modelling, analysis & control of vehicle suspension systems · · 2017-08-28executive summary...
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Department of Automatic Control & Systems Engineering
Modelling, Analysis & Control
Of Vehicle Suspension Systems
By:
Naveen Chadha B.Sc.
08/2017
Supervisor: Professor R.F.Harrison
A dissertation submitted in partial fulfilment of the requirements for the degree of M.Sc.
Advanced Control & Systems Engineering.
EXECUTIVE SUMMARY
INTRODUCTION
Since the invention of the automobile improving ride quality & the vehicle’s ability to keep good
road holding is an essential area within automotive engineering. Poor ride quality can cause
numerous health issues that stem from road disturbances such as musculoskeletal injuries,
especially to users that spend the majority of their time driving. Another problem is cost the of
advanced suspension systems; consequently, a system that replaces a passive system needs to
improve ride quality while keeping the manufacturing cost low for the general population.
This dissertation researches potential systems & implements a selected suspension system within a
quarter-car model subject to varying degrees of disturbances, subsequently describes & implements
an industry standard controller & is improved on via fuzzy logic control.
AIMS AND OBJECTIVES
The objectives for this project are as follows:
1. Review existing literature on controlled suspension systems for automobiles.
3. Model & simulate road disturbances set by an industry standard.
4. Retrieve a linearised quarter-car passive system & implement the feasible system with a degree
of non-linearity.
5. Design an industry standard controller.
6. Design a fuzzy logic controller
7. Simulate the new system with both controllers
8. Compare & analyse performance.
ACHIEVEMENTS
The main achievements of this project are reduced vertical acceleration, reduced standard
deviations by the new system & further improved via fuzzy controller for majority of road
disturbances. The fuzzy controller also shows very minute sacrifices concerning road holding
compared to the PID controller & uncontrolled system.
CONCLUSIONS / RECOMMENDATIONS
A MR damper that is controlled via PID & fuzzy logic is presented, the system is self-regulated
therefore there is no requirements from the driver & performance of the system was investigated via
simulated road disturbances set by the industry standard. The nature of the controlled semi-active
system allows a cost effective solution to enhance ride comfort along most road classes, where there
is hardly an improvement for very poor roads such as off-road terrain.
Recommendations to improve upon the system is to used optimised vehicle parameters tuned for
ride quality & make use of non-linear parametric identification to reduce any numerical error within
the semi-active system model.
ABSTRACT
This dissertation presents a magnetorheological damper to improve vehicle ride quality with a PID
& fuzzy when exposed to a range of road disturbances, the MR damper is currently implemented
within high-end automobiles for the purpose of performing along very smooth to average roads
often found in developed countries, thus the reason for the research to develop a controller that can
enhance the MR damper behaviour for both smooth & rough roads.
A non-linear model of the MR damper is implemented as the Dahl model, from which PID & fuzzy
controllers are applied. The effects of the controllers were investigated in a series of simulation
experiments, the results suggest that fuzzy control is more adaptive than the PID controller within
the MR damper, offering improved ride quality without sacrificing too much of road holding while
PID controller offers little improvement over the uncontrolled MR damper but shows satisfactory
road holding performance, the controllers show minimal improvement when exposed to very high
excitation levels which can be classed as off-road terrain/rocks, roads that are commonly found in
less developed countries. However the fuzzy controller shows satisfactory results when exposed to a
variation of roads which are made up of asphalt or tarmac.
Acknowledgements
I am deeply grateful to my partner Natasha Hulse for supporting, encouraging & giving me the
motivation to complete this intensive degree especially throughout this thesis, without her this
would have not been possible.
I would also like to express huge appreciation towards my family for providing support &
helping me during the difficult times & would like to thank some of my classmates, where I am
sure we will continue our friendships in the future.
Contents
1. Chapter 1 – Introduction ..................................................................................................................... 1
1.1. Introduction ..................................................................................................................................... 1
1.2. Structure .......................................................................................................................................... 3
1.3. Background & Motivation .............................................................................................................. 4
1.4. Aims & objectives ......................................................................................................................... 5
1.4.1. Aims ...................................................................................................................................... 5
1.4.2. Objectives ............................................................................................................................. 5
1.5. Project Management ....................................................................................................................... 5
1.5.1. Project Breakdown .............................................................................................................. 5
1.5.2. Project Gantt Chart ............................................................................................................. 6
1.5.3. Tools ..................................................................................................................................... 6
1.5.4. Management Review ........................................................................................................... 7
2. Chapter 2 - Literature Review ........................................................................................................... 9
2.1. Background & Introduction .......................................................................................................... 9
2.2. Suspension Systems ........................................................................................................................ 9
2.2.1. Passive Systems ................................................................................................................. 11
2.2.2. Active Systems .................................................................................................................... 11
2.2.2.1. Hydraulic Systems................................................................................................. 12
2.2.2.2. Pneumatic Systems ................................................................................................ 13
2.2.2.3. Electromagnetic Systems ...................................................................................... 14
2.2.2.4. Hybrid Active Systems .......................................................................................... 18
2.2.3. Semi-Active Systems .......................................................................................................... 21
2.2.3.1. MR Damper .......................................................................................................... 21
2.2.4. Conclusion ......................................................................................................................... 22
2.3. Modelling Review ........................................................................................................................ 24
2.3.1. Road Modelling ................................................................................................................. 24
2.3.2. MR Damper Modelling...................................................................................................... 26
2.3.3. Conclusion ........................................................................................................................ 30
3. Chapter 3 - Implementation ............................................................................................................. 31
3.1. Road Model ................................................................................................................................... 31
3.2. Passive Quarter-Car Model ........................................................................................................... 32
3.2.1. Model Verification ............................................................................................................. 34
3.2.2. Simulink Implementation ................................................................................................... 35
3.3. MR damper Implementation ........................................................................................................ 36
3.3.1. Dahl Model ........................................................................................................................ 36
3.3.2. Validation ........................................................................................................................... 37
3.4. System Parameters ....................................................................................................................... 39
4. Chapter 4 - Control ........................................................................................................................... 40
4.1. PID ................................................................................................................................................. 40
4.2. Fuzzy Control ................................................................................................................................ 41
5. Chapter 5 - Results ............................................................................................................................. 45
5.1. Dynamic Responses ..................................................................................................................... 45
5.2. Standard Deviations ..................................................................................................................... 46
5.2.1. Ride Quality ....................................................................................................................... 46
5.2.2. Road Holding ..................................................................................................................... 47
5.3. Potential Errors .............................................................................................................................. 49
6. Chapter 6 - Conclusion ...................................................................................................................... 51
7. Chapter 7 – Improvements & Future Work ................................................................................... 52
7.1. Improvements
7.1.1. Non-Linear Parametric Identification .............................................................................. 52
7.1.2. Passive System Optimisation ............................................................................................. 52
7.1.3. Fuzzy Controller Tuning ................................................................................................... 52
7.2. Future Work
7.2.1. User Adaptive Controller Design ..................................................................................... 53
7.2.2. Vehicle Body Roll Control ................................................................................................. 53
7.2.3. Improved Road Model ....................................................................................................... 53
7.2.4. ISO 2631 ............................................................................................................................ 54
7.2.5. Validation of Control Performance .................................................................................. 54
REFERNCES ............................................................................................................................................ 55
APPENDIX ................................................................................................................................................ 58
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Chapter 1 – Introduction
1.1. Introduction
The essential aspects of the design of commercial & passenger vehicles are how ergonomic, economic
& efficient they are, the comfort, ride quality & safety of the vehicle is considered to be one of the main
aspects for a vehicles marketability which is a branch of ergonomics. The broad aim of this report is to
review the current suspension systems that can possibly improve ride quality with an addition of a
controller, which could be implemented widely for more common vehicles due to the most expensive
vehicles which contain sophisticated suspension systems are out of budget for the majority of the
population.
Vehicle suspensions usually have the following requirements:
1. Isolate vehicle body from road disturbances to deliver improved ride quality where ride quality
can be measured by the vertical velocity of passenger locations/vehicle body, the existence of a
well-engineered suspension delivers isolation by reducing vibrational forces transmitted from
the axle to the vehicle body which results in chassis velocity reductions.
2. To reduce vertical acceleration of the wheels resulting in improved road holding, the
performance of a vehicle can be determined by traction abilities that stem from road holding.
3. Provide good road holding roll pitch are minimised by the suspension system.
4. To maintain support of vehicle static weight (Rajamani, 2014)
Vehicle suspension systems are characterised as types of passive, semi-active & active suspensions,
according to their function to supplement or subtract energy from external excitation resulting in a
smoother or rougher ride. (Gillespie, 1992). Within this project & report the focus is on the ride quality
from the passenger/driver point of view to minimise discomfort & reduce health risks discussed in
background & motivation, the ideal method of minimising this discomfort & improving ride quality is
by reducing vertical acceleration as the vehicle travels along the road, within the results the undamped
mass response which is the wheel is analysed briefly to discover any sacrifices or improvements were
made with road holding, which is how much contact the wheel as to the ground.
A comprehensive literature review was carried out to select the best suspension system to implement
both in passive & controlled manner, after which the suspension system & continuous road surfaces are
modelled, the new system that is controlled by a PID & fuzzy controller is analysed in terms of vertical
acceleration & standard deviations that indicates quality of ride.
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The suspension system of choice derived from the literature review is a magnetorheological damper
(MR Damper) that is added to a passive suspension system to form a semi-active system, which
contains magnetic fluid within the damper. Within the damper viscosity changes according to the
voltage input within the electromagnets resulting in a denser fluid that increases damping force resulting
in a damped ride quality which is seen as an improvement.
Within the results, the system is analysed without voltage & then with max voltage (12 Volts) to
discover the significance of the MR Damper over the passive system. Following is an analysis of a PID
controller which is seen as the benchmark controller across many industries & an analysis of a fuzzy
logic controller which is the preferred choice of a controller in the automotive industry in recent years.It
is used on a wide variety of applications such as anti-lock braking, engine control & automatic
transmission.
1.2. Structure
The structure of the thesis is composed of 7 chapters:
Chapter 1 introduces the thesis background, problem definition, aims & objectives, & project
management.
Within Chapter 2, the literature review is presented, which researches different suspension methods,
compares each method, deduct the best solution, furthermore road modelling & system modelling is
concisely presented.
In Chapter 3 describes the vehicle suspension multi-body system dynamics, mathematical equations of
the passive suspension system, model verification, research & implementation of chosen suspension
system model (MR Damper), additionally derive road models in accordance with ISO 8606 & analysis
of models.
In Chapter 4 control strategies & implementation of PID & fuzzy control are discussed with schematics
of Simulink model relating to the controllers.
Chapter 5 presents results of passive, passive MR damper, along with PID & fuzzy controllers a
comprehensive discussion about analysis & findings of the project.
Summary & conclusions are given within Chapter 6 describing the main points of the project, results &
reflecting on the project in relation to aims & objectives.
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Future work & recommendations are discussed within Chapter7, which highlights possible errors,
potential improvements over control & modelling furthermore suggestions to improve & take this thesis
further.
1.3. Background & Problem Definition
In addition to vehicle manufacturers improving ride quality for marketing purposes, it is also important
to address the health benefits/risks from good/poor ride quality. Automobiles & public transport such as
coaches & buses are widely used for social & commercial purposes; therefore a human body could
spend a significant time in the vehicle which comes with health issues that can be addressed with better
suspension. Vibration & vertical acceleration within a moving vehicle affects the human body by the
disturbances from the road. Within the body organs, bones & muscles are affected by the movement
which could cause micro fractures in the vertebrae, disc protrusion, nerve damage & acute lower back
pain (Bose, 2004).
Reduced ride quality affects the spine due to intervertebral discs serving as shock absorbers & becoming
more prone to injury over long durations, musculoskeletal injuries & back sprains or strains are the
single largest source of compensation claims in the workplace, according to the American journal of
industrial medicine. Biodynamic research has given evidence for an elevated risk of health impairment
due to long term exposure to high-intensity whole-body vibration, mainly the lumbar spine & the
connected nervous system may be affected, metabolic & other factors originating from within may
have an additional effect on the degeneration (ISO 2631, 2003).
During the ISO 2631 study, reactions & rider perspective was assessed at various magnitudes depending
on passenger expectations in regard to the purpose of trip & duration which is shown in Table (1). It can
be deducted from the study & Table (1) that the increase in acceleration results in passenger discomfort,
over a continuous road it leads to constant vibration, therefore a better suspension system decreases
vertical acceleration, resulting in reduced vertical velocity & vibration.
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Motion sickness, vertigo, difficulty of concertation, headache, back pain & general discomfort are the
most common health issues resulting from poor ride quality & safety issues while driving, as a person
ages they become more disposed to these injuries, during an evaluation of vehicle motion sickness due
to vehicle vertical velocity & vibration, it is established that pitch irregularities causes wider sensory
discrepancy than other movements such as roll or yaw, the study also found motion sickness occurs
between 0.1hz & 0.5hz. (Atsumi, 2002). Furthermore, a majority of the older population relies on
public transportation such as buses, using a controlled suspension method to improve ride quality would
reduce chances of exhibiting previous musculoskeletal conditions or chances of developing new ones
depending on the regularity of public transport usage & duration.
Therefore the purpose of the thesis is to improve ride quality using a standard industry controller;
proportional-integral-derivative (PID) & improve upon the controller using fuzzy logic control which is
common within the automotive industry. Improvements with the controllers can reduce vertical
acceleration thus reducing health risks mentioned above.
1.4. Aims & Objectives
1.4.1. Project Aims:
The aim of the project is to research, model, simulate, analyse & control a quarter vehicle suspension
systems, select an appropriate semi-active or active suspension system & use a benchmark controller
such as PID to reduce vertical acceleration & attempt to improve the system via fuzzy control methods.
Academic knowledge gained from systems engineering approach is to be utilised within a practical &
real world scenario. Secondly, the project also seeks to improve one’s knowledge of vehicle suspension
systems, project management skills & report writing skills.
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1.4.2. Objectives:
Firstly the objective is to research what constitutes as poor ride quality & problems associated with it,
market demand & manufacturers target audience for such systems is a factor in when selecting an
appropriate suspension system method. The second objective is to carry out a comprehensive literature
review of suspension systems & road models, where passive, semi active & active suspension systems
will be researched along with appropriate road models.
Thirdly the objective is to mathematical model, verify & simulate a passive system & road model, &
also the active/semi-active system along with any non-linearities.
Fourth objective is to design a benchmark controller which would be a PID & implement a fuzzy
controller to find out if there is any improvement over the PID controller & passive system.
The fifth objective is to fully analyse results of controllers, highlight findings & potential errors. The
final objective is to create a report presenting the findings & prepare an oral presentation.
1.5. Project Management
Change of project commencing 14th July 2017, original project was from 14th June 2017 – 13th July
2017 the reason for change is due to the timeframe the original objective was not achievable due to
coming across unforeseen obstacles & errors is previous research papers, therefore, forcing model the
system from scratch which results in hardly any time allowance for linearising & control. Non-linear
models previously established did not take in account important aspects that were crucial to the initial
project, thus a different problem was formulated & researched that is achievable within a month while
showcasing modelling & control techniques which have been taught across all the modules during the
M.Sc. degree.
1.5.1. Project Breakdown
A breakdown of the project is described below, an initial breakdown of the project is important to form
a more manageable task list important to project management; a clear instruction set list for the project
gives an opportunity to foresee potential problems. The following describes planned out general project,
research, modelling & implementation tasks:
1. Problem understanding & definition
2. Aims & Objectives formulation
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3. Planning & preparation • Structure of tasks • Resources • Project structure/Gantt chart
4. Literature Review
• Research , study & compare passive, semi-active & active suspension systems • Discuss advantages & disadvantages of these systems. • Research into control effort, cost & actuators required. • Select the suspension system based on the above reasons & research further into
the system & non-linear models. • Research appropriate road models
5. System Modelling
• Passive system modelling, equations of motion & validation • Road profile mathematical model & validation • New suspension system modelling & validation. • Simulink/Matlab implementation
6. Controller Design
• PID controller design • Fuzzy controller design
7. Results • Analysis of suspension systems, uncontrolled, PID & fuzzy • Description & reasons for the results • Parametric & Non-Parametric analysis.
8. Project Delivery
• Dissertation write up • Matlab/Simulink code layout • Oral Presentation
1.5.2. Gantt Chart
The Gantt chart displayed in Figure (1) shows the timeline & deadlines of tasks described above. It is a
widely used project management tool where a chart uses a series of horizontal lines to show what work
needs to be completed within a specified time frame, this can help the user decide on the feasibility of a
project depending on the user’s deadline.
1.5.3. Tools
Tools that would be used to carry out this research would be software program MATLAB for
implementing the mathematical model along with Simulink to further simulate the system & implement
the suspension system along with the controlled system. The system & experiment can be implemented
through MATLAB code alone, although Simulink provides enhanced efficiency in terms of
mathematical flexibility, analysis speed & debugging. Simulink is a time domain platform, thus, a
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mathematical formulation is only required of the system. MATLAB is used to help with statistical
analysis & model validation.
1.5.4. Management Review
Implementation & results were fully achieved & validated by 24th August & report (first draft) was
completed by 24th August which does not align with the Gantt chart shown in Figure (1), issues that
prolonged the delivery of the project was primarily researching & implementing the non-linear model
of the MR damper, testing out different models, gaining results took longer than expected due to lack of
computation power, with certain road models such as the rougher road models, it took much longer to
simulate the controlled system with these models, using a trial & error method for finding appropriate
PID values for the system. Time limit of the project sacrificed further improvements on the controllers,
more in depth statistical analysis & inclusion of road handling response of the system.
As an engineer, project management could have been improved, by creating a more clearer structure,
further research prior to starting the project & using a validated established model to quickly get a
Simulink model up & running, thus, more time allowance in fine tuning the controllers for improved
results.
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Figure (1): Initial Gantt chart of project, using project breakdown to aid planning of the project.
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Chapter 2 - Literature Review
2.1. Background & Introduction
The purpose of the literature review is a comprehensive research & study of suspension systems for the
purpose of improving ride quality, the categories of suspension systems that are studied are passive,
active & semi-active systems, from the research the most suitable system & method would be
selected based on advantages/ disadvantages, cost, & control effort. Road modelling strategies would
be researched, investigate industry standard models, implementation additionally research into
appropriate benchmark controllers & fuzzy control is conducted.
2.2 Suspension systems
The suspension assembly within a ground vehicle is made up of the following:
Spring
Dampers
Sprung & Unsprung mass
Sprung mass or also known as damped mass is known as the vehicle body where the passenger
occupies, this is connected by an unsprung mass which is called an undamped mass, which is placed
vertically below the damped mass, connected via various rods, bars & a spring damper system known as
the shock absorber or “damper”.
Springs are employed to absorb the bumps & shocks transmitted from the road surface & prevent these
disturbances from reaching the main body of the vehicle, these are made with different materials which
include various characteristics & spring coefficient. Dampers are utilised for when the vehicle
experiences a disturbance from the road, the spring deflects & oscillates & this oscillation can cause
issues with traction & ride quality consequently a damper reduces these oscillations thus improving the
ride & road holding of the vehicle. Figure (3) displays the process of how road disturbance affects ride
perception; the focus of the project is to reduce this disturbance experienced by damped mass.
If the damped mass of the vehicle is high in terms of distance from the unsprung mass, the occupants of
the vehicle will experience a smoother ride, consequently if the damped mass is placed quite low similar
to a sports car the suspension system will have to work harder to control the movement of the undamped
mass (wheel) therefore the damped mass of the vehicle will oscillate more as the vehicle travels over
rough roads. (Hillier, Coombes, 2004)
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The type of suspension put in place & the parameters chosen of the suspension set up (soft or stiff
springs) affects the ride quality of the vehicle. Within this thesis a model is used to represent parameters
of car type, which is the most popular type in the United Kingdom; a hatchback, according to Society of
Motor Manufacturers & Traders, one of the benefits of using this vehicle is that the parameters are very
similar to many popular cars that are very affordable in the UK & globally, therefore an improved
suspension system if integrated in best-selling cars with minimal cost could benefit most of the
population.
Within Figure (2) quarter car models of each suspension system that would be investigated within the
literature review, firstly what comprises of a passive suspension system is researched, secondly active
suspension systems are investigated which include parallel active suspension systems & electromagnetic
systems, followed by semi- active systems, the arrow within in Figure (2) represents the actuator
manipulated by a controller. Advantages & disadvantages of active & semi-active systems are discussed
within the conclusion section where a suitable system is selected.
Figure (3): Disturbance transferring through the vehicle affecting ride perception
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2.1.1 Passive Suspension System:
A passive suspension system consists of spring & damper mounted on each wheel of the vehicle with no
controller or actuator. The objective of a spring is to absorb the energy entering into the body due to the
motion of the vehicle & simultaneously support the weight of chassis. Purpose of a damper is to
dissipate any extra energy stored in the spring.
Figure (4): McPherson strut, the most common type of passive suspension system.
McPherson strut illustrated in Figure (4), is the most common set up for suspension systems, due to the
simplicity, no need of an external power source, low manufacturing costs, used worldwide & provides
isolation which is deemed satisfactory among smooth roads. The disadvantages of the passive system
are inherent performance limitations, the system can only absorb & dissipate little amount of energy
from the disturbances of the road, thus, the need for a further improved system to control a broad range
disturbances.
2.2.2. Active Suspension Systems
Active suspension systems are classified by a controller which is constantly active due to adjusting the
damping force, ride height or spring coefficient, or any combination of the three. An active system
makes use of the controller to reduce variations in disturbances constantly allowing a far greater degree
of road holding & ride quality by the actuator controlling the dampening at each wheel than a
conventional passive system. Active systems are classified as follows:
1. Hydraulic systems
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2. Pneumatic systems
3. Electromagnetic system
4. Hybrid-Active systems
2.2.2.1. Hydraulic Active Suspension
Hydraulic based active suspension system uses the hydraulic pressure that stems from a liquid within
the damper to manipulate force that consequently improves ride quality & road holding. The
implementation of a hydraulic actuator where a bladder the can be filled quickly with fluid, it is attached
to a compressor which displaces liquid into the actuator with a specified amount of force resulting it to
expand at the rate it requires to control the ride quality. This method of suspension control was
pioneered in the industry & used across many models by Mercedes-Benz, which have patented the
system & is known as Active Body Control (ABC). In Figure (5) a control system layout describes how
the system is interconnected with the mass & hydraulic piston.
Figure (5): Active Body Control system schematic
The ABC system uses an on-board computer that detects body displacement from sensors positioned
throughout the vehicle which it uses within the controller to send signals to the servomechanisms that
control the hydraulic piston to adjust damping force.
Disturbance from the road acts as input, it first meets the wheel which is the unsprung mass, the
controller regulates the distance of the sprung mass to ensure there is limited displacement, vibration &
vertical acceleration for ride comfort, the controller feeds suitable input into the pressure regulator
which in turn regulates the piston force, hydraulic force to the servomechanisms is generated by a high-
pressure circular piston hydraulic pump. This also takes into account displacement of unsprung mass to
accurately change the force produced in the piston for improved road holding. Either road holding or
ride quality priority is usually a pre-set chosen by the driver within the cockpit. 13 sensors constantly
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monitor chassis motion, chassis level & provide the controller with new information every 10ms. There
are four level-keeping sensors, one at each wheel to measure the damped mass level, three
accelerometers to measure the vertical body acceleration, an acceleration sensor measure the longitude
acceleration & finally one sensor detects transverse body accelerations. (Dahiphale, Chopade, Pathan,
2016)
Within each hydraulic cylinder under there is a sensor that monitors pressure, as the controller collects
& processes data, it operates four hydraulic servos, & each mounted in a series on a spring strut beside
each wheel. Rapidly the controlled suspensions generate counter forces to body roll & pitch while it is
not stationary, a suspension strut is connected in parallel in addition to the hydraulically controlled
fluctuating cylinder between the body & the wheel. This adjusts the cylinder in the direction of the
suspension strut & changes the length, in turn, creates a force which acts upon the suspension &
dampening of the vehicle in the frequency range up to 5 Hz. Figure (6) displays the improvement of the
ABC over a passive system. (Merker, Girres, Thriemer, 2002)
Figure (6): Active Body Control while aggressive cornering (left) normal passive suspension system
(right).
2.2.2.2. Pneumatic Suspension systems
Pneumatic systems work similar to hydraulic systems but replaces fluid with gas to produce a
mechanical force, therefore the components are less prone to shock wear & tear. Vehicles that use air
suspension today are usually high end manufacturers or used on top of the range models such as
Maybach, Mercedes, Lexus, Porsche, Audi, Ford & Lexus. A pneumatic system can be seen as
adjusting the spring stiffness coefficient instead of controlling the damper.
Air suspension system has a chamber of air that replaces the passive road spring, where each suspension
strut is fitted with an air chamber; the air which is under pressure is contained within the air chamber by
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a flexible diaphragm, the system utilises an electronically controlled system similar to the ABC system,
where an on-board air compressor, along with sensors & controllers monitor & manage the pressure
within the air chamber. The unique characteristic of a pneumatic system is that the control system can
modulate the spring pressure to provide a constant static deflection meaning the vehicle is self-levelling
compensating for any extra load; this function is of use in vehicles where the gross weight varies
regularly such as buses, coaches, passenger cars & commercial vans. (Stone, Ball, 2004)
The height of the vehicle can be adjusted by increasing or decreasing the pressure within the strut,
increase of air results in height rise, vice versa a decrease of air produces a reduction in height between
the suspension & body; the electronically controlled actuator regulates the amount of air exiting or
entering the struts. (Hiller, Coombes, 2004). The construction of the pneumatic suspension or “spring”
is encased in an aluminium cylinder to prevent dirt from getting into the system shown in Figure (7), a
twin tube gas filled damper with continuous electrical control is used. (Audi AG, 2002).
Figure (7): Construction of a pneumatic suspension system
2.2.2.3. Electromagnetic suspension
The electromagnetic suspension is a ground breaking system that provides almost near perfect road
holding & ride quality at the same time without each characteristic affecting each other. The concept &
research started in 1980 & in 2004 the suspension system was completed. Dr. Bose who carried out the
mathematical study to find the most ideal promising performance of a vehicle suspension system,
without any concerns of suspension hardware limitations. The research result between 1980 & 1985
shown that it was promising to achieve performance results that was a substantial improvement above
any other suspension system, also meanwhile evaluating conventional, active & semi-active suspension
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systems it was found that no other suspension system had the arrangement of swiftness, force, &
adaptiveness that is required to deliver the ideal results. The research led to the study of
electromagnetics as a suspension system as the chosen approach to achieve ideal results. (Bose®
Suspension System, 2004)
Figure (8): Electromagnetic suspension system layout
The system utilises the concept of magnetic levitation & electromagnets to create a system where the
damped mass is floating on air over the undamped mass, magnetic levitation is achieved by creating a
clearance between two permanent magnets placed within the damper, one bar is placed below & the
other is allowed to levitate with a help of a frame, this clearance gives the system adequate space to
adjust according to the road disturbance. However, Earnshaw’s Theorem states that “a magnetic body
cannot stay stationary at stable equilibrium when placed in any situation of gravitational & magnetic
field or fields”. Electromagnetic system utilises the voltage & the magnetic field (See Figure (9)) is
supervised by a control system & feedback to continually manipulate the voltage sent to the
electromagnets to achieve stable levitation, these permanent magnets used do not have any power
dissipation & the electromagnet stabilises the effect & road disturbances. (Van Der Sande, 2011)
As it can be observed in Figure (8) “linear electromagnetic motors”, which are magnets & coils of wire
are attached to each wheel, combined with power amplifiers, & a set of control algorithms control
electrical power delivered to the motor by a power amplifier in response to signal from the controller,
the bidirectional power amplifier allows power to flow into the linear electromagnetic motor & allows
power to be returned from the motor. When a voltage is applied to the coils surrounding the magnets, the
motor extends & retracts, creating motion between the undamped mass & damped mass, the system
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allows the damped mass to be almost level, with the wheels of the car displaces to accommodate road
disturbance & the control algorithm keeps the levitation stable. For instance, when the wheels travels
over a pothole, power is used to extend the linear magnetic motor & isolate the damped mass from the
disturbance, as the vehicle moves over the pothole the motor operates as a generator & returns power
back through the amplifier resulting in a level movement across the pothole. (Bose® Suspension
System, 2004)
Figure (9): A basic diagram of voltage passing through electromagnets to achieve levitation.
Figure (10): Automobile with standard suspension over bumps showing the damped mass response.
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Figure (11): Exact automobile now fitted with the electromagnetic system showing significant
improvement.
Electromagnetic suspension can improve ride quality within the roll axis, in Figure (12) a car with a
passive suspension system executes an aggressive left turn which results in the body roll towards the
right however in Figure (13) the electromagnetic system compensates for the force pushing the car’s
body towards the right by increasing the displacement on the right-hand side of the car between the
undamped & damped mass.
Figure (12): Car with passive suspension turning a corner at high velocity.
Figure (13): Exact car fitted with the Bose system, negotiating a corner at the same velocity.
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2.2.2.4. Hybrid Active Suspension Systems
Hybrid active suspension systems can be classified as systems that use both liquids & gasses which
constantly adjusts the dampening of the vehicle. In this thesis, the following is researched for possible
options to improve ride quality:
1. Hydrolastic suspension
2. Hydrogas suspension
Hydrolastic Suspension
Hydrolastic suspension system composes of a rubber type suspension arrangement with its main focus
on reducing vehicles pitch, the Hydrolastic system is pressurized with a liquid after any air has been
extracted from the system. The liquid consists of water, alcohol & an anti-corrosive agent (Hillier,
Coombes, 2004). The system replaces the separate springs & dampers of a conventional suspension
system with integrated, space efficient, fluid filled displacer units which are interconnected between the
front & rear wheels. The displacer unit at each wheel contains a rubber spring therefore damping is
attained by the displaced fluid travelling through the rubber valves, this fluid travels to the displacer of
the paired wheel resulting in dynamic interaction between front & rear wheels. For example, a vehicle
that experiences a disturbance via the front wheel the fluid is transferred the corresponding rear
displacer then lowers the rear wheel thus lifting the rear of the vehicle minimising pitch associated with
the disturbance, the process is vice versa when the rear wheel experiences the disturbance before the
front wheels. This effect is predominantly efficient on small cars as shorter wheelbases are more
affected by pitching. (Moulton, 1962)
Figure (14): Hydrolastic suspension system components
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The main improvement over a conventional suspension is that the front/rear interconnection allows the
vehicle to be stiffer in roll than in pitch, therefore, a compliant suspension system can be designed
offering comfortable ride without suffering a penalty in terms of excessive roll when cornering. In roll,
there is no transference of fluid from the displacers, & hence its internal pressure rises. The only slack or
allowance in the suspension occurs because of the inherent flexibility of the rubber springs which are
originally stiff. In terms of pitch as detailed above, fluid is transferred front to rear therefore the pressure
in the system stays effetely the same producing a compliant suspensions system.
Hydragas suspension
Hydragas suspension which has been developed from the Hydroelastic type system, the main difference
the rubber spring is replaced by a pneumatic spring. The units are interconnected in pairs by a fluid
pipeline, which links the front unit with the rear unit on the same side of the vehicle (refer to Figure
(16)), this line allows the liquid fluid pressure in the two units to equalise thus reducing the fore & after
pitch motion, which is most noticeable on short wheelbase cars, Hydragas unit consists of three main
parts; nitrogen acts as the spring, a fluid displacer & a damper valve block with bump & rebound valves.
Rubber spring is removed completely from the Hydrolastic system, the fluid is still in place, a separating
diaphragm is placed above the fluid, & above that is a cylinder or sphere which contains nitrogen gas,
the nitrogen acts as spring & damping unit whilst fluid is still allowed to run between front & rear units.
The Hydragas system utilises gas filled spring units also known as Hydragas Springs, which is present
at each wheel. Each unit has a sealed chamber containing a quantity of nitrogen gas at high pressure.
Below this chamber is a displacement chamber filled with a water-based fluid. When the wheel meets a
bump the fluid is pushed, compressing the gas, this action provides the springing effect. The two units
on each side of the car are also interconnected front to back, resulting in when the left from wheel meets
a bump, a part of the fluid from the left from unit is forced through a pipe to the left rear unit & left rear
wheels therefore that side is improved. (Rajput, 2007)
Citroën cars are known for this system which not only allows the driver to adjust ground clearance of
the body & vehicle but also maintains this set clearance despite any extra load on the vehicle, the
pressure gauge helps monitor the vehicle level. Spheres shown in Figure (15) & Figure (16) are not
prone to mechanical wear but can be subject to a drop in pressure typically due to nitrogen
disseminating through the membrane, the manufacturer states that the spheres would need replacing
between 60,000km & 100,000 km.
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Figure (15): Hydragas suspension system components
Figure (16): Hydragas suspension system components
1 - Gas, 2 – Fluid, 3 – Sphere, 4 - Cylinder, 5 - Arm, 6 -Piston.
The Hydragas system is a somewhat linear spring rate like suspension; the further it is compressed the
stiffer the suspension response is. Due to the inherent properties of gasses, where a volume of a gas is
halved the pressure is doubled, the suspension is very soft initially but as it compresses the stiffness
increases. When the suspension is active, the system pushes oil into the sphere, thereby altering the
volume, hence the pressure of the gas. Usually, steel-sprung cars are either too soft or stiff or some
intermediate compromise, while Hydragas offers the driver to adjust to their needs. (Haynes, 2004)
The system includes a self-levelling function where there is the same amount of suspension
characteristics even when gross weight is increased or decreased. Likewise, the self-levelling function
also removes unwanted compromises associated with suspension design of passive sprung cars as the
suspension is constantly operating around a prearranged position. A Hydragas suspension operates at
near to ideal angles at all times & under all conditions. Nitrogen is used as the gas to be compressed, due
to the possibility of corrosion is less likely, a nitrogen resolver with an adjustable volume yields the
spring with nonlinear force deflection behaviour. (Haynes, 2004)
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2.2.3. Semi-Active Suspensions
2.2.3.1. Magnetorheological Damper
A magnetorheological damper (MR damper) is a shock absorber/damper filled with magnetorheological
fluid that contains metallic particles, manipulated by a magnetic field originating from an
electromagnet; it can transform the liquid into a semi-solid state within milliseconds. The fluid itself
comprises of magnetisable particles the size of a micron, usually made up of iron, placed in a liquid
such as mineral oil, synthetic oil, or water. The MR damper allows for energy absorption in mechanical
systems & due to the semi-passive nature where the damper works as a passive system when there is no
voltage within the electromagnet, therefore it can be seen as a fail-safe device. (Bajaj, Birdi, Ugale,
2014). The damper contains channels or chambers shown in Figure (17) which allows the fluid to pass
through it while the damper piston moves according to road disturbance; allowing damping
characteristics constantly controlled by varying power of the electromagnet. Fluid viscosity increases
within the damper as electromagnet strength increases.
Delphi Cooperation developed this system for use in the commercial market, branded as MagneRide
active suspension. An electronic control unit, along with sensors maintains the ride quality & voltage
passing through the electromagnet to adjust the dampening accordingly, it can be adjusted once every
millisecond. It is a system used across the automotive industry by manufacturers such as Chevrolet,
Ford, Audi, Ferrari & Lamborghini, aiming for very smooth to urban road surfaces.
In Figure (18) top of the diagram shows the MR damper in a passive state, where no electric voltage is
passing through hence creating magnetic repulsion/attraction, when a voltage is passed through the
metallic particles stiffens the fluid (bottom of the diagram) via metallic particles creating a barrier within
the piston so the fluid is denser hence stiffens the dampening to reduce force transmitted from
undamped mass to the damped mass.
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Figure (17): Illustration showing the inside of an MR damper, note the holes/rings where the fluid can
pass through.
Figure (18): MR damper fluid response to voltage
.
2.2.4. Conclusion
Here advantages & disadvantages are explored with each suspension system which will lead to a choice
of system for the thesis. Firstly the hydraulic system, the advantages are that it can be adjustable &
customisable, very responsive & provide an enhanced smooth ride quality, adjustment & ride height can
be controlled via an LQR method, or fuzzy logic. However the disadvantages are: due to it being a
solely active system if a component breaks or the fluid leaks, the system would lose the pressure within
the fluid subsequently leading to the vehicle sagging, this renders the vehicle immobile, the mass of the
Page | 23
system is quite large hence need of a large control force leading to more expenses in manufacturing, &
maintenance requires specialised tools & knowledge which can lead to large repair costs.
Secondly, the pneumatic air suspension advantages are that it can always be self-levelling despite any
extra load, the ride quality is described as gliding over bumps, adjustable settings by the user &
improved tire life from less vibration absorbed from the wheel. Nonetheless, the cons of this system are
higher manufacturing costs & repair costs. Air bag or air strut failure caused by wet rust, wear & tear or
moisture within the system that corrodes it internally, seals & rubber components may dry out,
punctures within the air bag caused by road debris, over extension of the air sprung could lead to failure
via tearing of the flexible layers, when the system loses pressure it can render the vehicle immobile. Air
compressor failure can occur due to a leak within the air springs/struts, the compressor can burn out
trying to maintain the correct air pressure in a leaking system, & finally dryer failure can occur, the
purpose of this is to remove the moisture from the system, but can become saturated hence the system
will experience moisture build up. Thirdly vehicles with Hydrolastic suspension have a tendency to
squat under acceleration & dive under breaking this increases the complexity of a mathematical model
along with issues that occur with pneumatic systems in terms of component failure & cost.
Fourthly, speed, response, concentrated strength within a small area allowing it to counter act vehicle
forces shows electromagnetic suspension is the most advanced & improved system for vehicles, but the
disadvantages within a commercial application are numerous such as the cost to produce custom
neodymium magnets the cost of this is quite high & already places this system more costly than any
other explored within this paper. Additionally wear & tear from components or electronic failure can
cost a small fortune to repair, it is a complex system that requires high precision machinery & skilled
engineers to manufacture from any wear & tear if parts fail or the system fails it can cost a small
fortune to repair it, this complex system & requires high precision machinery & skilled engineers to
manufacture.
Finally, in conclusion, the suspension system that will be chosen for this thesis would be the MR
damper system owning to the overall cost of the system is much less than the other systems, ease of
installation, the semi-active nature of the system means it can be a fail-safe system, it does not require
large actuator forces thus lighter in weight compared to the other options, resulting in cost savings. It is
deemed as an excellent compromise between active & passive system.
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2.3. Modelling Review
2.3.1. Road Modelling
There are multiple sources from which reduces ride quality within a vehicle, these generally fall into
two classes; road surface & vibration caused by vehicle components which are powertrain, wheels &
other moving components (Gillespie, 1992). Within this thesis, the main focus is developing a
suspension system to reduce disturbances from the road from the rider perspective thus forming an
accurate road model is essential to fully analyse the response & form an accurate control system for the
environment. Road roughness is defined by the elevation profile along the vehicle’s wheels as it travels,
it can be viewed as a deterministic signal in vector form, random signals that are limited by pre-
determined values thus to model the road a useful tool is the Power spectral density function (PSD) (D.
Gillespie, 1992).
The vector form of signals is used as an excitation source in vehicle simulations to assess ride quality,
while it is computationally inefficient & unfeasible to simulate a vehicle travelling over a long distance
of a measured surface with very high accuracy, it is favourable to consider the road profile as a
particular realisation of having a random probability distribution which is a good average that may
be analysed statistically. (Turkay, Akcay, 2015). Prior knowledge of disturbance aids the automotive
engineer in making informed choices early in the design process.
The usage of the “ISO 8608 standard” for road profiling is based on the theory that a given road has
identical statistical properties along a section to be classified. While the spectral analysis of road
profiles is relatively new to road engineering, it has been employed by automotive engineers for
several decades. In the ISO 8608 report, 5 classes of roads are acknowledged. By comparing the
PSDs associated with the classes, roads that have a minor degree of roughness are defined of best
quality while roads that have a high degree of roughness are regarded as very poor, similar to off-
road tracks. (Andren, 2006)
While this simple parametric PSD may not precisely estimate the road roughness spectrum for the
whole range of frequencies; conversely, it will correctly estimate the energy for the frequencies in
the range which may excite the vehicle response. (Turkay, Akcay, 2015).
The profile of elevation is measured over by a length of road using the Fourier transform to turn it into a
sequence of sine waves fluctuating in amplitudes and phase relationships. Plotting of the amplitude vs
spatial frequency is the power spectral density, the spatial frequency specified as wave-number with
units of 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐/𝑚𝑚𝑐𝑐𝑚𝑚𝑐𝑐𝑟𝑟2 is the inverse of the wavelength of the sine wave it is based (ISO 8606, 2005).
Page | 25
Using a single slope elevation profile can help identify acceleration within the pitch axis of the vehicle,
double slope elevation profile which uses varying degrees of difference between 2 tracks, one for the
right hand side & one for the left hand side usually appears quite similar to average but the focus of the
thesis is within vertical acceleration, if one was to measure roll within the car, a double slope profile
would be advantageous.
Longitudinal profiles which classification based on ISO (8606) paved roads are generally to be among
road classes A to D, while road E is classified as rough paved road/off road terrain, the PSD of roads
characterise drop in magnitude with the wave number, to determine PSD it is necessary to measure the
surface profile with respect to a reference plane.
(1). Φ(Ω) = Φ(Ω0) � ΩΩ0�−𝑤𝑤
or Φ(𝑛𝑛) = Φ(𝑛𝑛0) � 𝑛𝑛𝑛𝑛0�−𝑤𝑤
,
Where,
(2). Ω = 2 ∗ πL
(3). Φ0 ≜ Φ(Ω0)
(4). 𝑛𝑛 = Ω2π
= spatial frequency, 𝑛𝑛0 = 0.1cycle/m,
Equation (2). Rad/m is the angular spatial frequency, L is the wavelength. Equation (3). In 𝑖𝑖𝑛𝑛 𝑚𝑚2/
(rad/m) is the values of the PSD at the reference wave number Ω0 = 0.1 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐/𝑚𝑚, w is waviness, for
most road surfaces w is 2.
Table (2): Road Roughness values classified by ISO 8606.
According to the research an estimation for the roughness of a road surface is given by the following;
new road surfaces such as concrete or asphalt surfaces or very well maintained surfaces are assumed to
Degree of roughness Φ(𝑛𝑛0)(10−6𝑚𝑚2/(𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐/𝑚𝑚)) 𝑤𝑤ℎ𝑐𝑐𝑟𝑟𝑐𝑐 𝑛𝑛0 = 0.1 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐/𝑚𝑚
Road Class Lower Limit Geometric Mean Upper Limit
A(Very Good) - 16 32
B (Good) 32 64 128
C (Average) 128 256 512
D (Poor) 512 1024 2048
E (Very Poor) 2048 4096 8192
Page | 26
have a road quality that fits in with A & B in Table(2) , secondly older road surfaces, which are not as
maintained regularly, or non-highway roads can be seen to fit in within C in Table(2) & finally roads
that have a large number of potholes, speed bumps, or cobblestones can be classified within D & E in
Table(2). Within this report, it is important to remember the values that will be chosen for road classes
fall into the upper limit for the purpose of worst case scenario in terms of road roughness for each road.
Figure (19): A real world example of very poor road which ISO approximates within Class E
2.3.2. MR damper modelling
A MR damper displays behaviour known as hysteresis, which is the difference of magnetic flux density
of a ferromagnetic material stemming from an external magnetic field. When this field is changed
through a complete cycle, the response not only depends on the current state but also based upon the
past history known as the hysteresis effect. The complexity of modelling MR damper is due to the
significant non-linear response that is exhibited when the model is subjected to input excitation, also
dependent on the voltage which increases the difficulty of mathematical modelling the system. Tt is
crucial that the selected mathematical model can describe its non-linear behaviour in order to develop a
feasible semi-active controller (Braz-Cesar, Barros, 2013). MR damper dynamics are highly complex
which has resulted in various mathematical models that approximately recreate the force –velocity
response, the damping force varies with the velocity & the magnitude of the magnetic field.
(Iskandarani, Karimi, 2011). In order to model & control an MR damper system with a degree of
accuracy a model would have to be included in the system to model the process of hysteresis, subject to
a magnetising signal which is voltage & the response of the magnetic fluid, the following models are
researched:
1. Bingham Model
2. Dahl Model
Page | 27
3. Bouc-Wen Model
Figure (20): (a).Components and schematic of an MR damper, (b). Working principle diagram
illustrates the schematics of the mathematical model; where in the middle would be MR damper
model describing hysteresis.
Bingham Model
(5). 𝑓𝑓𝑎𝑎 = 𝑓𝑓𝑐𝑐 𝑐𝑐𝑠𝑠𝑛𝑛�̇�𝑥𝑑𝑑 + 𝑐𝑐𝑜𝑜 + 𝑓𝑓𝑜𝑜
One of the first MR damper models that were developed to describe rheological properties in fluids is
the Bingham plastic model, modified by (Stanway, 1985) in equation (5) proposes an idealised
mechanical model, The Bingham model comprises of a Coulomb friction element that is placed in
parallel with the passive system, where Co is the damping coefficient, �̇�𝑥𝑑𝑑 is the damped mass velocity,
𝑓𝑓𝑐𝑐 is the frictional force related to the fluid yield stress, and offset in the force 𝑓𝑓𝑜𝑜 is the zero-mean
measurement of force owning to the fluid accumulator (Spencer,Dyke,Sain,Carlson, 1996). The
Bingham model is a heavily simplified model of the MR damper, which is linear shown in Figure(21),
it shows little or no amount of adaptiveness & does not take into account previous dynamics of fluid,
therefore no hysteresis (Iskandarani, Karimi, 2011).
Page | 28
Figure (21): Bingham model implemented using the suspension system discussed in Chapter 3 with band-limited
white noise based on ISO PSD.
Dahl Model
The dahl model formulated in (Dahl, 1968) shown below where 𝐹𝐹𝑚𝑚𝑚𝑚 is exerted force from the MR
damper, w is the dynamic hysteresis.
(6). 𝐹𝐹𝑚𝑚𝑚𝑚 = 𝑘𝑘�̇�𝑥𝑑𝑑 + (𝑘𝑘𝑤𝑤𝑎𝑎 + 𝑘𝑘𝑤𝑤𝑤𝑤𝑣𝑣)𝑤𝑤
(7). �̇�𝑤 = 𝜌𝜌(�̇�𝑥𝑑𝑑 − |�̇�𝑥𝑑𝑑|𝑤𝑤), note results of (𝑘𝑘𝑤𝑤𝑎𝑎 + 𝑘𝑘𝑤𝑤𝑤𝑤𝑣𝑣) is voltage dependent & the parameters can
be estimated using a trial & error method to form the correct shape of graph of force vs velocity:
hysteresis behaviour of magneto-rheological. (Sahin, Engin, Cesmeci, 2010).
𝑣𝑣 Is the control voltage, 𝑘𝑘,𝑘𝑘𝑤𝑤𝑎𝑎,𝑘𝑘𝑤𝑤𝑤𝑤 & 𝜌𝜌 are parameters that control the shape of the hysteresis loop in
turn affecting force when voltage is applied. Dahls first paper states “The origin of friction is in quasi
static bonds that are continuously forms & subsequently broken” (Iskandarani, Karimi, 2011). A basic
schematic of the Dahl model presented in Figure (22) will be implemented in Chapter 4.
Page | 29
Figure (22): Dahl model schematic
Bouc-wen model
The Bouc-Wen model was originally formulated by (Bouc, 1971) & generalised by (Wen,1976), is
explored as an option for modelling the MR damper due to it being a common choice of MR damper &
a highly effective model to describe the hysteric performance of an MR damper. It is an extremely
versatile and can demonstrate a wide verity of hysteric behaviour. Adjustment of the parameters of the
model 𝛾𝛾,𝛽𝛽, τ, can control the linearity & smoothness of the transition between the pre-yield forces of
the fluid to the post-yield region. (Spencer, 1996). The force generated by the MR damper can be
described by equations(8-13) damping force component which is also known as the yield stress of the
MR fluid according to the evolutionary /ever changing variable Z that traces history dependence of the
response. (Cesar, Barros, 2013).
(8). 𝑧𝑧 = −𝛾𝛾 | 𝑥𝑥�̇�𝑑 − 𝑥𝑥�̇�𝑢 |𝑧𝑧 | 𝑧𝑧|𝑛𝑛−1 − 𝛽𝛽(𝑥𝑥�̇�𝑑 − 𝑥𝑥�̇�𝑢)|𝑧𝑧|𝑛𝑛 + τ(𝑥𝑥�̇�𝑑 − 𝑥𝑥𝑢𝑢)̇
(9). 𝐹𝐹𝑚𝑚𝑚𝑚 = 𝐶𝐶1(𝑣𝑣) 𝑥𝑥�̇�𝑑 + 𝑘𝑘1(𝑥𝑥𝑑𝑑 − 𝑥𝑥0)
(10). 𝐶𝐶1(𝑣𝑣) = 𝐶𝐶1𝑎𝑎 + 𝐶𝐶1𝑤𝑤𝑣𝑣
(11). 𝐶𝐶0(𝑣𝑣) = 𝐶𝐶0𝑎𝑎 + 𝐶𝐶0𝑤𝑤𝑣𝑣
(12). 𝛼𝛼(𝑣𝑣) = 𝛼𝛼𝑎𝑎 + 𝛼𝛼𝑤𝑤𝑣𝑣
(13). 𝑣𝑣 = −𝑁𝑁(𝑣𝑣2 − 𝑣𝑣1)
Where 𝑣𝑣 is the voltage applied to the constant current driver component, within this model there is a
total of 14 parameters to form the MR damper. In Figure (23) an attempt was made to implement a
simplified version of the Bouc-Wen model based on (Eshkabilov, 2013) still the computational
power available could not process the Bouc-Wen model using road classes B-E in an adequate time
Page | 30
limit thus due to exhausting the computational power & increased potential of error concerning the
parameters of the Bouc-wen model. High fidelity models comprise of numerous parameters that
require an accurate parameter identification procedure to resourcefully approximate parameters &
reduce errors. Estimation of such parameters can be established via mathematical models, the most
common is the least square method (Cesar, Barros, 2013).
Figure (23) Bouc-Wen MR damper as a semi-active suspension system
2.3.3. Conclusion
In conclusion the Dahl model is chosen to be implemented as the MR damper model, due to it
displaying accurate hysteresis & as commonly used as the Bouc-Wen model; the Dahl model relies on
voltage input from which one could adjust easily avoiding excessive use of computational power. The
Bouc-Wen model is the highest fidelity, self-experimentation with this model within Simulink using
edited parameters from (Eshkabilov, 2013) within the implemented passive model has proved that it
is quite computationally tasking, taking up to 30 minutes to simulate a step response for road
models B to E. The Bingham model is very linear, proven in Figure (21) with system implemented
in Chapter 4, therefore due to displaying no hysteresis the Bingham model is avoided within this
thesis.
Page | 31
Chapter 3 – Implementation
3.1. Road Modelling
Previously in the literature review, using an ISO defined model for road roughness levels was
established, therefore, band-limited white noise block is utilised within Simulink to form a deterministic
signal according the ISO data. Band-limited white noise produces normally distributed random numbers
that are suitable for continuous systems & provide satisfactory averages of road models, the signal
produced is an approximation of the PSD signals that stem from Table(2). Band-limited white noise
generation allows one to create an improved approximation by generation of a signal is close to the
correlation of the PSD road models. Parameters defined by Table (2) with sample time of 0.1, &
choosing the upper mean of each road classification (32e-6, 128e-16, 512e-6, 2048e-6, 8192e-6)
represents road classification A,B,C,D,E respectively.
For a deeper view of the road models, an example was generated within MATLAB code to demonstrate
the differences in elevation for a road model. Road (C) is used as an example illustrated by Figure (24)
& a band-limited white noise simulation of the same road in Figure (25).
Figure (24): Showing an example PSD of road surface (C) according the ISO standard
with Elevation Vs road length.
Page | 32
Figure (25): Showing an example of road surface (C) according the ISO standard, as a band-
limited white noise representation (Note within the Simulink model the Y axis is elevation & X axis
is time)
3.2. Passive Quarter-Car Model
Primarily the passive model is to be used as a linearised mass spring damper system of a quarter car
model (see Figure (26)), taking into account the damping & spring effects of the suspension system
along with the masses of the system. The undamped mass which is the wheel & components is
characterised by the undamped mass, a small damping value to describe the damping behaviour of the
tyre & spring stiffness of the tyre.
The model would be based on a previous schematic described in a journal (Florin, Ioan-Cozmin ,
Liliana, 2013) but using parameters that describe a modern hatchback, which is the most popular type
of car amongst the general population.
Page | 33
Figure (26): Passive model to be used for modelling & control.
LaGrange Equations
Instead of deriving equations of motion from a free body diagram, for more complex systems LaGrange
equations are used for multiple degrees of freedom system, using partial differentiation of the systems
kinetic energy, dissipation & potential, the equations of motion in equation 20 & 21 are formed, using
the system parameters & using equations 14 to 19 in MATLAB, a state space is formed describing the
behaviour of the damped mass in Figure (26).
(14.) 𝑀𝑀 = �𝑚𝑚2 00 𝑚𝑚1
� , (15). 𝐾𝐾 = �𝑘𝑘𝑑𝑑 + 𝑘𝑘𝑢𝑢 −𝑘𝑘𝑢𝑢−𝑘𝑘𝑑𝑑 𝑘𝑘𝑢𝑢 + 𝑘𝑘𝑑𝑑
�,
(16). 𝐶𝐶 = �𝑐𝑐𝑑𝑑 + 𝑐𝑐𝑢𝑢 −𝑐𝑐𝑢𝑢−𝑐𝑐𝑑𝑑 𝑐𝑐𝑢𝑢 + 𝑐𝑐𝑑𝑑
�
(17). 𝐴𝐴 = �−𝑀𝑀−1𝐶𝐶_𝑑𝑑 −𝑀𝑀−1𝐾𝐾𝐼𝐼 0
�, (18). 𝐵𝐵 = � 𝑀𝑀−1
0 � , (19). 𝐶𝐶 = [ 0 0 1 0]
(20). 𝑚𝑚𝑑𝑑�̈�𝑥𝑑𝑑 + 𝑘𝑘𝑑𝑑 (𝑥𝑥𝑑𝑑 − 𝑥𝑥𝑢𝑢 ) + �̇�𝑐𝑑𝑑(�̇�𝑥𝑑𝑑 − �̇�𝑥𝑢𝑢) = 0
(21). 𝑚𝑚𝑢𝑢�̈�𝑥𝑢𝑢 + 𝑘𝑘𝑢𝑢𝑥𝑥𝑢𝑢 + 𝑘𝑘𝑑𝑑 (𝑥𝑥𝑑𝑑 − 𝑥𝑥𝑢𝑢 ) + 𝑐𝑐𝑢𝑢�̇�𝑥𝑢𝑢 − 𝑐𝑐𝑑𝑑(�̇�𝑥𝑑𝑑 − �̇�𝑥𝑢𝑢) = 𝑐𝑐𝑢𝑢�̇�𝑥𝑚𝑚 + 𝑘𝑘𝑢𝑢𝑥𝑥𝑚𝑚
Page | 34
3.3.1. Model Verification
Analysis of the system to verify that the whole system is stable shows that the eigenvalues are < 1,
MATLAB’s eig function proves this, additionally controllability & observability of the system is
analysed. A system described by the matrices (A, B) can be said to be controllable is there exists an
unconstrained control input that can transfer any initial state to any desired location for the system.
(Dorf, Bishop, 1998). Equation 22 can indicate to one that if the system is controllable, a solution may
not exist if the system is not controllable. (Ogata 1997). Observability refers to the ability to estimate a
state variable; a system may be observable if the output has a component due to each state variable,
(Dorf, Bishop, 1998). The concept of observability (equation 23) is useful in solving the problem of
reconstructing unmeasurable state variables from measurable variables in the minimum possible length
of time, which can be useful in developing optimizing based controllers. . It is important because in
practice the difficulty encountered with state feedback control is that some of the state variables are not
accessible for direct measurement with the result that it becomes a requirement to estimate the
unmeasurable state variables in order to construct the control signals. (Ogata 1997). For the system in
question both equations rank result in the value 4.
(22). 𝑊𝑊𝑚𝑚 = [𝐵𝐵 𝐴𝐴𝐵𝐵… .𝐴𝐴𝑛𝑛−1𝐵𝐵] (23). 𝑊𝑊0 = �
𝐶𝐶𝐶𝐶𝐴𝐴…
𝐶𝐶𝐴𝐴𝑛𝑛−1�
Figure (27): Bode diagram of sprung mass of transmissibility passive system.
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3.2.2. Simulink Implementation
Figure (28): Simulink implementation of equations 20 & 21.
Figure (29): Example response of the passive damped mass over road classification(A),
Acceleration 𝑐𝑐𝑚𝑚/𝑐𝑐2, Velocity(cm/s) , Displacement(cm) are represented by the green, orange, blue
lines respectively.
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3.3. Semi-Active System/MR Damper
Figure (30): The semi active suspension shown has a sensor detecting the vehicle body vertical
acceleration movement, via an accelerometer; originally the schematic included the input of undamped
mass acceleration into the controller but was removed for simplification.
(25). 𝑚𝑚𝑑𝑑�̈�𝑥𝑑𝑑 + 𝑘𝑘𝑑𝑑 (𝑥𝑥𝑑𝑑 − 𝑥𝑥𝑢𝑢 ) + �̇�𝑐𝑑𝑑(�̇�𝑥𝑑𝑑 − �̇�𝑥𝑢𝑢) = 𝐹𝐹𝑚𝑚𝑚𝑚
(26). 𝑚𝑚𝑢𝑢�̈�𝑥𝑢𝑢 + 𝑘𝑘𝑢𝑢𝑥𝑥𝑢𝑢 + 𝑘𝑘𝑑𝑑 (𝑥𝑥𝑑𝑑 − 𝑥𝑥𝑢𝑢 ) + 𝑐𝑐𝑢𝑢�̇�𝑥𝑢𝑢 − 𝑐𝑐𝑑𝑑(�̇�𝑥𝑑𝑑 − �̇�𝑥𝑢𝑢) = −𝐹𝐹𝑚𝑚𝑚𝑚 + 𝑐𝑐𝑢𝑢�̇�𝑥𝑚𝑚 + 𝑘𝑘𝑢𝑢𝑥𝑥𝑚𝑚
Equations 25 & 26 represent the adjusted equations of motion that accommodates 𝐹𝐹𝑚𝑚𝑚𝑚 which now
represents the semi-active suspension system, 𝐹𝐹𝑚𝑚𝑚𝑚 is the force exerted by the controller, shown in
Figure (31) schematic.
3.3.1. Dahl Model
The Dahl model in Figure (31) is integrated within the Simulink passive system taking into account
changes of equation 20 & 21 to accommodate equations 25 & 26
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Figure (31): Simulink model implementing Dahl’s equations stated in equation 6 & 7.
3.3.2. Validation
Eigenvalues are still < 1, rank of controllability & observability produces the value: 5, therefore the dahl
model is stable & can be linearised & controlled. The validation of the MR damper can be seen in
hysteresis loops for Force vs velocity (Figure (33)); when the velocity changes, the force of the
damper does not change instantly the fluid provides resistance to the damper until the force allow
the fluid bonds to be broken it takes into account pre-yield stress & post yield stress of the fluid,
stated in (Dahl, 1968). (Iskandarani, Karimi, 2011). Figure (33) demonstrates the effect of voltage
on the MR damper, loosely speaking the additional voltage applied the more resistance the damper
offers therefore increase in vertical velocity of the damped mass is reduced. The varying response of the
MR damper force to road disturbance is established & verified by observing Figure (34).
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Figure (32): Bode plot showing stability margins a linearised state space of the System with the
addition of the Dahl model.
Figure (33): Force response of the MR damper with a step input, showing hysteresis implemented
within the Simulink model, blue, red, yellow, purple & green lines that represent input of 0, 2, 2.5,3,6
volts respectively.
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Figure (34): Simulink response graph showing constantly changing force of the MR damper due to the
classified very poor road response as disturbance.
3.4. System Parameters
Table (3): System parameters
Model Parameters
𝑀𝑀2 Damped Mass 341.3 kg
𝑀𝑀1 Undamped Mass 47.4 kg
𝐾𝐾𝑢𝑢 Undamped Spring Constant 170000 N/m
𝐾𝐾𝑑𝑑 Damped Spring Constant 32000 N/m
𝐶𝐶𝑢𝑢 Undamped Spring Constant 30 N/m
𝐶𝐶𝑑𝑑 Damped Spring Constant 1000 N/m
𝜌𝜌 Dahl parameter 1500
𝐷𝐷𝑘𝑘 Dahl parameter 350
𝑣𝑣 Voltage Varies with controller
𝐾𝐾𝑤𝑤𝑎𝑎 Dahl parameter 80
𝐾𝐾𝑤𝑤𝑤𝑤 Dahl parameter 80
𝑥𝑥𝑑𝑑 Displacement of Damped mass Vector response from road input
𝑥𝑥𝑢𝑢 Displacement of undamped mass Vector response from road input
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Chapter 4 - Controllers
4.1 PID
Use of a PID controller is chosen due to the simplicity & ease of implementation amplified by the
Simulink model.
Figure (35): PID controller to minimise vertical velocity, hence vertical acceleration, note saturation block included to provide correct constraints of the voltage (0 to 12 Volts).
Figure (35.1): Hysteresis of PID response to road C indicates that the PID controller within the system is validated & showing similar non-linear characteristics of the MR damper.
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From trial & error the values of the PID are 5𝑐𝑐−6, 0.012, & 1𝑐𝑐−8 respectively, the values are selected
in order to achieve best voltage values to alter the damping force of the MR damper to reduce the
amount of vertical acceleration from the damped mass.
4.2 Fuzzy Logic
Fuzzy sets & logic theory introduced by Lofti Zadeh in 1973, states “As the complexity of a system
increases, our ability to make precise & significant statements about its behaviour diminishes until a
threshold is reached beyond which precision and relevance becomes almost mutually exclusive
characteristics which translates into ‘The closer one looks at a real world problem, the fuzzier becomes
it’s solution (Mahfouf, 2016). Where the increased non-linearity of a system, the difficulty increases
when attempting to control it.
Fuzzy logic is a powerful method of implementing controllers for many applications & most
importantly in automotive engineering, by using engineering expertise into products in a short amount
of time, where the design relies on both engineers & test drivers. Control systems within automobiles
are complex & require multiple parameters, the optimisation of most systems are based on engineering
expertise in the industry rather than mathematical models , such as “good ride quality” “good road
handling “ are optimisation goals, which cannot be defined mathematically (Altrock, 1997).
For example, anti-Lock braking systems, engine control units, & automotive gearboxes are usually
controlled by fuzzy logic & widely used by nearly every automotive manufacturer, to overcome the
complexity & computationally exhaustive mathematical models (Altrock, 1997).
Main benefits of fuzzy logic are the ease to model control procedures, ability to deal with uncertainty &
non-linearity, ease of implementation & use of linguistic variables. PID controller are used due to their
simple structure & effortlessness controller design when the system is linear or linearised around an
operating point, although most real world systems are non-linear in the whole operating range this is
where fuzzy logic has the advantage. (Passino,Yurkovich, 1998). The self-tuning nature & on-line
adaptation to non-linear, time varying & uncertain systems of fuzzy controllers offers a promising
option for industrial applications.
The fuzzy logic control system is applied to the MR damper system to achieve regulation of the
viscosity of the MR damper via altering the voltage depending on the input vertical velocity of the
damped mass, the values of the fuzzy control system are a collection of rules & fuzzy set membership
functions, the schematic of the fuzzy controller implementation is displayed in Figure(36).
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Using MATLAB fuzzy logic designer shown in Figure (37-39) allows changing parameters within the
fuzzy controller with ease, producing a voltage from 0 to 12 volts. The choice of parameters began from
even distribution of velocity measurements to voltage in Figure (37), then using trial & error adjust the
values and membership functions for improved ride quality, to allow increased adaptiveness of the
controller across various excitation levels.
Figure (36): Basic fuzzy controller schematic
Figure (37): Fuzzy logic designer tool within MATLAB receives the input, allows membership functions
to be designed, along with a rule base dictating the behaviour of the controller based on output
membership functions.
Figure (38): Fuzzy input set to definition of damped mass velocity response that would
result from road disturbance.
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Figure (39): Fuzzy output set for a quarter car suspension model depending on input
velocity, dictating voltage input into the electromagnet.
Using Mamdani interference to develop rules listed below, values of velocity & voltage are used to
control the behaviour of the MR damper at different operating points. The Mamdini type of fuzzy rules
processing was formed from when E.H.Mamdini built the first fuzzy controller in 1974 to control a
highly non-linear plant without any knowledge of process dynamics. (Mafouf, 2016). Using these
concepts the following general basic set of fuzzy rules were formed below for the MR damper:
1. IF (Velocity is Small) THEN (Voltage) is Low Volts 2. IF (Velocity is AN) THEN (Voltage) is Low Volts
3. IF (Velocity is Average) THEN (Voltage) is Medium Volts 4. IF (Velocity is AP) THEN (Voltage) is High Volts 5. IF (Velocity is Big) THEN (Voltage) is High Volts
AN & AP refers to average negative & average positive of the velocity, potentially the fuzzy
controller can be adjusted to be more intricate by seperating the velocity into more catogories,
which leads to the controller adapting to more scenarios, the voltage applied is general ranging from
low volts to high, again the controller can be modified to include a range of voltage ranges to
become more adaptive & optimising damper response across all the road surfaces.
Figure (40): Dahl model of MR damper that includes a fuzzy controller
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Figure (41): Response of the fuzzy logic controller subject to average road disturbance, comparing the
response to the passive & PID controller, the fuzzy system is validated & functions in the correct manner.
Figure (41.1): Hysteresis of fuzzy controlled MR damper subject to an average road surface indicates the controller is valid & achieving preliminary validation requirements.
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Chapter 5 - Results
5.1. Dynamic Responses
Dynamic responses of each road classification were recorded for each mode of MR damper: 0 volts, 12
volts, MR damper with PID & Fuzzy controller. The simulation duration for all was 20 seconds, 10
seconds or less was deemed too short to gain accurate responses & anything over 30 seconds required
too much computational power that was available especially for road classes C to E, taking up to 30
mins for a simulation.
Firstly the MR damper is simulated as a “passive” state with 0 volts & 12 volts as the voltage input,
showing both minimal damping resistance & maximum damping resistance, then the PID & fuzzy
controllers were simulated, calculated averages of vertical acceleration is displayed in Table(4).
However it is not established what the optimal voltage of the system is, thus 0 volts & 12 volts are used.
MR damper with constant 12V A B C D E
𝑐𝑐𝑚𝑚/𝑐𝑐2 3.6 17.7 3.1 6.5 1.5
PID Fuzzy A B C D E A B C D E
𝑐𝑐𝑚𝑚/𝑐𝑐2 8.2 7.4 10.2 5.5 8.49 7.6 7.3%
4.6 37.8%
5.4 47.1%
4.6 16.4%
3.83 54.8%
Table(4): Mean responses of acceleration of the MR damper comparison of MR damper with 0 volts ,
with 12 volts, the implemented PID controller & fuzzy controller, with percentage improvement noted of
fuzzy controller vs PID.
From responses of mean accelerations, it shows the fuzzy controller shows significant improvement
over the PID controller with road classes B, C & E, indicating it is more adaptive over a smooth road,
average road, and roads/surfaces akin to very rough trails, however concerning the road profiles,
constant 12V provides best performance within A, C & E roads, but shows very poor performance
within B & D, the damper at 0V shows poor performance compared to the fuzzy controller for all roads
apart from road C. The fuzzy controller shows constant adaptability across the road profiles, with finer
tuning of the controller the results can potentially show improvement over the constant 12V concerning
road A,C & E.
Passive MR damper at 0V A B C D E
𝑐𝑐𝑚𝑚/𝑐𝑐2 7.8 5.2 4.6 6.9 9.8
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5.2. Standard Deviations
Average of accelerations takes into account negative value accelerations also; leading to a
questionable reliability of analysis therefore standard deviations can show a much clearer & reliable
analysis of the results.
5.2.1. Ride Quality
Standard deviations of
Vertical acceleration
Passive MR damper at 0V A B C D E
3.13 6.2 12 23.5 46.3 MR damper with constant 12V
2.75 5.81 11.5 22.7 46.2 PID
3.2 6.2 12 24 46.3 Fuzzy
2.25 4.9 11.1 23.5 46.1 Original Passive system(No MR damper)
3.3 6.6 13.1 26 51.6 Table (5): Standard deviations for each MR damper, PID, Fuzzy & original passive system
A. Fuzzy controller shows improvement over the PID controller by 29.6%, over the MR damper
with 0V, & 12V by 28.1%, 18.2% respectively, & 31.8 % improvement over the original
passive system.
B. Fuzzy controller shows improvement over the PID controller by 21%, over the MR damper
with 0V, & 12V by 21%, 15.7% respectively, & 25.8 % improvement over the original passive
system.
C. Fuzzy controller shows improvement over the PID controller by 8%, over the MR damper with
0V, & 12V by 8%, 3.5% respectively, & 15.3 % improvement over the original passive
system.
D. Fuzzy controller shows 0% improvement between MR damper at 0 volts & decrease in
performance compared to 12 volts by 3.5% although shows improvement over PID, & original
passive system by 2.1% & 9.6% respectively.
E. For the very poor road class which shows a large amount of excitation to the system, the
differences between 0 volts, 12 volts, PID & fuzzy all amount to less than 1% , while the
biggest improvement over the original passive system is the fuzzy system at 10.6%
Standard deviations of acceleration of the damped mas show that the fuzzy logic controller improves
ride quality over all road profiles, the most significant improvement occurs within road class A to C
with minor improvement occurring at road D. Within road E there very small changes between
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deviations of each model, this indicates that despite the controller or constant voltage within the MR
damper, with enough disturbances shown the MR damper will not be worth implementing if the
majority of roads fall within this category. Within most western countries commercial drivers usually
spend time on highways & urban areas, which represent roads A to C, therefore relating to addressing
health issues that stem for long durations of driving the system with a fuzzy controller is an attractive
option.
The results establish that a fuzzy controller can offer better performance & could lead to further
increased performance if more rules & membership functions are introduced, concerning ride quality.
Figure (41.2): Voltage analysis in yellow compared to vertical acceleration in green, & velocity in
orange, for a fuzzy controlled system using road C.
Within Figure (41.2) shows the effect of damped mass responses feeding into the fuzzy logic controller
to generate a voltage level, voltage response takes 0.1 seconds.
5.2.2. Road Holding
In Table (6) wheel/undamped mass standard deviations in terms of acceleration is recorded, as
previously stated in the objectives road holding of the MR damper system will be analysed. Overall the
PID shows best performance when road handling is concerned, shortly followed by the fuzzy controller.
A constant 12V shows the worst performance, especially with road E.
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Standard
deviations of Vertical
acceleration of the wheel within road
A
Passive MR damper at 0V 46.9
MR damper with constant 12V 48.7 PID 44.2
Fuzzy 45.5
Standard deviations of
Vertical acceleration of the wheel within road
B
Passive MR damper at 0V 89.9
MR damper with constant 12V 93.7 PID 85.3
Fuzzy 88.8
Standard
deviations of Vertical
acceleration of the wheel within road
C
Passive MR damper at 0V 168.3
MR damper with constant 12V 176 PID
162.9 Fuzzy 164.1
Standard deviations of
Vertical acceleration of the wheel within road
D
Passive MR damper at 0V 326.7
MR damper with constant 12V 330.9 PID
321.8 Fuzzy 324.9
Standard
deviations of Vertical
acceleration of the wheel within road
E
Passive MR damper at 0V 642.0
MR damper with constant 12V 660.4 PID
632.1 Fuzzy 638.2
Table (6): Standard deviations of undamped mass (wheel) in terms of vertical acceleration, increased
values indicate poor road handling performance compared with lower values.
Comparing results from the damped mass & undamped mass standard deviations of vertical
accelerations it shows that the MR damper improves performance compared to the conventional system,
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especially when a fuzzy controller is implemented, the controller shows constant improved performance
concerning ride quality & even though the PID shows better road handling qualities, the differences are
minimal, thus, due to the project work concentrating on ride quality the fuzzy controller is the prevailing
option.
Concerning road E, there are minor differences between the controllers & modes, if the controllers are
tuned further & similar results are shown, it can suggest a performance limitation of the MR damper
within very rough terrain/off-road surfaces.
5.3. Potential Errors
Very late into the thesis the non-linear MR damper modelling is not fully accurate due to k in equation 6
is actually formed via = 𝑘𝑘𝑎𝑎 + 𝑘𝑘𝑤𝑤 𝑣𝑣 , within this thesis the a fixed value was assigned to k, for a more
accurate non-linear model 𝑘𝑘𝑎𝑎 + 𝑘𝑘𝑤𝑤 𝑣𝑣 can be placed within equation 6, forming:
(26). 𝐹𝐹𝑚𝑚𝑚𝑚 = ( 𝑘𝑘𝑎𝑎 + 𝑘𝑘𝑤𝑤 𝑣𝑣 ) �̇�𝑥𝑑𝑑 + (𝑘𝑘𝑤𝑤𝑎𝑎 + 𝑘𝑘𝑤𝑤𝑤𝑤𝑣𝑣)𝑤𝑤
The model will be affected accurately by the voltage, due to transforming the equation results in a total
of 5 estimated parameters, to improve this further, non-linear parametric identification can be utilised
which is discussed in further detail for improvements in chapter 7.
The adjustment of the Dahl model transforms the Simulink in Figure (31) model into Figure (42):
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Figure 42: Increased accuracy of the Dahl model over the one implemented within the thesis,
where the model depencney on voltage is increased.
However as stated within Chapter 3, the model was implemented from equations 6 & 7 & still produced
correct relationship between velocity & damping force in line with previous established research by
Dahl. The most advantageous aspect of correcting this oversight is with non-linear parametric
identification, with a more accurate model can produce reliable parameter estimation.
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Chapter 6 - Conclusion
In summary a review of potential suspension systems to increase ride quality has been carried out, the
literature shows that the MR damper was a suitable replacement for a conventional passive suspension
system compared to active systems, due to cost saving traits, thus, addresses the issue of being within
budget for vehicles that the general population can afford & benefit from, another attribute is the ability
to adjust damping force according to road excitation, while exhibiting a fail-safe features. Road profiles
were modelling using the power spectral density based on ISO 8608 then simulated via band-limited
white noise within Simulink.
The MR damper was implemented based on a passive quarter-car suspension system; the model was
adjusted to accommodate the Dahl Model, a non-linear model describing the behaviour of the MR
damper. The hysteresis of the model was then validated based on previous research; previous
established test data was not available, thus parameter identification was carried out by a manual trial &
error method to emulate previous research papers showing the hysteresis of the Dahl model.
Once the models have been validated a PID controller was implemented, tuning the parameters to
reduce overall vertical accelerations & standard deviations for a specified time. Subsequently a fuzzy
logic controller was designed, this was chosen due to fuzzy logic becoming more prominent in industry,
especially in automotive engineering. The results improvement over the PID controller, concerning
mean vertical accelerations & standard deviations, however PID controller shows better performance
when standard deviations of the undammed mass are analysed indicating better road holding
performance, due to the project aim of improving ride quality, the fuzzy system is most advantageous
showing improved adaptability across different road excitations. Fuzzy system shows most
improvements for road classes A to D, with hardly any improvement with road E/off-road terrain. This
suggests that the controllers need further tuning for increased robustness.
Active/semi-active suspension systems still remain in a duality between ride quality & road holding,
thus frequent trade-offs are required in the design of the controller therefore suggestions to improve the
research are discussed in Chapter 7.
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Chapter 7- Improvements & Future work
7.1. Improvements
7.1.1. Non-Linear Parametric Identification
The estimation of the parameters manually could lead to numerical inaccuracy; therefore non-linear
parametric identification is suggested to increase the accuracy of the Dahl model that
estimates: 𝑘𝑘𝑎𝑎,𝑘𝑘𝑤𝑤, 𝑘𝑘𝑤𝑤𝑎𝑎,𝑘𝑘𝑤𝑤𝑤𝑤 & 𝜌𝜌. This will be most beneficial once a prototype is developed & test
data is available leading to using measured data to estimate parameters or the model itself, known as
white-box estimation.
7.1.2. Passive System Optimisation
A potential area for improvements would be editing the original passive system, optimising
performance of ride quality & road holding across the road classifications, therefore once that the spring
& damping coefficients are optimised for the vehicle & roads A to E, forming an MR Damper thereafter
& results of the experiment can assure if the MR damper is truly an improved system over the
conventional MacPherson suspension set up.
7.1.3. Fuzzy Controller Tuning
Improvement with the fuzzy controller is another area that can be improved, by adding membership
functions & more rules so that the controller manipulates the MR damper more effectively over all road
models, especially D & E. It can go one step further, by adding Sugeno type fuzzy processing, which is
adding a second input to the controller & edit the voltage output accordingly, it can use linguistic
vatable such as OR & AND rendering the controller more robust & diverse.
For example, it can include undamped/wheel vertical velocity to take into account road holding by the
following rules:
1. IF Wheel Velocity is very low AND Mass Velocity is very high THEN Big voltage increase
2. IF Wheel Velocity is medium AND Mass Velocity is low THEN voltage small decrease
3. IF Wheel Velocity is very high AND Mass Velocity is very low THEN voltage Big decrease
4. IF Wheel Velocity is medium AND Mass Velocity is medium THEN voltage medium(constant)
Observing the voltage response in Figure (41.2), further intricate membership functions & rules can use
a broader range of the voltage spectrum that can solve the issue of performance of the fuzzy controller
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within road classes D to E, that increase ride comfort for very poor roads/off road terrain, pushing the
performance of the MR damper close to it’s mechanical limitations.
7.2. Future Work
7.2.1. User Adaptive Controller Design
A potential avenue to explore is further design of fuzzy logic controllers within the MR damper that
changes the behaviour based on input from the user which prioritise & optimise ride quality & road
holding.
For example a vehicle may have 3 settings the user can choose from within the cockpit of the car:
1. Terrain
2. Urban
3. Performance
If the driver selects “Terrain” this indicates driver is to encounter off-road terrain, in most cases at low
speeds thus road holding is not a priority, therefore a fuzzy controller can be designed to optimise ride
quality to the maximum it can be, secondly selecting “Urban” may indicate that the driver is driving
through the city where road classes fall in between C to D, where an another set of fuzzy rules can be
applied to increase road holding ability while keeping a high level of comfort. Finally if “Performance”
mode is selected a fuzzy controller can be designed to maximise road holding, this could sacrifice ride
comfort, but that is the duality of semi-active suspension systems.
7.2.2. Vehicle Body Roll Control
Future work can include control & analysis of a half car model that can help analyse & develop
controllers to adjust the MR damper force according to both vertical acceleration & acceleration
within the roll axis, adjusting the left & right side MR dampers to control vehicle body roll offering
a more stable ride experience & road holding. Use of vehicle speed & steering angle can help
design the controller.
7.2.3. Improved Road Model
If one is to analyse a half or full car model to control pitch & roll affects the use of a 2 track/slope
road model is a requirement due to both wheels acting independently of one another. The current
spectrum model chosen from the ISO 8608 study provides a simplified approximation. However a
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two slope spectrum known as the MIRA (Motor Industry Research Association), this contains
higher degree of accuracy suitable for analysing system response to uneven road surfaces that occur
on both sides of the vehicle. The MIRA & ISO classes are the most prevailing in industry.
7.2.4. ISO 2631
Using vibrational analysis, ISO 2631 frequency considerations listed in Table(1) can be addressed
to asses motion sickness & comfort, aiding the engineer in designing a system addressing health
concerns of the user in a more detailed manner.
7.2.5. Validation of control performance
Use of a demonstration model of a MR Damper can be utilised as a prototype to validate control
performances of both PID & fuzzy controller.
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REFERENCES
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[18]. Rajput, R. (2007). A Text Book of Automobile Engineering. New Delhi: Laxmi Publications. [19]. Citroenet.org.uk. (2017). Citroen hydropneumatic suspension - overview. [online] Available at: http://www.citroenet.org.uk/miscellaneous/hydraulics/hydraulics-1.html [Accessed 26 Aug. 2017]. [20]. Moulton, Alex. (1962). “Hydrolastic Springing”. Automobile Engineer. September 1962 [21]. Stone, R. and Ball, J. (2004). Automotive Engineering Fundamentals. Warrendale, Pennsylvania: SAE International. [22]. Dahiphale, M., Chopade, Y., Patil, C. and Pathan, F. (2016). Active Body Control Suspension. International Journal of Advanced technology in engineering & science, 4(03), pp.389 - 395. [23]. Haynes, J. (2004). Citroen: Daring to be Different. Haynes Manuals Inc. [24]. Active Body Control (ABC)The DaimlerChrysler Active Suspension & Damping SystemThomas Merker, Gaston Girres & Olaf Thriemer [25]. Audi AG, (2002), Adaptive Air suspension in the Audi A8, Home Study program 292,T007/02, Ingolstadt: Audi [26]. Turkay, S. and Akcay, H. (2015). Spectral Modeling of Longitudinal Road Profiles. 28th Electrical and Computer Engineering (CCECE). [27]. van der Sande, T. (2011). Control of an automotive electromagnetic suspension system. Masters. Eindhoven University of Technology. [28]. Andren, P. (2006). Power spectral density approximations of longitudinal road profiles. International Journal of Vehicle Design, 40(1/2/3), p.2. [29]. Sequeirac, A., Benny, B., Karanth P, N. and D’Souzaa, R. (2016). Hysteresis Modeling of Amplified Piezoelectric Stack Actuator for the Control of the Microgripper. American Scientific Research Journal for Engineering, Technology, and Sciences, 15(1), pp.265-281. [30]. Braz-Cesar, M. and Barros, R. (2013). Experimental & Numerical Analysis of MR Dampers. PHD. University of Porto. [31]. Iskandarani, Y. and Karimi, H. (2011). Hysteresis modeling for the rotational magnetorheological damper. Recent Researches in Geography, Geology, Energy, Environment and Biomedicine, pp.479 - 485. [32]. Andronic Florin, Manolache-Rusuioan-Cozmin, Patuleanuliliana,(2013), Passive Suspension Modelling using MATLAB, Quarter Car Model, Input Signal Step Type, New Technologies & Products in Machine Manufacturing Technologies, University of Suceava 2013. [33]. Dahl P.R. (1968) A solid friction model. Technical Report, TOR-158(3107-18) (El-Segundo, CA: The Aerospace Corporation), 1968.
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[34]. Mahfouf, M (2016), Fuzzy Logic Modelling & Control, Theortical & practical aspects of fuzzy systems, Automatic Control & Systems Engineering, University of Sheffield [35]. Spencer, B., Dyke, S., Sain, M. and Carlson, J. (1996). Phenomenological Model of a Magnetorheological Damper. ASCE Journal of Engineering Mechanics, pp.1- 22. [36]. Hingane, A., Sawant, S., Chavan, S. and Shah, A. (2017). Analysis of Semi active Suspension System with Bingham Model Subjected to Random Road Excitation Using MATLAB/Simulink. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), pp.1-6. [37]. Jantzen, J. (1999). Design Of Fuzzy Controllers. Lyngby: Technical University of Denmark. [38]. Ghorbany, D. (2011). MR Damper hysteresis characterization for the semi-active suspension system. Masters. University of Agder. [39]. Passino, K. and Yurkovich, S. (1998). Fuzzy Control. California: Addison Wesley Longman, Inc. [40]. Zapateiro, M., Luo, N., Rodellar, J. and Rodríguez, A. (2017). Modelling and identification of hysteretic dynamics of my Dampers & application to semi active vibration control of smart structures. In: The 14th World Conference on Earthquake Engineering.
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APPENDIX
Overall layer of the Simulink model used in the thesis:
Adjusted (highlighted in red) passive system to accommodate the dahl model:
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Fuzzy hysteresis response to all road disturbances:
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PID hysteresis response to all road disturbances
Code:
%{ **Naveen Chadha **08/2017 **Modelling, Analysis & Control of vehicle suspension **University of Sheffield %} clc; clear; fuzzy=readfis('SuspensionFuzzy.fis'); %% Vehicle Parameters % m2 = 450; % m1 = 68; % kd = 28500; % ku = 293900; % cd = 2700; % cu = 6; m2 = 341.3; m1 = 47.4; kd = 32000;%8000; ku = 170000;%80000; cd = 1000; cu = 30; %% MR damper Hysteresis Parameters - Bouc-Wen Gamma = 1.2e7;
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Beta = 1e7; Tau = 15; n = 2; Ko=300; Co= 650; u = 5; Alpha = 8e4; Fo= 0; %% dahl model parameters ud = 1.5; D_Ro = 1500; D_Gain= 350; Kwa= 80; Kwb=80; %% Bingham Model Parameters d=10; Fc = 210; %% Langarian method for passive system %% ---------------- %Mass M= [m2 0 ; 0 m1]; %Springs Spring = [kd+ku -ku; -kd kd+ku]; %Dampers C_d = [cd+cu -cu; -cd cu+cd]; I = eye(2); %% State Spaces %% --------------------------------------- A = [-(inv(M)*C_d) -(inv(M)*Spring); I zeros(2)]; B = [ inv(M); zeros(2)]; C = [0 0 1 0]; D =[0 0]; sys = ss(A,B,C,D); C_V = [0 0 0 1]; sys_v = ss(A,B,C_V,D); %% Transfer functions %% ---------------------------------- tf('s'); [num,dum]=ss2tf(A,B,C,D,2); systf = tf(num,dum); %% Zero Pole Gain %% --------------------------------------- [z_tf,p_tf,k_tf] = tf2zp(num,dum); G = zpk(z_tf,p_tf,k_tf);
rankreach = rank(ctrb(A,B)); rankobsv = rank(obsv(A,C)); syseig= eig(sys); %Less than 0 = stable [wn,zeta]=damp(sys); figure(1) bode(systf); grid on;
%% ISO Road Roughness
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% Cycles Omega0 = 0.1; % PSD ISO Gd_0 =32*(10^-6); % W – fluctuations in road w = 1; % Length of Road L = 100; N = 1000; Omega_L = 0.004; % 1 = complete flat road Omega_U = 0.8; %frequency of roughness % % % % delta = 1/L; %Spatial Frequency Band Omega = Omega_L:delta:Omega_U; % Power Spectral Density of road Gd = Gd_0.*(Omega./Omega0).^(-w); % calculate amplitude using formula(8) in the article %Amp = sqrt(2*Gd*delta_n); k = 3; Ro = sqrt(delta) * (2^k) * (10^-3) * (Omega0./Omega); Psi = 2*pi*rand(size(Omega)); % intervals 0 to L Phi = 0:0.5:100; H= zeros(size(Phi)); for i=1:length(Phi) H(i) = sum( Ro.*cos(2*pi*Omega*Phi(i) + Psi) ); end H_R = H*1000; %speed initally calculated from mm/s figure(2) plot(Phi, H_R,'r'); xlabel('Distance m'); ylabel('Elevation (mm)'); grid on