Internal Model Controller Design for a Internal Model Controller Design for a Robot armRobot arm

By Vishal KumarBy Vishal KumarAdvisor: Gary L. DempseyAdvisor: Gary L. Dempsey

5/6/085/6/08Bradley UniversityBradley University

Department of Computer and Electrical EngineeringDepartment of Computer and Electrical Engineering

Senior Project

Senior ProjectSenior Project

1.1. Functional DescriptionFunctional Description

2.2. Project FocusProject Focus

3.3. Functional Requirements and Functional Requirements and SpecificationsSpecifications

4.4. Lab work and comparison of resultsLab work and comparison of results

Functional DescriptionFunctional Description

Individual ComponentsIndividual Components

• 1.46 GHz Windows Based PC with plenty 1.46 GHz Windows Based PC with plenty of RAMof RAM

• Quanser Plant SRV-02 with embedded Quanser Plant SRV-02 with embedded position sensors, gripper and motorposition sensors, gripper and motor

• Q8 High-Performance H.I.L Control Board Q8 High-Performance H.I.L Control Board and I/O port interfaceand I/O port interface

• Power Module PAO103Power Module PAO103

Functional DescriptionFunctional Description

Functional DescriptionFunctional DescriptionQ8 High-Performance H.I.L Control BoardQ8 High-Performance H.I.L Control Board

8 A/D / 8 D/ASimultaneous Sampling of all A/D and Simultaneous Update to all D/ASupported by Real-Time Targets – RTX, xPC

Functional DescriptionFunctional Description

Acquisition Board Port InterfaceAcquisition Board Port Interface

Functional DescriptionFunctional Description

Power ModulePower Module

High Level System Block DiagramHigh Level System Block Diagram

Project AbstractProject Abstract

The goal of this Electrical Engineering Senior Capstone Project is to design a Internal Model Controller for controlling the non-linear 6th order Quanser Plant in the level configuration.

The disturbance rejection capability of Internal Model Control architecture is capable of controlling high-order plants despite their non-linearities and external disturbances.

Project DescriptionProject Description

Internal Model Control Open-LoopInternal Model Control Open-Loop

Let Gp(s) = approx(Gp(s))And Gc(s) = approx(Gp(s)) ^ -1Then Gp(s)*Gc(s) = approx(Gp(s)) * approx(Gp(s)) ^ -1 = 1

Project DescriptionProject Description

Internal Model Control Closed-LoopInternal Model Control Closed-Loop

Project DescriptionProject Description

Internal Model Control AdvantagesInternal Model Control Advantages Provides time-delay compensationProvides time-delay compensation

At steady-state, the controller will give offset free At steady-state, the controller will give offset free responses(perfect control at S.S)responses(perfect control at S.S)

The controller can be used to shape both the input tracking and The controller can be used to shape both the input tracking and disturbance rejection responsesdisturbance rejection responses

The controller is the inverse of the plant without non-invertible The controller is the inverse of the plant without non-invertible components(time-delay)components(time-delay)

Perfect Tracking is achieved despite model-mismatch, as long Perfect Tracking is achieved despite model-mismatch, as long as the controller is the perfect inverse of the model. as the controller is the perfect inverse of the model.

Project DescriptionProject Description

Model Implementation TechniquesModel Implementation Techniques22ndnd order model(Linear) order model(Linear) used for used for

Proj. Proj. Look-up Tables(Linear and Non-Linear)Look-up Tables(Linear and Non-Linear)State-Space Model(Linear)State-Space Model(Linear)Adaline model(Linear)Adaline model(Linear)Non-Linear Perceptron model(Non Non-Linear Perceptron model(Non

Linear)Linear)

PrespectivePrespective

What makes this project different?What makes this project different?

New ToolsNew Tools• Simulink/Real Time Execution(RTX) Simulink/Real Time Execution(RTX)

WorkshopWorkshop• WinCon Client and WinCon Server WinCon Client and WinCon Server

environmentenvironment• Implementing an advanced controller Implementing an advanced controller

architecture – IMC – basis for adaptive controlarchitecture – IMC – basis for adaptive control

ApplicationsApplications

Adaptive Signal ProcessingAdaptive Signal ProcessingFlight Control – Adaptive models are of Flight Control – Adaptive models are of

importanceimportanceHydraulics – disturbance rejection is of Hydraulics – disturbance rejection is of

importanceimportance

Functional RequirementsFunctional Requirements

1.1. Single Loop – Proportional , Single Loop – Proportional , Proportional–Derivative ControllerProportional–Derivative Controller

2.2. FD Design for P, PD, PI controllersFD Design for P, PD, PI controllers

3.3. Internal Model ControlInternal Model Control

4.4. Internal Model Control with Adaptive Internal Model Control with Adaptive ModelModel

Performance SpecificationsPerformance Specifications

Percent Overshoot Percent Overshoot 5% max5% maxTime to PeakTime to Peak 50ms max50ms maxTime to settle Time to settle 200ms max200ms maxClosed Loop Bandwidth Closed Loop Bandwidth 2Hz min2Hz minClosed Loop Frequency Resp.Closed Loop Frequency Resp. 3dB max 3dB maxGain Margin Gain Margin 5.0 min5.0 minPhase Margin Phase Margin 60 degrees 60 degrees

minminSteady State Error Steady State Error 1 degree max1 degree maxController Execution Time Controller Execution Time 1ms max1ms max

Fall ’07 WorkFall ’07 Work

System Identification without armSystem Identification without arm

)150/(

69)(

)35(

ss

esGp

mss Experimental

Simulation

Fall ’07 WorkFall ’07 Work

Proportional Controller Design without Proportional Controller Design without armarm

Gc(s) = K = 0.3Gc(s) = K = 0.3

1.5 1.55 1.6 1.65 1.7 1.75-5

0

5

10

15

20

25

30

35

Time

Deg

rees

Proportional ControlGc(s) = .3

Fall ’07 WorkFall ’07 WorkProportional – Derivative Controller Design Proportional – Derivative Controller Design

without armwithout armGc(s) = 0.61(s + 61.5)/(s+120)Gc(s) = 0.61(s + 61.5)/(s+120)

Spring ‘08 WorkSpring ‘08 Work

System Identification with ArmSystem Identification with Arm

45.73 e^ ( -0.110s)45.73 e^ ( -0.110s)

Gp(s) = --------------------------Gp(s) = --------------------------

s(s/30.0 +1.0)s(s/30.0 +1.0)

Gain and Delay found by experimental dataGain and Delay found by experimental data

Pole found by multiple simulation best fit methodPole found by multiple simulation best fit method

This is the best fit 2This is the best fit 2ndnd order model for the plant. order model for the plant.

System Identification with ArmSystem Identification with Arm

Experimental vs. Model – results are close but not perfectExperimental vs. Model – results are close but not perfect

Spring ’08 Work

0 1 2 3 4 5 6-5

0

5

10

15

20

25

30

35

Experimental

Simulation

Spring ‘08 WorkSpring ‘08 Work

F.D.Design – P controllerF.D.Design – P controllerF.D. Design – PD controllerF.D. Design – PD controllerF.D. Design – PI controllerF.D. Design – PI controllerF.D. Design – Optimum Phase Margin PI F.D. Design – Optimum Phase Margin PI

controllercontroller

Standard Classical Control TechniquesStandard Classical Control Techniques

Design, Simulate, Implement, EvaluateDesign, Simulate, Implement, Evaluate

Spring ‘08 WorkSpring ‘08 Work

-60

-50

-40

-30

-20

-10

0

10

20

30

40

Mag

nitu

de (

dB)

100

101

102

-180

-135

-90

-45

0

Pha

se (

deg)

Bode Diagram

Frequency (rad/sec)

Uncompensated

Partially Compensated PI

Proportional Controller

Compensated PI

Optimum PI

Spring ‘08 WorkSpring ‘08 Work

IMC Controller Design

Spring ‘08 WorkSpring ‘08 Work•Final Design by Tuning

Spring ‘08 WorkSpring ‘08 Work

IMC step Response

Spring ‘08 WorkSpring ‘08 Work

SpecificationSpecification ValueValue Spec. Spec. Met?Met?

Percent Overshoot Percent Overshoot 5% max5% max YesYes

Time to Peak(max) Time to Peak(max) 50ms max50ms max NoNo

Time to settleTime to settle 200ms max200ms max NoNo

Closed Loop Bandwidth Closed Loop Bandwidth 2Hz min2Hz min YesYes

Peak CL Frequency Resp.Peak CL Frequency Resp. 3dB max3dB max YesYes

Gain MarginGain Margin 5.0 min5.0 min YesYes

Phase MarginPhase Margin 60 degrees min60 degrees min YesYes

Steady State ErrorSteady State Error 1 degree max1 degree max YesYes

Controller Execution TimeController Execution Time 1ms max1ms max YesYes

ConclusionConclusion

Internal Model Control(IMC) provides excellent performance for stable Internal Model Control(IMC) provides excellent performance for stable plants. Due to a integration in the plant model, meaning that the plants. Due to a integration in the plant model, meaning that the plant is marginally stable/unstable, the controller architecture plant is marginally stable/unstable, the controller architecture reaches limitations and has to be modified. reaches limitations and has to be modified.

As shown above, in the Simulink Block Diagram, the new architecture As shown above, in the Simulink Block Diagram, the new architecture provides velocity and position feedback with Internal Model for the provides velocity and position feedback with Internal Model for the velocity of the plant. Literature analyzing controller design provides velocity of the plant. Literature analyzing controller design provides no insight for controlling unstable plants. no insight for controlling unstable plants.

The aforementioned technique has powerful implications for controlling The aforementioned technique has powerful implications for controlling unstable plants using the IMC architecture. unstable plants using the IMC architecture.

Questions? Comments?Questions? Comments?