ece16513 sm15 lecture 1

7/21/2019 ECE16513 SM15 Lecture 1

http://slidepdf.com/reader/full/ece16513-sm15-lecture-1 1/47

Control Systems

16 513 - 011

Lecture 1

Mufeed MahDECE, UML, Summer 2015

7/21/2019 ECE16513 SM15 Lecture 1


Course Outline

Tentative Course Description

•

Introduction to Control Systems & Mathematical Models of Systems• Review Linear Algebra and Matrix operations

• State Variable Models

• Feedback Control System Characteristics

• The Performance of Feedback Control Systems

• The Stability of Linear Feedback Systems

• The Design of State Variable Feedback Systems

Prerequisite

16:413 Linear Feedback Systems

Tentative Textbooks• Modern Control Systems, 10/e by Richard C. Dorf and Robert H. Bishop. ISBN:

9780131457331

• Design of Feedback Control Systems by Raymond T. Stefani, Bahram Shahian. ISBN-13:

978-0195142495 ISBN-10: 0195142497

• Any other Control systems Textbook

ECE16513 Summer I -2015 Mufeed MahD, ECE, UML

7/21/2019 ECE16513 SM15 Lecture 1


Course OutlineGrading Policy

• Exam 1 and 2 50%

• Final Exam 50%

Remarks

• All exams are OPEN book (only assigned textbook)

• No makeup exams. If you missed an exam due to legitimate reasons, weight will be

scaled to other attempted work

• No showing up for the final exam is an immediate F in the course.

Instructor

Mufeed Mahd, PhD PEng

ECE, UMASS Lowell, Ball Hall 321,Tel (978)934-3317

Email: [email protected]

Subject: ECE16513-SM2015

Office Hours: By appointment

ECE16513- Summer I -2015 Mufeed MahD, ECE, UML

7/21/2019 ECE16513 SM15 Lecture 1


Control Concept

(a) A plant or process to be controlled.

(b) An open-loop control system.

(c) Example of an open-loop control system.

(d) Engine speed versus throttle angle curves.


Introduction to Control Systems - Foundations

7/21/2019 ECE16513 SM15 Lecture 1


Feedback Control Concept

(a) A closed – loop or feedback control

(b) A closed-loop engine control system



7/21/2019 ECE16513 SM15 Lecture 1


Feedback Control Concept- Advantages



7/21/2019 ECE16513 SM15 Lecture 1


Modeling

A mathematical model that behaves similarly as the actual system within some

operating range.



7/21/2019 ECE16513 SM15 Lecture 1


Modeling- Linearization

Instead of nonlinear mathematical equation, a linear model that operates near

some value called (xo) can be obtained using

Taylor Series Approximation.



7/21/2019 ECE16513 SM15 Lecture 1


Modeling- Electric Systems

• Governed by KCL and KVL

• Can be solved using Nodal or Mesh Analysis or any other techniques learned

in circuit theory

• Normally systems are LTI, and can be solved using Laplace Transform.



7/21/2019 ECE16513 SM15 Lecture 1


Modeling- Electric Systems

• Components and Sources permit superposition principle.



7/21/2019 ECE16513 SM15 Lecture 1


Modeling- Electric Systems- Example

Solving using Mesh Analyses

Mesh 1

Mesh 2

Collecting Terms



7/21/2019 ECE16513 SM15 Lecture 1



Solving using Mesh Analyses



7/21/2019 ECE16513 SM15 Lecture 1



Solving using State Variables Approach

It is when the Differential Equations were written in terms of ENERGY STORED

in the capacitors and inductors instead of voltage current relationship.

Select inductors currents i1 and i2 AND capacitor voltage vc.

Then, we have



7/21/2019 ECE16513 SM15 Lecture 1



Solving using State Variables Approach



7/21/2019 ECE16513 SM15 Lecture 1



Nodal Analysis

Arranging terms

Laplace Transform



7/21/2019 ECE16513 SM15 Lecture 1


Modeling- Electric Systems- Op Amp



7/21/2019 ECE16513 SM15 Lecture 1



Lag Impedance Circuit

which can be written in a general form as

note: a should be > b. to have the pole (-b)

to the right of the zero ( – a).



7/21/2019 ECE16513 SM15 Lecture 1





7/21/2019 ECE16513 SM15 Lecture 1



Op Amp circuits are very important in the Design Problem.

Primarily used in system compensation to improve system behavior (stability or

time response).

Example: Create the circuit

Solution: since the zero to the right of the pole, select the lead configuration.



7/21/2019 ECE16513 SM15 Lecture 1


Translational Mechanical Components

A method of analysis for the translational mechanical systems include these

steps:

a) Spring-mass-damper translational mechanical system at equilibrium

b) Free body diagram



7/21/2019 ECE16513 SM15 Lecture 1


7/21/2019 ECE16513 SM15 Lecture 1


Translational Mechanical Components- Example

Equating forces for mass(es)

Collecting terms and Laplace Transform

The vibration damper transfer function can be expressed as



7/21/2019 ECE16513 SM15 Lecture 1



State Variable Approach

Select your states variables as (x1) and (x2) as well as

The state space representation for the translational system is



7/21/2019 ECE16513 SM15 Lecture 1




Select your states variables as (x1) and (x2) as well as

The state space representation for the translational system is



7/21/2019 ECE16513 SM15 Lecture 1




Laplace Transform

Using Cramer's’ rule to solve for X1(s)



7/21/2019 ECE16513 SM15 Lecture 1


Rotational Mechanical Components

Torque- Angle Relationship

a) Rotational-Spring-Mass-Damper Systems at Equilibrium


c) Gear Train



7/21/2019 ECE16513 SM15 Lecture 1



Analysis Procedure



7/21/2019 ECE16513 SM15 Lecture 1


Rotational Mechanical Components- Example

a) Rotational Mechanical Systems




7/21/2019 ECE16513 SM15 Lecture 1



Node Equivalent circuit

Mesh equivalent circuit



7/21/2019 ECE16513 SM15 Lecture 1



Equating Torques

Collecting terms

Laplace Transform



7/21/2019 ECE16513 SM15 Lecture 1



Nodal Analogy

Compare the mechanical equations for mass and inertial to the electricaladmittance at a node

We have,



7/21/2019 ECE16513 SM15 Lecture 1



Nodal Analogy

Compare the mechanical equations for mass and inertial to the electricalimpedance at a node

We have,



7/21/2019 ECE16513 SM15 Lecture 1



Gear Train and Transformers

The torque ( 1) is

The torque( 2) is



7/21/2019 ECE16513 SM15 Lecture 1




The gear relationship

Solving for ( 1) and substituting to get equation in terms of the input torque ( )



7/21/2019 ECE16513 SM15 Lecture 1




KVL for the primary and secondary side of idea transformer

Turn ratio for the transformer

Then, one KVL equation referred to the primary side



7/21/2019 ECE16513 SM15 Lecture 1




Gear-Transformer Analogy



7/21/2019 ECE16513 SM15 Lecture 1


Electromechanical Components



7/21/2019 ECE16513 SM15 Lecture 1



Electrical equation for DC control motor driving an Inertia load

Mechanical equation, neglecting the damping friction B,Laplace transform with zero IC, we get

note: this model is also good for AC control motor



7/21/2019 ECE16513 SM15 Lecture 1



Motor Driving an Inertia Load via a Gear train

Electrical equation for DC control motor driving an Inertia load

Mechanical equation, neglecting the damping friction B,

where

Then,



7/21/2019 ECE16513 SM15 Lecture 1



The DC generator model is governed by



7/21/2019 ECE16513 SM15 Lecture 1





7/21/2019 ECE16513 SM15 Lecture 1



Note: The rate of change of angular momentum

of a system is equal to the applied torque

Alternatively,



7/21/2019 ECE16513 SM15 Lecture 1



Fundamental Gyroscope law: A torque about any axis other than the spin axisproduces a velocity about the axis that is orthogonal to the applied torque axis.

The gyro is an important instrument for measuring torques (Qx=Hwy) by

measuring this orthogonal or precession velocity.



7/21/2019 ECE16513 SM15 Lecture 1




ece16513 sm15 lecture 1

Documents