Fall 2013 -- ECEN 4138/5138 -- Control Systems Analysis.

Instructor: Harry Hilgers

Course Overview

·         Analysis and design of continuous time control systems using frequency (classical) and time domain (state space) methods.

·         Develop equations of motion for mechanical and electrical systems.

·         Laplace transforms

·         Transfer functions and block diagrams.

·         Stability, dynamic response and steady-state analysis.

·         Analysis and design of control systems using root locus and frequency response methods (Gain/Phase Margin, Nyquist diagrams, Nichols Charts).

·         If time permits: Introduction to Digital Control via difference equations and z-transform.

·         Computer aided design and analysis with Matlab/Simulink (during lecture periods as well as in homework)

·         Course details will be on D2L

REQUIRED Course Material

1)      Norman S. Nise, Control Systems Engineering, 6th Edition, Wiley, 2011, ISBN 13 978-0470-54756-4

2)      Katsuhiko Ogata, Matlab for Control Engineers, ISBN 978-0-13-615077-0

3)      Student version of Matlab/Simulink R2013a. This must reside on your laptop computer (you will need this during lectures and exams).

Detailed Syllabus

1.     Introduction

What is a Control System

What is a Control Systems Engineer

What are the Control System Objectives

What is the Control System Design Process

2.     Modeling in the frequency domain

Short review of the Laplace Transform

The transfer function – what is it?

Equations of motion and subsequent transfer functions of

Electrical Networks

Mechanical Systems

Translational

Rotational

Analogs between electrical and mechanical equations of motion

Linearization

Case Study

3.     Modeling in the time domain

State Space Representation

Conversion between Transfer Function and State Space

Linearization

Case Study

4.     Time Response

Poles, zeros

System order

First Order

Second order

Critically, Over, Under damped

Effect of zeros

Effects of nonlinearities

Laplace Transform solution of the State Equations

Time domain solution of the State Equations

Case Study

5.     Reduction of Multiple Subsystems

Block diagrams

Feedback systems

Signal Flow Graphs

Similarity Transformations

Case Study

6.     Stability

S-plane stability

Routh Hurwitz Criterion

Stability in State Space

Case Study

Position, Velocity and Acceleration steady-state errors

Steady-State Error for Unity Feedback systems

Static Error Constants and System Type

Specifications

For Disturbances

For Non-Unity Feedback Systems

System Sensitivity

Steady- State errors in State Space

Case Study

8.     Root Locus Techniques

Definition

Properties

Sketching the Root Locus by hand

Drawing the Root Locus with Matlab

Pole Sensitivity

Case Study

9.     Design via Root Locus

Improving Steady State and Transient Response

Physical Realization of the Compensators

Case Study

10.  Frequency Response Techniques

Review of Bode Plots

Nyquist Criterion

Stability via Nyquist Diagram

Gain and Phase Margin via Nyquist Diagram

Stability, Gain and Phase Margin via Bode Plots

Relation between

Closed Loop Transient and Closed Loop Frequency Responses

Closed and Open Loop Frequency Responses

Closed Loop Transient and Open Loop Frequency Responses

Steady State Error Characteristics from Frequency Response

Systems with Time Delay

Obtaining Transfer Functions Experimentally

Case Study

11.  Design via Frequency Response

Case Study

12.  Design via State Space

Controller Design

Controllability

Observer Design

Observability