FEEDBACK CONTROL SYSTEMS

 Lecture: Tuesdays and Thursdays 3:00 - 4:20 pm SH 212

 Lab: Fridays 2:30 - 4:20 p.m. HH B301

 Matlab Tutorial URL: http://brie.library.cmu.edu/ctms/
 

Professor Qiao Lin Office: Scaife Hall 312 Phone: 268-3641 Email: qlin@andrew.cmu.edu Office hours: Thursdays 4:30-6:30 pm or by appointment	Secretary: Kate McClintock Office: Scaife Hall 317 Phone: 268-3050 Email: km63@andrew.cmu.edu
TA/Grader: Leanne Crosbie Phone: 521-7755 Email: crosbie@andrew.cmu.edu.

Purpose

Objectives

The major objectives of 24-451 are the following:

1. Be familiar with the inputs, outputs, and components of a control system. Know the difference between open-loop and closed-loop (feedback) control systems and understand the advantages of feedback control.
2. Understand the utility of Laplace transforms and transfer functions for modeling complex interconnected systems.
3. Understand the relationship of poles of a transfer function to the stability of a system, and more generally understand the concept of poles and zeros of a transfer function and how they affect the physical behavior of a system.
4. Understand the role of integral control and generally why more than simple proportional control is often needed in a control system.
5. Know the effect of sample-rate on the stability of computer controlled (discrete-time) systems, and more generally the fundamental differences between continuous-time and discrete-time control systems.

• Derive mathematical models of a variety of electrical, mechanical, and electro-mechanical systems.
• Understand the concept of stability of a dynamic system.
• Draw the pole-zero diagram and the root loci, which are the change in location of the poles as parameters are of a system are varied.
• Understand the concept of frequency response and the related concepts of bandwidth, disturbance sensitivity, and noise sensitivity. Be able to draw Bode plots and understand their significance.
• Use frequency domain techniques to design controllers.
• Estimate time response of systems to impulse, step, ramp, and sinusoidal inputs from the transfer function.
• Understand the meaning of proportional control, integral control, and derivative control, lag compensation, and lead compensation, and how to use them to achieve desired stability, steady-state error, and frequency response.
• To use Matlab® with facility to aid in the analysis and design of control systems.
• To construct simple feedback circuits using op-amps.

Text

References

• Dorf, R. and Bishop, R.Modern Control Systems
• Messner, W. and Tilbury, D. Controls Tutorials for MATLAB and Simulink
• Ogata, K., Discrete-Time Control Systems
• Strang, G., Linear Algebra

Rough Course Plan

The plan largely follows the order in which material is covered in the text. Chapter numbers refer to Nise.

 

1. Introduction to Control Systems (Chapter 1 -- 1 lecture)
2. Modeling
1. Laplace Transforms (Chapter 2 -- 1 lecture)
2. Modeling of Op-amps and Electric Motors (1 lecture)
3. State Space Representation (Chapter 3 -- 1 lecture)
4. Transfer Functions and Block Diagram Algebra (Chapter 5 -- 2 lectures)
3. Time Response
1. Rise Time, Settle Time, Overshoot. (Chapter 4 -- 3 lectures)
2. Stability (Chapter 6 -- 1 lecture)
3. Steady State Error (Chapter 7 -- 1 lecture)
4. Root Locus Techniques
1. Definition, Properties, and Sketching Rules (Chapter 8 -- 2 lectures)
2. Design via Root Locus (Chapter 9 -- 2 lectures)
5. Frequency Response Techniques
1. Bode Plots (Chapter 10 -- 2 lectures)
2. Design via Frequency Response (Chapter 11 -- 3 lectures)
6. Introduction to Discrete-Time Control (Chapter 13 -- 4 lectures)
1. Components of a Computer Control System
2. Difference Equations and the Z-transform
3. Basic Discrete-Time Controller Design

Tentative Lab Schedule

 
This course will have a laboratory component. The Lab will meet on certain Fridays 2:30-4:30 p.m. p.m. in the Undergraduate Measurement Lab, Hamerschlag B301.
 

Lab 1. Motor Identification

Lab 2. Proportional Speed Control

Lab 3. Proportional plus Integral Speed Control

Lab 4. Motor Speed Control with Lead Compensation and Integral Control