Course description :

This course introduces classical concepts of continuous-time feedback system modeling, analysis, compensation techniques, as well as root-locus, Bode diagrams and Nyquist plots as methods of establishing stability of systems. Introduction to computer-aided design tools for control systems will be given throughout the entire course, where relevant. The digital control system topics include z-transforms and state variable representation of discrete-time systems, generating models for mixed continuous and discrete-time systems, modeling asynchronous sampling, analysis and design by root locus, frequency response, and state-space techniques, as well as controllability, observability and observer design.

Prerequisite : EEE 147 Signals and Systems, ES 101 Mechanics of Particles and Rigid Bodies

Course objectives :

At the end of this course, the student should be able :
To construct a mathematical model, block diagram and signal flow graph for a physical lumped parameter system. To perform stability and sensitivity analysis on systems, design cascade and feedforward compensators to meet transient and frequency response specifications. To use computer- aided control tools to verify root locus, transient and frequency response characteristics of a system.

Text :

Dorf and Bishop. Modern Control Systems, 8th edition. Addison-Wesley.

References :

B.C. Kuo.  Automatic Control Systems, 5th edition.
D'Azzo and Houpis.  Linear Control System Analysis and Design :
Conventional and Modern, 3rd edition.
R.C. Dorf.  Modern Control Systems, 6th edition.
Shahian and Rasul.  Control System Design Using Matlab.

Grading :

2 Long exams 50 %
2 (or 3) Laboratory exercises 30 %
Homeworks and quizzes  20 %

Grading scale :

92 -  100    1.0
88 - < 92    1.25
84 - < 88    1.5
80 - < 84    1.75
76 - < 80    2.0
72 - < 76    2.25
68 - < 72    2.5
64 - < 68    2.75
60 - < 64    3.0
< 60           5.0

Course outline :

1. Introduction, Class Policies, Grading, References

2. Introduction to Control Theory

• What is control systems theory?

• Motivation for control.

• Examples of control systems.

• Basic feedback system.

• Why feedback?

3. Closed-loop Systems

• Open-loop vs. closed-loop.

• Advantages and disadvantages of a closed-loop system.

• Control system design overview.

4. Mathematical Modeling of Dynamic Systems

• What is a model? What is a dynamic system?

• Electrical systems, mechanical systems (translational and rotational), thermal systems and liquid-level systems

5. LTI systems and Differential Equations

• Linear time-invariant systems.

• State-space representation.

• Linearization.

6. Laplace Transforms and Octave

• Forcing functions.

• Familiarization with Octave

7. Block Diagrams and Transfer Functions

• block diagrams and block diagram transformations

• transfer function

8. SFG and Mason Gain Rule

• Comparison of block diagrams and SFGs.

• SFG transformations.

• Mason gain rule.

9. General Control Systems

• Some more about transfer functions.

• General control system, definitions and objectives.

• LTI response to forcing functions.

10. LTI Steady-state Response

• System type.

• Steady-state error.

11. Time Domain Specifications

• Pole position and time domain relationships

• Typical time domain specifications

• First-order systems

• Second-order systems

12. Performance Specifications

• Time domain exercises for second-order systems.

• Characteristic equation.

• Dominant poles and design issues.

13. Stability

• Different aspects of stability.

• BIBO and BIBS stability

• Pole locations and stability

14. Routh-Hurwitz Stability Test

• Hurwitz determinants

• Routh-Hurwitz stability criterion

• Why do you want to use Routh-Hurwitz stability test?

• Some examples and issues on using R-H stability test.

15. Root Locus Basics

• Basic properties

• Root locus construction

16. Advanced Root Locus

• Effect of adding poles and zeros.

• Root contour.

• Time delay.

• Root sensitivity.

17. PID Controller

• Proportional control

• PD control

• PID control

18. Introduction to Frequency Response

• LTI Response to a sinusoid.

• Magnitude and phase responses.

• Frequency response of first and second order systems.

• Polar plots.

19. Bode Plots

• Charateristics of Bode plots

• Standard Bode plots

• Asymptotic plots

20. Bode Plots and Transfer Functions

• Review of standard Bode plots.

• Building an asymptotic Bode plot.

• Identifying a transfer function from a Bode plot.

21. Compensation Using Bode Plots

• Why use Bode plots to identify transfer functions?

• Performance parameters in the frequency domain.

• Compensation techniques.

• Interpreting Bode plots.

22. Frequency Response Methods : Stability

• Why study in terms of frequency response?

• Contour mapping in the complex plane.

• Cauchy’s theorems.

• Nyquist stability criterion.

23. Nyquist Diagrams, Gain Margins

• Practical aspects of using the Nyquist stability criterion.

• Examples on Nyquist stability criterion.

• Gain margin.

24. Nyquist Diagrams and Phase Margins

• Review of gain margin.

• Phase margin.

• Remarks about gain margin and phase margin.

• Put it all together.

25. Digital Control Introduction

• Definition, advantages, disadvantages

• Examples

• z-transform

26. System representation

• Simulation diagram

• SFG

• State-space representation

• Transfer function

27. Sampling and reconstruction

• Ideal sampler

• Starred transform

• Data reconstruction

28. Pulse transfer function

• z-transform and starred transform

• Open-loop transfer function

32. Closed-loop transfer function

• Derivation using SFGs

• State variable forms