Course description :

Transfer functions. Block diagrams. Signal flow graphs. Root locus,Bode, Nyquist and polar plots. Sensitivity. Stability. Compensation techniques. Multivariable systems. Disturbance rejection. Robust control. Adaptive control. State-variable representation and feedback. State-space design. Optimal control, computer simulations. Design projects

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 physical systems. To perform stability and sensitivity analysis on systems, design cascade and feedforward compensators to meet transient and frequency response specifications using root locus, Bode and Nyquist plots. To explain key concepts in multivariable control, robust control, adaptive control and quadratice optimal control. To use computer-aided control tools to verify root locus, transient and frequency response characteristics of a system.

Text :

Ogata. Modern Control Engineering, any edition, Prentice Hall.

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  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

• Overview of EE 231 topics

• Control system

2. Mathematical Modeling of Dynamic Systems

• Electrical systems,

• Mechanical systems (translational and rotational),

• Thermal systems and liquid-level systems

3. LTI systems, Differential Equations, Laplace Transforms

• Linear time-invariant systems.

• State-space representation.

• Linearization.

4. Block Diagrams and Transfer Functions

• block diagrams and block diagram transformations

• transfer function

5. SFG and Mason Gain Rule

• Comparison of block diagrams and SFGs.

• SFG transformations.

• Mason gain rule.

6. General Control Systems

• Some more about transfer functions.

• General control system, definitions and objectives.

• LTI response to forcing functions.

7. LTI Steady-state Response

• System type.

• Steady-state error.

8. Time Domain Specifications

• Pole position and time domain relationships

• Typical time domain specifications

• First-order systems

• Second-order systems

9. Performance Specifications

• Time domain exercises for second-order systems.

• Characteristic equation.

• Dominant poles and design issues.

10. Stability

• Different aspects of stability.

• BIBO and BIBS stability

• Pole locations and stability

11. Root Locus Basics

• Basic properties

• Root locus construction

12. Advanced Root Locus

• Effect of adding poles and zeros.

• Root contour.

• Time delay.

• Root sensitivity.

13. PID Controller

• Proportional control

• PD control

• PID control

14. Introduction to Frequency Response

• LTI Response to a sinusoid.

• Magnitude and phase responses.

• Frequency response of first and second order systems.

• Polar plots.

15. Bode Plots

• Charateristics of Bode plots

• Standard Bode plots

• Asymptotic plots

16. Bode Plots and Transfer Functions

• Review of standard Bode plots.

• Building an asymptotic Bode plot.

• Identifying a transfer function from a Bode plot.

17. Compensation Using Bode Plots

• Why use Bode plots to identify transfer functions?

• Performance parameters in the frequency domain.

• Compensation techniques.

• Interpreting Bode plots.

18. Frequency Response Methods : Stability

• Why study in terms of frequency response?

• Contour mapping in the complex plane.

• Cauchy’s theorems.

• Nyquist stability criterion.

19. Nyquist Diagrams, Gain Margins

• Practical aspects of using the Nyquist stability criterion.

• Examples on Nyquist stability criterion.

• Gain margin.

20. Nyquist Diagrams and Phase Margins

• Review of gain margin.

• Phase margin.

• Remarks about gain margin and phase margin.

21. Multivariable Control.

22. Robust Control

23. Adaptive Control

24. Quadratic Optimal Control