Theory of Dynamic Systems

The course is a substitute for:

Theory of Dynamic Systems (35TDS)

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The notion of system serves to describe and understand complex engineering,

natural, economic, and social phenomena; it facilitates a connected study of

these phenomena.

A definition of system is proposed; description and realization of systems

are presented. Internal dynamics, input and output constraints are studied.

Methods of altering the system dynamics are explored.

The theory is illustrated by examples. Laboratory experiments include

modeling and control of electromechanical, hydraulic, pneumatic, heating and

magnetic small-scale systems in real time using RT MATLAB.

Requirements:

Basic knowledge of Linear algebra, Basic knowledge of control theory.

Syllabus of lectures:

1. System theory, State space equations. Linearization

2. State-space and input-output description. of SISO and MIMO systems.

3. Poles and zeros of thesystem. Singular systems

4. System realization. State transformations.

5. Interconnected systems. Mason's rule. Algebraic loops.

6. Solution of state space equations. System modes. Impulse response matrix.

7. Continuous and dicscrete time description, Sampling and holding.

8. Reachability and controlability

9. Observability and reconstructibility.

10. Ljapunov and asymptotic stability. Stability tests. Robust stability.

11. Modification of system dynamics. State feedback. State reconstruction. Observers.

Separation principle.

12. Algebraic methods of control. Polynomial equations. Stabilizable controllers.

13. Unification of algebraic approach to continuous and discrete time systems.

14. System realization.

Syllabus of tutorials:

1. Introduction, requisite knowledge from X35SAM and X35SRI.

2. Dynamical properties of continuous and discrete time systems.

3. Examples of economic, natural and engineering systems.

4. Linear systems, linearization, realization.

5. Interconnected systems.

6. Solution of state space equations, numerical methods.

7. Sampled-data systems.

8. Reachability and observability tests.

9. Stability and robust stability criteria.

10. State feedback, examples.

11. State observer design.

12. Examples of nonlinear systems. Analysis of nonlinear systems.

13. Properties of stochastic systems.

14. Realization of random signals, factorization algorithms.

Study Objective:

Study materials:

1. T. Kailath: Linear Systems. Prentice Hall, Englewood Cliffs, New York,

1980.

2. P.J.Antsaklis, A.N.Michel: Linear Systems. The McGraw-Hill Co., 1997.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory course)
• Cybernetics and Measurements - Artificial Intelligence- structured studies (compulsory course)
• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory course)
• Cybernetics and Measurements - Aeronautical Engineering and Control Systems- structured studies (compulsory course)