Modern Control Theory

The course is a substitute for:

Modern Control Theory (X35MTR)

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The objective of the subject is to introduce a general design methodology how to translate an engineering problem into an optimization task and interpret the mathematical results. This approach is illustrated on methods developed during last three decades (state-space and algebraic methods for LQ, time optimal and model matching problems, adaptive control). Basic methods of uncertainty description are introduced and the effect of uncertainty on design is analyzed. The official website it http://dce.felk.cvut.cz/mtr/.

Prerequisities: Linear system theory, control system, linear algebra.

Requirements:

Syllabus of lectures:

1. Introduction to MTR. Motivation to MTR (advantages and disadvantages compered with the classical control aproaches (PID), posibilities of MTR. Deterministic discrete-time LQ control: optimality principle, (DRE) diference Riccati equation for LQ controller, .

2. Deterministic discrete-time LQ control: (ARE) algebraic Riccati equation (relation to DRE and to Lyapunov equation), steady Kalman gain computation methods, quadratic optimal tracking, quadratic optimal asymptotic tracking, frequancy properties of disrete-time LQ controller.

3. Deterministic continuous-time LQ control: diferential Riccati equation, frequancy properties of continuous-time LQ controller.

4. Model predictive control (MPC) and feedback control strategy, predictive LQ controller.

5. MPC controller - including the system variables constraints.

6. Linear stochastic system: mean value and covariance developement, MS and LMS estimation, formulation of system state estimating problem of stochastic systems based on system input and system output.

7. Optimal filtering based on state space description (Kalman filter): correlated/uncorrelated process and measurement noise, filtration and prediction step of Kalman filter, continuous time Kalman filter with discrete time system output measuring, extended Kalman filter.

8. Application of modern control method in industry.

9. Extended Kalman filter, Kalman filter for coloured process and measurement noise, properties of Kalman filter, Kalman filter and spectral factorization.

10. LQG controller: LQ controller for stochastic system, LQ controller + Kalman filter for stochastic system, separation principle, influence of state observer to robustness.

11. Introduction into uncertainty description, structured and unstructured uncertainty, small gain theorem, robust stability.

12. Robust quality.

13. Statistical identification methods: ARX, ARMAX and OE model, identification of ARX model by least squares method, online system parameters identification (forgetting).

14. Introduction to adaptive control.

Syllabus of tutorials:

1. Matlab and Matlab toolboxes.

2. Norms of signals and systems.

3. Sensitivity functions.

4. Robust controller.

5. Set of all stabilizing controllers.

6. Polynomial quadratic controller.

7. LQ controller.

8. LQ controller, tracking.

9. Predictive control.

10. Predictive control, variables constraints.

11. Stochastic system.

12. Kalman filter.

13. Modern controller design for real process.

14. Result presentations, započet.

Study Objective:

Study materials:

[1] Lewis, F.L.: Optimal Control. J.Wiley and Sons, N.Y. 1994

[2] Kučera, V.: Analysis and design of discrete linear control systems. Academia, Prague 1991

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Technická kybernetika-inženýrský blok (compulsory course)
• Technická kybernetika-inženýrský blok (compulsory course)