Algebraic Design Methods

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The course offers an alternative design method for linear control systems. The method is based on transfer functions, expressed in fractional form. All controllers are parametrized that stabilize a given plant. The optional parameter appears linearly in all closed-loop transfer functions. Additional design requirements, like those of optimality or robustness, can be achieved by a suitable choice of the parameter. Development of modern reliable algorithms makes it possible to extend the applicability of these methods in last years.

Requirements:

Syllabus of lectures:

1. Proper and stable rational functions

2. Diophantine equations

3. Solution algorithms

4. Systems and signals, norms

5. Feedback systems

6. Stabilizing controllers

7. Optimal systems

8. H2 norm minimization

9. Hinf norm minimization

10. Robust stabilization

11. Reference tracking

12. Pole placement

13. Multi-input multi-output systems

14. Parametrization of stabilizing controllers

Syllabus of tutorials:

1. Polynomials and rational functions

2. Divisibility

3. Solution of polynomial equations

4. Solution of rational equations

5. Computing the norms

6. Written test

7. Parametrization of stabilizing controllers

8. Optimal disturbance attenuation

9. Spectral factorization and the H2 norm

10. Interpolation and the Hinf norm

11. Robust stabilization and tracking

12. Pole placement, finite impulse response

13. Written test

14. Conclusion

Study Objective:

Study materials:

[1] Vidyasagar, M.: Control System Synthesis: A Factorization Approach. MIT Press, Cambridge 1985

[2] Doyle, J.C., Francis, B.A., Tannenbaum, A.R.: Feedback Control Theory. Macmillan, New York 1992

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