Stability of linear control systems

Module overview. Stability is the base requirement for the design of a control system. This module gives a first insight into the design of closed-loop systems and the problem of their stability. It is shown by definitions what stability means. Then the most important stability criteria using the characteristic polynomial (Hurwitz, Routh) are introduced. Most emphasis is put on the Nyquist criterion, which can be used with Nyquist and Bode diagrams to design stable closed-loop systems with given stability margins. To simplify the stability test in the frequency domain with Nyquist or Bode diagrams several rules are given. All terms, techniques and rules are illustrated by examples.

Module objectives. When you have completed this module you should be able to:

1. Understand the stability of linear dynamical systems.
2. Understand the algebraic stability criteria for linear systems.
3. Know how to test the stability of linear systems described by transfer functions.
4. Know how to test the stability of linear systems described by frequency-response characteristics.
5. Know how to test the stability of a closed loop from open-loop data.

Module prerequisites. Transfer function, characteristic polynomial,determinants, frequency response, Bode diagram, Nyquist diagram.