H∞ robust controller for self-tuning control applications Part 2. Self-tuning and robustness

A relatively simpleH∞ control law was defined in Part I (Grimble 1987). If a polynomial involving the cost-weights is strictly Hurwitz the control law simplifies even more. This is the situation which is exploited in the non- H∞, generalized minimum-variance control law found in most of the existing self-tuning control schemes. In systems having a unit time-delay the calculations for the H∞ controller become trivial. The cost-weights may be chosen to place some of the poles of the closed-loop system in desired locations if pole placement is required. The self-tuning algorithm presented is very similar to the indirect self-tuners based on LQG control laws. The choice of the cost-weights to improve the disturbance rejection and stability robustness properties of the design is discussed and the conditions when LQG and H∞controllers give a similar performance are established.