| Summary: | This thesis presents two design methods for multiple robust controllers (MRC) and a design method for switched robust controllers that can be used for linear systems with parametric uncertainty. These methods are helpful in enhancing the performance of feedback control systems beyond the performance limitations associated with conventional design methods for uncertain linear systems.
MRC have been introduced to overcome the performance limitations imposed by the requirements for robustness. The design of MRC involves dividing the uncertainty set of a linear system into a number of subsets, as well as synthesizing of a robust controller for each subset. We propose two methods for the design of the uncertainty set divisions and controllers. The first method determines each controller and each subset in subsequent steps, and can deal with only time-invariant parametric uncertainties. In the second method, we find both each controller and each subset simultaneously. This method can handle both time-invariant and time-varying uncertainties.
Switched robust controllers, on the other hand, have the potential to advance the existing performance limitations of a single linear time-invariant robust controller by switching among a set of linear time-invariant controllers. We introduce a new concept, robust finite-time tracking, that is a property of closed-loop uncertain systems. Robust finite-time tracking focuses on the transient response, as opposed to the steady-state response (as in Lyapunov-based techniques). We formulate an optimization problem for the design of switched robust finite-time tracking controllers.
The controller design methods that discussed above include nonsmooth non-convex optimization problems. In order to find a local optimum to the problems, nonsmooth optimization techniques are utilized.
We compare the performance of developed methods to existing methods in the literature through several numerical examples, such as inverted pendulum and mass-spring-damper systems. Moreover, to demonstrate the advantages of our method for MRC over traditional robust controllers in a practical example, we design multiple robust track-following controllers for hard disk drive servo-systems.
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