This paper is concerned with the problem of designing robust state derivative feedback control laws in discrete time. The main contribution consists of a method for recasting a continuous time state space model in the form of a discrete time model formulated in terms of the state derivative. Uncertain input delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the resulting state derivative model. Therefore, robust control techniques originally developed for discrete time state space models can be directly employed to design the state derivative feedback law. Three computational examples are presented for illustration. The first example highlights the importance of accounting for the effect of sampling in the design procedure. More specifically, a linear quadratic regulation problem involving the state derivative is addressed. The second example involves the design of a robust predictive controller in the presence of input constraints and uncertain time delay. Finally, the third example is concerned with robust pole placement in the presence of parametric uncertainty.

This paper is concerned with the predictive control of water level in an experimental pilot plant, in the presence of input constraints and uncertain time delays. Robustness is achieved by casting the delay uncertainty into a polytopic form and using a predictive control formulation based on linear matrix inequalities. Integral action is introduced into the controller to ensure offset-free tracking of step changes in the setpoint. Moreover, an integrator resetting procedure based on the concept of regions of guaranteed cost is proposed to improve the resulting transient response. The results show that the introduction of robustness into the predictive control formulation is indeed of value to avoid closed-loop instability in the presence of time delays. In addition, the integrator resetting procedure was found to provide substantial performance improvements in terms of overshoot and settling time.

No abstract

No abstract

No abstract