The effects of computational delay in descriptor-based trajectory tracking control

摘要

Descriptor Predictive Control (DPC) has been shown to be a useful method for solving nonlinear tracking problems. A rigorous analysis of local stability and performance characteristics of this method has been achieved previously by studying the linear plant under the assumption that the delay introduced in the control due to numerical computation can be neglected. It was shown that, if the plant is controllable and minimum phase, stability is guaranteed and tracking is achieved exponentially with any desired rate of convergence. It was also shown that sometimes DPC must include a specially designed preliminary feedback. In this paper, we carry out a similar analysis by taking into account computational delay, which is unavoidable in actual implementation of DPC. We show, in particular, that under the same assumptions, and provided the special preliminary feedback is used, that the closed loop system remains stable as long as the delay is smaller than a threshold and that exponential tracking is achieved. However, the rate of convergence of the tracking error cannot be chosen arbitrarily because it is constrained by the plant zeros. The delay analysis is used to explain experimental observations in the literature about the occasional failure of previous implementations of the DPC approach at small sampling periods. A nonlinear robotics problem is worked in detail.