A MIMO Sampling Rate Dependent Controller

Abstract

A sampling-rate-dependent (SRD) controller is proposed for the uniform output tracking problem of multiinput multioutput discrete time-varying linear systems. A proportional-integral-derivative (PID) controller is a special case of the proposed controller. The SRD controller aims at achieving uniform output tracking in the sense of attaining arbitrary small steady-state errors as well as arbitrary small settling time. The SRD controller makes use of higher sampling rates for larger variations in the desired trajectories. An analytic approach for finding the parameters of the SRD controller that guarantees reference output trajectory tracking is presented. Four different numerical examples and two different experimental applications are provided in order to illustrate the output tracking capability of the proposed SRD controller. Performance is compared to a PID controller with fuzzy gain scheduling, four multivariable PID controllers, an H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> optimal controller, and an iterative-learning-control algorithm.