Control Design for Disturbance Rejection in the Presence of Uncertain Delays

This paper is concerned with control of processes with uncertain delays for disturbance rejection. The effect of the uncertain delays on the stability is studied. First, the method to compute the maximum uncertain delay that a given controller can tolerate is described. Second, in the case of PI/PID controller, all of the admissible controller parameters stabilizing a system with uncertain but bounded delays are determined. Meanwhile, we propose a simple method to construct the parameter space satisfying a given robustness index for the nominal model. In the admissible regions satisfying various objectives, the global optimum controller is achieved for disturbance rejection in the presence of uncertain delay. As a result, the MIGO ( Ms-constrained Integral Gain Optimization) method is revisited in the case of uncertain delay, and the rule of selecting the value of maximum sensitivity function is proposed in terms of the bound on the uncertain delay. Two simulation examples and an experiment are given to demonstrate the effectiveness and advantage of the proposed method.