Synthesis of sampled-data H∞ servo controller with generalized hold

In this paper, we consider type 1 sampled-data feedback control system synthesis problems by sampled-data hoc technique, where the hold is a design parameter as well as the discrete-time controller. The feedback control system consists of a continuous-time plant and a discrete-time controller with sample and hold devices which must achieve the following three design specifications: 1) internal stability, 2) desired feedback characteristics such as robust stability, sensitivity reduction and disturbance attenuation, and 3) robust tracking and/or robust disturbance rejection for step-type exogenous signals. Two types of type 1 servo problems, namely the output regulation type and the disturbance rejection type, are formulated to adopt the above requirements. We show that the output regulation type problem has no solution for any hold while the disturbance rejection type problem is well defined. We also develop a synthesis method of type 1 digital controller together with generalized hold based on the sampled-data H_∞ control. The resultant optimal hold is composed of that for the sampled-data H_∞ regulation problem and ZOH, while the discrete-time controller has the internal model.