Multi-rate Control System for Improvement in Intersample Response Based on State-space Representation

Abstract

The decision of sampling and hold intervals is an important issue in the design of sampled-data control systems, in which a continuous-time plant is controlled using a digital computer in discrete time, and the selection of intervals greatly influences the control quality. However, it is not easy to set these intervals arbitrarily because of hardware constraints. This paper proposes a new method for the design of a multi-rate single-input single-output sampled-data control system under the constraint that the sampling interval of the plant output in continuous time is an integer multiple of the hold interval of the control input, which is updated in discrete time. In the design of the multi-rate control system, the intersample plant output can possibly oscillate even if the sampled plant output converges to its reference input. In conventional design methods, to improve intersample ripples, both the sample and the intersample responses are simultaneously designed, and then, the original sample response might be deteriorated even though the intersample response is improved. In this study, a multi-rate control law, which stabilizes a closed-loop system, is extended on the basis of state-space representation, and the multi-rate control system is redesigned such that the steady-state intersample response is improved independently of the sample response. As a result, the sample response is maintained and the intersample response is improved in the steady state. Numerical examples demonstrate the effectiveness of the proposed method.