Design of a multi-rate control system in state-space representation using input redundancy

Abstract

This paper discusses a design method for controlling a single-input single-output linear time-invariant sampled-data multi-rate control system, where the sampling interval of a plant output is longer than the holding interval of a control input. In such a sampled-data control system, the control input can be changed between the sampling instants. Hence, even if the sampled output converges to the reference input, the intersample output may oscillate. Such an intersample oscillation is eliminated when the control input is constant. In a conventional method, a control law is extended using an additional signal which is independent of the reference response in the discrete time, and the additional signal is designed so that the control input is constant in the steady state. The conventional method is designed based on the transfer function model, on the other hand, the proposed method is designed using the state-space model. Furthermore, a new design method of the additional input is proposed using the input redundancy which is defined by strongly input redundant or weakly input redundant. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

Keywords

• multi-rate system
• state-space representation
• input redundancy
• strong input redundancy
• weak input redundancy
• ripple
• intersample output