Optimal Preview Control for Discrete-Time Systems in Multirate Output Sampling

Fucheng Liao,Yujian Guo

doi:10.1155/2016/6924324

Abstract

This paper studies the disturbance preview optimal control problem for discrete-time systems with multirate output sampling. By constructing the error system and using the discrete lifting technique, we reduce the multirate preview control problem to a single-rate one for a formal augmented system. Then, applying preview control theory, the optimal preview control law of the augmented error system is obtained. Meanwhile, we introduce a discrete integrator to eliminate the static error. Then we study a method to design a controller with preview action for the original system. And the existence conditions of the controller are also discussed in detail. Finally, numerical simulation is included to illustrate the effectiveness of the proposed method.

Highlights

In multirate output control systems, each component of the input vectors only changes once, and each component of the output vectors is detected several times during one sampling period
References [3, 4] studied the design of the multirate output sampling functional observer and periodic output feedback controller based on fast output sampling, respectively
This paper studies the disturbance preview optimal control problem for linear discrete-time systems in multirate output sampling

Summary

Introduction

In multirate output control systems, each component of the input vectors only changes once, and each component of the output vectors is detected several times during one sampling period. In [16], it has been shown that there is an advantage in updating feedforward control input at a higher rate in track-seeking control These cases motivate the research work for preview control theory of multirate systems. Liao et al presented an LQ optimal preview servomechanism design method for linear discrete-time systems with time-delay in a multirate setting. Reference [18] discussed the optimal preview control problem for a class of multirate sampled systems with state time-delay. Reference [19] applied preview control theory to solve the optimal preview control problem for discrete-time descriptor causal systems in a multirate setting. This paper studies optimal preview control for discrete-time systems in multirate output sampling.

Problem Description and Related Assumptions

The Derivation of the Augmented Error System

Existence Conditions of the Controller

Design of an Optimal Preview Controller for the Original System

Numerical Example

Conclusion