Fundamental Limit of Discrete-Time Systems in Tracking Multi-Tone Sinusoidal Signals

作     者：Weizhou Su~1 Li Qiu~2 Jie Chen~3 1 Center for Control and Optimization, South China University of Technology Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology 3 Department of Electrical Engineering, University of California Riverside, CA 92521-0425 USA 

会议名称：《第二十四届中国控制会议》

会议日期：2005年

学科分类：080904[工学-电磁场与微波技术] 0810[工学-信息与通信工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 081105[工学-导航、制导与控制] 081001[工学-通信与信息系统] 081002[工学-信号与信息处理] 0825[工学-航空宇航科学与技术] 0811[工学-控制科学与工程] 

基　　金：This work is supported by the Hong Kong Research Grants Council under the grant HKUST6212/03E  NSFC Project 60474028 and NSF/USA under the Grant ECS-9912533 

关 键 词：Performance limitation optimal control tracking nonminimum phase zeros 

摘      要：正 This paper studies the tracking performance of linear time-invariant multivariable discrete-time systems. The specific problem under consideration is to track a multi-tone sinusoidal reference signal consisting of linear combinations of a step and several sinusoidal signals, whereas the tracking performance is measured by the energy of the error response between the output of the plant and the reference signal. Our purpose is to find the fundamental limit for the best attainable performance, under any control structures and parameters, and we seek to determine this limit analytically in terms of the given plant and reference characteristics. Both the full-information and partial-information tracking schemes are formulated and investigated to address these goals, which are concerned with whether or not the reference information is fully available for tracking. Analytical expressions are developed in full generality under full-information tracking, and for a more specialized case under partial-information scheme;in particular, an optimal cheap control design is constructed to show that the performance limit can be attained asymptotically in the full-information case. The results show that in general plant nonminimum phase zeros and reference modes can interact to fundamentally constrain a system’s tracking ability. They also show that absence of full reference information can degrade the tracking performance, thus demonstrating an intrinsic trade-off between the tracking objective and the availability of the reference information.