On Stability Of Zeros Of Discrete-Time System With GSHF

Zeros play an important role in control-system design. The unstable zeros limit the performance which the controlling system can be achieved, and limit the application of control technology. When a continuous-time system is discretized by the use of a sampler and a hold, the mapping between the discrete-time poles and their continuous-time counterparts is very simple. There is unfortunately no simple transformation between the discrete-time zeros and their continuous-time ones. The different signal reconstruct device will influence the position of zeros, so the research of zeros stability which base on the different signal hold and controlling system design which base on the different signal hold is very important.The paper is supported by Chongqing Natural Science Fund item"The research of digital control theory and application based on multirate signal reconstruction mechanism". We research the properties of the PC GSHF zeros in this paper, which is a special form of GSHF. At first, we analyze the discretized time model in the condition of PC GSHF ,give out the specific forms of discretized time system's state equation when N =3,4,5,6, and research the account method of the conversion from continuous time system to discretized time system. Secondly ,we analyze the properties of limiting zeros in the condition of PC GSHF when Tâ†'0, give out the stability condition when N =2,3, and research the Simulation of discretized time model tracking control based on ZOH and PC GSHF. We research the zero's properties and stability of discretized time system in the condition of having time delay. The research indicate that the zeros stability can be preserved through choosing the design parameter of PC GSHF. Through researching we find that the PC GSHF is better than ZOH and FROH in the condition of zeros'stability condition...