Deriviation of the z-transfer Function of Optimal Digital Controller Using an Integral-Square-Error Criterion with the continuous-data Model in Linear Control Systems

선형연속데이터형 제어계통의 플랜트와 디지털모델의 오차자승적분지표에 의한 최적디지탈제어기의 전달함수유도

In this paper, an attempt is made to match the continuous state trajectory of the digital control system with that of its continuous data model. Matching the state trajectories instead of the output responses assures that the performances of the internal variables of the plant as well as the output variables are preserved in the discretization. The mathematical tool used in this research is an extended maximum principle of the Pontryagin type, which enables one to synthesize a staircase type of optimal control signals, such as the output signal of a zero-order hold asociated with a digital controller. A general mathematical expression of the digital controller which may be used to replace the analog controller of a general system while preserving as mauch as possible the performance characteristics of the original continuous-data control system is derived in this paper.