Abstract
A design method will be useful if it calls for a minimum amount of knowledge about the controlled process, since identification of the state equation is not an easy task especially in the field of process control. The author previously developed a method for the continuous-time case which involves only a limited number of the controlled process parameters corresponding to the number of the controller parameters. In this paper the method is applied to sampled-data control systems.
The controlled process is usually time-continuous even in a sampled-data control system. Thus, the system is working on the continuous-time basis. Here, sampled-data control systems are approximated into continuous-time ones, and the previously developed method is employed to give the design formulas.
The control system to be designed is to meet the following specifications:
(C1) It has zero steady-state error.
(C2) It has adequate damping characteristics.
(C3) It has the shortest rise-time on satisfying (C1) and (C2).
The design formula gives rise to a sampled-data system which approaches to a continuous-time one with an increasing response speed but without changing its damping characteristics as the sampling period reduces to zero. Zero sampling period reduces the formulas to the previously obtained ones for the continuous-time systems.
Formulas for the PID and the I-PD control schemes are derived according to the method. Some designed samples are demonstrated in step response curves, which show effectiveness of the method. The sampling period T is assumed in advance to be less than half the rise-time of the controlled process, otherwise a system with T=0, that is, a continuous-time system will result because of the specification (C3) above.
