A describing function technique for sampling period selection and controller discretisation

Abstract

Most industrial processes that are to be controlled are continuous in nature. A very> extensive range of well tried methods for control systems analysis and design, together with the associated algorithms for implementation, are in continuous time form. Digital control algorithms can be produced by translation of the analogue designs or they can be developed using digital design techniques. Discretisation of analogue controllers can be done in many well known ways. In general the stability of the resulting system cannot be guaranteed, both because of inherent approximation and lack of guidance on choice of sampling period. The criticalfactor is the sampling period, too high a value and the system is unstable, too low and the controller is overdesigned.

A discretisation method for translation from analogue to digital is given here where, subject to certain constraints, the sampling period can be chosen so as to guarantee stability. Following on this, the Z transfer function of the controller is taken as the ratio of the zero order hold equivalent transfer function of the combined process and controller, to that of the process alone.