Open-loop discretization methods for control systems design

Abstract

In this paper, a unified theory is presented which addresses essential aspects of the open-loop discretization procedure. Initially, factors which affect the generation and propagation of discretization errors are identified by analytical, heuristic and experimental arguments. Following this, a discretization algorithm is presented which takes these factors into account. The fundamental idea of the discretization method is the replacement of the analogue integrators of the prototype continuous-time system by discrete-time approximations. This is done in such a way as to optimize a given cost function with respect to a given input. Unlike many discretization schemes presented in the literature, the procedure developed attempts to first determine the magnitude of the expected discretization errors, and then discretize with an appropriate complexity, giving the designer control over the order of the discrete-time system. This appears to be an effective means of designing filters with low complexity which still retain essential properties of the prototype system. An emphasis of this work is to view the discretization process from a control theory and engineering perspective. This results in a number of new perspectives relating to the discretization process.