Transient Response Analysis of a Nonlinear Sampled-Data Control System

Transient response and limit cycle characteristics associated with a wide range of nonlinear sampled-data systems can be rigorously computed by implementing a straightforward numerical approach. Based upon the piecewise-linear analytical technique, a set of continuous open-loop equations are formulated to describe all analog system components. Digital and/or purely numerical processes are defined in terms of standard recursion formulae. The final analytical-routine consists of a combination of both analog and digital equations, written in a difference equation format; as such, the ultimate computational requirements are ideally suited for high speed electronic digital computer simulation. Physical system nonlinearities are reflected in corresponding nonlinear difference equation coefficients, while all time varying relationships and time delay parameters (transport lags, etc.) are easily incorporated within the framework of a digital computer program mechanization. The technique is demonstrated by means of an illustrative example. In particular, both the transient response profile and steady state limit cycle characteristics of a nonlinear sampled-data controller are computed by invoking a formalistic step-by-step procedure. A brief review of the sampled-data theory is presented through a qualitative description of the z-transform, sampler, zero order hold and digital compensator. A linear sampled-data follower is next analyzed, and the results compared to those obtained through conventional z-transform techniques. The extension to systems containing non-linearities at various positions within the loop is demonstrated.