Design of sampled-data control systems for minimum probabilistic error

THE ¿PROBABILISTIC ERROR¿ or ¿end-sigma error,¿ meaning the average penalized error for such times when the output is actually being used, has been proposed as a measure of control system performance in an earlier publication.1 A companion paper2 presents a complete design process to find the time invariant continuous linear system which possesses the minimum probabilistic square error in a given environment of random and deterministic signals and random noise. A corresponding design process is presented in this paper for impulse-sampled systems. The result of this design is a linear digital filter to be used with a given plant in order to keep the probabilistic square error to a minimum. Working equations are presented, which were developed with digital computer programing and solutions in mind. Such solutions can be obtained for very general signal input and noise environments. However, the proposed method works best when the output is being utilized within a time interval including a nonexcessive number of samples.