Performance analysis of linear regulators with non-Gaussian Markovian disturbances†

Abstract

Abstract Due to the complexity of non-Gaussian design, most control systems are designed via assumptions of Gaussian disturbances, oven for cases of non-Gaussian disturbances. Similarly, performance evaluations of systems designed via a Gaussian assumption when inputted with non-Gaussian disturbances are most difficult and rarely made. The present paper therefore presents a method for analysing such performances by deriving output probability structures for cases of input disturbances belonging to a class of non-Gaussian Markovian processes that are common to many chemical engineering processes. The analysis is based on considering the Chapman—Kolmogorov and the Fokker-Planck equations related to a two-state Markov process and its results are compared with the ease of Gaussian disturbances to facilitate the determination of the discrepancy between the performance expected by the Gaussian assumption and the actual performance.