Robustness effects of sampling in model referencesand minimum variance control

This paper investigates several issues relating to the effect of sampling in model reference and minimum variance control. It is shown that, in the case of stochastic systems, the continuous time response resulting from digital control is cyclostationary. A method is presented for computing the time-varying covariance between sampling instants. The results are used to examine the performance of several digital control algorithms including the minimum variance control strategy. It is shown that these algorithms can have poor continuous time responses especially for lightly damped systems. The fact that one step ahead controllers applied to lightly damped systems are overly responsive between sampling instants is well known but these issues have been largely overlooked in much of the recent literature on stochastic and adaptive control. We suggest that it may be preferable to use alternative design procedures which give suboptimal performance at the sampling instants but which actually result in superior continuous time results. The theoretical results in the paper are substantiated by both computer simulation studies and a practical application.