Optimal Sampling-Rates of Digital LQ and LQG Tracking Controllers with CostsAssociated to Sampling

摘要

In this paper it is shown that if costs are associated to sampling operationswhich are added to a performance criterion, the minimization of this new performance criterion results in a controller operated at an optimal sampling rate. This, under the assumptions that the system is periodically sampled, the applied control is kept fixed between every two sampling instances and some technical conditions are met. In case the considered planning horizon in the performance criterion is finite, an algorithm is devised which calculates in a finite number of steps the optimal sampling period. It is shown that the technical conditions mentioned above are satisfied by the finite planning horizon time-varying LQG tracking problem. Since stability is a major requirement in controller design, the authors also consider the case of an infinite planning horizon. This analysis is focused on the time-invariant digital LQ tracking problem. Given some mild regularity conditions, a numerical algorithm is presented that approximates the optimal solution within any prespecified error norm. It is also shown that in this case an optimal sampling-rate exists. The algorithm for determining the optimal sampling period if the planning horizon is finite is illustrated in an economic example.