Multirate generalized predictive control for sampled-data systems

In the generalized predictive control (GPC) scheme, we study a practical case of multirate systems involving fast A/D conversion and slow D/A conversion. We formulate the GPC problem as a sampled-data one with the performance index expressed in terms of continuous-time signals, capturing the inter-sample behavior. We convert such a multirate sampled-data GPC problem into an equivalent discrete-time GPC problem and then give an explicit solution for the optimal multirate control law. In an example, we first compare performance of this multirate GPC controller with that using conventional discrete-time multirate scheme, then with those using single-rate sampling schemes at the fast and slow rates, thus establishing its advantages.