The purpose of this study is to drive the adaptive multirate GPC for multivariable systems in a stochastic framework. Modeling disturbances as white noise is inadequate for process control because most disturbances encountered in process control are colored or non-stationary in nature. For that reason we first propose stochastic parallel model identification algorithm for multirate sampled system. No attempt is made in it to identify the noise model. Hence the algorithm is applicable to any measurement noise case. The measurement noise can be arbitrary(for example, colored or non-stationary noise), except for the assumption that it and control inputs are stochastically uncorrelated. Projected stochastic gradient algorithm and least squares algorithm are proposed. A estimation is at least bounded by proportional to the parameter estimation and it approached zero if the parameter estimation error approached zero. We extend the GPC to multirate systems by calculating an estimate for the output at intersampling instants. The technique utilizes intersampling control inputs and available model parameters to generate the intersampling output estimates. When stochastic parallel model is used, the estimates of outputs can be easily generates at input(fast) sampling instants without affecting the properties of the parameter estimates. This is in contrast to estimation based on ARMAX model where the unbiasedness of the parameter estimates of the dynamical part of the system crucially depends on the identification of the noise model and estimates and/or predicted values of the output are affected the parameter estimates at intersampling instants. Deadtime is implicitly handled in the formulation. In order to demonstrate the effectiveness of the proposed control algorithm simulation study is carried out. The closed-loop performance are excellent. Both outputs track changes in the reference signals very well despite of the presence of the measurement noise. These simulation results show that the proposed control scheme makes the performance of the multirate control system approach that of the single rate(fast rate) control system.
