Adaptive model predictive control of multivariable time-varying systems

In this work, we develop a novel adaptive model predictive control (AMPC) formulation for multivariable time-varying systems. A two-tier modeling scheme is proposed in which the deterministic and stochastic components of the model are updated on-line by two separate recursive pseudolinear regression schemes. To incorporate good long-range prediction capability with respect to manipulated inputs, we propose to identify a parametrized form of an output error (OE) model using the input-output data. To account for unmeasured disturbances, the residuals generated by the OE model are modeled as ARMA processes. To address the admissibility issue and the parameter-drift problem in on-line estimation, we propose to use a combination of a novel constrained recursive estimation scheme and the conventional recursive methods for model parameter estimation. An interesting feature of the proposed modeling scheme is that it allows separation of stationary and nonstationary components of the unmeasured disturbances. The deterministic and stochastic components of the model are then combined to form a linear time-varying state-space model, which is then used to formulate the predictive control problem at each sampling instant. A novel feature of the proposed controller is that we develop an infinite-horizon MPC formulation with a time-varying objective function in the adaptive-control framework for dealing with the grade-transition problems in continuously operated plants. The applicability of the proposed approach to the control of semibatch and continuously operated large-scale industrial processes is demonstrated by carrying out simulation studies on the production of penicillin and on the benchmark Tennessee Eastman control problem. The proposed modeling and control scheme is also validated by conducting experiments on a benchmark quadruple-tank setup. The analysis of the simulation and experimental results reveals that the proposed two-tier modeling scheme successfully captures time-varying system dynamics with respect to manipulated inputs as well as unmeasured disturbances over a wide operating range. The proposed AMPC scheme is able to achieve tight control of time-varying semibatch processes and is capable of managing large transitions in the operating conditions of a continuously operated complex multivariable process