Robust offset-free control of nonlinear systems using model predictive control and integral action

Model Predictive Control (MPC) is an advanced control setup that uses optimization to determine the controlled input. The MPC was initially a linear approach that has grown to include non-linear systems, robust stability, and offset-free control, which have increased the complexity through; more intricate modeling requirements, increased tuning demands, and a higher computational load. In this work, the aim is to reduce the aforementioned complexities when applying MPC to nonlinear processes. The first step is to use multiple linear models as a way of describing the non-linear process. The piecewise linear (PWL) description captures the nonlinear process without requiring a non-linear model. The first objective is to use the PWL for a multi-model description of the process giving rise to multiple model predictive control (MMPC). The PWL models are combined, using a Bayesian approach, into a single model for use in the optimization in MPC. The technique is not a new approach, but one that had not been applied to a pH-control system before. For the next objective, an MMPC-I approach is developed to introduce integral action into the MMPC, to handle uncertainties such as disturbances and modeling errors. The new method is suggested to circumvent the complications associated with the tuning of an observer. The combination of MPC and the integral controller was further developed by using the multi-model in a min-max approach to get min-max MPC-I. The min-max configuration using the worst-case scenario for the models rather than weighing them together. This objective would improve the handling of parametric uncertainties, reducing overshoots and oscillations. The final objective was to develop a Robust MPC-I controller. The disturbance, parametric uncertainty, and integral controller are all accounted for in the input to state practical stability (ISpS) approach. A proof is given that the Robust MPC-I is indeed ISpS for nonlinear systems with bounded uncertainties. The different combinations of MPC and integral controllers were tested on the pH-control system and compared to PID and observer-based MPC. The MMPC showed excellent behavior when set-point tracking giving at least 25% improvement compared to PID, concerning rise time, settling time and overshoot. However, the MMPC would not achieve offset-free control when disturbances or model errors were present. The inclusion of integral action removed the offset for both MMPC-I and the min-max MPC-I. The MMPC-I managed to reduce the settling time and overshoot for set-point tracking, disturbance rejection and model errors, leading to a 15% reduction in root mean square error (RMSE) compared to the PID. The min-max MPC-I showed similar improvements compared to the PID, though RMSE improvement were just 10%. The reduction compared to the observer-based MPC was even more significant (22%) as it could not achieve offset-free control for all cases. The Robust MPC-I was proven to be stable through mathematical proof, as well as showing improvement compared to the min-max MPC-I. The RMSE was reduced by a further 10%. Lastly, it was shown that the Robust MPC-I reduced the computational time compared to the observer-based MPC by an average of 25%. A model predictive controller with adaptive I-controller is presented in this thesis to reduce the complexity of the controller. The steps needed in controller tuning and the computational times have been improved compared to the observerbased controller. The robust min-max-MMPC-I is shown to produce better control compared to PID and the observer based model predictive controller.

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