A novel strategy for model predictive control tuning considering nonsquare systems, with more outputs than inputs, and set points or ranges for controlled variables, is introduced. This methodology is applicable for any predictive control algorithm, since it has adjustable parameters according to the implementation, and is divided in three parts that consists of, initially, the determination of the best attainable closed-loop performance function for the multiscenarios, generated from the complete model, including performance and robustness metrics as additional constraints. Based on the attainable closed-loop function, the second step is the calculation of the optimal scaling for the process and, finally, the controller weights are tuned leading the process to the best operating condition. This constrained strategy was applied in the controller design of the Shell heavy oil fractionator benchmark showing good results for zone region tracking.

In the literature, the available techniques for MPC tuning usually consider a specific operating point (OP), while in real plants, controllers should be robust in a wide operating region facing different plant behaviors that arise due to disturbances, saturations, and nonlinearities. In this work, a method for MPC tuning proposed in our previous work is extended for a robust tuning for classical (square) MPCs. This technique applies to any predictive control algorithm, and it considers multi-scenarios based on the closed-loop attainable performance of the system. The sequential procedure is applied, where initially the attainable performance for each scenario (herein, different OPs are used) is determined, and an estimate of the closed-loop potential is computed. In the end, the optimum scaling for the model and the MPC tuning parameters are calculated, solving an optimization problem that uses the attainable trajectories for each scenario as a reference. The selection of the controller’s process model is also determined according to constraints of the attainable performance determination. This robust and constrained strategy is applied to the controller design of two nonlinear systems: (i) the quadruple-spherical tank system and (ii) a continuous stirred tank reactor with separation column and recycle. The proposed approach was successful in tuning the MPC capable of working with all proposed OPs, including those with critical operational conditions for the process controllability, such as nonminimum phase dynamics and model-plant mismatches.

The process model has the most relevant role in model predictive control (MPC) design since it is responsible for capturing system dynamics and behavior for control action calculation. Besides that, in real-time optimization (RTO), an accurate model allows the estimation of the optimum values that will lead the plant to optimal operation. Related to linear models, the linearization point sometimes is not capable of tracking the process trajectory in different regions, jeopardizing the entire representation. Regarding these issues, it is proposed in this paper to employ an augmented unscented Kalman filter to update the linear process model used in the MPC and the steady-state nonlinear model used in the hybrid RTO, at each sampling time, to capture the true process behavior and the updated economic cost. The cost function, solved in the RTO layer, is handled in the MPC layer as a process output, a new variable combined by the measurements, that must be driven to the provided optimum value, respecting constraints. The extended MPC approach is capable of handle zone tracking and set-point/target tracking. The Williams−Otto reactor scheme was employed to corroborate the proposed approach since it presents structural and parametric discrepancies between the model and the plant. The presented results showed that the approach was able to track the true value of the optimal cost operation, respecting the soft-constraints (or range) for the process outputs without exceeding manipulating efforts.

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