Abstract
A tuning procedure for a model predictive controller (MPC) is presented for multi-input multi-output systems. The approach consists of two steps based on a hybrid method: the goal attainment method and a variable neighborhood search. In the first step, the weights of the MPC objective function are obtained, minimizing the square error between the closed-loop response of the internal controller model and a predefined desired reference trajectory. In the second step, the integer variables of the problem (prediction and control horizons) are obtained, minimizing the square error between the closed-loop response and an optimal trajectory, aiming a controller with low computational cost and good performance. The proposed method was tested in two benchmark processes using different MPC formulations, showing satisfactory results.
Highlights
Model predictive control (MPC) is an advanced control structure that uses an openloop model to predict future process behavior over a predefined horizon by solving an optimization algorithm at each time step [1]
The MPC tuning method used in this work is achieved through the synergy of the goal attainment method (GAM) and variable neighborhood search (VNS) algorithms, which results in a hybrid approach that allows one to estimate the controller parameters based on the desired performance of the system
To assure a robust method, the tuning parameters in this work can be adjusted in different ways since GAM and VNS algorithms use the internal model of the MPC: (i) it is possible to use the same robust formulation of the MPC in the Model Predictive Control Tuning Approach (MPCT) to find the tuning parameters, e.g., through minimax optimization formulations in both algorithms; (ii) it is possible to estimate the tuning parameters under a worst-case control problem using a family of models that represent the dynamic behavior of the process, and ; (iii) robustness can be considered through the result of a conservative performance since the MPCT algorithm employs a reference trajectory defined by the user
Summary
Model predictive control (MPC) is an advanced control structure that uses an openloop model to predict future process behavior over a predefined horizon by solving an optimization algorithm at each time step [1]. This paper shows that the algorithm can be applied to any formulation of MPC control; the tuning algorithm is capable of dealing with model mismatch and system noise by adjusting parameters based on the worst-case scenario from the family models of the process, using a robust MPC formulation in the MPC tuner, or via the predefined desired trajectory in the system; according to the performance criteria, which are pre-established by the user, the tuning algorithm can provide a quick parameter adjustment, presenting a low computational cost; the algorithm works in conjunction with the internal MPC optimizer to obtain adequate system performance and robustness; improvement of the objective function for obtaining the adequate length of prediction and control horizons, using the VNS algorithm to reach the desired closed-loop dynamic; reduction of the computational cost of the algorithm by removing an optimization stage in the calculation of the utopia point of the goal attainment method algorithm; and since this work proposes a sequential optimization method, better results were attained by executing the GAM algorithm first, followed by the VNS algorithm.
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