Enhanced MPC based on unknown state estimation and control compensation

The model predictive control (MPC) method is widely used in multivariable process control due to its optimization control nature and easy engineering realization. Aiming at the large control error fluctuations caused by various noises, unmeasurable states, and disturbances under the MPC method in practice, this paper proposes a novel enhanced MPC (En-MPC) method that uses Kalman filter to estimate unknown states and combines with the state gain matrix for control compensation. Firstly, given the difficulty of measuring some key states of actual industrial processes, the unknown states are estimated online through Kalman filter technology; Secondly, the state estimation values are used as the initial value of the prediction model to obtain the future output information of the system, and the open-loop optimization solution is calculated in the finite horizon by solving the optimization objective function. The relationship equation between the state variance and the state gain matrix is established and optimized to obtain the optimal gain matrix, which is multiplied by the state estimation as the output of the compensation controller. Finally, the solution of the basic optimization controller and the solution of the compensator is added together to act as the final control input to the controlled plant. The upper bounds of the state variables of the proposed method are proved by the induction method in the root-mean-square sense, and the stability of the system under the algorithm is demonstrated. Simulations and sewage treatment process data experiment show the effectiveness and practicability of the proposed method.