Model Predictive Control for Nonlinear Systems With Two-Time Scales

Model predictive control (MPC) has been successfully applied to multivariable nonlinear systems with operational constraints. However, the control performance of MPC is hindered by the different time scales of controlled variables. A two-time scale MPC (TTSMPC) strategy is developed to address the challenge caused by two-time scale characteristics, and ultimately improve the control accuracy. Two-time scale models based on fuzzy neural network (FNN), including slow-sampling FNN (S-FNN) with time scale conversion mechanism and fast-sampling FNN (F-FNN), are constructed to model the two-time scale nonlinear system. Then, the predicted outputs of all controlled variables are obtained at the fast time scale. On this basis, the multiobjective optimal control problem (MOCP) is also solved at the fast time scale to improve control accuracy. Besides, the corresponding convergence and stability conditions of TTSMPC are proved in theory. Finally, the experiment results on the benchmark example of wastewater treatment process (WWTP) illustrate that TTSMPC can achieve satisfactory operation performance at the fast time scale. Note to Practitioners—The motivation of this paper is to overcome the negative impact of two-time scales on MPC in terms of control accuracy. Considering the scenario of an unknown nonlinear system with two-time scales, a TTSMPC scheme is put forward to improve the control accuracy. The implementation of TTSMPC scheme includes four steps. First, establish an FNN-based fast sampling model to compute the predicted output of the fast-sampling controlled variable at the fast time scale. Second, construct a S-FNN with time scale conversion mechanism to calculate the predicted output of the slow-sampling controlled variable at the fast time scale. Third, solve the MOCP on the fast time scale to obtain the control input and apply it to the controlled system. Fourth, correct the parameters of S-FNN and F-FNN at the sampling instants of slow-sampling controlled variable and fast-sampling controlled variable, respectively. Finally, experiments on the benchmark platform of WWTP show the superiority of TTSMPC in terms of control accuracy.