Robust fuzzy predictive switching control for nonlinear multi-phase batch processes with synchronous vs asynchronous cases

Multi-phase batch processes (MPBP) have the characteristics of nonlinearity and various cases of switching, where the switching between two adjacent phases can be divided into synchronous vs asynchronous cases. The present study introduces a robust fuzzy predictive method for switching control to ensure that an MPBP can still operate stably in the above two cases. First, considering the multi-phase characteristics of MPBP, multiple stable sub-models are established under the synchronous case. On this basis, unstable sub-models are established between adjacent phases under the asynchronous case. Second, in order to deal with the inherent nonlinearity of MPBP, each sub-model is locally linearized and a mixed Takagi-Sugeno (T-S) model is established. Third, using a mapping relationship between controller and local subsystem including direct mapping and fully associative mapping, a global output control law is designed. By combining the Lyapunov stability theory, linear matrix inequality (LMI) theory, mode-dependent average dwell time method, etc., corresponding LMI conditions are derived by the mapping relationship of different cases, making each phase asymptotically stable and each batch exponentially stable. Then, the distribution compensation gains of the corresponding controllers, the shortest operating time of the stable subsystem and the longest operating time of the unstable subsystem can be obtained by solving corresponding LMI conditions in a synchronous or an asynchronous case. Finally, if the MPBP is in an asynchronous case, according to the longest operating time of the unstable subsystem, a time compensation method based on the obtained operating time is proposed to avoid the occurrence of an unstable subsystem. The simulation results demonstrate that the proposed method has greater advantages than the reference methods.