Two-dimensional optimization design of constrained minmax model predictive tolerant-fault control for nonlinear batch processes

The presence of actuator faults and disturbances, coupled with the nonlinear characteristics inherent in batch processes, poses challenges to the design of high-precision control algorithms, especially for variables that vary over a large range. To solve this issue, we propose a two-step 2D constrained model predictive fault-tolerant control method that integrates the theory of min-max optimization. First, the original nonlinear batch process is approximated at different operating points and transformed into multiple polytopic systems (MPSs), which includes the "worst case" scenario, i.e., a case with all internal effects. Next, according to its characteristics and by introducing an output tracking error and batch state differences, an equivalent model of a MPS is created and an iterative learning control law was used. Based on this model, a quadratic performance index function, including anti-external disturbances, is designed, which is divided into two parts covering the entire infinite horizon. The linear state feedback control law plus the initial free control moves comprise the control law. In this way, the optimal control inputs are generated, and the system can be controlled with a greater margin, improving feasibility. Moreover, for closed-loop stability, a parameter-dependent Lyapunov function is constructed. An allowable range of actuator faults that the designed controller can resist is also considered and constructed. The advantage of the proposed control algorithm is that it fully considers the repetitive characteristics of batch processes, and for the first time, a 2D two-step control strategy related to time and batch directional information is designed, which greatly improves the system output tracking performance. Using a nonlinear batch reactor as an example, the method proposed in this study demonstrates its superiority tracking performance and ability to resist external disturbances than that of the traditional method.