Linear Quadratic Predictive Fault-Tolerant Control for Multi-Phase Batch Processes

This paper proposes a linear quadratic predictive fault-tolerant control (LQPFTC) scheme for multi-phase batch processes with input time-delay and actuator faults. First of all, according to a given model with input time-delay, a new variable is introduced and the given model is transformed into an extended state-space model without time delay. And then, a new 2D switched system model based on an equivalent 2D-Roesser model is constructed by introducing the state error and the output tracking error to solve the actuator fault and realize the optimal control performance. By adjusting the variable in the function, a quadratic performance function based on the model is designed and a linear predictive fault-tolerant controller by combining with the principle of predictive control is proposed. Then, using the Lyapunov function and the average dwell time method, the sufficient conditions for the robust exponential stability of the system along the time and batch direction, and the minimum running time of each phase are derived. Finally, taking the injection molding process as an example, different fault values are selected for simulation. The results show that the 2D controller designed can realize tracking control with different actuator fault values and even a serious one.