Predictive fault-tolerant control for nonlinear batch processes with small time delays via iterative learning control: A Lyapunov–Razumikhin approach

Abstract

For batch processes with small time delays and actuator partial fault, the existing methods based on iterative learning control still have some limitations, including the conservative and computationally burdensome of stability conditions and the limited fault-tolerant control capabilities. For this background, an iterative learning robust predictive fault-tolerant control method is developed, which integrates the Lyapunov–Razumikhin function method and derives stability conditions based on robust positive definite invariant set and terminal constraint set. With small time delays, the stability conditions of the system deduced using the Lyapunov–Razumikhin function are solved at a lower computational cost, which is due to the fact that the dimensionality of the stabilization condition is directly related to the size of the time delay, and thus the small time delay implies a lower dimensionality. Especially, the computational effort for solving the stability conditions online is reduced, allowing real-time control law gains to be obtained and combined with historical batches of control inputs, reducing the learning cycles of the system, and realizing stable tracking of the setpoints within shorter operating batches. Moreover, the robust positive invariant set and the set of terminal constraints are able to constrain the state of the system within a safe range for all possible uncertainties, bounded disturbances, and faults. This makes the proposed methods based on them more robust and fault tolerant. Finally, a nonlinear batch reactor is used as an example to demonstrate the effectiveness and feasibility of the developed method.