A stable self-learning PID control for multivariable time varying systems

A stable self-learning PID (proportional+integral+derivative)(proportional+integral+derivative) control scheme for multivariable nonlinear systems with unknown dynamics is proposed in this paper. The control scheme is based on a neural network (NN) model of the plant. The NN model is adapted by an extended Kalman filter (EKF) to learn plant dynamic change, while the PID control parameters are adapted by the Lyapunov method to minimize squared tracking error. Therefore, the model output is guaranteed to converge to the desired trajectory asymptotically, and the plant output also tracks the desired trajectory due to model adaptation. The proposed scheme is evaluated by applying it to a simulated multivariable continuous stirred tank reactor (CSTR). The self-learning PID controller is also compared with a fixed parameter PID controller for a single-input single-output CSTR and the superiority of the self-learning PID is demonstrated.