A New Adaptive PID Controller for Non-Linear Systems

A.S. Zayed, M. Elfandi, and M. Twiel (Libya)


PID control, zero pole-placement control, self-tuning control, Nonlinear control, Neural networks.


This article presents a new non-linear PID adaptive controller algorithm incorporating a radial bases function (RBF) neural network based generalised learning model (GLM) . The GLM assumes that the unknown non-linear plant is represented by an equivalent model consisting of a linear time-varying sub-model plus a non-linear RBF neural networks sub-model. The parameters of the linear sub-model are identified by a recursive least squares algorithm with a directional forgetting factor, whereas the unknown non-linear sub-model is modelled using the RBF neural network resulting a new non-linear controller with a generalised minimum variance performance index. In addition, the proposed controller has a PID structure and overcomes the shortcomings of other linear designs and provides an adaptive mechanism which ensures that both the closed-loop poles and zeros are positioned at their pre-specified places. It can track set point changes with the desired speed of response, penalises excessive control action, and can be applied to non-minimum phase systems and unstable systems. Example simulation results using a non-linear plant model demonstrate the effectiveness of the proposed controller.

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