An adaptive grey PID-type fuzzy controller design for a non-linear liquid level system

Product-sum-type fuzzy controllers are known to have similar characteristics to PD-type controllers. In the case of type-0 control systems, PID-type fuzzy controllers have been proposed in the literature in order to eliminate the steady-state error. However, these control methods, essentially based on conventional PID theory, have no predictive capabilities. The concept of grey system theory, which has a certain prediction capability, offers an alternative approach for various kinds of conventional control methods, such as PID control and fuzzy control. This paper proposes a grey prediction-based fuzzy PID controller that can overcome the stated shortcomings. In order to obtain a better controller performance, another fuzzy controller is designed to change the step size of the grey predictor. A non-linear liquid level system is taken as a test bed. The grey model developed is examined under several different conditions and it is shown that the proposed grey fuzzy PID controller can predict the future output value of the system. It is clear that the proposed adaptive PID-type fuzzy controller is effective in controlling such a non-linear system accurately by changing the step size adaptively for real-time working.