Optimal Predicted Fuzzy PI Gain Scheduling Controller of Constant Turning Force Systems with Fixed Metal Removal Rate

The dynamic behaviour of the turning process is nonlinear and time-varying owing to variations in cutting depth. This paper proposes an optimal predicted fuzzy PI gain scheduling controller to control the constant turning force (CTF) process with a fixed metal removal rate (MRR) under various cutting conditions. The predicted fuzzy PI gain scheduling control scheme consists of two parts: the fuzzy PI gain scheduling controller; and the grey predictor. First, the optimal parameters of both the grey predictor and the optimal PI gains corresponding to each desired cutting depth in the range of operation, are designed off-line by using the proposed optimal combined method, i.e. Taguchi–RGA method, which integrates the Taguchi method and a real-coded genetic algorithm (RGA). Then, before the parameters of both the grey predictor and the PI gains are scheduled on-line, by fuzzy inference in terms of the changes of cutting depth, the optimal set of triangular-type membership functions of the fuzzy inference mechanism for scheduling the parameters of both the grey predictor and the PI gains are also designed off-line by using the Taguchi–RGA method. Computer simulations are performed to verify the applicability of this optimal predicted fuzzy PI gain scheduling control scheme for controlling the CTF process with a fixed MRR under various cutting conditions. It is shown that such an optimal predicted fuzzy PI gain scheduling control scheme can achieve satisfactory performance and better results than those reported recently in the literature.