Optimal fuzzy control system using the cross-entropy method. A case study of a drilling process

This paper focuses on the optimal tuning of fuzzy control systems using the cross-entropy precise mathematical framework. The design of an optimal fuzzy controller for cutting force regulation in a network-based application and applied to the drilling process is described. The key issue is to obtain optimal fuzzy controller parameters that yield a fast and accurate response with minimum overshoot by minimising the integral time absolute error (ITAE) performance index. Simulation results show that the cross-entropy method does find the optimal solution (i.e. input scaling factors) very accurately, and it can be programmed and implemented very easily (few setting parameters). The results of a comparative study demonstrate that optimal tuning with the cross-entropy method provides a good transient response (without overshoot) and a better error-based performance index than simulated annealing [17], the Nelder–Mead method [14] and genetic algorithms [33]. The experimental results demonstrate that the proposed optimal fuzzy control provides outstanding transient response without overshoot, a small settling time and a minimum steady-state error. The application of optimal fuzzy control reduces rapid drill wear and catastrophic drill breakage due to the increasing and oscillatory cutting forces that occur as the drill depth increases.