Optimal Fuzzy Proportional-Integral-Derivative Control for a Class of Fourth-Order Nonlinear Systems using Imperialist Competitive Algorithms

The proportional integral derivative (PID) controller has gained wide acceptance and use as the most useful control approach in the industry. However, the PID controller lacks robustness to uncertainties and stability under disturbances. To address this problem, this paper proposes an optimal fuzzy-PID technique for a two-degree-of-freedom cart-pole system. Fuzzy rules can be combined with controllers such as PID to tune their coefficients and allow the controller to deliver substantially improved performance. To achieve this, the fuzzy logic method is applied in conjunction with the PID approach to provide essential control inputs and improve the control algorithm efficiency. The achieved control gains are then optimized via the imperialist competitive algorithm. Consequently, the objective function for the cart-pole system is regarded as the summation of the displacement error of the cart, the angular error of the pole, and the control force. This control concept has been tested via simulation and experimental validations. Obtained results are presented to confirm the accuracy and efficiency of the suggested method.