No abstract

Soft computing techniques are frequently used in modeling and control applications of nonlinear systems. However, the fuzzy cognitive map method, which is one of the soft computing techniques, is rarely used in control applications as a main controller. In this study, a fuzzy cognitive map based PD controller structure is introduced and used for the stabilization of an inverted pendulum system which is a nonlinear, unstable, and under-actuated system. The proposed controller has two inputs which are the error and the change of error. In the proposed PD controller structure, the crisp input values are fuzzified to be handled in a fuzzy cognitive map process. Then, causal relationships between fuzzified inputs and a control output are defined by using weight parameters. Finally, the crisp control output value which will be applied to the system is obtained by using an activation function. The types of membership functions used for the fuzzification process and the activation function determine the nonlinear characteristics of the proposed fuzzy cognitive map based PD controller. The proposed controller has three tuning parameters which are one output gain and two weight parameters. To show the effectiveness and robustness of the proposed fuzzy cognitive map based PD controller, simulation studies are performed on an inverted pendulum system. Additionally, the performance of the proposed controller is compared with a PD controller. All controller parameters are determined by using a genetic algorithm. Comparison results indicate that the proposed fuzzy cognitive map based PD controller shows better control performance than the classical PD controller.

Linear proportional-integral-derivative (PID) controllers are the most widely used process controllers in industrial applications due to their simple structures and effective performances. However, performances of these controllers reduce as the nonlinear characteristics or the system orders of the industrial processes increases. Therefore, various nonlinear PID controller models are proposed in literature to improve the control performances of linear PID controllers. In this study, a new nonlinear PID controller design approach is proposed based on the fuzzy cognitive map (FCM) method. Two different FCM based PID controller models are introduced. The first controller model is in the conventional parallel PID structure with three inputs as the error, the derivative of the error, and the integral of the error. On the other hand, the second controller model is in the conventional fuzzy PID form with two inputs as the error and the derivative of the error. In the proposed method, each input signal is firstly fuzzified by using a membership function. Then, causal relationships between inputs and the output are determined by using weight parameters. Finally, the FCM inference is performed by using an activation function. Therefore, the proposed nonlinear PID controllers have four and six tuning parameters, respectively. Simulation studies are performed on a fourth order linear system in order to evaluate the performance of the proposed FCM based PID controller models. The performances of these controller models are compared with a conventional PID controller and a fuzzy PID controller. The comparison results show that the proposed FCM based PID controller models outperform the conventional PID and fuzzy PID controllers.