Optimization of setpoint-based fuzzy gain scheduling and its application to a linear stage

PID controllers have been employed in servo systems for decades. It is well known that an underdamped system has a fast response but accompanied by undesired overshoot, whereas an overdamped system has no oscillation at all but its response is too slow. We propose a setpoint gain scheduling scheme for PD-type controllers using fuzzy logic, which is simple and effective to implement in the industry, to take the advantages of fast response and oscillation suppression. Our objective is to move a positioning system to a target position and have it settle down as soon as possible. In order to optimize the parameters, we use Powell´s method to provide conjugate direction search and the golden section method to find the optimal step size along the search direction. A ballscrew linear stage is used to demonstrate the effectiveness of our proposed scheme successfully. In an experiment of 80 mm movement, it takes additional 0.01 s only to settle down after 0.32 s move time by using the proposed method, whereas it takes additional 0.23 s to settle down by using the auto-tuned conventional PD-type controller.