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.