A novel design of positive position feedback controller based on maximum damping and H 2 optimization

Abstract

Positive position feedback is an attractive control law for the control of plants having no high frequency roll-off. The tuning of the parameters of the positive position feedback to obtain the desired closed-loop performance is quite challenging. This paper presents a technique to design the positive position feedback controller with the optimal damping. The technique is demonstrated on a single degree-of-freedom system. The poles of the positive position feedback are tuned using the method of maximum damping, which states that the maximum damping is achieved when both closed-loop poles of the system are merged. The parameters of the positive position feedback are dependent on the desired target damping in the closed-loop system. However, arbitrary choice of target damping results in high response at the frequencies lower than the tuning frequency. The optimal value of the target damping is obtained by minimizing the $H_2$ norm of the closed-loop transfer function of the system. The influence of the various parameters of the positive position feedback on the closed-loop response of the system is also studied. Finally, the experiments are conducted to verify the effectiveness of the proposed technique.