PID guidance law design using short time stability approach

In this paper, a PID guidance law utilizing short time stability approach is designed considering control loop dynamics. The kinematic model demonstrates a feedback formation so that it can be separated into two parts, a linear time-invariant (LTI) element in forward path, and a time-varying gain in feedback. Thus, the circle criterion can be employed for stability analysis of the guidance loop dynamics and stability conditions give an analytical bound for the flight up time in which stability can be insured. The stability bound of the proposed guidance law is less conservative than proportional navigation (PN) and proportional-derivative navigation (PDN) and proportional-integral navigation (PIN) guidance laws. Also, this approach can be used as a tool to design guidance law parameters. Finally, three-dimensional simulation results demonstrate the effectiveness and robustness of the new guidance law against the maneuvering target.