Synthesis of robust PID controller for controlling a single input single output system using quantitativefeedback theory technique

In this paper, the modeling and control of a rotary missile that uses the proportional navigation law is proposed, applying the Quantitative Feedback Theory (QFT) technique. The dynamics of a missile are highly uncertain; thus, application of robust control methods for high precise control of missiles is inevitable. In the modeling section, a new coordinate system has been introduced, which simplies analysis of rotary missile dynamics equations. In the controlling part, application of the QFT method leads to the design of a robust PID controller for the highly uncertain dynamics of a missile. Since missile dynamics have multivariable nonlinear transfer functions, in order to apply the QFT technique, these functions are converted to a family of linear time invariant processes with uncertainty. Next, in the loop shaping phase, an optimal robust PID controller for the linear process is designed. Lastly, analysis of the design procedure shows that the robust PID controller is superior to the commonly used PID scheme and multiple sliding surface schemes, in terms of both tracking accuracy and robustness.