By frequency-domain approach, a synthesis methodology of single-input-single-output optimal control system is developed to ensure closed-loop stability and to minimize a linear quadratic cost function. Furthermore, the equivalent two-degree-of-freedom system is designed so that the feedback-loop can satisfy the return difference equality, i.e., this system possesses the system performance with the optimal control sense and the stability margins properties as in time-domain approach LQR optimal systems. The F-4E flight control system is considered as the design example to illustrate the validity of the design method.

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