PID controller design based on FBR and two-degree-of-freedom optimal servomechanism

The authors proposed a design method of a PID controller based on plant model reduction by fractional balanced reduction and integral-type optimal servomechanism (IOS), which was synthesized using the method proposed by Smith and Davison. In the IOS synthesis, the variables included in the cost function for controller design are not the plant inputs and outputs themselves but their first and second-order derivatives. Although the derivatives are given the physical meaning as frequency-weighted variables, the magnitude of the inputs and outputs is not evaluated in the control design. Another problem arises when the integral of the control error is included in the augmented state variables and hence in the cost function, i.e., the problem of indefiniteness of the steady-state value of the integral. Those inconveniences were resolved by the two-degree-of-freedom type optimal servo-system (2DOF-IOS). In this paper, the 2DOF-type IOS has been employed instead of the Smith-Davison type IOS to design a PID controller and then the resulting controller has been applied to flight control of the lateral-directional motion of the F-16.