Abstract
This paper proposes a new method to tune a fractional order PID controller. This method
utilizes both the analytic and numeric approach to determine the controller parameters. The
control design specifications that must be achieved by the control system are gain crossover
frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new
design specification suggested by this paper. These specifications results in three equations in
five unknown variables. Assuming that certain relations exist between two variables and
discretizing one of them, a performance index can be evaluated and the optimal controller
parameters that minimize this performance index are selected. As a case study, a third order
linear time invariant system is taken as a process to be controlled and the proposed method is
applied to design the controller. The resultant control system exactly fulfills the control design
specification, a feature that is laked in numerical design methods. Through matlab simulation,
the step response of the closed loop system with the proposed controller and a conventional PID
controller demonstrate the performance of the system in terms of time domain transient response
specifications (rise time, overshoot, and settling time).
utilizes both the analytic and numeric approach to determine the controller parameters. The
control design specifications that must be achieved by the control system are gain crossover
frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new
design specification suggested by this paper. These specifications results in three equations in
five unknown variables. Assuming that certain relations exist between two variables and
discretizing one of them, a performance index can be evaluated and the optimal controller
parameters that minimize this performance index are selected. As a case study, a third order
linear time invariant system is taken as a process to be controlled and the proposed method is
applied to design the controller. The resultant control system exactly fulfills the control design
specification, a feature that is laked in numerical design methods. Through matlab simulation,
the step response of the closed loop system with the proposed controller and a conventional PID
controller demonstrate the performance of the system in terms of time domain transient response
specifications (rise time, overshoot, and settling time).
Keywords
Fractional order PID controller; gain crossover frequency; phase margin; peak magnitude at resonant frequency.