Robust fractional order PIλDμ controller design and parameter tuning

This paper deals with the robust control problem for linear systems with both gain and time constants variations under fractional order PI
^λ
D
^μ
controller. A robustness specification to the parameters variations is proposed. For those systems with more than one uncertain time constant, the robustness specifications are analyzed and simplified. To minimize the phase offset nearby the crossover frequency, the PI
^λ
D
^μ
parameters tuning is formulated as a nonlinear optimization problem with the specifications and controller structure constraints, meanwhile the initial values of optimization is preprocessed by solving nonlinear equations. Numerical examples have illustrated the effectiveness of the tuning method and advantages of the proposed PI
^λ
D
^μ
controller.