Fractional order PIλDµA controller design based on Bode’s ideal function

The fractional order proportional, integral, derivative and acceleration (PIλDµA) controller is an extension of the classical PIDA controller with real rather than integer integration action order λ and differentiation action order µ. Because the orders λ and µ are real numbers, they will provide more flexibility in the feedback control design for a large range of control systems. The Bode’s ideal transfer function is largely adopted function in fractional control systems because of its iso-damping property which is an essential robustness factor. In this paper an analytical design technique of a fractional order PIλDµA controller is presented to achieve a desired closed loop system whose transfer function is the Bode’s ideal function. In this design method, the values of the six parameters of the fractional order PIλDµA controllers are calculated using only the measured step response of the process to be controlled. Some simulation examples for different third order motor models are presented to illustrate the benefits, the effectiveness and the usefulness of the proposed fractional order PIλDµA controller tuning technique. The simulation results of the closed loop system obtained by the fractional order PIλDµA controller are compared to those obtained by the classical PIDA controller with different design methods found in the literature. The simulation results also show a significant improvement in the closed loop system performances and robustness using the proposed fractional order PIλDµA controller design.