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This paper presents a new method for computationally effective implementation of a discrete-time fractional-order proportional&#x2013;integral&#x2013;derivative (FOPID) controller. The proposed method is based on a unique representation of the FOPID controller, where fractional properties are modeled by a specific finite impulse response (FIR) filter. The balanced truncation model order reduction method is applied in the proposed approach to obtain an effective, low-order model of the FOPID controller. The time-invariant FOPID controller implementation is presented first, and then the methodology is extended to the controller with time-varying gains. A comparative analysis shows that the proposed methodology leads to the effective modeling of discrete-time FOPID controllers. In addition to simulation runs, the effectiveness of the introduced methodology is confirmed in a real-life experiment involving the control of the DC motor servo system. The paper concludes with the implementation tools developed in the Matlab/Simulink environment.

A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller