Robust Fractional-Order PI/PD Controllers for a Cascade Control Structure of Servo Systems

In this paper, a cascade control structure is suggested to control servo systems that normally include a servo motor in coupling with two kinds of mechanism elements, a translational or rotational movement. These kinds of systems have high demands for performance in terms of fastest response and no overshoot/oscillation to a ramp function input. The fractional-order proportional integral (FOPI) and proportional derivative (FOPD) controllers are addressed to deal with those control problems due to their flexibility in tuning rules and robustness. The tuning rules are designed in the frequency domain based on the concept of the direct synthesis method and also ensure the robust stability of controlled systems by using the maximum sensitivity function. The M-Δ structure, using multiplicative output uncertainties for both control loops simultaneously, is addressed to justify the robustness of the controlled systems. Simulation studies are considered for two kinds of plants that prove the effectiveness of the proposed method, with good tracking of the ramp function input under the effects of the disturbances. In addition, the robustness of the controlled system is illustrated by a structured singular value (µ) plot in which its value is less than 1 over the frequency range.