Design Guidelines for Fractional Order Cascade Control in DC Motors: A Computational Analysis on Pairing Speed and Current Loop Orders Using Oustaloup’s Recursive Method

Nested, or cascade speed and torque control has been widely used for DC motors over recent decades. Simultaneously, fractional-order control schemes have emerged, offering additional degrees of control. However, adopting fractional-order controllers, particularly in cascade schemes, does not inherently guarantee better performance. Poorly paired fractional exponents for inner and outer PI controllers can worsen the DC motor’s behavior and controllability. Finding appropriate combinations of fractional exponents is therefore crucial to minimize experimental costs and achieve better dynamic response compared to integer-order cascade control. Additionally, mitigating adverse couplings between speed and current loops remains an underexplored area in fractional-order control design. This paper develops a computational model for fractional-order cascade control of DC motor speed (external) and current (internal) loops to derive appropriate combinations of internal and external fractional orders. Key metrics such as overshoot, rise time, and peak current values during speed and torque changes are analyzed, along with coupled variables like speed drop during torque steps and peak torque during speed steps. The proposed maps guide the selection of effective combinations, enabling readers to deduce robust or adaptive designs depending on specific performance needs. The methodology employs Oustaloup’s recursive approximation to model fractional-order elements, with MATLAB–SIMULINK simulations validating the proposed criteria.