A novel mixed technique for order abatement in linear time invariant systems and robustness analysis of DC motor

This work presents a novel mixed technique for order abatement (OA) of linear time-invariant (LTI) systems. The proposed approach utilizes the Honey Badger algorithm (HBA) to compute the numerator polynomials, while the stability equation (SE) method determines the denominator polynomials of the abated system (AS). The Integral of squared error (ISE) is employed as the objective function to minimize the error between the high-order system (HOS) and the AS, ensuring accurate coefficient estimation. To evaluate the effectiveness of the proposed mixed approach, various performance and transient parameters were compared against well-established techniques from the literature. The results from tested examples demonstrate the superior accuracy and stability of the proposed method in approximating system dynamics. Additionally, the study explores the implementation of an HBA-tuned PID controller for DC motor speed control, with the integral of time-weighted absolute error (ITAE) serving as the objective function. A robustness analysis was conducted by varying the motor parameters, and the transient response of the HBA/PID technique was compared with existing methods. The findings reveal that HBA/PID achieves lower rise time and settling time, leading to an overall improvement in the motor's response. These results highlight the effectiveness of the proposed approach in both order abatement and robust control applications.