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    Reference model-based optimization of sliding mode control for second-order systems
    (Sage Publications Ltd, 2025) Teke, Ibrahim Halil; Tan, Nusret
    In this study, the design of Sliding Mode Control (SMC) has been carried out based on a second order reference model with a specified transfer function. The primary objective of this study is to determine the SMC controller parameters according to the desired time response in the output signal. The aim is to determine the optimal control gains that minimize the difference between the reference and plant outputs in a systematic way. By minimizing the error between the reference model and the SMC controlled system model, the optimal SMC parameters, specifically the sliding surface slope ( lambda ) and the switching function coefficient ( K ), are obtained. Integral performance criteria were used to minimize the error. Both the reference system and the system controlled by the SMC have second-order transfer functions. While the natural frequency ( omega n ) in the reference model system remains constant, the damping ratio ( zeta ) was varied between 0.5 and 1. For each zeta value in the reference system, the optimal SMC parameters ( lambda and K ) were obtained by using the Fmincon optimization algorithm to minimize the error between the two systems based on the selected integral performance criteria. By applying the obtained SMC parameters to the controlled system, unit step responses were obtained in the output of the controlled system. T optimization process was performed based on the transfer functions of two different known systems, and the variation of the optimal SMC parameters according to the damping ratio of the reference model was presented in tables and graphs. The simulation results confirm that the proposed method significantly improves the accuracy and robustness of tracking compared to conventional SMC tuning approaches. These results demonstrate the effectiveness of the proposed method for designing reliable and efficient controllers for second-order dynamic systems. The success of the reference model-based second-order system controlled by the SMC method is clearly demonstrated by the generated graphs and tables. This study introduces a new optimization-based SMC design approach by establishing an explicit analytical relationship between the damping ratio and the controller parameters. In the proposed method uses regression, which avoids the need for iterative tuning and repeated calibration.
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    Sliding Mode Control Design Using PIR Sliding Surface for Second Order Systems
    (Ieee-Inst Electrical Electronics Engineers Inc, 2026) Teke, Ibrahim Halil; Tan, Nusret
    This study proposes a new Sliding Mode Control (SMC) approach in which a proportional-integral-retarded (PIR) structure is employed as the sliding surface for second-order dynamical processes. Unlike conventional sliding surfaces that rely on proportional-derivative structures, the proposed PIR sliding surface integrates proportional, integral, and intentional delay terms directly into the surface definition, thereby eliminating explicit derivative action while improving transient shaping capability and noise robustness. The proposed PIR sliding surface offers an alternative sliding surface design perspective by embedding delay-based dynamics directly into the surface formulation, enabling derivative-free implementation and enhanced design flexibility, rather than aiming for universal performance dominance over existing PID/PI-based sliding surface designs. A complete analytical formulation is provided, including the derivation of the PIR-based sliding surface, the associated closed-form SMC control law, and a Lyapunov-based stability analysis ensuring finite-time convergence and closed-loop stability. The controller parameters are optimally tuned using the MATLAB fmincon algorithm based on four integral performance criteria, namely ISE, IAE, ITSE, and ITAE. The proposed PIR-SMC scheme is evaluated through comprehensive simulation studies on a second-order electromechanical system. The results demonstrate fast reference tracking, reduced overshoot, and accurate steady-state performance. Robustness is further assessed by applying +/- 10% variations to the process parameters without retuning, where consistent dynamic behavior is maintained. Additionally, by delivering an external disturbance at various time instants, the suggested controller's disturbance rejection capability is examined. In all cases, the PIR-SMC-controlled system suppresses the disturbance effectively and restores the output to the reference value within 0.5-1 s without steady-state error. Comparative analyses indicate that ISE-based optimization provides superior transient performance, while ITAE-based optimization minimizes long-duration errors. Overall, the proposed PIR sliding surface-based SMC offers a robust and flexible control framework suitable for second-order processes and represents a viable alternative to conventional sliding surface based designs.