Reference model-based optimization of sliding mode control for second-order systems

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 ( λ ) 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 ( ω n ) in the reference model system remains constant, the damping ratio ( ζ ) was varied between 0.5 and 1. For each ζ value in the reference system, the optimal SMC parameters ( λ 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.