This chapter presents reaching laws utilizing difference equation with minimum function for discrete-time sliding mode control. The proposed approach combines the characteristics of an altered Gao’s methodology when away from the sliding manifold and Utkin’s method when nearby the manifold. By eliminating chattering and ensuring precise adherence of the system states to the sliding hyperplane, the method effectively controls the rate of change of the switching function through a tunable gain. Consequently, the derived control signal is less aggressive for large initial conditions compared to Gao’s method. The proposed discrete-time sliding mode control is applicable to both unperturbed and perturbed systems. For unperturbed systems, the sliding variable reaches zero in finite time, whereas for perturbed systems, it remains confined within a neighborhood of the sliding hyperplane. The effectiveness of the proposed reaching law is validated through simulations, including both a numerical example and a practical example involving a pendulum system. Additionally, a detailed comparative analysis with existing methods and the approach discussed in the previous chapter is provided, offering a comprehensive evaluation.

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Reaching Laws Based on Difference Equations with Minima and Rate-Regulatory Function

  • Shyam Kamal,
  • Parijat Prasun

摘要

This chapter presents reaching laws utilizing difference equation with minimum function for discrete-time sliding mode control. The proposed approach combines the characteristics of an altered Gao’s methodology when away from the sliding manifold and Utkin’s method when nearby the manifold. By eliminating chattering and ensuring precise adherence of the system states to the sliding hyperplane, the method effectively controls the rate of change of the switching function through a tunable gain. Consequently, the derived control signal is less aggressive for large initial conditions compared to Gao’s method. The proposed discrete-time sliding mode control is applicable to both unperturbed and perturbed systems. For unperturbed systems, the sliding variable reaches zero in finite time, whereas for perturbed systems, it remains confined within a neighborhood of the sliding hyperplane. The effectiveness of the proposed reaching law is validated through simulations, including both a numerical example and a practical example involving a pendulum system. Additionally, a detailed comparative analysis with existing methods and the approach discussed in the previous chapter is provided, offering a comprehensive evaluation.