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        Variable Gains Sliding Mode Control

        Sergio Alvarez-Rodríguez,Gerardo Flores,Noé Alcalá Ochoa 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.3

        In this paper a sliding mode control with variable gains is proposed. Such a controller has chatteringeffect reduction without detriment to the robustness properties of the sliding modes. The key idea behind the control design is that the variable gains magnitude is proportional to the trajectory tracking error magnitude. Also, this design establishes a connection between both the first and the second order sliding modes control. It is demonstrated that the proposed controller does not overestimates disturbances, which significantly reduces the control energy used. Finally, a stability analysis in the sense of Lyapunov is developed to demonstrate finite time convergence to the origin; simulations experiments are carried out to show the effectiveness and robustness of the proposed controller.

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        PID Principles to Obtain Adaptive Variable Gains for a Bi-order Sliding Mode Control

        Sergio Alvarez-Rodríguez,Gerardo Flores 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.10

        A new model to obtain adaptive variable gains for a bi-order Sliding Mode Control is proposed in this work. The variable gains for the controller are designed to dynamically adapt their values, using principles of the well-known Proportional-Integral-Derivative control technique, where the magnitude of the tracking error is the signal feedback. According to the way to tune parameters, it can become a first-order or a second-order controller. This design takes into account the actuators’ constraints (operational limits of the plant to control). As a result of theadaptive properties of the proposed scheme, the new controller significantly reduces the energy consumption in control processes, and it rejects the so-called chattering-effect, simultaneously maintaining the main robust properties of the Sliding Mode strategy. In order to show the feasibility and effectiveness of the proposed design, simulation results are presented, where the performance of the proposed controller is compared with the conventional Sliding Modes of order one and two, and also with the classical PID controller. A strong stability analysis in the sense of Lyapunov is presented, showing global exponential stability for the equilibrium point of the closed-loop control system when the proposed control design is used.

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