In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured uncertainty, is able to guarantee the finite time stability. The main advantage of this second order sliding mode control is reaching to sliding surface with high precision without chattering in control signal. In simulation section, the proposed algorithm is compared with the boundary layer sliding mode control and then is applied to designing a finite time nonlinear guidance law that is robust with respect to target maneuvers. Simulation results show that the control input in this algorithm is smooth and has no chattering and by applying this method, sliding variables will converge to zero in a given desired finite time.

This paper studies the uncertain nonlinear dynamics of a MEMS optical switch addressing electrical, mechanical and optical subsystems. Recently, MEMS optical switch has had significant merits in reliability, control voltage requirements and power consumption. However, an inherent weakness in designing control for such systems is unavailability of switch position information at all times due to the saturated output characteristics, which is aggravated by considering disturbances. In order to circumvent this problem, two nonlinear observers based on the first order and second order sliding mode approach are designed to estimate the state variables of the device subject to external disturbances. The nonlinear observers are then utilized in the control system to maintain robust stability and tracking performances. The newly invented second order sliding mode controller can remove the chattering phenomena as the main drawback of the first order sliding mode controller. Furthermore, since second order sliding mode control is not robust against disturbances/uncertainties which vary with states, a new time-varying second order sliding mode control is proposed to enhance the robust performance of the controller without estimating any switching time. Simulation results show that the proposed observer and control have good tracking ability and robustness against disturbances.

This paper proposes a new uncertainty cancellation based second-order sliding mode control law to control uncertain nonlinear systems in a finite time. The presented algorithm consists of a term that not only estimates the uncertainty based on sliding mode observer theory but also provides second-order sliding mode behaviour. Therefore, the Recommended algorithm is robust in the presence of uncertainties. Additionally, it offers a smooth control signal, ensuring that chattering does not appear. In this method, the finite-time convergence of the closed-loop system error is guaranteed by using mathematical relations. For this aim, a Lyapunov candidate function is first defined based on the sliding variable and the estimation error. Then, by establishing the finite time stability condition, the stability of sliding variable and estimation error is ensured. Additionally, the convergence time is explicitly determined. This particular design is applied to a thrust vector-based flying object to track the pitch angle. The efficiency of the thrust vector system will be demonstrated through computer simulations and compared with two other observer-based sliding mode methods.

Grid-tied Neutral-Point-Clamped (NPC) inverters have been widely used in various applications recently. A superior control method is required to achieve the desired performance of a grid-connected NPC inverter. Accordingly, a second-order sliding mode control (SOSMC) method, which is designed in the stationary frame, is utilized for achieving this aim in this paper. The super-twisting second-order sliding mode control is used for solving the chattering problem of conventional first-order sliding mode control (FOSMC). In comparison to control methods which are applied in rotation frame, this method is not required transformation from rotating frame to a-b-c frame and vice versa and decoupling of d and q components. The Lyapunov stability analysis is used for designing of this controller. The performance of proposed method is evaluated by simulation results implemented in MATLAB/Simulink software. The performance of the SOSMC is also compared with FOSMC. The results show that the incorporation of SOSMC can improve current reference tracking of the NPC inverter in different scenarios.

In this paper, a chattering-free sliding-mode control is mainly proposed in a second-order discrete-time system. For achieving this purpose, firstly, a suitable control law would be derived by using the discrete-time Lyapunov stability theory and the sliding-mode concept. Then the input constraint is taken into account as a saturation function in the proposed control law. In order to guarantee the closed-loop system stability, a sufficient stability condition would be addressed in the presence of unstructured uncertainties. Hence the states of the discrete-time system are moved to a predefined sliding surface in a finite sampling time. Then the system states are asymptotically converged to the origin through the sliding line. The suggested SMC is successfully applied in two discrete-time systems (i. e. regulation and tracking problems). The effectiveness of the proposed method will be verified via numerical examples.

This paper investigates fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems in the presence of matched and mismatched disturbances. Using estimation of the mismatched disturbance estimated by a fixed-time disturbance observer, a novel nonlinear dynamic sliding surface is designed. This estimation is utilized in designing a completely novel nonlinear dynamics sliding surface whereby the fixed-time convergence of the sliding motion is guaranteed in spite of mismatched disturbance. The convergence time of the closed-loop system including disturbance observer and control system is guaranteed to be uniform with respect to initial conditions. Moreover, the proposed controller avoids chattering phenomenon by producing a continuous control signal.