Smooth Second-order Sliding Mode Control Research Articles

Smooth second-order sliding mode control for fully actuated multirotor aerial vehicles

The present paper is concerned with the robust and smooth attitude-position tracking control of fully actuated multirotor aerial vehicles equipped with fixed rotors and subject to matched model uncertainties and disturbances. The vehicle coupled dynamic equations representing the translational and rotational motions are thoroughly derived using the multibody approach, considering the external torque and force disturbances as well as the uncertainties in the inertia parameters of the airframe and the rotors. From this model, it is shown that the overall disturbances and uncertainties can be lumped into an additive-matched plant-model discrepancy. Then, based on a geometrically consistent description of the control error in SE(3), a novel joint geometric attitude-position control law is designed using a multi-input smooth second-order sliding mode strategy. The latter uses a high-order sliding mode disturbance observer to guarantee the overall system robustness. The second-order sliding mode is proved to exist using vector-field homogeneity, and the tracking error is shown to exponentially converge to the origin. The method is extensively evaluated via numerical simulations using a fully actuated hexacopter with tilted rotors, showing advantages with respect to state-of-the-art alternatives.

Fast Smooth Second-Order Sliding Mode Control with Disturbance Observer for Automatic Shell Magazine

This paper studies practical control design for a novel automatic shell magazine (ASM) with a new fast smooth second-order sliding mode (FSSOSM) control based on disturbance observer. The dynamic model of the ASM with parameter perturbations and nonlinear friction is established. A higher order sliding mode disturbance observer based on super-twisting algorithm is utilized as a robust compensator to estimate the lumped uncertainties. The proposed FSSOSM control is performed to obtain the continuous sliding mode control law and inhibit the chattering phenomenon. The finite time convergence is investigated by utilizing the Lyapunov stability theorem. Three controllers, the traditional sliding mode controller, the proposed FSSOSM controller and a continuous fixed-time second-order sliding mode (CFTSOSM) controller, are compared. Extensive comparative simulation results under three typical working conditions (no-loaded, half-loaded and full-loaded) demonstrate that the proposed control strategy has a high dynamic tracking performance along with a good robustness against model uncertainty.

Global smooth sliding mode controller for flexible air-breathing hypersonic vehicle with actuator faults

A global smooth sliding mode controller (GSSMC) is proposed for flexible air-breathing hypersonic vehicle (FAHV) under actuator faults and parametric uncertainties, consisting of global fast finite-time integral sliding surface (GFFIS), generalized smooth second-order sliding mode reaching law (GSRL) and smooth fixed-time observer. Firstly, nonlinear control-oriented model of FAHV is processed using input/output feedback linearization with flexible effects and actuator faults modeling as lumped matched disturbances. Secondly, a GFFIS is established to ensure finite-time convergence of states without singularity based on a newly proposed fast finite-time high-order regulator (FFR). The FFR is improved from standard finite-time high-order regulator via dilation rescaling, which can accelerate response speed avoiding complicated parameters selection. Meanwhile, GFFIS can eliminate initial reaching phase to enhance robustness of system due to characteristic of global convergence. Thirdly, a GSRL is presented to ensure finite-time convergence of sliding mode vector and its derivative without chattering based on a generalized smooth second-order sliding mode control algorithm, the stability and finite convergence time of which is analyzed via Lyapunov criteria in detail. Then, a smooth fixed-time observer is applied to estimate lumped disturbances in fixed time and avoid effects of parametric uncertainties. With the three components, GSSMC can drive FAHV subject to actuator faults and parametric uncertainties to follow desired values in finite time with smooth control signals. Ultimately, three sets of simulations are performed to verify the effectiveness of the methods proposed.

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

ABSTRACTA fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.

Fast smooth second-order sliding mode control for systems with additive colored noises.

In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the controller. The finite-time convergence of the prescribed sliding variable dynamics system is proved by using stochastic Lyapunov-like techniques. Then the proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are presented comparing with smooth second-order sliding mode control to validate the analysis.

Finite-time convergent terminal guidance law design based on stochastic fast smooth second-order sliding mode

A novel finite-time convergent terminal guidance law, based on stochastic fast smooth second-order sliding mode control theory, is proposed in order to handle the track imprecision caused mainly by inertial lag, model uncertainties and atmospheric environment disturbances, as well as the stochastic noise caused by target maneuver term. The missile-interceptor guidance system against targets performing evasive maneuvers is considered. The target maneuver model is employed to alleviate the dependence of the perfect knowledge of the range to target and the range rate as well as the limitation to target normal acceleration. Considering that the system is driven by additive noise, which do not have any equilibrium, a new concept of finite-time mean-square practical convergence is presented. And based on this concept, the finite-time convergence property of proposed guidance law is deduced. The availability and effectiveness of the proposed guidance law is illustrated through computer simulations. The results show that the proposed guidance law can realize finite-time convergence, and it has strong robustness against bounded uncertainties as well as the stochastic noise. The proposed guidance law does not has violent high-frequency chattering, which guarantees the tracking accuracy.

Adaptive smooth second-order sliding mode control method with application to missile guidance

This paper proposes an adaptive smooth second-order sliding mode control law for a class of uncertain non-linear systems. The key point of this control law is ensuring a smooth control signal considering parametric uncertainty and disturbances with unknown bounds. The proposed control method is obtained by introducing a continuous function under the integral and using adaptive gains. The switching function and its derivative are forced to zero in finite time. This is achieved using a smooth control command and without the prior knowledge of upper bound parameters of uncertainties. The finite-time stability is proved based on a quadratic Lyapunov approach and the reaching time is estimated. This structure is used to create a homing guidance law and the efficiency is evaluated via simulations.

Global Finite Time Synchronization of Two Nonlinear Chaotic Gyros Using High Order Sliding Mode Control

In this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order sliding mode control (HOAMSC). It is proved that the proposed controller is robust to mismatch parametric uncertainties. Also it is shown that the method have excellent performance and more accuracy in comparison with conventional sliding mode control. Based on Lyapunov stability theory, the proposed controller and some generic sufficient conditions for global finite time synchronization are designed such that the errors dynamic of two chaotic behaviour satisfy stability in the Lyapunov sense. The numerical results demonstrate the efficiency of the proposed scheme to synchronize the chaotic gyro systems using a single control input.

Guidance and Control of Missile Interceptor using Second-Order Sliding Modes

A new smooth second-order sliding mode control (SSOSM) is proposed and proved for a system driven by uncertain sufficiently smooth disturbances. The main target application of this technique, the missile interceptor guidance-control system against targets performing evasive maneuvers, is considered to demonstrate benefits of this design for a two-loop integration of guidance and flight control systems. The designed guidance-control system performance is verified via computer simulations using a miniature hypervelocity kinetic energy endo-atmospheric interceptor planar model.

Smooth second-order sliding modes: Missile guidance application

A new smooth second-order sliding mode control is proposed and proved using homogeneity-based technique for a system driven by sufficiently smooth uncertain disturbances. The main target application of this technique—the missile-interceptor guidance system against targets performing evasive maneuvers is considered. The smooth second-order sliding mode control-based guidance law is designed and compared with augmented proportional navigation guidance law via computer simulations of a guided missile intercepting a maneuvering ballistic target.