Discontinuous Sliding Mode Control Research Articles

Smooth sliding control to overcome chattering arising in classical SMC and super-twisting algorithm in the presence of unmodeled dynamics

The earlier smooth sliding control (SSC) is revisited. New global stability and chattering alleviation analysis is presented under the more general situation of simultaneous presence of plant uncertainty, unmodeled dynamics and external disturbance. Based on an appropriate prediction error loop, it delivers a smooth filtered control signal to the plant. New explicit conditions are presented for SSC to eliminate chattering. Considering numerical examples recently used in a lively debate between continuous and discontinuous sliding mode control options, the SSC is shown to overcome chattering arising in both classical first-order sliding mode (FOSM) control and the super-twisting algorithm (STA) in the presence of unmodeled dynamics. Besides the original theoretical contribution, one main purpose here is to stir new research about chattering avoidance in both classical and higher-order sliding mode algorithms for uncertain systems.

Secure Data Transmission Based on Adaptive Chattering-Free Sliding Mode Synchronization of Unified Chaotic Systems

This paper is concerned with a novel secure data transmission design based on adaptive synchronization of master and slave unified chaotic systems. First, by introducing an augmented error state, an adaptive continuous sliding mode control (SMC) is derived to guarantee the synchronization of unified chaotic systems. Then, the secret message embedded in the master chaotic system can be transmitted from transmitter to receiver. Different from previous works using discontinuous SMC, the undesired chattering phenomenon can be fully eliminated, and it becomes possible to precisely recover the embedded secret message at the receiver. Last, an example is given to illustrate the success of secure data transmission with the continuous SMC developed in this paper.

Robust Control Design for an Active Magnetic Bearing System Using Advanced Adaptive SMC Technique

Fast rotating machines require special attention to ensure accurate rotor placement within the air gap. For this reason, the active magnetic bearings (AMB) system is used to levitate the rotor in the air gap using an electromagnetic feedback control force. The contact-less support AMB system improves the rotor dynamic performance and helps in the success of machine operations. However, the control design for the five degrees-of-freedom (DOF) AMB system is intricate because of its complex nonlinear dynamics. Moreover, these systems are often subjected to model uncertainties, harmonic disturbances, and sensor noises. Therefore, this paper proposes a robust control strategy using an adaptive second-order non-singular fast terminal sliding mode control (SMC) design. The proposed control law employs the higher-order SMC scheme to alleviate the chattering problem from the discontinuous SMC input, which would otherwise restrict its practical applicability. Further, a non-singular fast terminal sliding surface is selected to achieve a faster system response. The adaptive law estimates the switching gain to relax the upper bound assumption of disturbance. The theoretical stability analysis of the proposed methodology proves the finite-time convergence of system states to a small residual bound in the neighborhood of zero. The numerical analysis with a comparative study is also carried out to illustrate the efficacy of the proposed strategy.

Experiential Integral Backstepping Sliding Mode Controller to achieve the Maximum Power Point of a PV system

Maximum Power Point Tracking (MPPT) strategy is necessary to extract the maximum power production of a Photovoltaic (PV) system. Since the PV has nonlinear dynamics, it is more suitable to use a nonlinear MPPT controller to improve the tracking efficiency. The modelling and control of most systems in real-time are not fully precise and introduce some variations such as : the steady state error and ripples in the system outputs. In this paper, a classical sliding mode controller has been designed and applied experimentally to the PV system to achieve the Maximum Power Point (MPP). The results show that the system responses present chattering phenomena with no negligible state error. In order to reduce these drawbacks (chattering and steady-state error), an Integral Backstepping combined with a discontinuous Sliding Mode Controller (IBSMC) is proposed and applied experimentally to the PV system. The obtained experimental results for the two controllers are compared under the same weather conditions, in terms of chattering phenomena and state error. As a result, the proposed hybrid controller (IBSMC) has achieved high dynamic system performances. Moreover, the stability of this system has been proved using Lyapunov stability criteria.

Speed control of inspection pig in gas pipelines using sliding mode control

Constant speed is a necessary condition for inspection pigs because they have enough time to get data from their installed sensors. Keeping the pig in constant speed is very important especially in gas pipelines because of high velocity of the fluid. This paper suggests a simple method based on sliding mode control, which is a time-domain robust control method, for speed control of an inspection pig in gas pipelines. A bypass valve is installed in the pig’s body which can be closed or opened by controller input. Dynamic equations of pig’s motion in two-dimensional gas pipeline is derived and written in the normal state-space form at first. Then, continuous control input for two-dimensional pipelines in two cases is obtained using a smoothed approximation of the discontinuous sliding mode control. The designed control system is simulated numerically using the MATLAB software. The simulation results show that this type of controller can keep the pig’s speed perfectly constant at desired value during the pig’s motion in the gas pipelines.

Grid-Connected Shunt Active LCL Control via Continuous Sliding Modes

An LCL grid-connected three-phase and three-wire shunt active filter (SAF) is studied and controlled. It is known that SAFs generate distortive components caused by the high switching frequency of a voltage source inverter (VSI). In order to prevent the spread of these distortive components to the grid, the LCL filter (usually controlled by a linear control feedback) is used; while a parasitic phase shift/lag between the reference and injected currents emerges and severely deteriorates the filtration quality. In this study, the inherently robust sliding mode controller (SMC) is used in the SAF, for reducing the phase-shift effects over the broad bandwidth, while improving robustness to system's disturbances. Furthermore, in order to prevent very high frequency switching of the SMC that can severely hurt the switching elements, two different continuous SMCs are employed and studied. In the first solution, a signum function used in discontinuous SMC is replaced by a continuous sigmoid function. The second proposed solution uses an artificial increase of input-output relative degree that allows designing the SMC in terms of the control derivative, while the actual SMC function becomes continuous by integrating the discontinuous SMC. The output of the continuous SMC is pulse width modulated (PWM) in order to provide a fixed given frequency of control switching, required for the VSI safe operation. The proposed approach was validated on a mathematically modeled conventional nonlinear load and a real textile factory (Aleppo, Syria) via simulation based on real measurements coming from power quality analyzers. A new modeling approach of nonlinear loads is proposed and the efficacy of the proposed controllers for SAF/ LCL filter, even under unbalanced conditions, is validated via simulations.

Adaptive Chattering‐Free Sliding Mode Control of Chaotic Systems with Unknown Input Nonlinearity via Smooth Hyperbolic Tangent Function

The design of adaptive chattering‐free sliding mode controller (SMC) for chaotic systems with unknown input nonlinearities is studied in this paper. A smooth hyperbolic tangent function is utilized to replace the discontinuous sign function; therefore, the proposed adaptive SMC ensures that not only the chaos phenomenon can be suppressed effectively but also the chattering often appearing in the traditional discontinuous SMC with sign function is eliminated, even when the unknown input nonlinearity is present. A sufficient condition for stability of closed‐loop system is acquired by Lyapunov theory. The numerical simulation results are illustrated to verify the proposed adaptive sliding mode control method.

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

SummaryProfessor Utkin proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics (stable actuators) in some systems governed by the First‐Order Sliding‐Mode Controller is lower than that produced by the Super‐Twisting Algorithm. This example served to motivate this paper reconsidering the problem of comparison of chattering in systems with stable actuators, and driven by Discontinuous Sliding‐Mode Controllers (DSMCs) and Continuous Sliding‐Mode Controllers (CSMCs). Comparison of chattering produced by DSMC and CSMC taking into account their amplitudes, frequencies, and average power (AP) needed to maintain the system into real‐sliding modes, allowing to conclude the following: (i) for systems with slow actuators, the amplitude of oscillations and AP produced by DSMC be smaller than those caused by CSMC; (ii) for bounded disturbances with fixed Lipschitz constant, there exist sufficiently fast actuators for which the amplitude of oscillations and AP produced by CSMC be smaller than those caused by DSMC.

Finite-time sliding mode and super-twisting control of fighter aircraft

The development of two nonlinear robust higher-order flight control systems for roll-coupled maneuvers of fighter aircraft with uncertain parameters is discussed in this article. The objective is to independently control the output variables (roll angle, pitch angle and sideslip angle) using aileron, elevator and rudder control surfaces. For a nominal model of aircraft, first a finite time stabilizing (FTS) control law, based on the notion of geometric homogeneity, is designed. Then for robust control in the presence of parameter uncertainties, (i) a discontinuous sliding mode (DSM) control law and (ii) a super-twisting (STW) continuous control law is designed. It is shown that in the composite closed-loop system consisting of either (a) the FTS and DSM control laws or (b) the FTS and STW control systems, the output trajectory tracking error and its first-order derivative converge to the origin in finite time. Digital simulation results for a swept-wing fighter aircraft, including the two composite control systems, are obtained. These results show that each of the designed flight controllers accomplishes precise simultaneous large longitudinal and lateral maneuvers, despite uncertainties in the aerodynamic and inertia parameters, turbulence, and partial loss of control surface effectiveness.

Finite-time stabilization of chaotic gyros based on a homogeneous supertwisting-like algorithm

This paper presents a finite-time stabilization scheme for nonlinear chaotic gyros. The scheme utilizes a supertwisting-like continuous control algorithm for the systems of dimension more than one with a Lipschitz disturbance. The algorithm yields finite-time convergence similar to that produces by discontinuous sliding mode control algorithms. To design the controller, the nonlinearities in the gyro are treated as a disturbance in the system. Thanks to the dissipativeness of chaotic systems, the nonlinearities also possess the Lipschitz property. Numerical results are provided to illustrate the effectiveness of the scheme.

Neural network-based H∞ sliding mode control for nonlinear systems with actuator faults and unmatched disturbances

Abstract By combining integral sliding mode control with nonlinear H∞ optimal control theory, a novel nonlinear control scheme is proposed for uncertain nonlinear systems with actuator faults and unmatched disturbances. The effect of the actuator faults and the separated matched disturbance component can be reduced by a properly designed discontinuous sliding mode controller, while unmatched disturbance component is attenuated by a nonlinear H∞ control obtained by approximately solving HJI equations for equivalent sliding mode dynamics. An adaptive dynamic program (ADP) algorithm based on three neural networks (NNs) is applied to solve the HJI equation. Lyapunov techniques are used to demonstrate the convergence of the NN weight errors in the sense of uniform ultimate bounded. Some simulation results are presented to verify the feasibility of the proposed control scheme.

A sliding mode vibration controller for lead screw drives

The conversion of rotary to translational motion in lead screw drives occurs at the meshing lead screw and nut threads. Adecreasing coefficient of friction with sliding velocity, may lead to instabilities in these drives. In this paper, a sliding mode controller is designed for a two degrees of freedom lead screw drive model. This controller has two objectives: to regulate the lead screw angular velocity to a preset value and to attenuate friction-induced vibrations. Only upper and/or lower bounds of system parameters are assumed to be known. In addition, in the development of the controller no specific model is assumed for the dependence of the coefficient of friction on the relative sliding velocity. Two modifications are applied to the basic discontinuous sliding mode controller to eliminate the inherent chattering problem and to limit thecontrolled input torque levels. Numerical simulation results are presented that show the applicability and the performance of the proposed controller.

Fuzzy boundary layer tuning for sliding mode systems as applied to the control of a direct drive robot

Chattering in the control signal is a significant problem in sliding mode control (SMC). The boundary layer approach is one of the many modifications proposed in the literature to avoid the chattering. In this approach, instead of the discontinuous SMC, a continuous feedback control law is employed in a boundary layer around the sliding surface. The thickness of the boundary layer is an important design parameter. This paper proposes a fuzzy online tuning method to adjust the boundary layer thickness for the best system performance without chattering. The method features the measurement of the chattering in the control signal. The paper validates the performance of the algorithm by experiments on a direct drive robot with a range of different payloads.

Discussion on: “Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty”

ðm p < nÞtheoutput; gðx,tÞisthematcheduncertainty and fðx,tÞ the unmatched uncertainty; ðxÞ is a known nonlinear vector function with ð0Þ¼0.The authors use the ideas of robust sliding modecontrol and incorporate a sliding surface originallyproposed by Edwards and Spurgeon [2]. The dis-continuous sliding mode control has been describedfully elsewhere (see, e.g. [4,7,9]). Using the estimatedstates and the system output, a dynamic slidingmode control is developed which is shown to satisfythe well-known reachability condition [7,9]. A non-linear asymptotic observer is proposed and this yieldsexponential state estimation error convergence basedon the solution to a constrained Lyapunov equation.Both matched and unmatched system uncertaintiesare considered. Like all sliding mode control systems,the following important property holds: the systembehaviour is invariant to the matched uncertaintyduring the sliding mode [9].The authors impose two realistic assumptions thatguarantee the existence of the output sliding mode[1,2]. Also assumed are the assumptions that the pair(A, C) is observable and that the nonlinear function ðxÞ is Lipschitz and that there exist known con-tinuous functions