Nonlinear Switching Surface Research Articles

An LMI adaptive-barrier function global sliding mode control of uncertain nonlinear systems with input saturation

This paper proposes a barrier function-based adaptive control strategy with a nonlinear sliding surface for a class of uncertain dynamic systems with input saturation. Its main objectives are to ensure robustness to parametric and non-parametric uncertainties whilst eliminating the reaching phase. A global nonlinear switching surface is defined and an adaptive barrier function sliding mode control approach is derived. The barrier strategy is adopted to ensure the convergence of the states to the desired values without overestimating the control gains. System stability is analyzed using the Lyapunov stability theory. The control parameters are obtained using the linear matrix inequality (LMI) approach. The control law is designed to remove the reaching phase. The effectiveness of the proposed approach was validated using a simulation study. The proposed control approach can easily be implemented to various nonlinear uncertain systems.

Current-Limited Suboptimal Sliding Mode Control for Voltage-Regulated Synchronous Buck Converters

This article proposes a new sliding mode control based on a nonlinear switching surface that provides a suboptimal current-limited start-up response in step-down converters. The main idea behind the design consists in combining different switching surfaces. The first one forces the system trajectories to track a constant current path until the output voltage error is small. A nonsingular terminal switching surface then drives the trajectories to the vicinity of the steady-state operating point. Finally, a first-order switching surface regulates the steady state providing very good rates of load and line regulation. The article presents the design guidelines of the suboptimal sliding mode control and the experimental evaluation that confirms the effectiveness of the proposal.

Wideband Series Harmonic Voltage Compensator for Enhancing Stability of Microgrids

A wideband series harmonicvoltage compensator (WSHVC) for mitigating the adverse effect of unknown grid impedance and load condition on the stability of microgrids with multiple grid-connected inverters (GCIs) is presented. The concept is based on extending the concept of series active power filter. A wideband series voltage source inverter is used to compensate for the high-frequency harmonic voltage caused by the impedance at the point of common coupling, thereby creating a virtually zero high-frequency impedance at the output of the GCIs. The system stability is then assured under any operating condition. The bandwidth of the WSHVC ranges from the second harmonic of the grid frequency to 8 kHz, which is sufficiently higher than the cut-off frequency of typical GCIs. Such fast dynamic behavior is realized by a novel fixed-frequency predictive control scheme with nonlinear switching surfaces. Since the WSHVC handles harmonic power only, its volt-ampere rating is lower than that of the entire system. A 500 VA prototype for a 6.5 kVA testbed with three commercial GCIs, nonlinear load, and adjustable grid impedance has been evaluated. The power dissipation of the WSHVC is less than 1% of the VA rating of the testbed. The effectiveness of the WSHVC on improving system stability is studied.

Passivity-based hierarchical sliding mode control/observer of underactuated mechanical systems

This paper investigates a passivity-based hierarchical SM control (PBHSMC) approach to solve the trajectory tracking issue of a special class of UMSs using unmeasured states and in presence of both unmatched and matched perturbations. First, a passivity-based SM observer (PBSMO) is designed for quick estimation of states in the UMS. Then, we develop a nonlinear two-layer switching surface using feedback passivation. The passivation-based approach ensures global asymptotical convergence of tracking error on the switching surface with the discontinuous term. Moreover, we develop an SMC law that can satisfy reaching mode and sliding mode conditions. Finally, to illustrate the performance of theoretical results, the developed control scheme is assessed by numerical simulation of two case studies including flexible-joint manipulator (FJM) and underactuated surface vessel (USV) systems. The simulation results indicate the superiority of the PBSMO-based PBHSMC scheme over the conventional SMO-based HSMC in suppressing unwanted oscillations of link, low tracking error and overshoot, short settling time, smooth and small control efforts, and also more accurate estimation of state variables with less chattering.

Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems

In this study, an adaptive nonsingular terminal sliding mode control technique according to the barrier function is designed for the performance improvement and robust stability of nonlinear systems with outdoor disturbances. For this reason, a novel nonlinear sliding surface is presented based on the states of the system. The nonlinear sliding surface forces the states of the system to converge from initial conditions to zero. Subsequently, a non-singular terminal sliding control scheme is advised for the purpose of finite-time stability of the nonlinear switching surface. Finite-time stabilization of the non-singular terminal sliding surface is verified by the Lyapunov theory. For improvement of the system performance against exterior perturbation, the barrier function adaptive technique is employed to estimate the unknown upper bounds of the exterior disturbance. Finally, the advantage and productivity of the recommended control method is investigated based on the simulation results. In the simulation part, the plasma torch jerk chaotic system is considered as a case study, such that the obtained results are given in different scenarios.

Simultaneous translation and rotation tracking design for sharp corner, obstacle avoidance, and time-varying terrain by hierarchical adaptive fixed-time saturated control

To fulfill the advantageous characteristics of omnidirectional mobile service robot (OMSR), i.e., simultaneous translation and rotation, the proposed hierarchical adaptive fixed-time saturated control (HAFTSC) is designed and implemented. To begin with, the path tracking model of an OMSR, including kinematics, mechanical dynamics with the friction of each wheel and the transformation between OMSR’s and world coordinates, and motor dynamics, is achieved. According to the model’s feature, the adaptive fixed-time virtual reference input (AFTVRI) for indirect mode is first designed to obtain the assigned task, and then an adaptive fixed-time tracking control (AFTTC) is designed to deal with high frequency motion behaviors, e.g., sharp corner tracking, obstacle avoidance, and time-varying terrain. The main features of the proposed control contain the nonlinear switching surface and nonlinear switching gains such that under suitable conditions the zero pose error is achieved at the expense of a compromised chattering input. Finally, compared experiments between nonlinear and constant switching gains, including the piecewise straight path with 90° corner, one obstacle or three mats on the desired path, validate the potency and robustness of the proposed control.

Min-Type Control Strategy of a DC–DC Synchronous Boost Converter

This paper presents the analysis and design of a min-type strategy to control a synchronous boost converter in continuous conduction mode. The strategy uses a nonlinear switching surface to establish the change of topology in the converter and is analyzed by means of a sliding-mode control approach. Subsequently, the min-type strategy is modified by a hybrid control formulation, which introduces a hysteresis width and a dwell-time to obtain a finite switching frequency in the start-up and steady-state, respectively. The hybrid control formulation is implemented digitally by means of a microprocessor which processes the samples of inductor current and capacitor voltage to provide the control signal that activates the power switch. Experimental results in a prototype validate the proposed control strategy and show its potential in transient time and steady-state.

Fuzzy Fixed-Time Learning Control with Saturated Input, Nonlinear Switching Surface and Switching Gain to Achieve Null Tracking Error

A class of generalized nonlinear dynamic systems is first approximated by $N$ fuzzy-based linear subsystems using the identification of input–output data or the linearizing system with respect to suitable operating points. To obtain null trajectory tracking error in fixed time, a fuzzy fixed-time control (FFTC) with nonlinear switching surface and switching gain is first designed. It can be said that the FFTC is based on a class of passive and distributive models with uncertainties. To compensate enormous uncertainties, a fuzzy fixed-time learning control (FFTLC) by learning two unknown coefficients for the upper bound of uncertainties in each subsystem is designed. As compared with radial basis function neural network, the computational complexity for the compensated uncertainties is much simple. It can be said that an FFTLC is based on a class of online active and distributive uncertain models. Due to the fixed-time control design, the transients often occur, particularly for the larger uncertainties or initial tracking error. Hence, the saturated input of nonlinear dynamic system is addressed and online compensated. Finally, the compared simulations and application to two-link robot manipulator confirm the effectiveness, robustness, and less computation as compared with previous studies.

Stabilization by a relay control using non-quadratic Lyapunov functions

In this article we consider the stabilization problem by a relay control using non-quadratic Lyapunov functions. First, a general result is proposed for the case of nonlinear systems. A full state relay feedback controller is designed in order to ensure the local asymptotic stability of the closed-loop system. Then, the result is applied to the particular case of LTI systems. A constructive method based on LMI conditions is given in order to design nonlinear switching surfaces and provide an estimation of a non-ellipsoidal domain of attraction. In addition, the approach is extended to observer-based relay feedback. Both linear and nonlinear switching surfaces dependent on the estimated state are designed while using a Luenberger observer. Finally, illustrative examples are proposed in order to show the efficiency of the proposed methods and simulations are performed for a Buck converter structure.

Constrained Near-Time-Optimal Sliding-Mode Control of Boost Converters Based on Switched Affine Model Analysis

Time-optimal (TO) control of dc–dc converters, using switching surface controllers, has been investigated extensively in the literature. Studies show that such controllers are of a minimum-switching and bang–bang nature and have the fastest possible response time. However, this method has three drawbacks: First, the inductors’ maximum current goes beyond practical limits. Second, due to a marginal status in existence condition of the switching surface, stability of the controller is sensitive to parameter changes. Third, its nonlinear switching surface needs high computational power and is hard to implement. To overcome these problems, the switched affine model of boost converters is used in this paper to study the time response and equilibrium states. Then, the current-constrained TO state trajectory is studied, and its optimality is discussed. A constrained near-optimal (CNO) controller is proposed with a piecewise linear switching surface to guarantee the robustness of stability and the simplicity of implementation. A general condition for the existence of sliding mode and a novel method to check finite time reaching are proposed for arbitrary switching surfaces. The Lyapunov stability for the CNO controller is also discussed. The proposed method is validated on an experimental setup with a boost converter prototype and a TMS320F2812 processor board.

A Variable Structure System Control and its Application in Underwater Vehicles

The paper proposes a new Variable Structure System (VSS) control algorithm and its application in underwater robotics. The main features of the proposed approach consist on the usage of coupled switching surfaces, and on the usage of an adaptive adjustment method for their parameters in order to accelerate the transient processes. The adaptive algorithm of linear and nonlinear switching surfaces coefficients, is based on the stabilization of the sliding mode parameter close to the reference value. In this paper, it is shown how the proposed approach improves the system transient processes and the energy efficiency in comparison with conventional VSS, neutralizing also some drawbacks. The proposed adaptive VSS algorithm is applied to control a Remotely Operated Vehicle (ROV), and simulation results confirm the advantages to apply it.

Lateral guidance and control of UAVs using second-order sliding modes

An innovative sliding mode based partially integrated lateral guidance and control scheme for UAVs is proposed in this paper. Guidance and control framework based on second order sliding modes is presented to solve the problem of two dimensional path-following. The overall closed-loop system generally consists of an inner control (designed considering system dynamics) and outer guidance (designed considering system kinematics) loop configuration. The main contribution of the technique presented here is the partial integration of the two loops i.e., a guidance and control system via series interconnection of two stable sliding manifolds. In the outer guidance loop, the proposed guidance scheme relies on a nonlinear switching surface with the real twisting algorithm derived at the kinematic level, generating roll error commands. The autopilot based on the super-twisting algorithm using a linear sliding surface forms the inner loop. Proof of existence of the 2-sliding mode, control boundedness and stability of the closed-loop, i.e., the overall guidance and control path-following system with the UAV kinematics and autopilot dynamics, is given. The proposed guidance and control system performance is verified via extensive flight tests of a scaled YAK-54 UAV. Flight results validate the proposed framework for guidance and control design.

Parameter-Dependent Relay Control: Application to PMSM

This brief presents a novel relay control design strategy for some classes of nonlinear systems. The main idea of this brief is to use a linear parameter-varying (LPV) modeling to design nonlinear switching surfaces. This modeling is motivated by the fact that numerical tools, such as linear matrix inequality (LMI), may be used by exploiting the quasi-linear structure of the system. Here, we propose an LMI formulation providing criteria for the design of switching surfaces. This design is seen as the synthesis of parameter-dependent relay. The second contribution of this brief is the implementation of this relay strategy for permanent magnet synchronous motors (PMSMs). Since the LPV framework can encompass the PMSM model, the obtained relay control depends on the motor speed variations. Experimental results on a PMSM are presented.

Digital Control of a Buck Converter Based on a Non-linear Switching Surface Technique

This paper proposes analysis and implementation of a digital control of a buck converter based on a non-linear switching surface technique. The on and off time intervals of a switching power device are evaluated by the novel switching criteria design. As a result, the output voltage can be completely preserved. The nonlinear-large signal performance for both continuous and discontinuous conduction modes of operation can be achieved with fast transient response and constant switching frequency. In order to verify the correctness of the mathematical approach, the simulation results are compared with the experimental ones. It is found that experimental results of a prototype well agree with the theoretical predictions.

Sliding Mode Control for Slosh-Free Motion Using a Nonlinear Sliding Surface

A new nonlinear switching surface is proposed for the design of a sliding mode controller for a class of mismatched uncertain systems. A control system for slosh-free motion of a partially filled liquid container is sought. This is representative of a broader class of systems to which the proposed methodology is applicable. A fundamental mode of lateral slosh is considered. A simple pendulum model is used to represent the lateral slosh. Given the difficulty of measuring the slosh states directly, a sliding mode observer is used for implementation of the resulting sliding mode control. The effectiveness of the theoretical developments is demonstrated via both simulation and experimental results.

Variable structure controller design for linear systems with bounded inputs

This paper studies the design of variable structure systems with saturation inputs. Sliding mode domain, reaching domain, and unescapable reaching domain of linear systems with variable structure are defined and investigated. When the state matrix of the linear system is Hurwitz, the stability of the variable structure systems is proven by using passivity theory. Moreover, variable structure systems with novel nonlinear switching surfaces are proposed for second order systems. Two strategies for designing variable structure control for high order linear systems are also proposed, such as stepby-step variable structure control and moving-surface variable structure control, which were found to guarantee that the reaching condition of the variable structure control is always satisfied. Finally, an illustrative example pertaining to the attitude control of a flexible spacecraft demonstrates the effectiveness of the proposed methods.

Design of Variable Structure Control with Bounded Inputs

The design of variable structure system inputs which are constrained by saturation is studied. For a LTI system which satisfies some conditions, it is shown that appropriate bounded controllers guarantee the system’s global stability and maximize the sliding mode domain on the switching surfaces. Stability conditions of variable structure systems with constrained inputs are relaxed, and the stability of the closed-loop system is guaranteed by using passivity theory of linear passive systems. Moreover, nonlinear sliding surfaces are discussed for variable structure controller design, and a novel nonlinear switching surface is proposed. Finally, the proposed methods are applied to a 2nd order LTI system to show their usefulness.

Discussion on: “Integral Sliding Mode Control for a Class of Uncertain Switched Nonlinear Systems”

The paper by Liana, Zhao, and Dimirovskid shows one of the latest advances in switched systems by incorporating sliding mode control with a nonlinear integral switching surface. It is worthwhile comparing two types of switching mechanisms employed in this work. The first type is the system structural switching with an average dwell time. Hence, the switching frequency should be finite, and the stable structures should dominate the system response. The second type is the controller structural switching around a pre-specified switching surface. In theory, the switching frequency of the SMC should be infinite so that the sliding motion can be guaranteed. On the other hand, the SMC can switch among unstable structures to yield a stable sliding mode. In the paper, only the stabilization problem is addressed. The extension to tracking problems is a non-trivial issue. Finally, it would be helpful to provide illustrative examples that have both stable and unstable structures, as this point is the focus of the paper.

Proximate Time-Optimal Digital Control for Synchronous Buck DC–DC Converters

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper introduces an approach to near time-optimal control for synchronous buck dc–dc converters. The proposed proximate time-optimal digital (PTOD) controller is a combination of a constant-frequency pulsewidth modulation (PWM) controller employing a linear PID compensator close to a reference point, and a linear or nonlinear switching surface controller (SSC) away from the reference, together with smooth transitions between the two. A hybrid capacitor current estimator enables switching surface evaluation and eliminates the need for current sensing. The SSC, which is implemented as a small Verilog HDL module, can be easily added to an existing digital PWM controller to construct the PTOD controller. In steady state, the controller operates exactly the same as a standard constant-frequency PWM controller with a linear PID compensator. Simulation and experimental results are shown for a 6.5 V-to-1.3 V, 10A synchronous buck converter. </para>

Robust tracking control for a class of MIMO nonlinear systems with measurable output feedback

AbstractThis paper proposes a robust output feedback controller for a class of nonlinear systems to track a desired trajectory. Our main goal is to ensure the global input‐to‐state stability (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. Our approach consists of constructing a nonlinear observer to reconstruct the unavailable states, and then designing a discontinuous controller using a back‐stepping like design procedure to ensure the ISS property. The observer design is realized through state transformation and there is only one parameter to be determined. Through solving a Hamilton–Jacoby inequality, the nonlinear control law for the first subsystem specifies a nonlinear switching surface. By virtue of nonlinear control for the first subsystem, the resulting sliding manifold in the sliding phase possesses the desired ISS property and to certain extent the optimality. Associated with the new switching surface, the sliding mode control is applied to the second subsystem to accomplish the tracking task. As a result, the tracking error is bounded and the ISS property of the whole system can be ensured while the internal stability is also achieved. Finally, an example is presented to show the effectiveness of the proposed scheme. Copyright © 2007 John Wiley &amp; Sons, Ltd.