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Showing papers on "Sliding mode control published in 2006"


Journal ArticleDOI
TL;DR: Using Linear matrix inequalities (LMIs) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system and a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time.
Abstract: In this note, we consider the problems of stochastic stability and sliding-mode control for a class of linear continuous-time systems with stochastic jumps, in which the jumping parameters are modeled as a continuous-time, discrete-state homogeneous Markov process with right continuous trajectories taking values in a finite set. By using Linear matrix inequalities (LMIs) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system. Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of coupled LMIs have solutions. A numerical example is given to show the potential of the proposed techniques.

613 citations


BookDOI
18 Jan 2006
TL;DR: In this article, the authors present an algorithm for adaptive linear design based on approximate approximator with linear linear design (ALD) and linear design with nonlinear design (NLD).
Abstract: Preface. 1. INTRODUCTION. 1.1 Systems and Control Terminology. 1.2 Nonlinear Systems. 1.3 Feedback Control Approaches. 1.3.1 Linear Design. 1.3.2 Adaptive Linear Design. 1.3.3 Nonlinear Design. 1.3.4 Adaptive Approximation Based Design. 1.3.5 Example Summary. 1.4 Components of Approximation Based Control. 1.4.1 Control Architecture. 1.4.2 Function Approximator. 1.4.3 Stable Training Algorithm. 1.5 Discussion and Philosophical Comments. 1.6 Exercises and Design Problems. 2. APPROXIMATION THEORY. 2.1 Motivating Example. 2.2 Interpolation. 2.3 Function Approximation. 2.3.1 Off-line (Batch) Function Approximation. 2.3.2 Adaptive Function Approximation. 2.4 Approximator Properties. 2.4.1 Parameter (Non)Linearity. 2.4.2 Classical Approximation Results. 2.4.3 Network Approximators. 2.4.4 Nodal Processors. 2.4.5 Universal Approximator. 2.4.6 Best Approximator Property. 2.4.7 Generalization. 2.4.8 Extent of Influence Function Support. 2.4.9 Approximator Transparency. 2.4.10 Haar Conditions. 2.4.11 Multivariable Approximation by Tensor Products. 2.5 Summary. 2.6 Exercises and Design Problems. 3. APPROXIMATION STRUCTURES. 3.1 Model Types. 3.1.1 Physically Based Models. 3.1.2 Structure (Model) Free Approximation. 3.1.3 Function Approximation Structures. 3.2 Polynomials. 3.2.1 Description. 3.2.2 Properties. 3.3 Splines. 3.3.1 Description. 3.3.2 Properties. 3.4 Radial Basis Functions. 3.4.1 Description. 3.4.2 Properties. 3.5 Cerebellar Model Articulation Controller. 3.5.1 Description. 3.5.2 Properties. 3.6 Multilayer Perceptron. 3.6.1 Description. 3.6.2 Properties. 3.7 Fuzzy Approximation. 3.7.1 Description. 3.7.2 Takagi-Sugeno Fuzzy Systems. 3.7.3 Properties. 3.8 Wavelets. 3.8.1 Multiresolution Analysis (MRA). 3.8.2 MRA Properties. 3.9 Further Reading. 3.10 Exercises and Design Problems. 4. PARAMETER ESTIMATION METHODS. 4.1 Formulation for Adaptive Approximation. 4.1.1 Illustrative Example. 4.1.2 Motivating Simulation Examples. 4.1.3 Problem Statement. 4.1.4 Discussion of Issues in Parametric Estimation. 4.2 Derivation of Parametric Models. 4.2.1 Problem Formulation for Full-State Measurement. 4.2.2 Filtering Techniques. 4.2.3 SPR Filtering. 4.2.4 Linearly Parameterized Approximators. 4.2.5 Parametric Models in State Space Form. 4.2.6 Parametric Models of Discrete-Time Systems. 4.2.7 Parametric Models of Input-Output Systems. 4.3 Design of On-Line Learning Schemes. 4.3.1 Error Filtering On-Line Learning (EFOL) Scheme. 4.3.2 Regressor Filtering On-Line Learning (RFOL) Scheme. 4.4 Continuous-Time Parameter Estimation. 4.4.1 Lyapunov Based Algorithms. 4.4.2 Optimization Methods. 4.4.3 Summary. 4.5 On-Line Learning: Analysis. 4.5.1 Analysis of LIP EFOL scheme with Lyapunov Synthesis Method. 4.5.2 Analysis of LIP RFOL scheme with the Gradient Algorithm. 4.5.3 Analysis of LIP RFOL scheme with RLS Algorithm. 4.5.4 Persistency of Excitation and Parameter Convergence. 4.6 Robust Learning Algorithms. 4.6.1 Projection modification. 4.6.2 &sigma -modification. 4.6.3 &epsis -modification. 4.6.4 Dead-zone modification. 4.6.5 Discussion and Comparison. 4.7 Concluding Summary. 4.8 Exercises and Design Problems. 5. NONLINEAR CONTROL ARCHITECTURES. 5.1 Small-Signal Linearization. 5.1.1 Linearizing Around an Equilibrium Point. 5.1.2 Linearizing Around a Trajectory. 5.1.3 Gain Scheduling. 5.2 Feedback Linearization. 5.2.1 Scalar Input-State Linearization. 5.2.2 Higher-Order Input-State Linearization. 5.2.3 Coordinate Transformations and Diffeomorphisms. 5.2.4 Input-Output Feedback Linearization. 5.3 Backstepping. 5.3.1 Second order system. 5.3.2 Higher Order Systems. 5.3.3 Command Filtering Formulation. 5.4 Robust Nonlinear Control Design Methods. 5.4.1 Bounding Control. 5.4.2 Sliding Mode Control. 5.4.3 Lyapunov Redesign Method. 5.4.4 Nonlinear Damping. 5.4.5 Adaptive Bounding Control. 5.5 Adaptive Nonlinear Control. 5.6 Concluding Summary. 5.7 Exercises and Design Problems. 6. ADAPTIVE APPROXIMATION: MOTIVATION AND ISSUES. 6.1 Perspective for Adaptive Approximation Based Control. 6.2 Stabilization of a Scalar System. 6.2.1 Feedback Linearization. 6.2.2 Small-Signal Linearization. 6.2.3 Unknown Nonlinearity with Known Bounds. 6.2.4 Adaptive Bounding Methods. 6.2.5 Approximating the Unknown Nonlinearity. 6.2.6 Combining Approximation with Bounding Methods. 6.2.7 Combining Approximation with Adaptive Bounding Methods. 6.2.8 Summary. 6.3 Adaptive Approximation Based Tracking. 6.3.1 Feedback Linearization. 6.3.2 Tracking via Small-Signal Linearization. 6.3.3 Unknown Nonlinearities with Known Bounds. 6.3.4 Adaptive Bounding Design. 6.3.5 Adaptive Approximation of the Unknown Nonlinearities. 6.3.6 Robust Adaptive Approximation. 6.3.7 Combining Adaptive Approximation with Adaptive Bounding. 6.3.8 Some Adaptive Approximation Issues. 6.4 Nonlinear Parameterized Adaptive Approximation. 6.5 Concluding Summary. 6.6 Exercises and Design Problems. 7. ADAPTIVE APPROXIMATION BASED CONTROL: GENERAL THEORY. 7.1 Problem Formulation. 7.1.1 Trajectory Tracking. 7.1.2 System. 7.1.3 Approximator. 7.1.4 Control Design. 7.2 Approximation Based Feedback Linearization. 7.2.1 Scalar System. 7.2.2 Input-State. 7.2.3 Input-Output. 7.2.4 Control Design Outside the Approximation Region D. 7.3 Approximation Based Backstepping. 7.3.1 Second Order Systems. 7.3.2 Higher Order Systems. 7.3.3 Command Filtering Approach. 7.3.4 Robustness Considerations. 7.4 Concluding Summary. 7.5 Exercises and Design Problems. 8. ADAPTIVE APPROXIMATION BASED CONTROL FOR FIXED-WING AIRCRAFT. 8.1 Aircraft Model Introduction. 8.1.1 Aircraft Dynamics. 8.1.2 Non-dimensional Coefficients. 8.2 Angular Rate Control for Piloted Vehicles. 8.2.1 Model Representation. 8.2.2 Baseline Controller. 8.2.3 Approximation Based Controller. 8.2.4 Simulation Results. 8.3 Full Control for Autonomous Aircraft. 8.3.1 Airspeed and Flight Path Angle Control. 8.3.2 Wind-axes Angle Control. 8.3.3 Body Axis Angular Rate Control. 8.3.4 Control Law and Stability Properties. 8.3.5 Approximator Definition. 8.3.6 Simulation Analysis. 8.4 Conclusions. 8.5 Aircraft Notation. Appendix A: Systems and Stability Concepts. A.1 Systems Concepts. A.2 Stability Concepts. A.2.1 Stability Definitions. A.2.2 Stability Analysis Tools. A.3 General Results. A.4 Prefiltering. A.5 Other Useful Results. A.5.1 Smooth Approximation of the Signum function. A.6 Problems. Appendix B: Recommended Implementation and Debugging Approach. References. Index.

479 citations


Proceedings ArticleDOI
01 Dec 2006
TL;DR: Simulations show that the control law robustly stabilizes a quadrotor and a sliding mode control is proposed to stabilize a class of cascaded under-actuated systems.
Abstract: In this paper, we present a new design method for the flight control of an autonomous quadrotor helicopter based on sliding mode control. Due to the under-actuated property of a quadrotor helicopter, the controller can make the helicopter move three positions (x, y, z) and the yaw angle to their desired values and stabilize the pitch and roll angles. A sliding mode control is proposed to stabilize a class of cascaded under-actuated systems. The global stability analysis of the closed-loop system is presented. The advantage of sliding mode control is its insensitivity to the model errors, parametric uncertainties and other disturbances. Simulations show that the control law robustly stabilizes a quadrotor.

437 citations


Book
07 Jul 2006
TL;DR: In this article, a DC-to-DC Power Converter Modeling and Controller Design Methods for AC Rectifiers is presented. But the model is based on an approximate linearization in the control of power electronics devices.
Abstract: Modelling.- Modelling of DC-to-DC Power Converters.- Controller Design Methods.- Sliding Mode Control.- Approximate Linearization in the Control of Power Electronics Devices.- Nonlinear Methods in the Control of Power Electronics Devices.- Applications.- DC-to-AC Power Conversion.- AC Rectifiers.

410 citations


Journal ArticleDOI
TL;DR: In this paper, a sliding-mode controller is derived for an integrated missile autopilot and guidance loop, motivated by a differential game formulation of the guidance problem, a single sliding surface, defined using the zero-effort miss distance, is used.
Abstract: A sliding-mode controller is derived for an integrated missile autopilot and guidance loop. Motivated by a differential game formulation of the guidance problem, a single sliding surface, defined using the zero-effort miss distance, is used. The performance of the integrated controller is compared with that of two different two-loop designs. The latter use a sliding-mode controller for the inner autopilot loop and different guidance laws in the outer loop: one uses a standard differential game guidance law, and the other employs guidance logic based on the sliding-mode approach. To evaluate the performance of the various guidance and control solutions, a two-dimensional nonlinear simulation of the missile lateral dynamics and relative kinematics is used, while assuming first-order dynamics for the target evasive maneuvers. The benefits of the integrated design are studied in several endgame interception engagements. Its superiority is demonstrated especially in severe scenarios where spectral separation between guidance and flight control, implicitly assumed in any two-loop design, is less justified. The results validate the design approach of using the zero-effort miss distance to define the sliding surface.

327 citations


Journal ArticleDOI
TL;DR: A simple unified approach to the design of fixed-frequency pulsewidth-modulation-based sliding-mode controllers for dc-dc converters operating in the continuous conduction mode is presented.
Abstract: This paper presents a simple unified approach to the design of fixed-frequency pulsewidth-modulation-based sliding-mode controllers for dc-dc converters operating in the continuous conduction mode. The design methodology is illustrated on the three primary dc-dc converters: buck, boost, and buck-boost converters. To illustrate the feasibility of the scheme, an experimental prototype of the derived boost controller/converter system is developed. Several tests are performed to validate the functionalities of the system

289 citations


Journal ArticleDOI
TL;DR: This paper presents several alternative methods for the control of power electronic buck converters applying fractional order control (FOC), and the fractional calculus is proposed in order to determine the switching surface applying a fractional sliding mode Control (FRSMC) scheme to theControl of such devices.

275 citations


Journal ArticleDOI
TL;DR: In this paper, an adaptive feed-forward control scheme that varies the hysteresis band according to the change of line input voltage and an adaptive feedback control scheme, which varies the control parameter (i.e., sliding coefficient) according to output load, is proposed to reduce switching frequency deviation in the events of line and load variations.
Abstract: A major disadvantage of applying sliding mode control to dc/dc converters is that the steady-state switching frequency is affected by line and load variations This is undesirable as it complicates the design of the input and output filters To reduce switching frequency deviation in the events of line and load variations, an adaptive feedforward control scheme that varies the hysteresis band according to the change of line input voltage and an adaptive feedback control scheme that varies the control parameter (ie, sliding coefficient) according to the change of the output load are proposed This paper presents a thorough investigation into the problem and the effectiveness of the proposed solutions In addition, methods of implementing the proposed adaptive control strategies are discussed Experimental results confirm that the adaptive control schemes are capable of reducing the switching frequency variations caused by both line and load variations

229 citations


Journal ArticleDOI
TL;DR: In this paper, a second-order sliding-mode observer based on the modified super-twisting algorithm providing finite time exact observation is applied for system identification, and the value of the equivalent output injection is used to identify perturbations directly.
Abstract: A second-order sliding-mode observer based on the modified super-twisting algorithm providing finite time exact observation is applied for system identification. The value of the equivalent output injection is used to identify perturbations directly. Continuous time versions of least square and forgetting factor methods are proposed to identify unknown time-invariant parameters respectively.

229 citations


Journal ArticleDOI
TL;DR: In this paper, a novel sliding mode control approach, Sliding Mode Control driven by SLiding Mode Disturbance Observers with Gain Adaptation, is presented for the reusable launch vehicle (RLV) flight control system design as a way to improve robustness to many phenomena such as modeling uncertainties and disturbances.
Abstract: The nation's goals to replace the aging Space Shuttle fleet and pursue exploration of our solar system and beyond will require more robust, less costly launch vehicles and spacecraft. This paper presents a novel Sliding Mode Control approach, Sliding Mode Control driven by Sliding Mode Disturbance Observers with Gain Adaptation, for the reusable launch vehicle (RLV) flight control system design as a way to improve robustness to many phenomena such as modeling uncertainties and disturbances, while retaining continuity of control without using high control gains. Due to the robustness to external disturbances (including wind gusts), mission guidance trajectories and modeling uncertainties, the proposed flight control system design also can reduce cost by requiring less time in design cycle and preflight analyses. This design is applied to Terminal Area Energy Management and Approach/Landing (TAL), a flight regime that has had little research effort in recent years. The multiple-loop, multiple time-scale design features low order disturbance observers that rely only on knowledge of the bounds of the disturbance. A gain adaptation algorithm is included in the disturbance observer design that provides the least gain needed for existence of the sliding mode. High fidelity 6 DOF computer simulations of the X-33 technology demonstration sub-orbital launch vehicle for nominal and severe wind-gust tests demonstrate improved performance over a more conventional, classical control system design.

229 citations


Journal ArticleDOI
İlyas Eker1
TL;DR: Experimental results that are compared with the results of conventional PID verify that the proposed sliding mode controller can achieve favorable tracking performance, and it is robust with regard to uncertainties and disturbances.
Abstract: In this study, a sliding mode control system with a proportional+integral+derivative (PID) sliding surface is adopted to control the speed of an electromechanical plant. A robust sliding mode controller is derived so that the actual trajectory tracks the desired trajectory despite uncertainty, nonlinear dynamics, and external disturbances. The proposed sliding mode controller is chosen to ensure the stability of overall dynamics during the reaching phase and sliding phase. The stability of the system is guaranteed in the sense of the Lyapunov stability theorem. The chattering problem is overcome using a hyperbolic function for the sliding surface. Experimental results that are compared with the results of conventional PID verify that the proposed sliding mode controller can achieve favorable tracking performance, and it is robust with regard to uncertainties and disturbances.

Journal ArticleDOI
TL;DR: In this paper, a magnetorheological brake (MRB) system with two rotating disks is proposed, which is based on a design optimization procedure using simulated annealing combined with finite element simulations involving magnetostatic, fluid flow and heat transfer analysis.

Journal ArticleDOI
TL;DR: The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.
Abstract: This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.

Journal ArticleDOI
TL;DR: In this paper, a Vehicle Dynamics Control (VDC) system is developed for tracking desired vehicle behavior, the cascade structure of control system consists of yaw moment major controller and wheel slip minor controller.

Journal ArticleDOI
01 Oct 2006
TL;DR: An integrated vehicle dynamics control system which aims to improve vehicle handling and stability by coordinating active front steering (AFS) and dynamic stability control (DSC) subsystems is developed in this paper.
Abstract: An integrated vehicle dynamics control system which aims to improve vehicle handling and stability by coordinating active front steering (AFS) and dynamic stability control (DSC) subsystems is developed in this paper. The DSC subsystem includes driveline-based, brake-based, and driveline plus brake-based DSC subsystems. The influence of varying forward speed and lateral acceleration on the lateral vehicle dynamics is investigated first. The AFS controller, which is used to improve vehicle steerability in the low to mid-range lateral acceleration, and the DSC controller, which manages to maintain vehicle stability during extreme driving situations, are then designed by using the sliding mode control (SMC) technique and phase plane method respectively. Based on the two independently developed controllers, a rule-based integration scheme is proposed to optimize the overall vehicle performance by minimizing interactions between the two subsystems and extending functionalities of individual subsystems. Computer simulation results confirm the effectiveness of the proposed control system and the overall improvements in vehicle handling and stability.

Proceedings ArticleDOI
01 Nov 2006
TL;DR: In this paper, a new controller based on backstepping and sliding mode techniques for miniature quadrotor helicopter is presented, which is formed by three inter-connected subsystems.
Abstract: This paper presents a new controller based on backstepping and sliding mode techniques for miniature quadrotor helicopter. The system is formed by three inter-connected subsystems. The first one which represents the under-actuated subsystem, gives the dynamic relation of the horizontal positions with the tilts angles. The second one, fully-actuated subsystem, gives the dynamics of the vertical position and the yaw angle. The last subsystem gives the dynamics of the propeller forces. The design methodology of the controller is based on the Lyapunov stability. To show the effectiveness of the proposed trajectory tracking control, simulation results are performed on the quadrotor model. The application of the proposed controller to a real miniature helicopter is also presented, some results are included to demonstrate the good performance of the proposed controller.

BookDOI
01 Jan 2006
TL;DR: Sliding Modes for Matched and Un-Matched Uncertainty, Observation and Identification, Discrete-Time Sliding Modes, and Applications.
Abstract: Mathematical Developments and VSC.- Higher Order Sliding Modes.- Sliding Modes for Matched and Un-Matched Uncertainty.- Observation and Identification.- Discrete-Time Sliding Modes.- Applications.

Journal ArticleDOI
TL;DR: A robust fuzzy neural network sliding-mode control based on computed torque control design for a two-axis motion control system is proposed and the motion tracking performance is significantly improved, and robustness to parameter variations, external disturbances, cross-coupled interference, and friction force can be obtained as well.
Abstract: A robust fuzzy neural network (RFNN) sliding-mode control based on computed torque control design for a two-axis motion control system is proposed in this paper. The two-axis motion control system is an x-y table composed of two permanent-magnet linear synchronous motors. First, a single-axis motion dynamics with the introduction of a lumped uncertainty including cross-coupled interference between the two-axis mechanism is derived. Then, to improve the control performance in reference contours tracking, the RFNN sliding-mode control system is proposed to effectively approximate the equivalent control of the sliding-mode control method. Moreover, the motions at x-axis and y-axis are controlled separately. Using the proposed control, the motion tracking performance is significantly improved, and robustness to parameter variations, external disturbances, cross-coupled interference, and friction force can be obtained as well. Furthermore, the proposed control algorithms are implemented in a TMS320C32 DSP-based control computer. From the simulated and experimental results due to circle and four leaves reference contours, the dynamic behaviors of the proposed control systems are robust with regard to uncertainties

Journal ArticleDOI
TL;DR: The chattering can be caused by fast dynamics which were neglected in the ideal model, and these `unmodeled' dynamics with small time constants are usually disregarded in models of servomechanisms, sensors and data processors.

Proceedings ArticleDOI
05 Jun 2006
TL;DR: In this paper, a feedback linearization-based controller with a high order sliding mode observer running parallel is applied to a quadrotor unmanned aerial vehicle, where the observer works as an observer and estimator of the effect of the external disturbances such as wind and noise.
Abstract: In this paper, a feedback linearization-based controller with a high order sliding mode observer running parallel is applied to a quadrotor unmanned aerial vehicle. The high order sliding mode observer works as an observer and estimator of the effect of the external disturbances such as wind and noise. The whole observer-estimator-control law constitutes an original approach to the vehicle regulation with minimal number of sensors. Performance issues of the controller-observer are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances.

Journal ArticleDOI
16 Jan 2006
TL;DR: In this article, a new approach implementing the sliding-mode controller is proposed for dc-dc converters, where the equivalent control input is used as the system control input, which results in a duty cycle regulation control system.
Abstract: A new approach implementing the sliding-mode controller is proposed for dc-dc converters. The equivalent control input is used as the system control input, which results in a duty cycle regulation control system. As designed, equivalent control input is maintained at a value between 0 and 1, similar to the desired duty cycle value. Thus, constant switching frequency can be achieved under changes of state conditions. Two sliding-mode controllers based on this method are designed for positive output elementary Luo converter. Traditional small-signal analysis is applied to study the close-loop system performance under proposed approach. Audio-susceptibility, control-to-output transfer functions and output impedance are derived on the basis of the small-signal model. It is shown that the proposed sliding-mode control approach retains the advantages of traditional sliding-mode control, as well as achieve constant switching frequency, which is decided by the input saw-tooth waveform. Results of the experiment are reported for both controllers and they verify the theoretical analysis.

Book
01 Dec 2006
TL;DR: In this paper, the authors present a model matching approach for measured output feedback control problems in the context of control problems with linearization and noninteracting control, as well as model matching.
Abstract: Methodology.- Preliminaries.- Modeling.- Accessibility.- Observability.- Systems Structure and Inversion.- System Transformations.- Applications to Control Problems.- Input-output Linearization.- Noninteracting Control.- Input-state Linearization.- Disturbance Decoupling.- Model Matching.- Measured Output Feedback Control Problems.

Journal ArticleDOI
TL;DR: Two flux observers for wide speed range direct torque control (DTC) of sensorless induction-motor drives are presented and compared and the accuracy, robustness, and high-dynamic performance of both observers when employed in sensorless DTC drives are proved.
Abstract: Two flux observers for wide speed range direct torque control (DTC) of sensorless induction-motor drives are presented and compared. The first one is a full-order sliding-mode observer with proportional plus integral (PI) compensation, without rotor speed adaptation. The second one is based on a zero phase-delay-improved integrator of the voltage model, which uses only a PI flux amplitude control with stator-flux reference magnitude in the correction loop. In both cases, an estimated dc offset is built up and memorized by the PI integral component and this totally compensates for all dc offsets and drifts originated in the acquisition channels. Two feasible solutions for on-line stator-resistance identification are proposed. Simulation and experimental results prove the accuracy, robustness, and high-dynamic performance of both observers when employed in sensorless DTC drives. The effectiveness of state estimation is confirmed by a steady state and transient sensorless operation at very low speed with rated load torque and step-speed reversal.

Journal ArticleDOI
TL;DR: In this paper, a model-free adaptive sliding controller is proposed to suppress the position oscillation of the sprung mass in response to road surface variation, which employs the functional approximation technique to establish the unknown function for releasing the model-based requirement.

Journal ArticleDOI
TL;DR: A 3D contour error estimation algorithm is presented for determining the geometric deviation from arbitrarily shaped toolpaths, and two spline fitting strategies are developed for smoothening sharp corners.
Abstract: This paper presents a trajectory planning strategy for maintaining the tool positioning accuracy in high speed cornering applications. A 3D contour error estimation algorithm is presented for determining the geometric deviation from arbitrarily shaped toolpaths. Two spline fitting strategies are developed for smoothening sharp corners. The under-corner approach reduces the toolpath length, and therefore the cornering time. This technique yields successful results when used with a high bandwidth servo controller (such as sliding mode control), capable of accurately tracking the commanded toolpath. The over-corner approach is based on stretching out the sharp corner with a smooth curve, which counteracts the ‘undercut’ caused by the large phase lag in low bandwidth servo controllers (such as P–PI control). The cornering feedrate is adjusted in the Virtual CNC platform, developed in the first part of this article, to ensure that contour error violation does not occur. The achieved cornering accuracy is verified in experiments, which are in close agreement with predictions obtained with the Virtual CNC.

Journal ArticleDOI
TL;DR: It is shown that the sliding mode in the estimation space can be attained in finite time and the sufficient condition for the asymptotic stability (in probability) of the overall closed-loop stochastic system is derived.

Journal ArticleDOI
TL;DR: The theory of vector Lyapunov functions is extended by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states, and presents a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem.
Abstract: Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. Moreover, using control vector Lyapunov functions, we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. Furthermore, we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law. Finally, the proposed control framework is used to construct decentralized controllers for large-scale nonlinear systems with robustness guarantees against full modeling uncertainty.

Journal ArticleDOI
TL;DR: In this article, a general procedure for the selection of a curved switching surface (SS) to control buck-type converters is presented, based on the normalized representation of ideal SSs for different loading conditions.
Abstract: A general procedure for the selection of a curved switching surface (SS) to control buck-type converters is presented in this letter. The analysis is based on the normalized representation of ideal SSs for different loading conditions. The normalization process leads to a unique representation of the SSs for any possible buck converter. A set of graphics in three dimensions is introduced to give a spatial sense of the behavior of the converter and its control requirements during transients. As a result of the investigation, a switching surface referred to in this letter as the natural unloaded SS is selected, providing excellent transient behavior and no overshoot during startup. For any buck converter with typical parameters, this control scheme produces, in one switching action, a minimum of 99% of the desired output voltage. The general concept of using second-order SS is also geometrically analyzed in this letter to clarify its characteristic features and disadvantages. Experimental results for a typical buck converter are presented to illustrate the transient behavior of the converter during startup and sudden load changes. The results confirm the virtues of the control scheme.

Journal ArticleDOI
TL;DR: In this article, two chattering-free sliding mode controllers (SMCs) are used to restrict the operation of the engine to the optimal efficiency region of the torque-speed curve.
Abstract: This study involves the improvement of overall efficiency in series hybrid-electric vehicles (SHEVs) by restricting the operation of the engine to the optimal efficiency region, using a control strategy based on two chattering-free sliding mode controllers (SMCs) One of the designed SMCs performs engine speed control, while the other controls the engine/generator torque, together achieving the engine operation in the optimal efficiency region of the torque-speed curve The control strategy is designed for application on a SHEV converted from a standard high mobility multipurpose wheeled vehicle (HMMWV) and simulated by using the Matlab-based PNGV Systems Analysis Toolkit (PSAT) The performance of the control strategy is compared with that of the original PSAT model, which utilizes PI controllers, a feedforward term for the engine torque, and comprehensive maps for the engine, generator and power converter (static only), which constitute the auxiliary power unit (APU) In this study, in spite of the simple modeling approach taken to model the APU and the optimal efficiency region, an improved performance has been achieved with the new SMC based strategy in terms of overall efficiency, engine efficiency, fuel economy, and emissions The control strategy developed in this work is the first known application of SMC to SHEVs, and offers a simple, effective and modular approach to problems related to SHEVs

Journal ArticleDOI
TL;DR: In this article, a second-order sliding mode control algorithm is presented for a class of MIMO nonlinear systems in input-output (I-O) form, which produces a dynamic control and does not require the derivative of the sliding variable, thus eliminating the requirement to design observers or peak detectors.