Search results for: adaptive sliding mode observer.

Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd Yatim

Abstract:

In this paper, a few chattering-free Sliding Mode Controllers (SMC) are proposed to stabilize an Active Magnetic Bearing (AMB) system with gyroscopic effect that is proportional to the rotor speed. The improved switching terms of the controller inherited from the saturation-type function and boundary layer control technique is shown to be able to achieve bounded and asymptotic stability, respectively, while the chattering effect in the input is attenuated. This is proven to be advantageous for AMB system since minimization of chattering results in optimized control effort. The performance of each controller is demonstrated via result of simulation in which the measurement of the total consumed energy and maximum control magnitude of each controller illustrates the effectiveness of the proposed controllers.

Keywords: Active Magnetic Bearing (AMB), Sliding Mode Control (SMC), chattering-free SMC.

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Authors: S. Reaz Ahmed, M. S. Kaiser

Abstract:

The tribological behavior of commercially used Perspex was evaluated under dry and wet sliding condition using a pin-on-disc wear tester with different applied loads ranging from 2.5 to 20 N. Experiments were conducted with varying sliding distance from 0.2 km to 4.6 km, wherein the sliding velocity was kept constant, 0.64 ms^-1. The results reveal that the weight loss increases with applied load and the sliding distance. The nature of the wear rate was very similar in both the sliding environments in which initially the wear rate increased very rapidly with increasing sliding distance and then progressed to a slower rate. Moreover, the wear rate in wet sliding environment was significantly lower than that under dry sliding condition. The worn surfaces were characterized by optical microscope and SEM. It is found that surface modification has significant effect on sliding wear performance of Perspex.

Keywords: Perspex, wear, friction, SEM.

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Authors: T.C. Manjunath, Student Member, B. Bandyopadhyay

Abstract:

This paper features the mathematical modeling of a single input single output based Timoshenko smart beam. Further, this mathematical model is used to design a multirate output feedback based discrete sliding mode controller using Bartoszewicz law to suppress the flexural vibrations. The first 2 dominant vibratory modes is retained. Here, an application of the discrete sliding mode control in smart systems is presented. The algorithm uses a fast output sampling based sliding mode control strategy that would avoid the use of switching in the control input and hence avoids chattering. This method does not need the measurement of the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement.

Keywords: Smart structure, Timoshenko beam theory, Discretesliding mode control, Bartoszewicz law, Finite Element Method, State space model, Vibration control, Mathematical model, SISO.

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Authors: A. Bennassar, A. Abbou, M. Akherraz, M. Barara

Abstract:

In this paper, we propose a sensorless backstepping control of induction motor (IM) associated with three levels neutral clamped (NPC) inverter. First, the backstepping approach is designed to steer the flux and speed variables to theirs references and to compensate the uncertainties. A Lyapunov theory is used and it demonstrates that the dynamic trajectories tracking are asymptotically stable. Second, we estimate the rotor flux and speed by using the adaptive Luenberger observer (ALO). Simulation results are provided to illustrate the performance of the proposed approach in high and low speeds and load torque disturbance.

Keywords: Sensorless backstepping, IM, Three levels NPC inverter, Lyapunov theory, ALO.

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Authors: Markus Reichhartinger, Martin Horn

Abstract:

In this paper, the application of sliding-mode control to a permanent-magnet synchronous motor (PMSM) is presented. The control design is based on a generic mathematical model of the motor. Some dynamics of the motor and of the power amplification stage remain unmodelled. This model uncertainty is estimated in realtime. The estimation is based on the differentiation of measured signals using the ideas of robust exact differentiator (RED). The control law is implemented on an industrial servo drive. Simulations and experimental results are presented and compared to the same control strategy without uncertainty estimation. It turns out that the proposed concept is superior to the same control strategy without uncertainty estimation especially in the case of non-smooth reference signals.

Keywords: sliding-mode control, Permanent-magnet synchronous motor, uncertainty estimation, robust exact differentiator.

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Authors: Ardeshir Karami Mohammadi

Abstract:

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

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Authors: A. N. K. Nasir, R. M. T. Raja Ismail, M. A. Ahmad

Abstract:

The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum-s angle and cart-s position. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. Two controllers are presented such as Sliding Mode Control (SMC) and Proportional- Integral-Derivatives (PID) controllers for controlling the highly nonlinear system of inverted pendulum model. Simulation study has been done in Matlab Mfile and simulink environment shows that both controllers are capable to control multi output inverted pendulum system successfully. The result shows that Sliding Mode Control (SMC) produced better response compared to PID control strategies and the responses are presented in time domain with the details analysis.

Keywords: SMC, PID, Inverted Pendulum System.

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Authors: M. Nayeripour, T. Niknam

Abstract:

Nonlinear and unbalance loads in three phase networks create harmonics and losses. Active and passive filters are used for elimination or reduction of these effects. Passive filters have some limitations. For example, they are designed only for a specific frequency and they may cause to resonance in the network at the point of common coupling. The other drawback of a passive filter is that the sizes of required elements are normally large. The active filter can improve some of limitations of passive filter for example; they can eliminate more than one harmonic and don't cause resonance in the network. In this paper inverter analysis have been done simultaneously in three phase and the RL impedance of the line have been considered. A sliding mode control based on energy feedback of capacitors is employed in the design with this method, the dynamic speed of the filter is improved effectively and harmonics and load unbalance is compensating quickly.

Keywords: Shunt active filter, harmonic, inverter, sliding mode control, energy feedback.

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Authors: Hossein Shahinzadeh, Ladan Darougaran, Ebrahim Jalili Sani, Hamed Yavari, Mahdi Mozaffari Legha

Abstract:

This paper present a new method for design of power system stabilizer (PSS) based on sliding mode control (SMC) technique. The control objective is to enhance stability and improve the dynamic response of the multi-machine power system. In order to test effectiveness of the proposed scheme, simulation will be carried out to analyze the small signal stability characteristics of the system about the steady state operating condition following the change in reference mechanical torque and also parameters uncertainties. For comparison, simulation of a conventional control PSS (lead-lag compensation type) will be carried out. The main approach is focusing on the control performance which later proven to have the degree of shorter reaching time and lower spike.

Keywords: Power system stabilizer (PSS), multi-machine power system, sliding mode control

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Authors: M. S. Kang, D. H. Kim, J. S. Yoon, B. S. Park, J. K. Lee

Abstract:

Since straightness error of linear motor stage is hardly dependent upon machining accuracy and assembling accuracy, there is limit on maximum realizable accuracy. To cope with this limitation, this paper proposed a servo system to compensate straightness error of a linear motor stage. The servo system is mounted on the slider of the linear motor stage and moves in the direction of the straightness error so as to compensate the error. From position dependency and repeatability of the straightness error of the slider, a feedforward compensation control is applied to the platform servo control. In the consideration of required fine positioning accuracy, a platform driven by an electro-magnetic actuator is suggested and a sliding mode control was applied. The effectiveness of the sliding mode control was verified along with some experimental results.

Keywords: Linear Motor Stage, Straightness Error, Friction, Sliding Mode Control.

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Authors: Dong Sang Yoo

Abstract:

The problem of finding control laws for underactuated systems has attracted growing attention since these systems are characterized by the fact that they have fewer actuators than the degrees of freedom to be controlled. The acrobot, which is a planar two-link robotic arm in the vertical plane with an actuator at the elbow but no actuator at the shoulder, is a representative in underactuated systems. In this paper, the dynamic model of the acrobot is implemented using Mathworks’ Simscape. And the sliding mode control is constructed using MATLAB and Simulink.

Keywords: Acrobot, MATLAB and Simulink, sliding mode control, underactuated systems.

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Authors: J. Ritonja, R. Brezovnik, M. Petrun, B. Polajžer

Abstract:

Many modern synchronous generators in power systems are extremely weakly damped. The reasons are cost optimization of the machine building and introduction of the additional control equipment into power systems. Oscillations of the synchronous generators and related stability problems of the power systems are harmful and can lead to failures in operation and to damages. The only useful solution to increase damping of the unwanted oscillations represents the implementation of the power system stabilizers. Power system stabilizers generate the additional control signal which changes synchronous generator field excitation voltage. Modern power system stabilizers are integrated into static excitation systems of the synchronous generators. Available commercial power system stabilizers are based on linear control theory. Due to the nonlinear dynamics of the synchronous generator, current stabilizers do not assure optimal damping of the synchronous generator’s oscillations in the entire operating range. For that reason the use of the robust power system stabilizers which are convenient for the entire operating range is reasonable. There are numerous robust techniques applicable for the power system stabilizers. In this paper the use of sliding mode control for synchronous generator stability improvement is studied. On the basis of the sliding mode theory, the robust power system stabilizer was developed. The main advantages of the sliding mode controller are simple realization of the control algorithm, robustness to parameter variations and elimination of disturbances. The advantage of the proposed sliding mode controller against conventional linear controller was tested for damping of the synchronous generator oscillations in the entire operating range. Obtained results show the improved damping in the entire operating range of the synchronous generator and the increase of the power system stability. The proposed study contributes to the progress in the development of the advanced stabilizer, which will replace conventional linear stabilizers and improve damping of the synchronous generators.

Keywords: Control theory, power system stabilizer, robust control, sliding mode control, stability, synchronous generator.

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Authors: Mohsen A. Bakouri, Andrey V. Savkin, Abdul-Hakeem H. Alomari, Robert F. Salamonsen, Einly Lim, Nigel H. Lovell

Abstract:

Physiological control of a left ventricle assist device (LVAD) is generally a complicated task due to diverse operating environments and patient variability. In this work, a tracking control algorithm based on sliding mode and feed forward control for a class of discrete-time single input single output (SISO) nonlinear uncertain systems is presented. The controller was developed to track the reference trajectory to a set operating point without inducing suction in the ventricle. The controller regulates the estimated mean pulsatile flow Qp and mean pulsatility index of pump rotational speed PIω that was generated from a model of the assist device. We recall the principle of the sliding mode control theory then we combine the feed-forward control design with the sliding mode control technique to follow the reference trajectory. The uncertainty is replaced by its upper and lower boundary. The controller was tested in a computer simulation covering two scenarios (preload and ventricular contractility). The simulation results prove the effectiveness and the robustness of the proposed controller

Keywords: robust control system, discrete-sliding mode, left ventricularle assist devicse, pulsatility index.

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Authors: Rong-Jong Wai, Chia-Ming Liu

Abstract:

Generally speaking, the mobile robot is capable of sensing its surrounding environment, interpreting the sensed information to obtain the knowledge of its location and the environment, planning a real-time trajectory to reach the object. In this process, the issue of obstacle avoidance is a fundamental topic to be challenged. Thus, an adaptive path-planning control scheme is designed without detailed environmental information, large memory size and heavy computation burden in this study for the obstacle avoidance of a mobile robot. In this scheme, the robot can gradually approach its object according to the motion tracking mode, obstacle avoidance mode, self-rotation mode, and robot state selection. The effectiveness of the proposed adaptive path-planning control scheme is verified by numerical simulations of a differential-driving mobile robot under the possible occurrence of obstacle shapes.

Keywords: Adaptive Path Planning, Mobile Robot ObstacleAvoidance

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Authors: Amer S. Al-Yahmadi, T.C. Hsia

Abstract:

This paper seeks to develop simple yet practical and efficient control scheme that enables cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The paper develops a sliding mode control law that provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Simulation results for two three joint arms moving a flexible beam, are presented to validate the theoretical results.

Keywords: Sliding mode control, cooperative manipulators.

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Authors: S. Kahvecioglu, A. Karamancioglu, A. Yazici

Abstract:

In this paper, a nonlinear model predictive swing-up and stabilizing sliding controller is proposed for an inverted pendulum-cart system. In the swing up phase, the nonlinear model predictive control is formulated as a nonlinear programming problem with energy based objective function. By solving this problem at each sampling instant, a sequence of control inputs that optimize the nonlinear objective function subject to various constraints over a finite horizon are obtained. Then, this control drives the pendulum to a predefined neighborhood of the upper equilibrium point, at where sliding mode based model predictive control is used to stabilize the systems with the specified constraints. It is shown by the simulations that, due to the way of formulating the problem, short horizon lengths are sufficient for attaining the swing up goal.

Keywords: Inverted pendulum, model predictive control, swingup, stabilization.

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Authors: Dongsu Wu, Hongbin Gu, Peng Li

Abstract:

A novel adaptive fuzzy trajectory tracking algorithm of Stewart platform based motion platform is proposed to compensate path deviation and degradation of controller-s performance due to actuator torque limit. The algorithm can be divided into two parts: the real-time trajectory shaping part and the joint space adaptive fuzzy controller part. For a reference trajectory in task space whenever any of the actuators is saturated, the desired acceleration of the reference trajectory is modified on-line by using dynamic model of motion platform. Meanwhile an additional action with respect to the difference between the nominal and modified trajectories is utilized in the non-saturated region of actuators to reduce the path error. Using modified trajectory as input, the joint space controller incorporates compute torque controller, leg velocity observer and fuzzy disturbance observer with saturation compensation. It can ensure stability and tracking performance of controller in present of external disturbance and position only measurement. Simulation results verify the effectiveness of proposed control scheme.

Keywords: Actuator saturation, adaptive fuzzy control, Stewartplatform, trajectory shaping, flight simulator

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Authors: Young-Seok Choi

Abstract:

We present a refined multiscale Shannon entropy for analyzing electroencephalogram (EEG), which reflects the underlying dynamics of EEG over multiple scales. The rationale behind this method is that neurological signals such as EEG possess distinct dynamics over different spectral modes. To deal with the nonlinear and nonstationary nature of EEG, the recently developed empirical mode decomposition (EMD) is incorporated, allowing a decomposition of EEG into its inherent spectral components, referred to as intrinsic mode functions (IMFs). By calculating the Shannon entropy of IMFs in a time-dependent manner and summing them over adaptive multiple scales, it results in an adaptive subscale entropy measure of EEG. Simulation and experimental results show that the proposed entropy properly reveals the dynamical changes over multiple scales.

Keywords: EEG, subscale entropy, Empirical mode decomposition, Intrinsic mode function.

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Authors: Markus Reichhartinger, Martin Horn

Abstract:

In this paper, the position control of an electronic throttle actuator is outlined. The dynamic behavior of the actuator is described with the help of an uncertain plant model. This motivates the controller design based on the ideas of higher-order slidingmodes. As a consequence anti-chattering techniques can be omitted. It is shown that the same concept is applicable to estimate unmeasureable signals. The control law and the observer are implemented on an electronic control unit. Results achieved by numerical simulations and real world experiments are presented and discussed.

Keywords: higher order sliding-mode, throttle actuator, electromechanicalsystem, robust and nonlinear control.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: P. Ramana , K. Alice Mary, M. Surya Kalavathi, M. Phani Kumar

Abstract:

This paper discusses two observers, which are used for the estimation of parameters of PMSM. Former one, reduced order observer, which is used to estimate the inaccessible parameters of PMSM. Later one, full order observer, which is used to estimate all the parameters of PMSM even though some of the parameters are directly available for measurement, so as to meet with the insensitivity to the parameter variation. However, the state space model contains some nonlinear terms i.e. the product of different state variables. The asymptotic state observer, which approximately reconstructs the state vector for linear systems without uncertainties, was presented by Luenberger. In this work, a modified form of such an observer is used by including a non-linear term involving the speed. So, both the observers are designed in the framework of nonlinear control; their stability and rate of convergence is discussed.

Keywords: Permanent magnet synchronous motor, Mathematicalmodelling, Rotor reference frame, parameter estimation, Luenbergerobserver, reduced order observer, full order observer

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Authors: Jaeho Han, Moonjung Kim, Won-Ho Kim, Chang-Ho Hyun

Abstract:

This paper introduces a high-gain observer based state of charge(SOC) estimator for lithium-Ion batteries. The proposed SOC estimator has a high-gain observer(HGO) structure. The HGO scheme enhances the transient response speed and diminishes the effect of uncertainties. Furthermore, it guarantees that the output feedback controller recovers the performance of the state feedback controller when the observer gain is sufficiently high. In order to show the effectiveness of the proposed method, the linear RC battery model in ADVISOR is used. The performance of the proposed method is compared with that of the conventional linear observer(CLO) and some simulation result is given.

Keywords: SOC, high-gain, observer, uncertainties, robust

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Authors: S. Sonkham, U. Pinsopon, W. Chatlatanagulchai

Abstract:

This paper presents a method of sliding mode control (SMC) designing and developing for the servo system in a dual-stage actuator (DSA) hard disk drive. Mathematical modeling of hard disk drive actuators is obtained, extracted from measuring frequency response of the voice-coil motor (VCM) and PZT micro-actuator separately. Matlab software tools are used for mathematical model estimation and also for controller design and simulation. A model-reference approach for tracking requirement is selected as a proposed technique. The simulation results show that performance of a model-reference SMC controller design in DSA servo control can be satisfied in the tracking error, as well as keeping the positioning of the head within the boundary of +/-5% of track width under the presence of internal and external disturbance. The overall results of model-reference SMC design in DSA are met per requirement specifications and significant reduction in %off track is found when compared to the single-state actuator (SSA).

Keywords: Hard Disk Drive, Dual-Stage Actuator, Track Following, HDD Servo Control, Sliding Mode Control, Model-Reference, Tracking Control.

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Authors: Hongji Tang, Yanbo Gao, Yue Yu

Abstract:

This paper presents a new nonlinear integral-type sliding surface for synchronizing two different chaotic systems with parametric uncertainty. On the basis of Lyapunov theorem and average dwelling time method, we obtain the control gains of controllers which are derived to achieve chaos synchronization. In order to reduce the gains, the error system is modeled as a switching system. We obtain the sufficient condition drawn for the robust stability of the error dynamics by stability analysis. Then we apply it to guide the design of the controllers. Finally, numerical examples are used to show the robustness and effectiveness of the proposed control strategy.

Keywords: Chaos synchronization, Nonlinear sliding surface, Control gains, Sliding mode control.

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Authors: Ekprasit Promtun, Sridhar Seshagiri

Abstract:

This paper considers the control of the longitudinal flight dynamics of an F-16 aircraft. The primary design objective is model-following of the pitch rate q, which is the preferred system for aircraft approach and landing. Regulation of the aircraft velocity V (or the Mach-hold autopilot) is also considered, but as a secondary objective. The problem is challenging because the system is nonlinear, and also non-affine in the input. A sliding mode controller is designed for the pitch rate, that exploits the modal decomposition of the linearized dynamics into its short-period and phugoid approximations. The inherent robustness of the SMC design provides a convenient way to design controllers without gain scheduling, with a steady-state response that is comparable to that of a conventional polynomial based gain-scheduled approach with integral control, but with improved transient performance. Integral action is introduced in the sliding mode design using the recently developed technique of “conditional integrators", and it is shown that robust regulation is achieved with asymptotically constant exogenous signals, without degrading the transient response. Through extensive simulation on the nonlinear multiple-input multiple-output (MIMO) longitudinal model of the F-16 aircraft, it is shown that the conditional integrator design outperforms the one based on the conventional linear control, without requiring any scheduling.

Keywords: Sliding-mode Control, Integral Control, Model Following, F-16 Longitudinal Dynamics, Pitch-Rate Control.

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Authors: Tohru Kawabe

Abstract:

In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: Sliding Mode Control, Model Predictive Control, Integral Action, Electric Vehicle, Slip suppression.

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Authors: Youcef Bekakra, Djilani Ben attous

Abstract:

This paper presents the study of a variable speed wind energy conversion system based on a Doubly Fed Induction Generator (DFIG) based on a sliding mode control applied to achieve control of active and reactive powers exchanged between the stator of the DFIG and the grid to ensure a Maximum Power Point Tracking (MPPT) of a wind energy conversion system. The proposed control algorithm is applied to a DFIG whose stator is directly connected to the grid and the rotor is connected to the PWM converter. To extract a maximum of power, the rotor side converter is controlled by using a stator flux-oriented strategy. The created decoupling control between active and reactive stator power allows keeping the power factor close to unity. Simulation results show that the wind turbine can operate at its optimum energy for a wide range of wind speed.

Keywords: Doubly fed induction generator, wind energy, wind turbine, sliding mode control, maximum power point tracking (MPPT).

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Authors: Martin Ringdorfer, Martin Horn

Abstract:

A robust wheel slip controller for electric vehicles is introduced. The proposed wheel slip controller exploits the dynamics of electric traction drives and conventional hydraulic brakes for achieving maximum energy efficiency and driving safety. Due to the control of single wheel traction motors in combination with a hydraulic braking system, it can be shown, that energy recuperation and vehicle stability control can be realized simultaneously. The derivation of a sliding mode wheel slip controller accessing two drivetrain actuators is outlined and a comparison to a conventionally braked vehicle is shown by means of simulation.

Keywords: Wheel slip control, sliding mode control, vehicle dynamics.

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

Abstract:

In this paper, stabilization of an Active Magnetic Bearing (AMB) system with varying rotor speed using Sliding Mode Control (SMC) technique is considered. The gyroscopic effect inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Also, transformation of the AMB dynamic model into a new class of uncertain system shows that this gyroscopic effect lies in the mismatched part of the system matrix. Moreover, the current gain parameter is allowed to be varied in a known bound as an uncertainty in the input matrix. SMC design method is proposed in which the sufficient condition that guarantees the global exponential stability of the reduced-order system is represented in Linear Matrix Inequality (LMI). Then, a new chattering-free control law is established such that the system states are driven to reach the switching surface and stay on it thereafter. The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active Magnetic Bearing (AMB), Sliding ModeControl (SMC), Linear Matrix Inequality (LMI), mismatcheduncertainty.

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Authors: Gabriel Sitler, Yousef Sardahi, Asad Salem

Abstract:

This paper presents an optimal and robust sliding mode controller (SMC) to regulate the position of the knee joint angle for patients suffering from knee injuries. The controller imitates the role of active orthoses that produce the joint torques required to overcome gravity and loading forces and regain natural human movements. To this end, a mathematical model of the shank, the lower part of the leg, is derived first and then used for the control system design and computer simulations. The design of the controller is carried out in optimal and multi-objective settings. Four objectives are considered: minimization of the control effort and tracking error; and maximization of the control signal smoothness and closed-loop system’s speed of response. Optimal solutions in terms of the Pareto set and its image, the Pareto front, are obtained. The results show that there are trade-offs among the design objectives and many optimal solutions from which the decision-maker can choose to implement. Also, computer simulations conducted at different points from the Pareto set and assuming knee squat movement demonstrate competing relationships among the design goals. In addition, the proposed control algorithm shows robustness in tracking a standard gait signal when accounting for uncertainty in the shank’s parameters.

Keywords: Optimal control, multi-objective optimization, sliding mode control, wearable knee exoskeletons.

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