Adaptive Backstepping Control Design for Semi-Active Suspension of Half-Vehicle With Magnetorheological Damper

This paper investigates the problem of controlling half-vehicle semi-active suspension system involving a magnetorheological(MR)damper.This features a hysteretic behavior that is presently captured through the nonlinear Bouc-Wen model.The control objective is to regulate well the heave and the pitch motions of the chassis despite the road irregularities.The difficulty of the control problem lies in the nonlinearity of the system model,the uncertainty of some of its parameters,and the inaccessibility to measurements of the hysteresis internal state variables.Using Lyapunov control design tools,we design two observers to get online estimates of the hysteresis internal states and a stabilizing adaptive state-feedback regulator.The whole adaptive controller is formally shown to meet the desired control objectives.This theoretical result is confirmed by several simulations demonstrating the supremacy of the latter compared to the skyhook control and passive suspension.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Tradeoff Analysis of Factors Affecting Longitudinal Carrier Landing Performance for Small UAV Based on Backstepping Controller

Tradeoff analysis of the factors,including external environment and unmanned aerial vehicle(UAV)aerodynamic attributes,which affect longitudinal carrier landing performance,is important for small UAV.First,small UAV longitudinal carrier landing system is established,as well as the nonlinear dynamics and kinematics model,and then the longitudinal flight control system using backstepping technology with minimum information about the aerodynamic is designed.To assess the landing performance,a variety of influencing factors are considered,resulting in the constraints of aerodynamic attributes of carrier UAV.The simulation results show that the severe sea condition has the greatest influence on landing dispersion,while air wake is the primary factor on impact velocity.Among the longitudinal aerodynamic parameters,the lift curve slope is the most important factor affecting the landing performance,and increasing lift curve slope can improve the landing performance significantly.A better system performance will be achieved when the lift curve slope is larger than 2per radian.

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.

Adaptive Observer Based Backstepping Controller Design for Dynamic Ship Positioning

Modified adaptive observer based backstepping control system for dynamic positioning of ship is proposed. As an improvement, the adaptive observer takes the first-order wave frequency model and the bias term which represent the slowly varying environmental disturbances and the unmodeled dynamics. Thus, the wave-frequency motions are filtered out, and only the reconstructed low-frequency motions are sent as inputs of the controller. Furthermore, as the ship dynamics parameters are unknown, the adaptive estimation law is designed for both the unknown ship dynamics and the unmeasured state variables. Based on the estimated states and parameters, backstepping controller considering the integral action is designed. Global exponential stability （GES） for the total system is proved using Lyapunov direct method. Simulation results show a good performance of the observer and control system.

Study of a smart platform based on backstepping control method

A structural model is significant for the verification of structural control algorithms. However, for nonlinear behavior, experiments are mostly destructive tests that are costly, and conducting repetitive structural experiments is difficult. Therefore, a repetitive structural vibration model is important for structural vibration control. In this study, a smart platform to realize different structural behaviors is developed based on the backstepping control algorithm. Lyapunov functions are used to derive the control law. Simulations show that the designed model can track the structural responses of different arbitrary linear structures very well. In addition, the proposed platform can track responses of different piecewise linear structures and desired models with various hysteresis very well. Numerical results verify the effectiveness of the proposed tracking controller through the backstepping method for the established platform.

A New Robust Adaptive Neural Network Backstepping Control for Single Machine Infinite Power System With TCSC

For a single machine infinite power system with thyristor controlled series compensation(TCSC) device, which is affected by system model uncertainties, nonlinear time-delays and external unknown disturbances, we present a robust adaptive backstepping control scheme based on the radial basis function neural network(RBFNN). The RBFNN is introduced to approximate the complex nonlinear function involving uncertainties and external unknown disturbances, and meanwhile a new robust term is constructed to further estimate the system residual error,which removes the requirement of knowing the upper bound of the disturbances and uncertainty terms. The stability analysis of the power system is presented based on the Lyapunov function,which can guarantee the uniform ultimate boundedness(UUB) of all parameters and states of the whole closed-loop system. A comparison is made between the RBFNN-based robust adaptive control and the general backstepping control in the simulation part to verify the effectiveness of the proposed control scheme.

Adaptive backstepping control for levitation system with load uncertainties and external disturbances

To explore the precise dynamic response of the levitation system with active controller, a maglev guide way-electromagnet-air spring-cabin coupled model is derived firstly. Based on the mathematical model, it shows that the inherent nonlinearity, inner coupling, misalignments between the sensors and actuators, load uncertainties and external disturbances are the main issues that should be solved in engineering. Under the assumptions that the loads and external disturbance are measurable, the backstepping module controller developed in this work can tackle the above problems effectively. In reality, the load is uncertain due to the additions of luggage and passengers, which will degrade the dynamic performance. A load estimation algorithm is introduced to track the actual load asymptotically and eliminate its influence by tuning the parameters of controller online. Furthermore,considering the external disturbances generated by crosswind, pulling motor and air springs, the extended state observer is employed to estimate and suppress the external disturbance. Finally, results of numerical simulations illustrating closed-loop performance are provided.

Wave Heave Compensation Based on An Optimized Backstepping Control Method

The vessel heave motion caused by wave action increases the difficulty of installing offshore wind equipment.On-board wave heave compensation devices have therefore become increasingly critical in ensuring the stability and safety of the gangway and working platform.This study accordingly improves the compensation effect of such devices by developing a wave heave compensation model and designing an optimized backstepping control method.First,a model of the compensation system including the servo motor and electric cylinder is established by using the mechanism method.Second,a backstepping control method is designed to track the vessel heave motion,and particle swarm optimization is applied to optimize the control parameters.Finally,MATLAB/Simulink is used to simulate the application of the optimized backstepping controller,then regular and irregular heave motions are applied as input to a Stewart platform to evaluate the effectiveness of the control method.The experimental results show that the compensation efficiency provided by the proposed optimized backstepping control method is larger than 75.0%.

Speed-assigned Position Tracking Control of SRM With Adaptive Backstepping Control

A novel speed-assigned method is applied to the position tracking control of switched reluctance motor(SRM).A speed control freedom can be drawn into the position control through speed assignment. Adaptive backstepping control is used to design the position controller for the SRM. The accuracy of position tracking of the SRM can be enhanced with speed assignment. A disturbance observer is further designed to enhance the estimation accuracy of the unknown load torque. Simulation results certify that the design scheme is right and effective.

Adaptive Backstepping Control for Uncertain Systems with Compound Nonlinear Characteristics

An adaptive backstepping multi-sliding mode approximation variable structure control scheme is proposed for a class of uncertain nonlinear systems.An actuator model with compound nonlinear characteristics is established based on the model decomposition method.The unmodeled dynamic term of the radial basis function neural network approximation system is presented.The Nussbaum gain design technique is utilized to overcome the problem that the control gain is unknown.The adaptive law estimation is used to estimate the upper boundary of neural network approximation and uncertain interference.The adaptive approximate variable structure control effectively weakens the control signal chattering while enhancing the robustness of the controller.Based on the Lyapunov stability theory,the stability of the entire control system is proved.The main advantage of the designed controller is that the compound nonlinear characteristics are considered and solved.Finally,simulation results are given to show the validity of the control scheme.

Backstepping Sliding Mode Control Based on Extended State Observer for Hydraulic Servo System

Hydraulic servo system plays an important role in industrial fields due to the advantages of high response,small size-to-power ratio and large driving force.However,inherent nonlinear behaviors and modeling uncertainties are the main obstacles for hydraulic servo system to achieve high tracking perfor-mance.To deal with these difficulties,this paper presents a backstepping sliding mode controller to improve the dynamic tracking performance and anti-interfer-ence ability.For this purpose,the nonlinear dynamic model is firstly established,where the nonlinear behaviors and modeling uncertainties are lumped as one term.Then,the extended state observer is introduced to estimate the lumped distur-bance.The system stability is proved by using the Lyapunov stability theorem.Finally,comparative simulation and experimental are conducted on a hydraulic servo system platform to verify the efficiency of the proposed control scheme.

Vibration Control of A Flexible Marine Riser System Subject to Input Dead Zone and Extraneous Disturbances

An observer-based adaptive backstepping boundary control is proposed for vibration control of flexible offshore riser systems with unknown nonlinear input dead zone and uncertain environmental disturbances.The control algorithm can update the control law online through real-time data to make the controller adapt to the environment and improve the control precision.Specifically,based on the adaptive backstepping framework,virtual control laws and Lyapunov functions are designed for each subsystem.Three direction interference observers are designed to track the timevarying boundary disturbance.On this basis,the inverse of the dead zone and linear state transformation are used to compensate for the original system and eliminate the adverse effects of the dead zone.In addition,the stability of the closed-loop system is proven by Lyapunov stability theory.All the system states are bounded,and the vibration offset of the riser converges to a small area of the initial position.Finally,four examples of flexible marine risers are simulated in MATLAB to verify the effectiveness of the proposed controller.

Command filtered integrated estimation guidance and control for strapdown missiles with circular field of view

In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier Lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The Lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.

Modeling and Backstepping-based Nonlinear Control Strategy for a 6 DOF Quadrotor Helicopter

In this article, a nonlinear model of an underactuated six degrees of freedom （6 DOF） quadrotor helicopter is derived on the basis of the Newton-Euler formalism. The derivation comprises determining equations of the motion of the quadrotor in three dimensions and approximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics. The derived model composed of translational and rotational subsystems is dynamically unstable, so a sequential nonlinear control strategy is used. The control strategy includes feedback linearization coupled with a PD controller for the translational subsystem and a backstepping-based PID nonlinear controller for the rotational subsystem of the quadrotor. The performances of the nonlinear control method are evaluated by nonlinear simulation and the results demonstrate the effectiveness of the proposed control strategy for the quadrotor helicopter in quasi-stationary flights.

Nominal Model-Based Sliding Mode Control with Backstepping for 3-Axis Flight Table

Based on nominal model, a novel global sliding mode controller （GSMC） with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.

Backstepping sliding mode control for uncertain strict-feedback nonlinear systems using neural-network-based adaptive gain scheduling

A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control（SMC） law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network（RBFNN） is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network（NN）, with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC.

Backstepping Control of Speed Sensorless Permanent Magnet Synchronous Motor Based on Slide Model Observer

This paper presents a backstepping control method for speed sensorless permanent magnet synchronous motor based on slide model observer. First, a comprehensive dynamical model of the permanent magnet synchronous motor(PMSM) in d-q frame and its space-state equation are established. The slide model control method is used to estimate the electromotive force of PMSM under static frame, while the position of rotor and its actual speed are estimated by using phase loop lock(PLL) method. Next,using Lyapunov stability theorem, the asymptotical stability condition of the slide model observer is presented. Furthermore, based on the backstepping control theory, the PMSM rotor speed and current tracking backstepping controllers are designed, because such controllers display excellent speed tracking and anti-disturbance performance. Finally, Matlab simulation results show that the slide model observer can not only estimate the rotor position and speed of the PMSM accurately, but also ensure the asymptotical stability of the system and effective adjustment of rotor speed and current.

Adaptive Backstepping Sliding Mode Control for Nonlinear Systems with Input Saturation

An adaptive backstepping sliding mode control is proposed for a class of uncertain nonlinear systems with input saturation.A command filtered approach is used to prevent input saturation from destroying the adaptive capabilities of neural networks (NNs).The control law and adaptive updating laws of NNs are derived in the sense of Lyapunov function,so the stability can be guaranteed even under the input saturation.The proposed control law is robust against the disturbance,and it can also eliminate the impact of input saturation.Simulation results indicate that the proposed controller has a good performance.

The Impulse Excitation Joint Servo Drive Design and Adaptive Backstepping Control of Humanoid Robots

This study aims to explore the humanoid robot joint servo drive integration design and adaptive backstepping control. To make the humanoid robot have explosive power as the human does, simply increasing the power output of the motor of a lightweight design cannot meet the demand of moving heavy objects and so on. Moreover, the backstepping control algorithm is designed to implement the dual-arm cooperative control. The joint servo drive is redesigned in the present study, which can drive the motor at a limitation state when needed output high-voltage pulse can stimulate the motor so that the motor can produce an instantaneous large torque. A miniature design scheme is presented in this study for the servo drive, explaining the design method of each part module. The ex- perimental data illustrate that the servo drive can produce an output torque greater than the rate of the high-voltage pulse that stimulates the motor. Knowledge of the control of humanoid robot moving a heavy object has important practical significance. The present study provides a complete actual problem and exhibits a real practical use case which can be used to speed up the explosive humanoid robot arms.