Conventional Backstepping Control Research Articles

Robust Backstepping Tracking Control of Mobile Robot Based on Nonlinear Disturbance Observer

This paper presents a robust backstepping control (BC) method based on nonlinear disturbance observer (NDOB) for trajectory tracking of the nonholonomic wheeled mobile robot (WMR) in the presence of external disturbances and parameters uncertainties. At first, a bounded Fuzzy logic based backstepping controller (BFLBC) is designed to control the WMR without considering the effects of the external disturbances and the parameters uncertainties. Typically, the conventional BC controller depends upon the state tracking errors analysis, where unbounded velocity signal is produced for the applications that have huge tracking errors. Therefore, a fuzzy logic controller (FLC) is introduced in this research in order to normalize the state tracking errors, so that the input errors to the BC are bounded to a finite interval. Finally, the designed BFLBC is integrated with the nonlinear disturbance observer in order to attenuate the external disturbances and model uncertainties. The simulation results show the effectiveness of the proposed controller to generate a bounded velocity signal as well as to stabilize the tracking errors to zero. In addition, the results prove that the proposed controller provide an excellent disturbance attenuation as well as robustness against the parameters uncertainties.

Compound Control Strategy for MDF Continuous Hot Pressing Electrohydraulic Servo System with Uncertainties and Input Saturation

A compound control strategy is investigated for Medium Density Fiberboard (MDF) continuous hot pressing electrohydraulic servo system (EHSS) with uncertainties and input saturation. Firstly, a hyperbolic tangent function is applied to approximate saturation nonlinearity in the system. And thus the mathematical model is continuous and differentiable. Subsequently, the slab thickness tracking controller is constructed by using a dynamic surface control (DSC) method, which introduces first-order low-pass filters to calculate derivatives of virtual control input in each step. Compared with the conventional backstepping controller, complexity of the design procedure is alleviated obviously. Moreover, a composite disturbance of uncertainties and input saturation is estimated by a nonlinear disturbance observer for compensation of the control law. Finally, an appropriate Lyapunov function is chosen to prove that all signals of the closed-loop system are semiglobally uniformly ultimately bounded and the tracking error converges to zero asymptotically. Numerical simulation results are also exhibited to authenticate and validate the benefits of the proposed control scheme.

Adaptive backstepping control for magnetic bearing system via feedforward networks with random hidden nodes

This paper presents an adaptive backstepping neural controller (ABNC) to achieve precise rotor position tracking for a nonlinear active magnetic bearing (AMB) system with modeling uncertainties and external disturbances. In the proposed ABNC, the single-hidden layer feedforward networks (SLFNs) are used to approximate the unknown nonlinearities of dynamic systems and then based on the approximated models, the neural controller is constructed. Different from the existing methods, the hidden node parameters of the SLFNs are determined using the recently proposed neural algorithm named extreme learning machine (ELM), where these parameters are assigned randomly without adjusting. This simplifies the controller design process. Using the Lyapunov theory, stable tuning rules are derived for the update of the output weights of the SLFNs and a proof of stability in the uniformly bounded sense is given for the resulting controller. Moreover, to relax the online computation burden existing in the ABNC, a simplified ABNC (Simpl_ABNC) with less parameters to be adjusted online is proposed to improve the control performance. Finally the simulation results demonstrate that the proposed ABNC and Simpl_ABNC achieve better tracking performance comparing with other controllers including PID controller, conventional backstepping controller and adaptive backstepping sliding mode controller. Also the results show that the Simpl_ABNC has much less computation complexity and also better tracking performance than the ABNC.

Finite-Time Output Feedback Tracking Control for Autonomous Underwater Vehicles

<?Pub Dtl=""?> In this paper, the finite-time output feedback trajectory tracking control problem for autonomous underwater vehicles (AUVs) is investigated. The vehicle model is constructed in six degrees of freedom and the vehicle attitude is represented by quaternions to avoid representation singularities. The control design consists of three steps. First, by using the finite-time control technique, two global finite-time stabilizing controllers based on state feedback are proposed for the vehicle translational and rotational tracking error subsystems, respectively. Second, considering the estimation problem of the vehicle translational velocities, a global finite-time convergent observer is employed to reconstruct the information of the vehicle translational velocities. Finally, based on the proposed state feedback controllers and the finite-time convergent observer, a finite-time output feedback trajectory tracking control scheme for AUVs is derived. Global finite-time stability of the closed-loop system is rigorously proved by using Lyapunov theory. Compared with the conventional backstepping control scheme via output feedback, the proposed finite-time output feedback control scheme offers not only a faster convergence rate but also a higher tracking accuracy for trajectory tracking control of AUVs. Simulations demonstrate the effectiveness of the proposed control scheme.

Intelligent Adaptive Gain Backstepping Technique

In this research, intelligent adaptive backstepping control is presented as robust control for continuum robot. The first objective in this research is design a Proportional- Derivative (PD) fuzzy system to compensate the system model uncertainties. The second objective is focused on the design tuning gain adaptive methodology according to high quality partly nonlinear methodology. Conventional backstepping controller is one of the important robust controllers especially to control of continuum robot manipulator. The fuzzy controller is used in this method to system compensation. In real time to increase the system robust fuzzy logic theory is applied to backstepping controller. To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. This method is applied to continuum robot manipulator to have the best performance.

Robust adaptive control of DC motor system fed by Buck converter

For the Buck-fed DC motor system with parameter uncertainties and external disturbances, an adaptive robust controller is proposed based on dynamic surface control and slide mode control method. The derived adaptive robust control guarantees the closedloop errors system is uniform ultimately bounded, and the parameters update laws are designed based on the uncertainty equivalence principle. The theoretical analysis and simulation results all reveal that the developed adaptive nonlinear robust controller is not sensitive to uncertainties of system, and owns simpler configuration and more accurate tracking performance than that of conventional backstepping control or PID control method.

Design of Fuzzy-Neural-Network-Inherited Backstepping Control for Robot Manipulator Including Actuator Dynamics

This study presents the design and analysis of an intelligent control system that inherits the systematic and recursive design methodology for an n-link robot manipulator, including actuator dynamics, in order to achieve a high-precision position tracking with a firm stability and robustness. First, the coupled higher order dynamic model of an n-link robot manipulator is introduced briefly. Then, a conventional backstepping control (BSC) scheme is developed for the joint position tracking of the robot manipulator. Moreover, a fuzzy-neural-network-inherited BSC (FNNIBSC) scheme is proposed to relax the requirement of detailed system information to improve the robustness of BSC and to deal with the serious chattering that is caused by the discontinuous function. In the FNNIBSC strategy, the FNN framework is designed to mimic the BSC law, and adaptive tuning algorithms for network parameters are derived in the sense of the projection algorithm and Lyapunov stability theorem to ensure the network convergence as well as stable control performance. Numerical simulations and experimental results of a two-link robot manipulator that are actuated by dc servomotors are provided to justify the claims of the proposed FNNIBSC system, and the superiority of the proposed FNNIBSC scheme is also evaluated by quantitative comparison with previous intelligent control schemes.

Fuzzy-Approximator-Based Adaptive Controller Design for Ship Course-Keeping Steering in Strict-Feedback Forms

Along with increasing marine transportation and logistics, the ship autopilot has become much important not only to lower the seaman's operating intensions, but also to reduce the seaman's deployment. It is still a challenge to design ship course-keeping controller because of ship's uncertain dynamics and time-varying environmental disturbance. This study focuses on backstepping adaptive course-keeping controller design for ship autopilot. Takagi-Sugeno (T-S) fuzzy approximator can formulate ship motion's uncertainties. Therefore, the proposed controller has no need of a priori knowledge about ship's system dynamics. Command filter can bypass the iterative differential manipulations in conventional ship course adaptive backstepping controller. The design can guarantee the ultimate uniform boundedness of the signals in closed-loop system. Finally, simulation study verifies the efficiency of the ship course-keeping design.

ℒ1 Backstepping for Robust Trajectory Tracking

This paper addresses the problem of making UAVs follow a prescribed trajectory in the presence of modeling uncertainties and external disturbances. The kinematics and dynamics of the trajectory tracking problem are in strict feedback form, appropriate for backstepping deisgn. While there is no uncertainty in the kinematics, rapidly changing uncertainties in the dynamics make this problem an ideal candidate for ℒ1 backstepping control. The trajectory tracking controller serves as the outer-loop in a cascaded design architecture and supplies a reference quaternion and thrust to the inner-loop controller. The inner-loop controller in turn generates a moment demand for the control allocation module. Such an inner-outer loop architecture is modular and does away with the requirement that the commanded trajectory be four times differentiable as would be required if a single monolithic backstepping control law were to be used. Simulations are used to demonstrate the performance of this controller in comparison to a conventional backstepping controller.

Adaptive fuzzy output feedback control for a single-link flexible robot manipulator driven DC motor via backstepping

In this paper, an adaptive fuzzy output feedback approach is proposed for a single-link robotic manipulator coupled to a brushed direct current (DC) motor with a nonrigid joint. The controller is designed to compensate for the nonlinear dynamics associated with the mechanical subsystem and the electrical subsystems while only requiring the measurements of link position. Using fuzzy logic systems to approximate the unknown nonlinearities, an adaptive fuzzy filter observer is designed to estimate the immeasurable states. By combining the adaptive backstepping and dynamic surface control (DSC) techniques, an adaptive fuzzy output feedback control approach is developed. Stability proof of the overall closed-loop system is given via the Lyapunov direct method. Three key advantages of our scheme are as follows: (i) the proposed adaptive fuzzy control approach does not require that all the states of the system be measured directly, (ii) the proposed control approach can solve the control problem of robotic manipulators with unknown nonlinear uncertainties, and (iii) the problem of “explosion of complexity” existing in the conventional backstepping control methods is avoided. The detailed simulation results are provided to demonstrate the effectiveness of the proposed controller.

Output feedback domination approach for finite-time force control of an electrohydraulic actuator

Force control of a single-rod electrohydraulic actuator is investigated. The model considers the friction effect of the actuator. First, a non-linear force controller using a feedback domination approach, which can globally finite-time stabilise the force tracking error system without the friction parameter uncertainties, is proposed. Then, another feedback domination controller is proposed to cope with the friction parameter uncertainties. To estimate the unmeasurable states, an observer with finite-time convergence is developed. Rigorous stability analysis is given. Compared with the conventional output feedback backstepping control method, the proposed output feedback domination control scheme provides a faster convergence rate and a higher tracking accuracy for force tracking. Numerical simulation results demonstrate the effectiveness of the proposed control design.

Adaptive backstepping controller for linear induction motor position control

PurposeThe purpose of this paper is to propose mover position control of linear induction motor (LIM) using an adaptive backstepping approach based on field orientation.Design/methodology/approachFirst, the indirect field‐oriented control LIM is derived. Then, an adaptive backstepping approach based on field‐oriented control of LIM is proposed to compensate the uncertainties which occur in the control. Mover position amplitude tracking objective is formulated, under the assumption of unknown total mass of the moving element, viscous friction, and load force, so that the position regulation is achieved.FindingsThe effectiveness and robustness of the proposed control scheme are verified by numerical simulation using Matlab/Simulink model. The numerical validation results of the proposed scheme have presented good transient control performances and robustness to uncertainties compared to the conventional backstepping control design.Originality/valueThe paper presents an adaptive backstepping approach for LIM control that achieves mover position amplitude tracking objective under mechanical parameter variation.

Backstepping Control Design with Actuator Torque Bound for Spacecraft Attitude Maneuver

BACKSTEPPING is a popular nonlinear control design technique [1,2]. It hinges on using a part of the system states as virtual controls to control the other states. Generating a family of globally asymptotically stabilizing control laws is the main advantage of this method that can be exploited for addressing robustness issues and solving adaptive problems. The term backstepping refers to the recursive nature of the control design procedure in which a control law and a control Lyapunov function are recursively constructed to guarantee stability. Backstepping has been considered for the spacecraft slew maneuvers [3,4]. The cascaded structure of spacecraft kinematics and dynamics makes the integrator backstepping a preferred approach for the spacecraft attitude maneuver problem, resulting in smooth feedback controls [5]. However, the typical control actuators used for this problem (such as reaction wheels, control moment gyros, or thrusters) have an upper bound on the control torque they can exert onto the system and the simple or conventional backstepping control method may result in excessive control input beyond that saturation bound. The issue has been addressed in the literature using other control methodologies such as nonlinear proportional–integral–derivative control [6], Lyapunovoptimal control [7] and variable structure control [8–11]. In this work, we design a nonlinear backstepping attitude controller using the inverse tangent-based tracking function [4] and a family of augmented Lyapunov functions [12]. Using this control law, we derive an analytical upper bound of the control torque norm. The bound is effectively used to tune the control parameters so that, for the given settling time specification, the upper bound of the control input is minimized. The performance of the proposed controller has shown improvements in minimizing the peak control torque and the settling time. The rest of the Note is organized as follows: First, the kinematics and dynamics of rigid spacecraft are summarized. Second, the details of the design procedure for the proposed controller and the analytical bounds for the control torque components are given. Third, the efficacy of the proposed scheme is demonstrated by the numerical simulations for the cases of attitude stabilization and tracking both. Finally, the conclusions are presented.

Development of Lyapunov-Based Genetic Algorithm Control for Linear Piezoelectric Ceramic Motor Drive

In general, the role of genetic algorithm (GA) is operated offline as a minor compensator or tuner in the control engineering because the systematic design and the latent stability problem of a GA-based control scheme are required to be solved. This paper originally designs a Lyapunov-based GA control (LGAC) scheme, and it applies for a practical control engineering example of the online motion control of a linear piezoelectric ceramic motor driven by a hybrid resonant inverter. In this control scheme, a GA control system via backstepping design technique is utilized to be the major controller, and adaptation laws derived from Lyapunov stability analyses are manipulated to adjust appropriate evolutionary steps. As a result, the system stability can be guaranteed directly without strict constraint conditions and detailed system knowledge. The effectiveness of the proposed drive and control system is verified by experimental results in the presence of uncertainties. From the measured results, the LGAC system performs superior high-precision motion control under wide operation range than conventional backstepping control system.

EXPONENTIAL STABILIZATION OF THE INERTIA WHEEL PENDULUM USING DYNAMIC SURFACE CONTROL

This paper considers the stabilization problem of Inertia Wheel Pendulum, a widely studied benchmark nonlinear system. It is a classical example of a flat underactuated mechanical system, for which the design of control law becomes a challenging task owing to its underactuated nature. A novel nonlinear controller design, fusing the recently introduced Dynamic Surface Control and the Control Lyapunov Function method, is presented as the solution. Stability is analyzed using concepts from Singular Perturbation Theory. The proposed design procedure is shown to be simpler and more intuitive than existing designs. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and verified using numerical simulations.

Final Comments by the Authors

This paper addresses the problem of making UAVs follow a prescribed trajectory in the presence of modeling uncertainties and external disturbances. The kinematics and dynamics of the trajectory tracking problem are in strict feedback form, appropriate for backstepping deisgn. While there is no uncertainty in the kinematics, rapidly changing uncertainties in the dynamics make this problem an ideal candidate for ℒ1 backstepping control. The trajectory tracking controller serves as the outer-loop in a cascaded design architecture and supplies a reference quaternion and thrust to the inner-loop controller. The inner-loop controller in turn generates a moment demand for the control allocation module. Such an inner-outer loop architecture is modular and does away with the requirement that the commanded trajectory be four times differentiable as would be required if a single monolithic backstepping control law were to be used. Simulations are used to demonstrate the performance of this controller in comparison to a conventional backstepping controller.

Real-time tracking control of a non-holonomic mobile robot

A novel tracking controller for real-time navigation of a non-holonomic mobile robot is presented. The proposed tracking controller is based on a backstepping model and a gated dipole model from a biological neural system. It is capable of generating smooth, bounded acceleration control signals to track a reference path. Unlike the conventional backstepping controllers, the proposed model can solve the velocity jump problem caused by a large initial tracking error. Unlike the existing tracking control methods that assume 'perfect velocity tracking', the proposed controller removes the unpractical assumption by considering the constraint of accelerations. In addition, the proposed controller can deal with complicated situations, e.g. the reference linear velocity or angular velocity is not constant. The effectiveness and efficiency of the approach are demonstrated by simulation studies.

A Biological Inspired Approach to Collision-Free Path Planning and Tracking Control of a Mobile Robot

In this paper, a novel biologically inspired neural network approach is proposed for real-time collision-free path planning and tracking control of a nonholonomic mobile robot in a dynamic environment. The real-time collision-free robot trajectory is generated by a topologically organized neural network, where the dynamics of each neuron is characterized by a shunting equation derived from Hodgkin and Huxley’s biological membrane equation. The dynamically changing environment is represented by the dynamic activity landscape of the neural network, where the neural activity propagation is subject to the nonholonomic kinematic constraint of the mobile robot. The tracking velocities for the mobile robot are generated by a novel neural dynamics based controller, which is based on two shunting equations and the conventional backstepping technique. Unlike the conventional backstepping controllers suffer from sharp jumps, the proposed tracking controller can generate smooth and continuous commands. The effectiveness and efficiency of the proposed approach are demonstrated through simulation and comparison studies.

퍼지 시스템을 이용한 이동로봇의 궤적제어

This paper describes a tracking control for the mobile robot based on fuzzy systems. Since the mobile robot has the nonholonomic constraints, these constraints should be considered to design a tracking controller for the mobile robot. One of the well-known tracking controllers for the mobile robot is the back-stepping controller. The conventional back-stepping controller includes the dynamics and kinematics of the mobile robot. The conventional back-stepping controller is affected by the derived velocity reference by a kinematic controller. To improve the performance of the conventional back-stepping controller, this paper uses the fuzzy systems known as the nonlinear controller. The new velocity reference for the back-stepping controller is derived through the fuzzy inference. Fuzzy rules are selected for gains of the kinematic controller. The produced velocity reference has properly considered the varying reference trajectories. Simulation results show that the proposed controller is more robust than the conventional back-stepping controller.