Adaptive Backstepping Design of a Microgyroscope.

In this article, a fuzzy-approximation-based adaptive backstepping control method for dual-arm of a humanoid robot was proposed. The purpose of this control system is to provide coordinated movement assistance to enable the humanoid robot’s human-like forearm to grab objects coordinately (or track any continuous desired trajectory), even in the presence of environmental disturbances and parametric uncertainties. We analyze the proposed adaptive backstepping by mathematical modeling and actually measure the robot dual-arm motion information of a number of case when they simulate the trajectory to verify the model. We design the adaptive fuzzy-approximation control strategy and combining the synthesis of the robust design, backstepping control, and Lyapunov function method, the proposed adaptive fuzzy backstepping control does not need to know the humanoid robot’s arms model precisely. In the control system proposed here, once the desired trajectories of the robot’s dual-arm positions are given, the adaptive fuzzy system was closed to any unknown functions and to the derivative of the virtual control law of the humanoid robot system. In this case, a robust design scheme was utilized to compensate for any approximation errors. With the proposed trajectory tracking, not only able to generate the coordinate motions for a humanoid robot’s two arms, but it can also control the arms to move to the desired positions. The proposed closed-loop system under the adaptive fuzzy backstepping control design was effective and that asymptotic stability was successfully achieved. The adaptive fuzzy-approximation backstepping control strategy should be more complete and intelligent and more actual test should be conducted to further evaluate the effect of the proposed trajectory tracking. The instability of dual-arm of humanoid robot system is systematically analyzed and a backstepping control strategy based on the adaptive fuzzy-approximation to improve the continuity of trajectory tracking of the robot’s arms is proposed.

A nonlinear constrained controller is designed for a reusable launch vehicle during re-entry phase in the presence of model uncertainty, external disturbance, and input constraint, via combining sliding mode control and adaptive backstepping control. Since the complex coupling between the translational and rotational dynamics of reusable launch vehicle, a control-oriented model derived from rotational dynamic is used for controller design. During the virtual control input design procedure, a dynamic robust term is utilized to compensate for the uncertainty. In addition, a filter is applied to handle “explosion of terms” problem during the actual control input design. To reduce the computational burden, adaptive law is used to evaluate the unknown norm bound of the lumped uncertainty. An auxiliary system is constructed to compensate for the input constraint effect. The stability of the closed-loop system is analyzed based on Lyapunov theory. Simulation results demonstrate the validity of the developed controller in providing stable tracking of the guidance command by numerical simulation on the 6-degree-of-freedom model of reusable launch vehicle.

In this paper, a nonlinear adaptive speed controller for permanent magnet linear synchronous motors based on a newly developed adaptive recursive Backstepping control approach for a permanent magnet synchronous motor drive is discussed and analyzed. The Backstepping technique provides a systematic method to address this type of problem. It combines the notion of Lyapunov function and a controller procedure recursively. The adaptive Backstepping control approach is utilized to obtain the robustness for mismatched parameter uncertainties. The overall stability of the system is shown using Lyapunov stability theorem. The simulation results clearly show that the proposed scheme can track the speed reference.

Robust adaptive integral backstepping control for opto-electronic tracking system based on modified LuGre friction model

This paper addresses the problem of fixed-time consensus tracking for a class of nonlinear multiagent systems (MASs) with disturbances. We establish a novel fixed-time consensus tracking protocol with adaptive disturbance rejection capabilities, leveraging adaptive selective disturbance elimination (ASDE) technology. This protocol consists of a distributed fixed-time observer (DFTO), a fixed-time disturbance observer (FTDO), and an adaptive selective disturbance elimination backstepping controller (ASDE) with adaptive lumped disturbance compensation abilities. The DFTO estimates the leader’s output using the communication network topology of each follower, while the FTDO rapidly observes the lumped disturbances and their derivatives. By adding disturbance indicator terms and disturbance observation attenuation terms to the control law, the beneficial and harmful effects of disturbance are distinguished. Under favorable disturbance conditions, lumped disturbances can be used to accelerate tracking speed. If disturbances are harmful, they are adaptively compensated to improve tracking accuracy. Furthermore, the fixed-time stability of each part of the protocol is analyzed using Lyapunov theory. Simulation results show that, under different initial states and command inputs, the proposed method achieves faster convergence and smaller tracking errors compared to the adaptive conditional disturbance negaton backstepping controller (ACDN), conditional disturbance negation backstepping controller (CDN), and non-smooth backstepping controller (NBCDC), verifying the effectiveness of the proposed method. The research outcomes serve as a reference for future multiagent adaptive anti-disturbance cooperative control technology.

In this paper, we present a nonlinear adaptive backstepping with extended state observer (ESO) trajectory tracking controller for a quadrotor unmanned aerial vehicle (UAV) subject to the multiple disturbances, which include the parametric uncertainties, actuator faults and external disturbance. First, a six-degrees of freedom quadrotor UAV model with the multiple disturbances function is built. Second, the adaptive backstepping controller is designed to track the desired trajectory command aim at internal disturbance. And the adaptive backstepping controller with ESO is designed to track the desired trajectory command aim at external disturbance. Third, the stability of the system is proved by the circle criterion. Finally, under different flight scenarios, simulation results are given to demonstrate the effectiveness of the proposed method.

Adaptive backstepping robust tracking control for stabilizing lateral dynamics of electric vehicles with uncertain parameters and external disturbances

This paper investigates a systematic modeling and control methodology for a multi-axis PZT (piezoelectric transducer) actuated servo stage supporting nano-manipulations. A sliding mode disturbance observer-based adaptive integral backstepping control method with an estimated inverse model compensation scheme is proposed to achieve ultra high precision tracking in the presence of the hysteresis nonlinearities, model uncertainties, and external disturbances. By introducing a time rate of the input signal, an enhanced rate-dependent Prandtl–Ishlinskii model is developed to describe the hysteresis behaviors, and its inverse is also constructed to mitigate their adverse effects. In particular, the corresponding inverse compensation error is analyzed and its boundedness is proven. Subsequently, the sliding mode disturbance observer-based adaptive integral backstepping controller is designed to guarantee the convergence of the tracking error, where the sliding mode disturbance observer can track the total disturbances in a finite time, while the integral action is incorporated into the adaptive backstepping design to improve the steady-state control accuracy. Finally, real time implementations of the proposed algorithm are applied on the PZT actuated servo system, where excellent tracking performance with tracking precision error around 6‰ for circular contour tracking is achieved in the experimental results.

This paper deals with the tracking control problem of quadrotor unmanned aerial vehicles (QUAVs) with external disturbances. First, because the QUAV model contains two non-integrity constraints, the dynamic model of the QUAV is decomposed into two subsystems which are independently controlled, so as to reduce controller design complexity. Secondly, the nonlinear disturbance observer (DOB) technique is integrated into a backstepping control method to design the controller for the first subsystem, in which a DOB is applied to estimate the lumped uncertainty. Based on the double power reaching law and the DOB, a multivariable sliding mode control (MSMC) scheme is developed for the second subsystem. Thirdly, based on Lyapunov theory, the closed-loop system is proved to be asymptotically stable. Finally, our comparative simulation results demonstrate that the presented control scheme behaves better in terms of tracking performance than the adaptive backstepping control (ABC) approach.

The control performance of quadrotor unmanned aerial vehicles (UAVs) in complex environments can be affected by external disturbances and other factors. In this paper, an adaptive neural network backstepping controller based on the barrier Lyapunov function (BLF) is designed for a quadrotor UAV with internal uncertainties, input–output constraints and external disturbances. Radial basis function neural networks are used to approximate the uncertainties in the dynamic model of the UAV, while the minimum parameter learning method is combined to accelerate the adjustment speed of neural network weights. A robust term is designed to balance the total system disturbance and improve the anti-interference performance. The BLF is used to handle the output constraint so that the constrained parameters cannot break the predefined constraints. An auxiliary system is introduced to solve input saturation and avoid the dependence of tracking error on the input amplitude in the method of approximating input saturation using the smoothing function. The stability of the control system is demonstrated by the Lyapunov method. The simulation results show that the proposed method has high tracking accuracy compared with the backstepping dynamic surface control method, and the input and output are in the predefined range.

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

Control-oriented modeling and adaptive backstepping control for a nonminimum phase hypersonic vehicle

Adaptive terminal synergetic-backstepping technique based machine learning regression algorithm for MPPT control of PV systems under real climatic conditions

A position tracking control method of permanent magnet synchronous motor (PMSM) is presented based on sliding mode control (SMC) and adaptive backstepping method. The adaptive backstepping controller is proposed for PMSM position loop and speed loop control. A adaptive backstepping observer is adopted to estimate the load torque. Regarding the current control of PMSM, the sliding mode controller with a novel sliding-mode exponential reaching law is presented. Finally, the stability of the entire system is verified by Lyapunov theory. The results of the experiment demonstrate that the proposed control algorithm achieves desirable position tracking property as well as good load disturbance attenuation.

In this article, we consider the adaptive fractional-order backstepping control problem for a class of high-order integer-order systems with uncertainties and unknown external disturbance. To obtain enhanced control performance, fractional-order calculus is integrated within the conventional backstepping controller design procedure. Theoretical proof is provided based on the Lyapunov stability theorem to ensure the global stability of the closed-loop system in the sense that all the closed-loop signals are uniformly ultimately bounded and the output tracking error to a reference signal converges to an adjustable arbitrarily small range by tuning certain design parameters. Both numerical simulation and experimental results verify the efficacy of the proposed adaptive fractional-order backstepping control scheme.