Observer‐based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

In this paper, a discontinuous projection‐based adaptive robust control (ARC) scheme is constructed for a class of nonlinear systems in an extended semi‐strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The form allows for parametric uncertainties, uncertain nonlinearities, and dynamic uncertainties. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed output tracking transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the output tracking error over entire time‐history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic output tracking is also achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

基于干扰观测器的机械臂广义模型预测轨迹跟踪控制

为实现对多自由度机械臂关节运动精确轨迹跟踪,提出一种基于非线性干扰观测器的广义模型预测轨迹跟踪控制方法。针对机械臂轨迹跟踪运动学子系统,采用广义预测控制（Generalized Predictive Control,GPC）方法设计期望的虚拟关节角速度。对于机械臂轨迹跟踪动力学子系统,考虑机械臂的参数不确定性和未知外界扰动,利用GPC方法设计关节力矩控制输入,基于非线性干扰观测器方法实时估计和补偿系统模型中的不确定性。在李雅普诺夫稳定性理论框架下证明了机械臂关节角位置和角速度的跟踪误差最终收敛于零的小邻域。数值仿真验证了所提出控制方法的有效性和优越性。     

Design of UDE‐based controllers from their two‐degree‐of‐freedom nature

The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two‐degree‐of‐freedom nature of UDE‐based controllers is revealed. The set‐point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE‐based control, the Laplace transform can be applied to some time‐varying systems for analysis and design because all the time‐varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time‐delay control, the UDE‐based control also brings better performance than the time‐delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings. Copyright © 2010 John Wiley & Sons, Ltd.     

基于一类饱和函数的机器人混合鲁棒/自适应控制

提出一类不需要线性PD反馈的混合鲁棒/自适应控制策略,用于不确定性机器人的轨迹 跟踪.其控制结构由一个补偿参数不确定性的自适应控制器和补偿非参数不确定性的鲁棒控 制器构成. 其主要特点是基于一类饱和型函数,提出了一类新颖的鲁棒控制器和非线性滑动 变量的设计方法.基于Lyapunov方法的理论分析和计算机仿真,均保证设计的控制策略能够消 除系统所有的不确定性影响,并达到全局的渐近稳定.     

Output feedback second‐order sliding mode control of the cart on a beam system

We propose an output feedback second‐order sliding mode controller to stabilize the cart on a beam system. A second‐order sliding mode controller is designed using a Lyapunov function‐based switching surface and finite‐time controllers, while the state estimator is designed based on the Luenberger‐like observer. The proposed observer extends the applicability of Luenberger‐like observer to nonlinear systems that are not input–output linearizable, but can be approximately input–output linearized. The approximation is based on the physical property of the system, wherein certain terms in the total energy are neglected. Extensive numerical simulations validate the robustness of the proposed controller to parametric uncertainties using estimated states. Copyright © 2009 John Wiley & Sons, Ltd.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Adaptive Output Feedback Control of Flexible-Joint Robots Using Neural Networks: Dynamic Surface Design Approach

In this paper, we propose a new robust output feedback control approach for flexible-joint electrically driven (FJED) robots via the observer dynamic surface design technique. The proposed method only requires position measurements of the FJED robots. To estimate the link and actuator velocity information of the FJED robots with model uncertainties, we develop an adaptive observer using self-recurrent wavelet neural networks (SRWNNs). The SRWNNs are used to approximate model uncertainties in both robot (link) dynamics and actuator dynamics, and all their weights are trained online. Based on the designed observer, the link position tracking controller using the estimated states is induced from the dynamic surface design procedure. Therefore, the proposed controller can be designed more simply than the observer backstepping controller. From the Lyapunov stability analysis, it is shown that all signals in a closed-loop adaptive system are uniformly ultimately bounded. Finally, the simulation results on a three-link FJED robot are presented to validate the good position tracking performance and robustness of the proposed control system against payload uncertainties and external disturbances.     

基于观测器的机械手神经网络自适应控制

提出了一种基于观测器的机械手神经网络自适应轨迹跟随控制器设计方法,这里机械手的动力学非线性假设是未知的,并且假设机械手仅有关节角位置测量.文中采用一个线性观测器重构机械手的关节角速度,用神经网络逼近修正的机械手动力学非线性,改进系统的跟随性能.基于观测器的神经网络自适应控制器能够保证机械手角跟随误差和观测误差的一致终结有界性以及神经网络权值的有界性,最后给出了机械手神经网络自适应控制器-观测器设计的主要理论结果,并通过数字仿真验证了所提方法的性能.     

Robust Tracking Control Of The Variable Stiffness Actuator Based On The Lever Mechanism

This paper is concerned with the design of a robust adaptive tracking control scheme for a class of variable stiffness actuators (VSAs) based on the lever mechanisms. For these VSAs based on the lever mechanisms, the AwAS‐II developed at Italian Institute of Technology (IIT) is chosen as the study object, and it is an enhanced version of the original realization AwAS (actuator with adjustable stiffness). Firstly, for the dynamic model of the AwAS‐II system in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance and input saturation constraints, by using the coordinate transformations and the static state feedback linearization, the state space model of the AwAS‐II system with composite disturbances and input saturation constraints is transformed into an uncertain multiple‐input multiple‐output (MIMO) linear system with lumped disturbances and input saturation constraints. Subsequently, a combination of the feedback linearization, disturbance observer, sliding mode control and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the AwAS‐II system. Under the proposed controller, the semi‐global uniformly ultimately bounded stability of the closed‐loop system has been proved via Lyapunov stability analysis. Simulation results illustrate the effectiveness and the robustness of the proposed robust adaptive tracking control scheme.     

An extended observer-based robust nonlinear speed sensorless controller for a PMSM

This work focuses on the problem of observer-based robust speed sensorless control of a 3-phase permanent magnet synchronous motor (PMSM). Nonlinear design techniques are employed for designing robust speed controller and observer that are able to withstand the effects of modelling uncertainties and load variations. A new cascaded observer scheme is proposed comprising a continuous sliding mode observer (SMO) and an extended high-gain observer (EHGO). The proposed cascaded observer reduces chattering, exhibits reasonable insensitivity to modelling inaccuracies and is capable of withstanding errors due to the finite boundary layer of continuous SMO. For the robust speed control, an integral sliding mode controller is designed that yields fast and accurate speed tracking performance even in the presence of bounded uncertainties and external disturbances. The complete scheme has been evaluated using simulations and experiments.     

State observer-based robust control scheme for electrically driven robot manipulators

By using a state observer, a new robust trajectory tracking control scheme is developed in this paper for electrically driven robot manipulators. The role of the observer is to estimate joint angular velocities. The proposed controller does not employ adaptation, but assures robust stability of tracking error between joint angles and desired trajectories. At sacrificing asymptotical stability of the tracking errors, the configuration of the proposed controller becomes very simple, compared with regressor-based adaptive controllers. It is shown in the closed-loop system using the proposed controller that the Euclidian norm of tracking errors arrives at any small closed region with any convergent rate by setting only one design parameter. Especially for the desired trajectories converging to constant ultimate values, it is assured that tracking errors converge to zero.     

Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties

In this paper, the integrated kinematic and dynamic trajectory tracking control problem of wheeled mobile robots (WMRs) is addressed. An adaptive robust tracking controller for WMRs is proposed to cope with both parametric and nonparametric uncertainties in the robot model. At first, an adaptive nonlinear control law is designed based on input–output feedback linearization technique to get asymptotically exact cancellation of the parametric uncertainty in the WMR parameters. The designed adaptive feedback linearizing controller is modified by two methods to increase the robustness of the controller: (1) a leakage modification is applied to modify the integral action of the adaptation law and (2) the second modification is an adaptive robust controller, which is included to the linear control law in the outer loop of the adaptive feedback linearizing controller. The adaptive robust controller is designed such that it estimates the unknown constants of an upper bounding function of the uncertainty due to friction, disturbances and unmodeled dynamics. Finally, the proposed controller is developed for a type (2, 0) WMR and simulations are carried out to illustrate the robustness and tracking performance of the controller.     

Robust nonlinear control of a three-tank system using finite-time disturbance observers

A finite-time disturbance observer-based robust control method is proposed for output tracking of the Inteco threetank system in the presence of mismatched uncertainties. The controller is designed in a backstepping manner. At each step of the virtual controller design, a robust feedback controller with some effective nonlinear damping terms is designed so that the system states remain in the feasible domain. The nonlinear uncertainty is compensated by a finite-time disturbance observer. And to avoid the shortcoming of “explosion of terms”, the dynamic surface control technique which employs a low-pass filter is adopted at each step of the virtual controller design. Attention is paid to reducing the measurement noise effects and to initialization technique of the system states and reference output trajectory. Theoretical analysis is performed to clarify the control performance. And the theoretical results are verified based on the experimental studies on the real Inteco three-tank system.     

Robust attitude tracking control of flexible spacecraft for achieving globally asymptotic stability

The three‐axis attitude tracking control problem in the presence of parameter uncertainties and external disturbances for a spacecraft with flexible appendages is investigated in this paper. Novel simple robust Lyapunov‐based controllers that require only the attitude and angular velocity measurement are proposed. The first controller is a discontinuous one composed of a nonlinear PD part plus a sign function, whereas the second one is continuous or even smooth by modifying the discontinuous part of the first one. For a general desired trajectory, both controllers can achieve globally asymptotic stability of the attitude and angular velocity tracking errors instead of ultimate boundedness. By using a two‐step proof technique, the partial stability of the proposed controllers for the resulting closed‐loop systems in the face of model uncertainties and unexpected disturbances is proven theoretically. To further enhance the control performance, a continuous controller is presented that utilizes the tracking errors for estimating the external disturbances. In addition, stability analysis is done. For all the developed controllers, numerical simulation results are provided to demonstrate their performance. Copyright © 2008 John Wiley & Sons, Ltd.     

基于模糊不确定观测器的四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性的四旋翼飞行器,提出了一种基于模糊不确定观测器（Fuzzy uncertainty observer,FUO）的自适应动态面轨迹跟踪控制方法.通过将四旋翼飞行器系统分解为位置、姿态角和角速率三个动态子系统,使得各子系统虚拟控制器能够充分考虑欠驱动约束;采用一阶低通滤波器重构虚拟控制信号及其一阶导数,实现四旋翼跟踪控制设计的迭代解耦;设计了一种模糊不确定观测器,用以估计和补偿未知外界扰动与系统不确定性,从而确保闭环系统的稳定性和跟踪误差与其他系统信号的一致有界性.仿真研究验证了所提出的控制方法的有效性和优越性.     

A robust guidance and control scheme of an autonomous scale helicopter in presence of wind gusts

This article deals with the problem of robust trajectory tracking for a scale model autonomous helicopter. A large class of uncertainties/disturbance is addressed, namely uncertain parameters and uniform time-varying tridimensional wind gusts occurring in the vicinity of the aircraft. Using an unknown input observer technique, it is shown that disturbances/uncertainties effects on the autonomous helicopter can be accurately reconstructed online. The analysis further extends to the design of a control law whose methodology takes the disturbance estimation procedure into account. Regarding passivity feature of the resulting model, a control law was designed using robust backstepping techniques. The approach proposed here significantly improves the performance of the control and the flight security by counteracting wind gusts in any flight phases. The framework proposed is applied to a non-linear six degree-of-freedom helicopter model. Consequently, a non-linear dynamic model of miniature helicopter is proposed, which focuses on the key effects in the dynamics of a miniature helicopter. Lyapunov stability analysis is then performed to keep the balance between robustness, short response time and large stability domain with a given security margin to guarantee obstacle avoidance during the tracking trajectory process. Simulations results are presented at the end of the article.     

Linearized min‐max robust model predictive control: Application to the control of a bioprocess

This work deals with the problem of trajectory tracking for a nonlinear system with unknown but bounded model parameter uncertainties. First, this work focuses on the design of a robust nonlinear model predictive control (RNMPC) law subject to model parameter uncertainties implying solving a min‐max optimization problem. Secondly, a new approach is proposed, consisting in relating the min‐max problem to a more tractable optimization problem based on the use of linearization techniques to ensure a good trade‐off between tracking accuracy and computation time. The developed strategy is applied in simulation to a simplified macroscopic continuous photobioreactor model and is compared to the RNMPC and nonlinear model predictive controllers. Its efficiency and its robustness against parameter uncertainties and/or perturbations are illustrated through numerical results.     

Robust Tracking Control of Helicopters Using Backstepping with Disturbance Observers

This paper addresses the robust and accurate trajectory tracking problem for unmanned helicopters in the presence of model uncertainties and external disturbances. First, the helicopter's model is simplified to a six‐degrees‐of‐freedom rigid body augmented with a simplified rotor dynamic model, with the model uncertainties and the external disturbances being treated as lumped unknown disturbances. Second, a nonlinear disturbance observer is designed to estimate this lumped disturbance. Then, a backstepping controller with disturbance compensation is designed to ensure robust and highly trajectory tracking. After that, the theoretical analysis of the efficiency of the designed disturbance observer‐based backstepping controller (Backstepping+DO) is shown by the Lyapunov theory. Finally, simulation results and conclusions are presented and discussed.     

Nonlinear output‐feedback control of torsional vibrations in drilling systems

This paper considers the design of a nonlinear observer‐based output‐feedback controller for oil‐field drill‐string systems aiming to eliminate (torsional) stick–slip oscillations. Such vibrations decrease the performance and reliability of drilling systems and can ultimately lead to system failure. Current industrial controllers regularly fail to eliminate stick–slip vibrations under increasingly challenging operating conditions caused by the tendency towards drilling deeper and inclined wells, where multiple vibrational modes play a role in the occurrence of stick–slip vibrations. As a basis for controller synthesis, a multi‐modal model of the torsional drill‐string dynamics for a real rig is employed, and a bit–rock interaction model with severe velocity‐weakening effect is used. The proposed model‐based controller design methodology consists of a state‐feedback controller and a (nonlinear) observer. Conditions, guaranteeing asymptotic stability of the desired equilibrium, corresponding to nominal drilling operation, are presented. The proposed control strategy has a significant advantage over existing vibration control systems as it can effectively cope with multiple modes of torsional vibration. Case study results using the proposed control strategy show that stick–slip oscillations can indeed be eliminated in realistic drilling scenarios in which industrial controllers fail to do so. Moreover, key robustness aspects of the control system involving the robustness against uncertainties in the bit–rock interaction and changing operational conditions are evidenced. Copyright © 2017 John Wiley & Sons, Ltd.     

Output feedback adaptive RISE control for uncertain nonlinear systems

In this article, committed to extending the robust integral of the sign of the error (RISE) feedback control to the working condition of output feedback, a novel output feedback controller with a continuously bounded control input which combines the adaptive control and integral robust feedback will be proposed for trajectory tracking of a family of nonlinear systems subject to modeling uncertainties. A novel adaptive state observer (ASO) with disturbance rejection performance is creatively constructed to derive real-time estimation of the unmeasured state signals. Moreover, a projection-type adaption law is integrated to handle parameter uncertainties and an integral robust term is employed to deal with external disturbances. It is shown that asymptotic estimation performance and meanwhile asymptotic tracking result can eventually be derived. Simulation validations are implemented to demonstrate the high tracking performance of the presented controller. Notably, the synthesized control algorithm can be readily extended to the Euler–Lagrange systems. Typically, it can be extended to practical electromechanical equipment such as three-dimensional vector forming robots to improve the real-time forming accuracy.