A performance oriented multi-loop constrained adaptive robust tracking control of one-degree-of-freedom mechanical systems: Theory and experiments

A performance oriented multi-loop approach to the adaptive robust tracking control of one-degree-of-freedom mechanical systems with input saturation, state constraints, parametric uncertainties and input disturbances is presented. The control system contains three loops. In the outer loop, constrained optimization algorithms are developed to generate a replanned trajectory on-line at a low sampling rate so that the converging speed of the overall system response to the desired target is maximized while not causing input saturation and the violation of state constraints. In the inner loop, a constrained adaptive robust control (ARC) law is synthesized and implemented at high sampling rate to achieve the required robust tracking performances with respect to the replanned trajectory even with various types of uncertainties and input saturation. In the middle loop, a set-membership identification (SMI) algorithm is implemented to obtain a tighter estimate of the upper bound of the inertia so that more aggressive replanned trajectory could be used to further improve the overall system response speed. Interaction of the three loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy. It is theoretically shown that the resulting closed-loop system can track feasible desired trajectories with a guaranteed converging time and steady-state tracking accuracy without violating the state constraints. Experiments have been carried out on a linear motor driven industrial positioning system to compare the proposed multi-loop constrained ARC algorithm with some of the traditional control algorithms. Comparative experimental results obtained confirm the superior performance of the proposed algorithm over existing ones.     

基于一阶不确定项估计律的机械臂鲁棒控制研究

针对多自由度机械臂控制系统的模型参数误差、关节摩擦力以及外部输入扰动等不确定项,设计了一类一阶误差估计律;结合基于机构动力学名义模型的输入输出反馈线性化控制算法,对六自由度刚性机械臂的时变轨迹跟踪控制进行了研究,理论上证明了设计的鲁棒控制器是全局渐进稳定的.仿真结果表明该控制策略对系统的各类不确定项具有很好的鲁棒性,能够实现高精度的轨迹跟踪控制.     

State Space Constrained Iterative Learning Control for Robotic Manipulators

Real‐life work operations of industrial robotic manipulators are performed within a constrained state space. Such operations most often require accurate planning and tracking a desired trajectory, where all the characteristics of the dynamic model are taken into consideration. This paper presents a general method and an efficient computational procedure for path planning with respect to state space constraints. Given a dynamic model of a robotic manipulator, the proposed solution takes into consideration the influence of all imprecisely measured model parameters, making use of iterative learning control (ILC). A major advantage of this solution is that it resolves the well‐known problem of interrupting the learning procedure due to a high transient tracking error or when the desired trajectory is planned closely to the state space boundaries. The numerical procedure elaborated here computes the robot arm motion to accurately track a desired trajectory in a constrained state space taking into consideration all the dynamic characteristics that influence the motion. Simulation results with a typical industrial robot arm demonstrate the robustness of the numerical procedure. In particular, the results extend the applicability of ILC in robot motion control and provide a means for improving the overall trajectory tracking performance of most robotic systems.     

Adaptive NN state error PCH trajectory tracking control for unmanned surface vessel with uncertainties and input saturation

A novel robust state error port controlled Hamiltonian (PCH) trajectory tracking controller of an unmanned surface vessel (USV) subject to time-varying disturbances, dynamic uncertainties and control input saturation is presented. The proposed control scheme combines the advantages of the high robustness and energy minimization of the state error PCH approach and the approximation capability of adaptive radial basis function neural networks (RBFNNs). Adaptive RBFNNs are used to the time-varying disturbances of the environment and unknown dynamics uncertainties of the USV model. The state error PCH control approach is designed such that the system can optimize energy consumption, and the state error PCH technique makes the designed trajectory tracking controller be easy to implement in practice. To handle the effect of the control input saturation, a Gaussian error function model is employed. It has been demonstrated that the proposed approach can maintain the USV's trajectory at the desired trajectory, while the closed-loop control system can guarantee the uniformly ultimate boundedness. The energy consumption model of the USV is constructed to reveal to the energy consumption. Simulation results demonstrate the effectiveness of the proposed controller.     

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.     

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

This paper aims at investigating the tracking control problem for a class of multi‐input multi‐output (MIMO) nonlinear systems with non‐square control gain matrix subject to unknown control direction and uncertain desired trajectory. By using the artificial neural network (NN) reconstructs the target trajectory with actual disguised trajectory, we are able to design a practical and stable tracking control scheme without the need for the unavailable desired trajectory. Nussbaum‐type function is incorporated in the control law to handle the unknown control direction. The remarkable feature of the proposed scheme is that it is robust against modeling uncertainties and tolerant to actuation faults, yet guarantees that the closed‐loop system is stable in the sense of ultimately uniformly bounded (UUB). The effectiveness of the proposed control schemes are illustrated through simulation results.     

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。     

Robust constrained predictive control using comparison model

This paper proposes a quadratic programming (QP) approach to robust model predictive control (MPC) for constrained linear systems having both model uncertainties and bounded disturbances. To this end, we construct an additional comparison model for worst-case analysis based on a robust control Lyapunov function (RCLF) for the unconstrained system (not necessarily an RCLF in the presence of constraints). This comparison model enables us to transform the given robust MPC problem into a nominal one without uncertain terms. Based on a terminal constraint obtained from the comparison model, we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints. Since this terminal condition is described by linear constraints, the control optimization can be reduced to a QP problem.     

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

A robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.     

Event‐triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach

This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example.     

一类不确定系统的自适应滑模迭代学习控制

本文针对一类在有限时间内执行重复任务的不确定非线性系统状态跟踪问题,提出一种自适应滑模迭代学习控制方法,在存在初始偏移的情况下也能实现对参考轨迹的完全收敛.本文通过设计全饱和自适应迭代学习更新律,估计参数和非参数不确定性以及未知期望控制输入,并将估计值限制在指定界内,避免估计值的正向累加.文章设计的自适应滑模迭代学习控制方法对系统模型的信息需求少,在对系统非参数不确定性的上界估计时不需要Lipschitz界函数已知.本文给出严格的理论分析,证明闭环系统所有信号的一致有界性以及跟踪误差的一致收敛性,并通过仿真验证所提控制方法的有效性.     

Robust Adaptive Fuzzy Control of Nonlinear Systems with Unknown and Time‐Varying Saturation

In this paper, a robust adaptive fuzzy control approach is proposed for a class of nonlinear systems in strict‐feedback form with the unknown time‐varying saturation input. To deal with the time‐varying saturation problem, a novel controller separation approach is proposed in the literature to separate the desired control signal from the practical constrained control input. Furthermore, an optimized adaptation method is applied to the dynamic surface control design to reduce the number of adaptive parameters. By utilizing the Lyapunov synthesis, the fuzzy logic system technique and the Nussbaum function technique, an adaptive fuzzy control algorithm is constructed to guarantee that all the signals in the closed‐loop control system remain semiglobally uniformly ultimately bounded, and the tracking error is driven to an adjustable neighborhood of the origin. Finally, some numerical examples are provided to validate the effectiveness of the proposed control scheme in the literature.     

Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems

In this work, we present a novel adaptive fault tolerant control (FTC) scheme for a class of control input and system state constrained multi‐input multi‐output (MIMO) nonlinear systems with both multiplicative and additive actuator faults. The input constraints can be asymmetric, and the state constraints can be time‐varying. A novel tan‐type time‐varying Barrier Lyapunov Function (BLF) is proposed to deal with the state constraints, and an auxiliary system is designed to analyze the effect of the input constraints. We show that under the proposed adaptive FTC scheme, exponential convergence of the output tracking error into a small neighbourhood of zero is guaranteed, while the constraints on the system state will not be violated during operation. Estimation errors for actuator faults are bounded in the closed loop. An illustrative example on a two degree‐of‐freedom robotic manipulator is presented to demonstrate the effectiveness of the proposed FTC scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Constrained dynamical systems,robust model reference adaptive control,and unreliable reference signals

ABSTRACT

In this paper, we address the robust control design problem for nonlinear dynamical systems tracking unreliable reference signals. Specifically, we present robust model reference adaptive control laws that guarantee uniform ultimate boundedness of the trajectory tracking error for nonlinear plants that are affected by matched, unmatched, and parametric uncertainties, and are subject to constraints on the state space and the measured output. These control laws guarantee satisfactory results even in case the reference trajectory or the reference output signal do not verify the given constraints and hence, may draw the plant's trajectory or measured output outside their constraint sets. A numerical example involving the attitude control of a spacecraft illustrates the feasibility of the theoretical results presented.     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

Robust output‐based controller design for enlarging the region of attraction of input saturated linear systems

The aim of this study was to design a constrained robust output feedback control strategy for stabilizing linear systems affected by uncertainties and output perturbations. The input is constrained by a saturation function. A classical Luenberger observer reconstructed the states from output observations. The state feedback control employed the estimated states given by the observer. This work proposed a Barrier Lyapunov Function (BLF) to manage the saturation problem in the control input. Moreover, an extended version of the attractive ellipsoid method (AEM) characterized the zone of convergence due the presence of perturbations in the output. A convex optimization procedure, formulated as a set of matrix inequalities, yielded the control parameters and the region of attraction for the close‐loop system as well as a minimal ultimately bounded set for the system trajectories. Numerical simulations supported the theoretical results formulated in this study.     

Robust fuzzy tracking control for robotic manipulators

In this paper, a stable adaptive fuzzy-based tracking control is developed for robot systems with parameter uncertainties and external disturbance. First, a fuzzy logic system is introduced to approximate the unknown robotic dynamics by using adaptive algorithm. Next, the effect of system uncertainties and external disturbance is removed by employing an integral sliding mode control algorithm. Consequently, a hybrid fuzzy adaptive robust controller is developed such that the resulting closed-loop robot system is stable and the trajectory tracking performance is guaranteed. The proposed controller is appropriate for the robust tracking of robotic systems with system uncertainties. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator.     

A Robust Tracking Controller for Electrically Driven Robot Manipulators: Stability Analysis and Experiment

 In this paper, a robust controller for electrically driven robotic systems is developed. The controller is designed in a backstepping manner. The main features of the controller are: 1) Control strategy is developed at the voltage level and can deal with both mechanical and electrical uncertainties. 2) The proposed control law removes the restriction of previous robust methods on the upper bound of system uncertainties. 3) It also benefits from global asymptotic stability in the Lyapunov sense. It is worth to mention that the proposed controller can be utilized for constrained and nonconstrained robotic systems. The effectiveness of the proposed controller is verified by simulations for a two link robot manipulator and a four-bar linkage. In addition to simulation results, experimental results on a two link serial manipulator are included to demonstrate the performance of the proposed controller in tracking a given trajectory.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

A robust constrained reference governor approach using linear matrix inequalities

The purpose of this paper is to examine and provide a solution to the output reference tracking problem for uncertain systems subject to input saturation. As well-known, input saturation and modelling errors are very common problems at industry, where control schemes are implemented without accounting for such problems. In many cases, it is sometimes difficult to modify the existing implemented control schemes being necessary to provide them with external supervisory control approaches in order to tackle problems with constraints and modelling errors. In this way, a cascade structure is proposed, combining an inner loop containing any proper controller with an outer loop where a generalized predictive controller (GPC) provides adequate references for the inner loop considering input saturations and uncertainties. Therefore, the contribution of this paper consists in providing a state space representation for the inner loop and using linear matrix inequalities (LMI) to obtain a predictive state-vector feedback in such a way that the input reference for the inner loop is calculated to satisfy robust tracking specifications considering input saturations. Hence, the final proposed solution consists in solving a regulation problem to a fixed reference value subjected to a set of constraints described by several LMI and bilinear matrix inequalities (BMI). The main contribution of the paper is that the proposed solution is a non-linear setpoint tracking approach, that is, it is allowed that the system goes into saturation facing the problem of setpoint tracking instead of regulating to the origin. An illustrative numerical example is presented.