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.     

Tracking control of electro-hydraulic servo multi-closed-chain mechanisms with the use of an approximate nonlinear internal model

This paper studied the trajectory-tracking problem of a hydraulic servo multi-closed-chain mechanism. The nonaffine nonlinear characteristic of the electro-hydraulic actuator and its time-varying uncertainty load resulting from the multi-closed-chain mechanism was taken into consideration in the proposed novel nonlinear control algorithm, that is, the approximate internal model control (AIMC) integrated with a position feedback control in cascade control design. This algorithm improves the trajectory-tracking performance of the hydraulic servomechanism (HSM). To reduce the difficulty in directly utilizing the AIMC for the HSM position trajectory, the complex electro-hydraulic mechanical system was divided into two subsystems: nonaffine nonlinear, and linear. The AIMC controller was designed for the nonaffine nonlinear subsystem to realize velocity trajectory tracking control, whereas a position feedback control was derived for the linear subsystem. The position trajectory tracking control was achieved by congruently combining the AIMC, and the position feedback control based on a recursive design idea. In addition, a complete state-space mathematical model for the HSM was developed and illustrated through simulations and experiments. Based on the proposed approach and the AIMC, the desired position and velocity trajectory tracking was examined on a hydraulic forging manipulator. The stability of the proposed method was analytically derived. Results of the simulations and experiments performed with the hydraulic manipulator demonstrated the effectiveness of the proposed approach.     

基于领导跟随的欠驱动船舶编队跟踪控制

针对具有三自由度欠驱动水面船舶编队控制问题,提出一种基于领导跟随 ( Leader /Follower) 结构的欠驱动水面船舶队形跟踪控制方法。当系统接收到队形控制指令, 每个欠驱动水面船舶按照自己在编队中的角色进行控制,其中Leader 根据任务中的队形指令 完成航迹跟踪控制,而Followers 则依据Leader 的信息和航行中任务中的队形指令完成航迹跟 踪控制。在航迹跟踪控制中,根据期望队形任务指令为每个船舶设计需要跟踪的参考路径和 速度指令; 基于Lyapunov 理论和重定义输出方法设计非线性速度控制器和路径跟踪控制器跟 踪设计路径和速度指令; 稳定性分析证明了队形跟踪误差是一致最终稳定的。仿真结果表明 船舶可以跟踪任意期望曲线队形,从而验证了方法的有效性。     

Feedforward digital tracking controllers for motion control applications

This paper reviews digital tracking control algorithms for motion control applications. In tracking control, the control objective is to steer the control object along the time-varying desired output. Two design approaches are presented for the case where the desired signal is known in advance, i.e. previewable. One approach is based on the mathematical inverse of a closed-loop system consisting of a controlled plant and a feedback controller. If the mathematical inverse is asymptotically stable, i.e. the closed-loop system does not possess zeros outside the unit circle (unstable zeros), it is an ideal feedforward controller for achieving perfect tracking under the preview assumption. For closed-loop systems with unstable zeros, a cancellation technique for the phase shift induced by unstable zeros is introduced. Another approach is based on linear quadratic optimal control and is known as finite optimal preview control. In this approach, the feedback controller and feedforward controller are determined simultaneously by minimizing a quadratic performance index which involves a tracking error term and a term related to the control effort. Applications of these tracking control algorithms to mechanical systems control are described.     

Predictor‐based repetitive learning control for a class of remote control nonlinear systems

In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. The proposed approach is to deal with the remote tracking control problem when the environment is periodic or repeatable over infinite time domain. Since there exist time delays in the two transmission channels: from the controller to the actuator and from the sensor to the controller, tracking a desired trajectory through a remote controller is not an easy task. In order to solve the problem caused by time delays, a predictor is designed on the controller side to predict the future state of the nonlinear system based on the delayed measurements from the sensor. The convergence of the estimation error of the predictor is ensured. The gain design of the predictor applies linear matrix inequality (LMI) techniques developed by Lyapunov Kravoskii method for time delay systems. The RLC law is constructed based on the feedback error from the predicted state. The overall tracking error tends to zero asymptotically over iterations. The proof of the stability is based on a constructed Lyapunov function related to the Lyapunov Kravoskii functional used for the proof of the predictor's convergence. By well incorporating the predictor and the RLC controller, the system state tracks the desired trajectory independent of the influence of time delays. A numerical simulation example is shown to verify the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Model-based iterative learning control strategies for precise trajectory tracking in gasoline engines

In this paper trajectory tracking algorithms for gasoline engines are devised. Specifically, precise reference tracking in engine speed and air-to-fuel ratio is enabled while satisfying initial and final conditions on the center of combustion. Such a tracking of multiple reference trajectories requires a coordinated control action for the air path, the fuel path, and the ignition timing actuators. Combining a dedicated feedforward and feedback controller structure and multivariable model-based norm-optimal parallel iterative learning control strategies, feedforward control trajectories are generated that enable a precise tracking of desired reference trajectories. Experimental results focusing on the termination of the catalyst heating mode show the effectiveness of the proposed methodology, resulting in a control error reduction above 85%.     

A sequential LQG approach to nonlinear tracking problem

A new approach, named the sequential LQG solution for nonlinear and nonstationary systems tracking problem, has been proposed in the article. Proposed method for tracking of a desired reference trajectory uses a state space model of the multivariable nonlinear/nonstationary system. The method involves three steps. The first step is the design of nominal trajectory using the predictive control technique. The second step is the sequential linearization of the nonlinear system around the fixed operating points, chosen in accordance to the plant dynamics changes. The third step involves the choice of the weighting matrices in the classical LQG controller design for the sequence of linearized models. The feasibility of the proposed method has been demonstrated through its application to the control of aircraft, represented by the six-degree-of-freedom model around the prespecified nominal trajectory.     

Output tracking control of switched nonlinear systems with multiple time-varying delays

In this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique.     

一种新型的移动机器人轨迹跟踪控制方法

主要是对非完整约束下移动机器人的轨迹跟踪控制进行了研究,提出了一种新型的基于移动机器人运动模型、具有全局渐近稳定性的跟踪控制方法。这种非线性控制方法主要分为前馈和反馈两个部分：前馈部分是一种滑模控制器,它是基于反演设计的思想设计了切换函数,采用指数趋近律,减少了滑模变结构控制的抖动,并使用Lyapunov第一法对控制系统进行了稳定性分析,证明了滑模跟踪控制器是稳定的;反馈部分是基于Lyapunov函数的方法设计的反馈控制器。通过前馈部分和反馈部分的相互作用,提高了移动机器人轨迹跟踪控制的精度。实验结果表明与一般的跟踪控制方法相比,控制效果明显改善,跟踪误差能在较短时间内收敛,具有很好的抗干扰性能。     

Swing-up of the double pendulum on a cart by feedforward and feedback control with experimental validation

The swing-up maneuver of the double pendulum on a cart serves to demonstrate a new approach of inversion-based feedforward control design introduced recently. The concept treats the transition task as a nonlinear two-point boundary value problem of the internal dynamics by providing free parameters in the desired output trajectory for the cart position. A feedback control is designed with linear methods to stabilize the swing-up maneuver. The emphasis of the paper is on the experimental realization of the double pendulum swing-up, which reveals the accuracy of the feedforward/feedback control scheme.     

Decentralized adaptive control of robot manipulators

A decentralized adaptive control scheme is proposed for the trajectory tracking of a general n-degree-of-freedom robot manipulator. The robot is considered as a set of decoupled second-order systems with disturbances. The controller consists of feedforward from the desired trajectory based on the “inverse system” of the model, PID feedback from the actual trajectory, and auxiliary input for the compensation of the neglected terms in modeling in each subsystem. The gain is derived in diagonal matrix form, and is adjusted by the model reference adaptive control theory based on the Lyapunov's direct method. The result is high accuracy in path tracking despite the high speed, load change, and sudden torque disturbances. Numerical simulations on.a planar two-link robot manipulator are presented to show the performance under various practical considerations.     

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

A New Nonlinear Controller for Trajectory Tracking of the Longitudinal Dynamics of a Small Scale Helicopter

A nonlinear control scheme is proposed for the trajectory tracking problem of a small scale helicopter’s longitudinal dynamics. The control scheme is based on a control design procedure that constructs static feedback regulators for nonlinear systems which are linearizable by dynamic feedback. Besides, the flatness characteristics of the helicopter’s longitudinal dynamics are used to design the desired trajectory. The controller proposed is based on the longitudinal model of the small scale helicopter including the main rotor and stabilizer bar dynamics. Sufficient conditions are given to guarantee asymptotic convergence to zero of the tracking error and to keep the main rotor thrust always negative assuming that all the helicopter’s parameters are known and that all helicopter’s states are measured. Numerical simulations are given to show the performance of the controller in the presence of the main rotor and stabilizer bar dynamics.     

Decoupling and tracking control for elastic joint robots with coupled joint structure

The paper deals with the modeling, identification, and control of a flexible joint robot developed for medical applications at the German Aerospace Center (DLR). In order to design anthropomorphic kinematics, the robot uses a coupled joint structure realized by a differential gearbox, which however leads to strong mechanical couplings inside the coupled joints and must be taken into account. Therefore, a regulation MIMO state feedback controller based on modal analysis is developed for each coupled joint pair, which consists of full state feedback (motor position, link side torque, as well as their derivatives). Furthermore, in order to improve position accuracy and simultaneously keep good dynamic behavior of the MIMO state feedback controller, a cascaded tracking control scheme is proposed, based on the MIMO state feedback controller with additional feedforward terms (desired motor velocity, desired motor acceleration, derivative of the desired torque), which are computed in a computed torque controller and take the whole rigid body dynamics into account. Stability analysis is shown for the complete controlled robot. Finally, experimental results with the DLR medical robot are presented to validate the practical efficiency of the approaches.     

基于误差系统的信息融合最优预见跟踪控制

针对期望轨迹和干扰可预见的最优跟踪问题, 提出了一种基于误差系统的信息融合最优控制方法. 将线性伺服系统转化为误差系统; 利用信息融合估计方法, 通过融合期望轨迹、干扰输入、误差系统状态等信息, 获得误差系统协状态以及控制增量的最优估计. 构建了由积分项、状态反馈控制项和预见前馈补偿项组成的最优预见控制系统. 线性直流电机系统的控制仿真结果表明, 信息融合最优预见控制下的位置跟踪精度比传统最优预见控制下的要高.     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

非完整移动机器人道路跟踪控制器设计及应用

讨论一类非完整约束条件下的移动机器人道路跟踪控制问题，综合后推方法与模糊滑模控制方法设计非完整移动机器人的状态反馈控制系统，并根据Lyapunov稳定性定理后推设计时变光滑反馈控制律，当存在较大侧向误差时，模糊滑模控制器确保移动机器人沿稳定的工作区域减小误差；当误差比较小时，时变光滑状态反馈控制实现对移动机器人的平稳镇定，采用移动机器人Amigobot作为实验平台，验证了控制器设计的有效性。     

基于倒转方法的欠驱动 Acrobot 系统稳定控制

针对欠驱动两杆体操机器人Acrobot, 提出一种新的稳定控制方法.首先,通过利用一个虚拟摩擦力矩为Acrobot 构造一条下摆轨迹;然后,运用倒转的思想为它设计出一条由垂直向下位置到垂直向上位置的期望运动轨迹, 并以此将系统的稳定控制问题转化为跟踪控制问题;最后, 基于最优控制理论来设计跟踪控制器,使Acrobot 能够沿期望轨迹渐近稳定在垂直向上位置处. 仿真结果验证了所提方法的有效性.     

Global approximate output tracking for nonlinear systems

Addresses the global output tracking problem for nonlinear systems with singular points. For nonlinear systems which satisfy a suitable observability condition, the authors identify a class of smooth output trajectories which the system can track using continuous open-loop controls. This class includes all output trajectories generated by smooth state feedback. They then study the problem of approximate output tracking using discontinuous time-varying feedback controllers. Given a smooth output trajectory for which exact tracking is possible, the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations. Finally, it is shown that their results can be applied to the control of a chain system, and some numerical results are presented to illustrate the performance of their controller     

Sliding Mode Rest-to-Rest Stabilization and Trajectory Tracking for a Discretized Flexible Joint Manipulator

In this article, a difference flatness approach is used for trajectory tracking tasks of an approximately (Euler) discretized model of a nonlinear, single link, flexible joint manipulator. The system's flat output is commanded to follow a prescribed trajectory achieving a desired angular position maneuver. A new robust discrete time feedback controller design technique, of the sliding mode type, is then proposed for the closed loop regulation of the link position around the prescribed trajectory. The effectiveness of the approach is illustrated by means of digital computer simulations in a rest-to-rest stabilization maneuver and in a sinusoidal reference trajectory tracking task.