Disturbance observer-based fixed-time prescribed performance tracking control for robotic manipulator

ABSTRACT

This paper investigates the fixed-time prescribed performance tracking control for the n-DOF uncertain manipulator. First, a novel Barrier Lyapunov Function (BLF) is proposed to guarantee the prescribed performance for the manipulator tracking error. Then, we introduce a disturbance observer to estimate the system uncertainty and disturbance accurately in a predefined time. Next, a composite controller based on the nonsingular fast integral terminal sliding mode is constructed. It is strictly proved that the closed-loop system is stable in fixed-time, which is independent of the initial conditions. Moreover, both transient and steady-state performances of the outputs can be preserved. Finally, numerical simulations and experimental studies are presented to demonstrate the effectiveness of the proposed methods.     

Finite‐time tracking control for a class of nonlinear systems with multiple mismatched disturbances

This article investigates the finite‐time output tracking problem for a class of nonlinear systems with multiple mismatched disturbances. To efficiently estimate the disturbances and their derivatives, a continuous finite‐time disturbance observer (CFTDO) design method is developed. Based on the modified adding a power integrator method and CFTDO technique, a composite tracking controller is constructed such that the system output can track the desired reference signal in finite time. Simulation results demonstrate the effectiveness of the proposed control approach.     

Reduced-order observer-based output feedback control of nonlinear time-delay systems with prescribed performance

This paper studies the problem of output feedback control for a class of nonlinear time-delay systems with prescribed performance. The system is in the form of triangular structure with unmodelled dynamics. First, we introduce a reduced-order observer to provide the estimate of the unmeasured states. Then, by setting a new condition with the performance function, we design the state transformation with prescribed performance control. By employing backstepping method, we construct the output feedback controller. It is proved that the resulting closed-loop system is asymptotically stable and both transient and steady-state performance of the output are preserved with the changing supply function idea. Finally, a simulation example is conducted to show the effectiveness of the main results.     

Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers

The distributed consensus output tracking problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances and uncertain nonlinear virtual control coefficients of the subsystems. The systems are under a directed communication graph, where the leader node is the root. The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid direct differentiation. At each step of virtual controller design, a prescribed performance controller is constructed to achieve prescribed transient performance so that the system states remain in the feasible domain. Then each virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the control system are analysed theoretically. It is clarified that the prescribed performance control technique ensures that the system signals stay in the feasible domain, whereas sufficiently small ultimate control errors can be achieved by the finite-time disturbance observers. Finally, the performance of the proposed methods is confirmed by numerical studies.     

Command filter-based finite-time adaptive tracking control for MIMO dynamic systems with external disturbances and prescribed performance constraints

This paper investigates command filter-based finite-time stability of multi-input multi-output (MIMO) dynamic systems with prescribed performance constraints and external disturbances. A novel finite-time differentiator is introduced into command filter-based control scheme, which improves transient performance of each subsystem. Meanwhile, disturbance observers are utilized to eliminate negative effects on control system caused by external disturbances. Furthermore, featured with a selected performance function, it can be guaranteed that tracking errors remain in prescribed performance region. Stability analysis of the proposed controller is presented by using a Lyapunov function including transformed filter errors, parameter errors of neural networks, and observed errors of lumped disturbances. Effectiveness of proposed control method is verified by a numerical example and a practical system of inverted pendulums, respectively.     

Global output regulation for strict‐feedback nonlinear systems with mismatched nonvanishing disturbances

This paper concerns the problem of global output regulation for a class of strict‐feedback nonlinear systems subject to mismatched nonvanishing disturbances. A composite control scheme is developed using a nonlinear disturbance observer‐based control approach. A novel idea is that the disturbance estimation is introduced into the design of virtual control laws in each step. Global stability analysis for the closed‐loop system is presented by the direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in the presence of mismatched nonvanishing disturbances without the requirement of solving any partial differential equations involved with the traditional output regulation theory. An application design example of a single‐machine infinite‐bus system with static var compensator is presented with simulation results to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

一类输出受限非线性系统的降维非递归预设性能控制策略

针对一类非匹配受扰非线性系统在输出受限条件下的跟踪控制问题, 本文在预设性能控制过程中引入非递归设计框架, 提出了一种降维非递归预设性能控制方案, 以缓解常用的递归预设性能控制过程中出现的复杂性爆炸问题, 大幅简化了系统的控制器设计过程, 便于实际工程应用. 本文设计的降维非递归控制策略能够实现控制器设计过程与稳定性分析的分离, 并且具有控制器形式简洁、控制参数选取机制简单的优点. 最后, 选取具有代表性的数值仿真和永磁同步电机位置跟踪控制实验阐释了所提出的控制策略的有效性及简洁性.     

一类不确定非线性系统的预定性能自适应控制

本文研究了一类不确定严格反馈非线性系统的预定性能控制问题.为保证系统预定性能,引入了一个简单的障碍型Lyapunov函数.结合反推设计法,给出了一种新的自适应控制算法.理论与实验结果表明,所得控制器不仅保证了系统预定性能,且使得闭环系统所有信号有界.     

非匹配扰动干扰下的无人直升机轨迹跟踪控制

针对小型无人直升机在飞行过程中容易受到非匹配扰动影响的特点,本文设计了一种基于新型滑模控制方法的轨迹跟踪控制器.首先,建立了无人直升机系统的非线性数学模型,并对该模型进行近似反馈线性化处理,同时将模型分为位置和偏航两个子系统;然后,利用扩展扰动观测器对复合扰动以及非匹配扰动的各阶导数的估计值,设计新型时变滑模面,得到滑模控制律,并给出了控制系统的稳定性分析;最后,仿真结果验证了控制方法的有效性和优越性.该新型滑模控制方法的优越性主要体现在:对非匹配扰动具有较强的鲁棒性,以及能有效地抑制抖振现象.     

基于观测器的受扰非线性系统近似最优跟踪控制

研究一类受扰非线性系统的最优输出跟踪控制问题.给出了有限时域最优输出跟踪控制律的近似设计算法.首先将求解受扰非线性系统最优跟踪控制问题转换为求解状态向量与伴随向量耦合的非线性两点边值问题,然后利用逐次逼近方法构造序列将其转化为求解两个解耦的线性微分方程序列问题.通过迭代求解伴随向量的序列,可得到由解析的线性前馈-反馈控制部分和伴随向量的极限形式的非线性补偿部分组成的最优输出跟踪控制律.利用参考输入降维观测器和扰动降维观测器,解决了前馈控制的物理可实现问题.最后仿真结果表明了该方法的有效性.     

Novel disturbance-observer-based control for systems with high-order mismatched disturbances

A novel disturbance-observer-based control method is investigated to attenuate the high-order mismatched disturbances. First, a finite-time disturbance observer (FTDO) is proposed to estimate the disturbances as well as the derivatives. By incorporating the outputs of FTDO, the original system is then reconstructed, where the mismatched disturbances are transformed to the matched ones that are compensated by feed-forward algorithm. Moreover, a feedback control law is developed to achieve the stability and tracking performance requirements for the systems. Finally, the proposed composite control method is applied to an unmanned helicopter system. The simulation results demonstrate that the proposed control method exhibits excellent control performance in the presence of high-order matched and mismatched disturbances.     

具有非匹配扰动的非线性变参数系统模型参考跟踪控制

本文研究了一类含有非匹配扰动的非线性变参数系统的跟踪控制问题.首先,设计非线性扰动观测器用于估计系统所受到的未知扰动.其次,在前馈–反馈跟踪控制器中引入扰动补偿控制项,提出一种基于扰动观测器的跟踪控制策略.利用依赖于状态和时变参数的线性矩阵不等式,导出保证闭环系统输入–状态稳定的充分条件,进而运用平方和凸优化技术解析地构造出扰动观测器和跟踪控制器.通过理论证明,所设计的控制策略能够实现非线性变参数系统输出对参考模型输出的跟踪,消除输出通道中非匹配扰动的影响.最后,由数值仿真例子验证了所提方法的有效性.     

Finite-time optimal tracking control for a class of nonlinear systems with prescribed performance

In this paper, a finite-time optimal tracking control scheme based on integral reinforcement learning is developed for partially unknown nonlinear systems. In order to realize the prescribed performance, the original system is transformed into an equivalent unconstrained system so as to a composite system is constructed. Subsequently, a modified nonlinear quadratic performance function containing the auxiliary tracking error is designed. Furthermore, the technique of experience replay is used to update the critic neural network, which eliminates the persistent of excitation condition in traditional optimal methods. By combining the prescribed performance control with the finite-time optimization control technique, the tracking error is driven to a desired performance in finite time. Consequently, it has been shown that all signals in the partially unknown nonlinear system are semiglobally practical finite-time stable by stability analysis. Finally, the provided comparative simulation results verify the effectiveness of the developed control scheme.     

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.     

Arbitrary settling time control with prescribed performance for high-order nonlinear systems

This paper studies an arbitrary convergence time tracking controller design problem for high-order nonlinear systems. Our aim is to enhance the existing free-will arbitrary time control (FATC), which cannot track time-varying reference signals. To do so, a new nonautonomous equation is firstly introduced to enable an arbitrary settling time stability for one-order systems. Then, a prescribed performance control (PPC) technology is integrated for general high order systems. By a backstepping Lyapunov analysis with iteratively contructed nonautonomous equations, it is proved that the closed-loop system satisfies the prescribed performance and all signals of the closed-loop system are arbitrary settling time stable (ASTS). Compared with the existing results, the tracking control problem with arbitrary convergence time is addressed by a continuous control law, which shows a better transient performance also. Simulation results confirm the effectiveness of the proposed control method.     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

Generalized extended state observer–based repetitive control for systems with mismatched disturbances

A generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive‐control system (RCS) for a class of single‐input, single‐output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO‐based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO‐based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance.     

含有非匹配干扰和未知动态的非仿射系统滑模控制算法

针对含有非匹配干扰和未知动态的非仿射系统控制问题,提出了一种基于扩张状态观测器(ESO)的改进滑模控制(SMC)方案.本文首先利用扩张状态观测器,将原系统转变为一个包含干扰的二阶积分级联系统,使含有未知动态的非仿射系统控制器设计问题转化为二阶积分级联系统的控制器设计问题,从而使得控制器在设计过程中不需要对对象模型完全已...     

Composite adaptive anti-disturbance control for MIMO nonlinearly parameterized systems with mismatched general periodic disturbances

In this paper, the problem of anti-disturbance control for a class of multi-input and multi-output (MIMO) nonlinearly parameterized systems with mismatched general periodic disturbances is investigated via a composite adaptive anti-disturbance control scheme. The composite adaptive anti-disturbance control method is presented by using disturbance observer technique, back-stepping method and adaptive control approach. A novel disturbance observer is designed to estimate the disturbances generated by a linear system with nonlinear output function. Rigorous stability analysis for the augmented closed-loop system is developed by direct Lyapunov stability theory. It is shown that the system outputs asymptotically converge to zero in the presence of mismatched general periodic disturbances. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.     

Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems under arbitrary switchings

This paper presents an adaptive neural tracking control scheme for strict-feedback stochastic nonlinear systems with guaranteed transient and steady-state performance under arbitrary switchings. First, by utilising the prescribed performance control, the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, radial basis function neural networks approximation are used to handle unknown nonlinear functions and stochastic disturbances. At last, by using the common Lyapunov function method and the backstepping technique, a common adaptive neural controller is constructed. The designed controller overcomes the problem of the over-parameterisation, and further alleviates the computational burden. Under the proposed common adaptive controller, all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded, and the prescribed tracking control performance are guaranteed under arbitrary switchings. Three examples are presented to further illustrate the effectiveness of the proposed approach.