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 control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design 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 controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Disturbance observer-based tracking control with prescribed performance specifications for a class of nonlinear systems subject to mismatched disturbances

This work investigates simultaneous prescribed performance tracking control and mismatched disturbance rejection problems for a class of strict-feedback nonlinear systems. A novel control scheme combining prescribed performance control, disturbance observer technique, and backstepping method is proposed. The disturbance estimations are introduced into the design of virtual control law design in each step to compensate the mismatched disturbances. To further improve the control performance, a prescribed performance function characterizing the error convergence rate, maximum overshoot, and steady-state error is used to construct the composite controller. The proposed controller guarantees transient and steady-state performance specifications of tracking error and provides much better disturbance attenuation ability simultaneously. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that all the states in the resulting closed-loop system are stable, and the tracking error evolves within the prescribed performance boundaries and asymptotically converges to zero even in the presence of mismatched external disturbances. Finally, theoretical results are illustrated and demonstrated by two simulation examples.     

基于有限时间指令滤波的非线性系统固定时间预设性能控制

针对一类严格反馈非线性系统,提出一种基于有限时间指令滤波的自适应固定时间预设性能控制策略.首先,引用非线性映射技术及适当的误差变换,建立等效的误差模型;其次,综合利用反步法、固定时间控制和自适应控制等方法,设计一种基于有限时间指令滤波的预设性能跟踪控制器.该策略应用指令滤波器解决了反步法中对虚拟控制律反复求导问题,减轻了计算负担.此外,预设性能控制和固定时间控制保证了系统的跟踪误差能够在固定时间内收敛到预设性能函数限定的范围内,其收敛时间与系统初始条件无关,且确保系统中全部信号在有限时间均达到有界区域.理论分析与仿真验证均表明了所提出设计方法的有效性.     

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.     

Robust estimation‐free decentralized prescribed performance control of nonaffine nonlinear large‐scale systems

In this paper, a low‐complexity robust estimation‐free decentralized prescribed performance control scheme is proposed and analyzed for nonaffine nonlinear large‐scale systems in the presence of unknown nonlinearity and external disturbance. To tackle the high‐order dynamics of each tracking error subsystem, a time‐varying stable manifold involving the output tracking error and its high‐order derivatives is constructed, which is strictly evolved within the envelope of user‐specialized prescribed performance. Sequentially, a robust decentralized controller is devised for each manifold, under which the output tracking error and its high‐order derivatives are proven to converge asymptotically to a small residual domain with prescribed fast convergence rate. Additionally, no specialized approximation technique, adaptive scheme, and disturbance observer are needed, which alleviates the complexity and difficulty of robust decentralized controller design dramatically. Finally, 3 groups of illustrative examples are used to validate the effectiveness of the proposed low‐complexity robust decentralized control scheme for uncertain nonaffine nonlinear large‐scale systems.     

Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique

In this study, a quasi-finite-time control method for designing stabilising control laws is developed for high-order strict-feedback nonlinear systems with mismatched disturbances. By using mapping filtered forwarding technique, a virtual control is designed to force the off-the-manifold coordinate to converge to zero in quasi-finite time at each step of the design; at the same time, the manifold is rendered insensitive to time-varying, bounded and unknown disturbances. In terms of standard forwarding methodology, the algorithm proposed here not only does not require the Lyapunov function for controller design, but also avoids to calculate the derivative of sign function. As far as the dynamic performance of closed-loop systems is concerned, we essentially obtain the finite-time performances, which is typically reflected in the following aspects: fast and accurate responses, high tracking precision, and robust disturbance rejection. Spring, mass, and damper system and flexible joints robot are tested to demonstrate the proposed controller performance.     

未知初始跟踪条件的非线性系统预设性能有限时间有界$H_infty$控制

研究一类具有外部扰动的非线性系统在初始跟踪条件未知情况下的预设性能有限时间有界$H_\infty$控制问题.针对预设性能控制设计,提出一个新的误差转换思想,并据此设计新的预设性能函数,解决预设性能控制依赖于系统被约束量初始条件的问题.基于所提出预设性能函数、有限时间控制理论以及有界$H_\infty$的设计方法,获得系统无需初始跟踪条件的预设性能有限时间有界$H_\infty$控制器,同时解决非线性系统在有界稳定情况下难以设计$H_\infty$控制器的问题,保证跟踪误差以预先设定的动态性能在有限时间内收敛至平衡点附近的小邻域内,并对外部干扰有较强的鲁棒性能.     

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.     

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.     

随机激励下板球系统建模与有限时间全状态预设性能跟踪控制

研究板球系统受到随机激励时的数学建模与轨迹跟踪控制问题. 首次建立了板球系统的随机数学模型, 并 结合backstepping方法、有限时间预设性能函数、全状态约束及新的预设性能推导方法设计了具有未知输入饱和的 随机板球系统实际有限时间全状态预设性能跟踪控制器, 实现了随机激励下板球系统的有限时间预设性能轨迹跟 踪控制. 所设计的控制器保证了系统跟踪误差能够被预先给定的有限时间性能函数约束, 并且能在任意给定的停息 时间内收敛到预先给定的邻域内. 最后通过仿真实验验证了所设计控制器具有更好的控制效果.     

一类p规范型非线性系统预设性能有限时间H∞ 跟踪控制

针对一类带有外部扰动的非严格反馈p规范型非线性系统, 在一种新的预设性能控制思想的基础上, 结合加幂积分技术、H_∞ 控制理论及神经自适应技术, 提出了一种自适应神经预设性能有限时间H_∞ 跟踪控制器的设计方法. 所设计的控制器能够保证系统的跟踪误差被有限时间性能函数约束, 并在任意给定的停息时间内收敛到平衡点的一个预先给定的邻域内, 且能够抑制外部扰动对系统的影响. 特别地, 该停息时间与系统初始状态无关. 两个仿真例子验证了所设计控制器的有效性和优越性.     

Barrier function based finite-time tracking control for a class of uncertain nonlinear systems with input saturation

In this article, a novel robust finite-time tracking control scheme is proposed for a class of uncertain nonlinear systems subject to the model uncertainty, external disturbance, and input saturation. A barrier function based disturbance observer (BFDO) with finite-time convergence performance is developed to estimate the non-smooth nonlinear compound disturbance, which includes the uncertainty, disturbance of system and input saturation. In addition, an adaptive continuous nonsingular terminal sliding mode controller, based on the barrier function and the estimate of the BFDO is developed. The Lyapunov stability and finite-time convergence of the proposed control scheme are proved. The effectiveness and performance advantage of the proposed control scheme is demonstrated by numerical simulations and comparison with existing works.     

Design of finite-time H∞ controller for uncertain nonlinear systems and its application

This paper studies the problem of finite-time H _∞ control for strict feedback nonlinear systems with external disturbance. The finite-time stability theory, H _∞ control method, backstepping technique, together with adding a power integrator tool are combined to design a finite-time H _∞ state feedback controller. The obtained controller can make the closed-loop system finite-time convergent, and the influence of the external disturbance is attenuated to a given degree. Two numerical examples are presented to show the effectiveness and feasibility of the proposed method. Meanwhile, the proposed method is also applied to robot manipulators.     

Improved prescribed performance control for nonlinear systems with unknown control direction and input dead-zone

In view of the input dead-zone, unknown control direction and difficulty in satisfying the prescribed performance that suffered in practical systems, an improved prescribed performance-based adaptive control scheme is stressed for uncertain nonlinear systems in this paper. Firstly, by adopting a characteristic function, the input dead-zone is linearized to a model with bounded perturbation. To settle the “computation complexity” issue, an adaptive controller is built via command filter design method, where the fuzzy logic systems are introduced to approximate the unknown nonlinearities. Meanwhile, the Nussbaum function is brought in controller design to counter the hardship of unknown control direction. Besides, the tracking error can be restricted in the prescribed boundary in finite time with the improved performance function. The presented control approach can not only ensure the finite-time convergence property of tracking error and the boundedness of all signals in the closed-loop system, but also easily implement in engineering. Finally, the simulation examples confirm the validity of the designed control scheme.     

基于预设性能的非仿射非线性系统自适应有限时间控制

针对一类具有死区的非仿射非线性系统,将预设性能控制与有限时间控制相结合,提出一种具有预设性能的自适应有限时间跟踪控制方法.基于Backstepping技术、模糊逻辑系统及有限时间Lyapunov稳定理论,给出使系统半全局实际有限时间稳定(semi-globally practically finite-time stable,SGPFS)的充分条件和设计步骤.该控制策略不仅使系统的输出误差在有限时间内收敛到一个预先设定区域,同时保证其收敛速度、最大超调量和稳态误差均满足预先设定的性能要求.最后通过仿真示例验证了所提出设计方法的有效性.     

基于有限时间预设性能的高超声速飞行器反演控制

针对存在参数不确定以及外界干扰的高超声速飞行器跟踪性能问题,提出一种基于有限时间预设性能的反演控制方案.首先,为便于控制器设计,将高超声速飞行器模型划分为速度和高度子系统,针对子系统分别设计预设性能控制器以提高系统的瞬态和稳态性能;然后,通过设计一种有限时间性能函数,使得跟踪误差能够在预设时间内收敛至稳态值;接着,考虑到反演设计中虚拟指令导数难以获取以及干扰项对系统的影响,基于干扰观测器提出一种扰动估计方法,目的是在取得良好的观测扰动效果的同时,使得控制器设计流程简化、复杂度降低;最后,基于Lyapunov稳定理论证明系统的跟踪误差最终一致有界,并通过仿真验证该方法的有效性.     

Finite time adaptive filter control of nonlinear systems with actuator faults and state constraints

The finite time adaptive filter control problem is studied for strict-feedback nonlinear systems with actuator faults and state constraints in this paper. First, with the aid of the backstepping technique, the controller and the adaptive laws are designed to compensate the actuator faults and parameter uncertainties. Then, the dynamic surface control is used to establish a first-order filter to alleviate computational burden for the reason of the derivative of virtual control laws. In addition, none of the system states violate predefined constraint boundaries by utilizing a log-type barrier Lyapunov function. Furthermore, the boundedness can be ensured for all the closed-loop signals, and better tracking performance of the system is obtained within a finite-time. Finally, the simulation examples are shown to prove the feasibility and effectiveness of the proposed strategy.     

永磁同步电机有限时间预设性能控制

为实现扰动作用下对永磁同步电机角位置伺服系统的高瞬态和稳态跟踪性能控制,本文提出一种具有预设性能约束的有限时间控制方法.首先,设计扰动观测器实现对负载力矩扰动的估计与补偿.其次,引入有限时间预设性能函数以保证角跟踪误差的动态性能,并通过可逆变换将受不等式约束的角位置跟踪误差转换为等效的无约束误差形式.然后,将有限时间指...     

输入饱和下的非线性积分系统的全局有限时间镇定

针对一类非线性积分系统, 利用有限时间控制技术, 提出了一种输入饱和情况下的全局有限时间控制方案. 首先, 基于有限时间 Lyapunov 稳定性理论, 设计镇定系统的全局有限时间递归控制器. 然后,将该递归控制器与饱和函数结合得到饱和控制器. 数学上严格证明了在该饱和控制器的作用下, 闭环系统满足全局有限时间稳定性. 仿真结果验证了该方法的有效性.