A New Robust Adaptive Control of Uncertain Nonlinear Systems and Pendulum Application

A new robust adaptive control of uncertain nonlinear systems is proposed in this paper. The proposed method combines sliding mode control with the immersion and invariance (I&I) adaptive scheme, and it has more available degrees of freedom than using the backstepping scheme. Via the proposed method, a class of nonlinear systems with mismatched parametric perturbations can be rendered asymptotically stable and the performance of the system can also be improved. Finally, the proposed method is applied to a simple pendulum with motor dynamics, and simulation results show the effectiveness and performance of the proposed method.     

Guaranteeing performance for uncertain nonlinear systems with bounded state constraint and mismatching condition

The control design problem for the uncertain nonlinear system with bounded state constraint and mismatching condition is considered in this paper. The uncertainty in the system, which may be due to unknown system parameters and external disturbance, is nonlinear and time‐varying. The state of the system is constrained to be bounded. The system does not satisfy the (global) matching condition. A creative one‐to‐one state transformation is proposed by converting the bounded states into the unbounded ones. A step‐by‐step state transformation is proposed to convert the mismatched system into a matched system. The robust control is then proposed based on the transformed system. The control is demonstrated to be able to guarantee the uniform boundedness and uniform ultimate boundedness of the system in the presence of uncertainty, while the state constraint can be always guaranteed.     

Composite adaptive dynamic surface control using online recorded data

This paper presents an online recorded data‐based design of composite adaptive dynamic surface control for a class of uncertain parameter strict‐feedback nonlinear systems, where both tracking errors and prediction errors are applied to update parametric estimates. Differing from the traditional composite adaptation that utilizes identification models and linear filters to generate filtered modeling errors as prediction errors, the proposed composite adaptation integrates closed‐loop tracking error equations in a moving time window to generate modified modeling errors as prediction errors. The time‐interval integral operation takes full advantage of online recorded data to improve parameter convergence such that the application of both identification models and linear filters is not necessary. Semiglobal practical asymptotic stability of the closed‐loop system is rigorously established by the time‐scales separation and Lyapunov synthesis. The major contribution of this study is that composite adaptation based on online recorded data is achieved at the presence of mismatched uncertainties. Simulation results have been provided to verify the effectiveness and superiority of this approach. Copyright © 2016 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.     

Numerical simulation of prestrain history effect on ductile crack growth in mismatched welded joints

Pipe reeling may lead to plastic pre‐deformation (prestrain) around existing cracks in components; therefore, investigating whether this process accelerates or counteracts ductile crack growth, especially for strength mismatched welded joints, is warranted. This study focused on the effect of prestrain history on ductile crack growth in mismatched welded joints. A single‐edge‐notched tension specimen was selected for numerical study, and the crack was assumed to have existed before a prestrain history was applied. Crack growth resistance curves for plane strain and mode I crack growth under large‐scale yielding conditions have been computed using the complete Gurson model. Meanwhile, symmetrical and non‐symmetrical prestrain cycle modes with different loading levels were applied to the overmatched specimens. The outcome demonstrated that the mismatch ratio (the ratio between the yield stress of the weld metal and base metal) showed a significant effect on fracture resistance regardless of the stage at which the prestrain cycle loading was located. By contrast, the processing of the crack growth was weakened by the increase of prestrain values, and the symmetrical prestrain cycle resulted in greater plastic damage than the non‐symmetrical prestrain cycle did. However, the initial crack length had a non‐significant effect on the ductile fracture considering the prestrain and mismatch effects.     

一类非线性严格反馈系统基于干扰观测器的抗干扰控制

针对一类带有干扰的非线性严格反馈系统, 研究其抗干扰控制问题. 系统干扰满足不匹配条件, 代表一类部分信息已知的干扰. 通过设计非线性干扰观测器, 提出基于非线性干扰观测器和back-stepping 的抗干扰控制方法来补偿干扰, 该方法可以保证闭环系统所有信号是半全局最终一致有界的. 最后, 通过与现有方法的对比验证了所提出方法的正确性和有效性.

     

基于广义扩张状态观测器的干扰不匹配离散系统状态反馈控制

针对一类干扰不匹配的线性离散时间系统, 研究基于广义扩张状态观测器的稳定化状态反馈控制器设计问题. 在经典的自抗扰控制器中, 扩张状态观测器主要针对干扰匹配的积分串联型系统. 然而, 在许多实际系统中往往存在干扰不匹配的情况, 例如存在采样抖动的离散时间控制系统. 针对这一问题, 基于一类存在不匹配干扰的离散时间系统, 提出广义扩张状态观测器和相应的稳定化状态反馈控制器设计方法. 最后通过永磁同步电机调速控制仿真实例验证了所设计的观测器和控制器的有效性.

     

非匹配不确定高阶非线性系统的滑模控制新方法

对具有非匹配不确定的高阶非线性系统,采用改进的高阶滑模微分器获取已知状态的任意阶微分估计值,再以恰当阶次的状态微分估计值之差,得到非匹配不确定项及其微分的估计值,证明了其误差任意小.为避免奇异性和抖振,采用两种方案设计了滑模控制器,并设计鲁棒项提高系统鲁棒性.基于Lyapunov~论证明了系统稳定性.同现有其他方法相比,该方法具有适用范围更广、收敛速度快、控制精度高、运算量小、保守性低等优点.最后仿真证明了本文所有结论.     

一类非线性系统的多面滑模控制器设计

针对一类非线性系统，提出了一种基于模糊小脑关联结构模型(CMAC)神经网络的多面滑模变结构控制算法，其特点是无需已知不确定性函数及其各阶导数的上界，并且允许控制矩阵存在不确定性．用Lyapunov稳定性定理证明了系统的状态及权值误差最终一致有界．与经典设计方法相比，所提出的方案允许非参数化不确定性．仿真实例显示了方法的有效性．