具有量化输入和边界扰动的柔性臂边界振动滑模控制

本文针对量化输入和有界扰动下柔性臂系统的振动抑制和边界滑模控制器设计问题开展研究. 柔性臂的动态特性由偏微分方程表示的分布参数模型描述. 对于具有未知有界干扰的柔性臂系统, 其主要控制目标是减小干扰的影响, 使柔性臂到达期望角度并同时抑制系统的振动. 首先, 利用边界输出信号构造滑模函数和滑模面. 其次, 结合所构造的滑模面, 设计一种边界滑模控制器, 并利用算子半群理论证明了闭环系统的适定性. 所提出的边界滑模控制策略保证了系统状态能够在有限时间内到达滑模面, 并且系统状态在滑模面上是指数收敛的. 最后, 通过物理实验验证了所提出控制策略的有效性.     

Synchronization of fractional-order uncertain chaotic systems with input nonlinearity

In this paper, sliding mode control has been designed for synchronization of fractional order uncertain chaotic systems with input nonlinearity. First, sliding mode control law has been taken from chaotic state error system which is asymptotically stable. Second, the shown sliding mode control ensures that fractional-order error system is asymptotically stable in the presence of uncertainty and nonlinear input. Simulation results using MATLAB software show that the designed controller is able to synchronize fractional-order chaotic systems in the presence of the mentioned factors.     

滑模变结构控制理论及其算法研究与进展

针对近年来滑模变结构控制的发展状况,将滑模变结构控制分为18个研究方向,即滑模控制的消除抖振问题、准滑动模态控制、基于趋近律的滑模控制、离散系统滑模控制、自适应滑模控制、非匹配不确定性系统滑模控制、时滞系统滑模控制、非线性系统滑模控制、Terminal滑模控制、全鲁棒滑模控制、滑模观测器、神经网络滑模控制、模糊滑模控制、动态滑模控制、积分滑模控制和随机系统的滑模控制等.对每个方向的研究状况进行了分析和说明.最后对滑模控制的未来发展作了几点展望.     

一类控制输入饱和受限的不确定系统滑模控制

本文研究控制输入饱和受限情况下不确定系统的滑模控制问题,其中,被控对象同时存在状态矩阵不确定性和控制增益矩阵不确定性.设计了一种积分型切换面和一个具有特殊结构的滑模控制律,可以在参数不确定和控制受限影响下保证系统状态轨迹有限时间内到达指定的切换面,利用等价控制律方法给出了滑模动态渐近稳定的充分条件.数值仿真例子验证了本文算法的有效性.     

不确定线性系统的鲁棒切换函数变结构控制

针对工程领域中常见的一类不匹配不确定系统,即不确定性不是发生在控制通道中的系统,如工程中具有执行器的控制系统,提出了一种建立鲁棒切换函数的方法,进面设计滑模变结构鲁棒控制策略,该策略可确保整个闭环系统的轨迹是一致最终有界并具有稳定性,最后以船舶减摇鳍控制系统为例,进行了变结构鲁棒控制器设计。     

量化参数不匹配的线性系统监督滑模控制设计

在量化控制系统中,量化器灵敏度参数的不匹配现象会造成系统的性能下降,严重时甚至会导致系统不稳定。另一方面,量化器灵敏度参数的不匹配现象也会增加控制设计的复杂性与难度。针对量化器灵敏度参数不匹配的不确定线性系统,研究监督策略下的量化反馈滑模镇定控制问题。应用监督控制策略,提出的鲁棒量化反馈滑模控制法能够有效消除量化灵敏度参数不匹配与模型不确定性带来的影响,进而确保系统轨迹能渐近收敛到原点。经过Matlab仿真实验验证了该方法的有效性与优越性。     

基于鲁棒观测器的非线性系统滑模控制

针对一类非线性不确定时滞系统,分别考虑了观测器的设计和控制器的设计问题.首先,基于扩张状态方程,设计鲁棒观测器;其次,基于观测器估计的状态值,融合H∞控制技术,设计了滑模控制器,并且将滑模控制器增益系数的计算问题转化为线性矩阵不等式的求解问题,而且所设计的滑模控制器不要求系统不确定项满足匹配条件,使得控制器具有广泛的使用范围;最后,给出数值算例,将设计的观测器和控制器应用算例中,仿真表明该方法的有效性.     

Robust Stabilization of Nonlinear PVTOL Aircraft with Parameter Uncertainties

In this work, the stabilization control problem is investigated for the planar vertical take‐off and landing (PVTOL) aircraft with unknown model parameters. To cope with the challenges caused by non‐minimum phase and parametric uncertainties, a new appropriate output, different from the general centroid position output, is carefully constructed to ensure the zero dynamics asymptotically stable, then the sliding‐mode technique is applied to design a state feedback control law. The proposed robust control law is proved able to asymptotically stabilize the PVTOL aircraft to the desired fixed position with null velocities and roll angle despite the unknown model parameters. Simulation examples illustrate the effectiveness of the proposed control algorithm.     

Sliding mode control for Markovian jumping systems with actuator nonlinearities

This article considers the design of sliding mode control for stochastic Markovian jumping systems with actuator nonlinearities. In the design of integral sliding surfaces, a set of specified matrices are employed such that the connections among sliding surfaces corresponding to each mode are established. And then, a sliding mode controller depending on the transition rates is synthesised such that the reachability of the specified sliding surface can be ensured. Moreover, sufficient conditions for the stability of the sliding motions are derived. It is shown that the effect of Markovian switching can be coped with by the present sliding mode control method. Finally, the simulation results illustrating the proposed method are provided.     

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum‐of‐squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite‐time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite‐time convergence of the sliding surface to a pre‐chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.