【作者】 李鹏；

【导师】 郑志强；

【作者基本信息】 国防科学技术大学 ， 控制科学与工程， 2011， 博士

【摘要】 不确定性条件下的控制问题是现代控制中的一个重要课题,因为在任何控制问题中,实际的控制对象和用于控制器设计的数学模型总是存在差异,这种差异主要来自于外界干扰、未知的对象参数和未建模动态。作为现代控制理论的一个重要分支,滑模控制以实现简单以及系统处于滑动模态时对满足匹配条件的外界干扰、模型的不确定性和未建模动态具有不变性而著称,且已成功应用于机器人、航空航天等领域。论文研究了传统滑模和高阶滑模控制问题,并将部分研究成果应用于机器人和飞行器的控制中。主要研究内容和创新点如下:(1)研究了传统滑模控制中采用Slotine形式的滑模面和积分滑模面,利用边界层和幂次趋近律来抑制抖振时,系统的稳态跟踪误差界问题。利用有界输入有界输出(BIBO)稳定的方法,推导出了比现有文献的结果更为精确的稳态跟踪误差界。进一步,通过给定的稳态跟踪误差要求,可以设计合适的边界层厚度或幂次趋近律参数,不用通过仿真实验来试凑。最后,所得到的结果应用到n关节机械臂的跟踪控制中。(2)为了减小稳态跟踪误差,不少学者将积分项引入到滑模面的设计中。然而,在大的初始误差条件下,积分会出现累积效应(Windup),引起大的超调和执行器饱和,甚至导致系统不稳定。因此,提出了一类具有“小误差放大,大误差饱和”功能的光滑非线性饱和函数以改进传统积分滑模控制,在保持传统积分滑模控制跟踪精度的同时获得更好的暂态性能。应用Lyapunov稳定性理论和LaSalle不变性原理证明了对常值或最终常值干扰可以完全抑制。并在此基础上提出了全程非线性积分滑模控制方法,消除了滑模的到达阶段,具有全程鲁棒性。(3)基于非光滑的类二次型Lyapunov函数,对二阶滑模Super-Twisting算法的有限时间收敛性进行了分析。系统受常值干扰时,通过Lyapunov方程证明了该算法有限时间收敛,并给出了收敛时间的最优估计;系统受时变干扰时,通过求解代数Riccati方程得出了一组保证该算法有限时间收敛的参数取值范围,并给出了收敛时间的估计值。同时,在此基础上提出自适应Super-Twisting算法,该算法不需要知道不确定性变化率的界。(4)证明了幂次趋近律本质上是二阶滑模,且趋近过程品质较好,但鲁棒性差。因此,设计了非齐次干扰观测器和快速幂次趋近律相结合的二阶滑模算法,这种二阶滑模算法适用于相对阶为1的系统。经与Shtessel在Automatica上提出的光滑二阶滑模算法进行比较,本算法具有更好的暂态性能。将该算法应用于一类无尾飞行器的姿态控制中,仿真结果表明了该算法的有效性。(5)利用有限时间控制技术中的齐次理论,并结合自适应控制思想,提出了一种鲁棒自适应二阶滑模控制方法,不需要知道系统不确定性的界。并设计了一类新的非线性函数替代齐次系统中的幂函数,克服了齐次系统在状态远离平衡点时收敛速度慢的缺陷,系统的状态能快速有限时间收敛。该算法形式简单,控制律的设计只需要系统的相对阶信息,并将其应用于Nubot全向移动机器人的轨迹跟踪控制中。(6)基于齐次理论和有限时间快速收敛Lyapunov函数,提出了鲁棒自适应任意阶滑模控制方法。将SISO系统的r阶滑模控制问题转化为受扰动的r重积分链的有限时间镇定问题,依据第七章的思路,将控制律的设计分成两个部分:名义控制部分和补偿控制部分。名义控制部分分别采用齐次理论和快速有限时间Lyapunov稳定性理论进行设计,补偿控制部分采用自适应一阶滑模方法,综合得到了鲁棒自适应任意阶滑模控制律,并应用于轮式移动机器人的控制中。更多还原

【Abstract】 Control in the presence of uncertainty is one of the main topics of modern control theory. In the formulation of any control problem there is always a discrepancy between the actual plant dynamics and its mathematical model used for the controller design. These discrepancies mostly come from external disturbances, unknown plant parameters, and unmodeled dynamics. Sliding mode control (SMC), one of the most significant branches in modern control theory, turns out to be characterized by high simplicity and invariance property which lies in its insensitivity to matched uncertainties when in the sliding mode. Thus, it has been widely implemented in many real systems such as robots, aeronautical and space vehicles.Traditional and higher order sliding mode (HOSM) control are investigated, and partial achievements are applied to robots and aircraft control. The main research contents and contributions are listed as follows:(1) For the traditional sliding mode tracking control of a class of uncertain nonlinear systems using boundary layer or power reaching rate law to suppress chattering, the steady-state error bounds are studied when use Slotine form sliding surface and integral sliding surface, respectively. Using the method of BIBO stability, the steady-state error bounds are obtained. Compared with the results reported in literatures, the steady-state error bounds in this dissertation is more accurate. Furthermore, by specifying the tracking error that is required, an appropriate saturation function or power reaching law to suppress chattering is designed without simulation experiments. A case study of an n-link robot manipulator model is presented to demonstrate the effectiveness of the analysis.(2) In order to decrease the steady-state error, many scholars introduced integral term in the sliding surface design. However, with the existence of large initial error, integrator windup would occur and give rise to overshoots and even lead to instability. Therefore, to promote the performance of traditional integral sliding mode control, a new nonlinear saturation function is proposed, which enhances small errors and be saturated with large errors in shaping the tracking errors. While maintaining the tracking accuracy of the traditional integral sliding mode control, this approach provides better transient performances. Using Lyapunov stability theory and LaSalle invariance principle, we proved that the proposed approach ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance. Furthermore, global nonlinear integral sliding mode control is proposed to provide a framework for eliminating the reaching phase, so that a sliding mode exists throughout the entire response.(3) The finite time convergence of the second order sliding Super-Twisting algorithm is analyzed using a non-smooth quadratic-like Lyapunov function. For the constant disturbance, the finite time convergence is proved through Lyapunov equation, and the optimal estimation of the convergence time is presented. For the time varying disturbance, the finite time convergence of Super-Twisting is guaranteed when the parameters satisfy the algebraic Riccati equation, and the estimation of the convergence time is provided. Finally, based on the non-smooth quadratic-like Lyapunov function, adaptive Super-Twisting algorithm is proposed that continuously drives the sliding variable and its derivative to zero in the presence of the disturbance with the unknown bounded variation.(4) It is proved that power rate reaching law, in essential, is second order sliding mode which has perfect reaching quality but poor robustness. Therefore, a robust second order sliding mode control scheme for first order dynamic systems is proposed. The controller has finite time convergent property and contains two parts. A part is fast power reaching law which is used to stabilize sliding variable and its derivative to zero in finite time without disturbance. The other part is a non-homogeneous disturbance observer, which can provide for exact estimation of the sufficiently smooth disturbance in finite time. As a result, a continuous second order sliding mode is established in finite time. Compared our method with the smooth second order sliding mode proposed by Shtessel in the Automatica, a better transient performance is obtained by our method. Simulation results using a tailless aircraft model show good performance even in actuator failure scenarios which validates the effectiveness and feasibility of the proposed method.(5) Using homogeneity and adaptive sliding mode concept, a robust adaptive second order sliding mode control scheme is proposed, and the bounds of uncertainties are not required to be known in advance. Power function in the homogeneous system is replaced by a proposed nonlinear function, thus, a fast convergence rate is guaranteed for any distance from equilibrium point. The convergence rate of the second order sliding mode can be hastened through tuning the controller parameters, and the robustness is ensured. The method is evaluated in simulations on an Omni-directional Mobile Robot (Nubot).(6) Based on homogeneity and finite-time convergent Lyapunov function, a robust adaptive arbitrary order sliding mode control method is proposed. It is shown that the problem is equivalent to the finite time stabilization problem for a perturbed chain of integrators. The control law contains two parts: the nominal part, which is designed using homogeneity technique and finite-time Lyapunov stability theory, respectively, achieves finite time stabilization of the chain of integrators without uncertainties; the compensating part, which is designed using adaptive sliding mode, rejects bounded uncertainties, and the bounds of uncertainties are not required to be known in advance. As a result, a finite time convergent arbitrary order sliding mode is established. An illustrative example of a wheeled mobile robots control shows the applicability of the method.更多还原