摘要
欠驱动系统是指系统控制量维数小于自由度维数的系统,是控制研究领域中非常常见的一类系统。由于其欠驱动特性,控制过程既要实现系统欠驱动部分的自稳定,又要实现驱动部分的稳定控制。这给控制理论带来了新的挑战,是控制理论的重要研究方向。由于欠驱动系统的多样性,除了部分反馈线性化方法外,很难找到对所有欠驱动系统均有效的控制方法。因此,对欠驱动系统的研究主要是针对某一种或者某一类系统。本文研究三类欠驱动系统：可变形线性物体的机器人操作系统、两轮自平衡小车UW-Car和欠驱动手臂acrobot。
本文研究滑模控制方法对欠驱动系统的稳定控制。基于欠驱动系统的动力学模型,研究一般欠驱动系统的控制方法。为了增强滑模控制器的鲁棒性,本文提出一种带有干扰观测器的滑模控制方法。通过干扰观测器估计外界扰动,并进行补偿,使得被控对象近似为无摄动无干扰的标准模型,再通过设计滑模控制器实现系统的稳定控制。该方法尤其适用于外界扰动较大或者扰动上界难以估计的环境。
本文采用基于滑模控制的可变形线性物体机器人操作过程中的末端抖振方法。采用有限元方法建立可变形线性物体的动力学模型。基于该动力学模型,提出基于滑模控制的可变形线性物体末端抑振控制方法。通过局部线性化、线性变换、Schur分解等一系列数学运算,解耦系统欠驱动部分和驱动部分。设计合适的滑模控制器满足系统的欠驱动部分能够自稳定在滑模面上,驱动部分能够满足滑模条件,从而实现可变形线性物体末端抑振控制。为了解决实际应用中存在输入饱和的问题,本文提出自适应滑模控制方法。通过设计合适的自适应规律,使得滑模控制器既能消除系统输入饱和特性对系统性能的影响,又能完成可变形线性物体末端快速抑振。我们采用MATLAB仿真验证上述理论分析,仿真结果表明,滑模控制方法能实现可变形线性物体末端快速抑振；自适应滑模控制方法在系统存在输入饱和特性的情况下也能够实现可变形线性物体末端的快速抑振。
两轮自平衡小车是一类重要的欠驱动系统,本文研究两轮自平衡小车UW-Car速度控制和最优刹车控制。通过对UW-Car系统机械结构分析,采用拉格朗日动力学方法建立UW-Car的动力学模型。基于该模型,计算得到UW-Car运动过程中的平衡点,通过设计终端滑模控制器,实现UW-Car的速度跟踪控制。刹车控制作为两轮自平衡小车重要的研究方向,本文提出一种基于最短刹车距离的最优刹车控制方法。通过设计切换滑模控制器,采用遗传算法求取最优参数,实现UW-Car的最优刹车控制。通过实验结果和MATLAB仿真比较,验证了UW-Car动力学模型的正确性,以及滑模控制器对UW-Car速度跟踪控制和最优刹车控制的有效性。
本文将带有干扰观测器的滑模控制方法应用在acrobot上。建立带有扰动的acrobot的动力学模型,采用干扰观测器估计系统扰动值并补偿,再采用滑模控制器实现acrobot的稳定控制。仿真结果表明,在外界扰动较大的环境下,通过与传统的滑模控制器控制效果比较,证明了带有干扰观测器的滑模控制器的控制效果更有效。欠驱动手臂acrobot是最简单的欠驱动系统,通过在acrobot应用,该方法可以逐步推广到更复杂的欠驱动系统
Underactuated systems are a class of control systems characterized by the presence of more degrees of freedom than control inputs, and are very common in the field of control research. Due to the particular characteristics of underactuated systems, in control processes, underactuated areas are self-stabilized while actuated systems are controller-stabilized. Ongoing development of such systems has brought about new challenges to control theory, and comprise an important research direction in the field of control theory. Given the diversity of underactuated systems, and aside from the partial feedback linearization method, there is a lack of a uniform solution to the control issue present in underactuated systems. Here we investigate three types of underactuated systems utilizing controllers designed for position and velocity tracking control:a deformable linear object robot operating system, a two-wheeled self-balance vehicle (UW-Car), and an underactuated acrobot arm system.
We adopt sliding mode control for stable control of underactuated systems. A sliding mode controller is designed for dynamic model of underactuated system in general form. In order to enhance the robustness of the sliding mode controller, this thesis proposes a type of disturbance observer incorporating a sliding mode control for a class of underactuated systems. By estimating and compensating for the disturbance by using a disturbance observer, the system is approximated as a standard model without perturbation and inference, and a sliding mode controller is thereby designed. This method is particularly suitable for large external disturbance environments or environments whose upper bounds are difficult to estimate.
We propose a sliding mode controller to dampen the vibration in the end of deformable linera object in this thesis. We obtain the dynamic model of a deformable linera object formulated by using finite element method. Based on this model, by using local linearization, linear transformation of variables and Schur decomposition of matrices, actuated and underactuated parts of the deformable linera object dynamic model are separated. Based on the decoupled dynamic model, a sliding mode controller is designed to force the underactuated state variables to converge to sliding mode hypersurface and actuated state variables satisfy the siding mode condition, and cause vibration at the end of the deformable linera object to dampen quickly. To solve the input saturation problem, an adaptive sliding mode control law is designed to suppress the damping at the end of deformable linera object. By designing a proper adaptive law, the adaptive sliding mode controller can both eliminate the effect of input saturation no the performance of the system and dampen the vibration at the end of a deformable linera object quickly. MATLAB simulations used to verify the theory analysis. The results show that the sliding mode controller can manage the vibration suppression at the end of a deformable linera object, and the adaptive sliding mode controller can suppress the vibration at the end of deformable linera object with input saturation.
The two-wheeled self-balance vehicle (UW-Car) is a characteristic example of underactuated system. Sliding mode controllers are designed for velocity control and optimal braking control of two wheeled vehicle UW-Car. Through mechanical structure analysis, the Lagrangian dynamics method is used to obtain the dynamic model of the UW-Car. Based on this model, the equilibrium point of the UW-Car while undergoing motion is calculated and the UW-Car's velocity tracking control is realized through terminal sliding mode controller. Taking speed reduction and braking as the UW-Car's primary research direction, we propose an optimal braking control method to achieve the shortest braking distance. A switching controller with optimal parameters calculated by genetic algorithm is designed. From comparisons between MATLAB simulation results and experiments, we arrive at the conclusion that the dynamic model of UW-Car is accurate and that the sliding mode controller for velocity tracking control and optimal braking control is effective.
The thesis presents a type of disturbance observer incorporating a sliding mode control applying to underactuated arm acrobot. Based on the dynamic mode of acrobot with disturbance, the disturbance observer is designed to estimate and compensate for the disturbance, and sliding mode controller is designed for the stable control of acrobot system. In large external disturbance environments, compare to simulation results of traditional sliding mode controller, the sliding mode controller with disturbance observer achieves greater effectiveness. Acrobot is the simplest underactuated system. By applying the controller to acrobot, the method can be gradually extended to more complex underactuated systems.
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