摘要
针对柔性机械臂系统的分布参数模型,研究了其位置控制、力/位置混合控制和协调运动控制问题。研究了以上三种控制问题基于确切动力学模型的控制方法,提出了基于Lyapunov函数方法和线性算子半群理论的构造性静态反馈和动态反馈控制策略;研究了以上三种控制问题存在参数不确定和外部干扰影响下的分布参数模型的鲁棒控制方法,提出了一种新的构造性的变结构控制方法,通过引入表征系统关节角、关节角速度和柔性臂根部应变的复合变量,基于Lyapunov理论和Barbalat引理给出了系统的递推性的控制器设计方法以及渐近稳定性证明;针对不确定参数界未知的情况,通过设计参数自适应更新律,提出了一种新的变结构自适应控制策略;针对以上算法分别进行了仿真研究,验证了算法的有效性。
Robot abilities increase greatly as the development of robot technology, and robot applications spread into more and more fields, so people hope they can complete more complex tasks. Recent years, the modeling and control for flexible manipulator charactered by large scale, high speed and light have been studied by many researchers. Flexible manipulator has been a new current of the robotic technology. Compared to the rigid manipulators, flexible ones have many advantages such as lower arm weight, better energy efficiency, higher operating speed and improved probability. However, flexible ones also have more complex dynamic behaviors and inherent bending vibration. In essence, flexible manipulator system is a nonlinear, strong coupling and infinite dimensional dynamic system, which including not only the global motion of large range, but also the local elastic deformation. Scholars in the world have deeply studied the flexible manipulators, but for the control objects, focus on the position control and have not paid more attention to the hybrid position/force control and cooperating control. For the control methods, many scholars have only designed the controller based on the simple lumped parameter model, which will inevitably lead to the so-called overflow problem. The overflow problem can be solved if the distributed parameter model is utilized; however there have few papers about this due to the complexity of the distributed parameter model, and major existing papers assume the model is exactly known. There are many challenging, just underway and marginal aspects, for example, hybrid position/force control, cooperating control, distributed parameter model, constructive control method design based on the distributed parameter model and robust control method. These problems still need scholars pay much attention and effort. Hence, it is very necessary and significant to study further on the flexible manipulator system.
This paper systemically studies on the position control, hybrid position/force control and cooperating control of flexible manipulators based on distributed parameter model, thus, the overflow problem is avoided. For the above three objects, the constructive control method based on the exact model and constructive robust control method based on the unknown model are studied. Main content and innovation are as follows.
The position control method of the horizontal flexible manipulator based on the distributed parameter model is studied. A novel static feedback controller is proposed. By introducing a new variable which is a linear combination of the rotation angle, rotation angle velocity and the root strain, the controller is derived by the stepping design method from the system’s energy. The blindness of the controller design method is avoided by the above constructive steps. By introducing an additive dynamic system, the input of which is the above defined combination variable, the dynamic feedback controller and disturbance rejection is studied by virtue of the positive real lemma. The robust controller is proposed considering the uncertain parameters and external disturbance of the system. A new constructive sliding mode variable structure controller is researched, and the sliding mode is also designed as the above mentioned combination variable. The controller is also derived by the stepping design method. The asymptotic stable of the closed loop system is proved by the Barbalat’s lemma. The sliding mode is proved to converge to zero in the finite times, thus, the closed loop system converge to a partial differential equation which has only the zero solution. The variable structure adaptive controller is proposed, the adaptive ability is enhanced by the designed parameter update law, and the adaptive controller need few assumptions. Simulation results verify the proposed algorithms are very more effective and advantageous.
The hybrid position/force control algorithm of the horizontal flexible manipulator based on the distributed parameter model is researched. A novel constructive static and dynamic feedback control method are proposed based upon the exact dynamic model, also a new constructive sliding mode variable structure and variable structure adaptive controller are derived based upon the uncertain dynamic model. In these methods, the geometry constrained condition is transformed to a new boundary condition of the partial differential equation which describing the vibration. This boundary condition makes the stepping design method can be accomplish, and the constructive algorithm of the position control system can be extended to the position/force control system. The blindness of the controller design method is avoided by the above constructive algorithm. The dynamic feedback controller resolves the problem of disturbance rejection. The problem of robust control is resolved by the constructive variable structure and variable structure adaptive controllers.
The cooperating control algorithm of the horizontal flexible manipulator based on the distributed parameter model is researched. A novel constructive static and dynamic feedback control method are proposed based upon the exact dynamic model, also a new constructive sliding mode variable structure and variable structure adaptive controller are derived based upon the uncertain dynamic model. In these methods, the geometry constrained condition is transformed to a new boundary condition of the partial differential equation which describing the vibration, and the other new boundary condition is obtained by eliminating the coupling Lagrange multiplier. These boundary conditions make the steeping design method can be accomplish, and the constructive algorithm of the position control system can be extended to the cooperating control system. The blindness of the controller design method is avoided by the above constructive algorithm. The efficiency of the proposed methods is verified by the simulation results.
The corresponding control algorithm of the three control objects have the similar construction, thus, it is confirmed that the control algorithm proposed in this paper is a uniform method which is applicable to the different three control objects. The conclusion and the perspective of future research are given at the end of the paper.
引文
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