Abstract The solution of a case study problem of suspended payload sway damping by moving a pivot base in vertical direction is presented. Unlike for the classical problem of anti-sway control for moving the base in the horizontal direction, implemented e.g. in cranes, a direct solution by using control feedback theory for linear systems is not possible. Once the model is linearized, it becomes uncontrollable. Thus, a derivation of a nonlinear controller is needed to solve the task. In this context, two solutions are proposed. The first solution is based on imposing harmonic motion of the base with double frequency of the payload natural frequency. Synchronization of the base and the payload deflection angle is done either by proportional time-delay controller or by proportional-derivative delay free controller. Secondly, the Lyapunov’s second method is directly applied to derive a nonlinear controller. For both cases, balancing the dissipated energy, rules for determining equivalent damping are explicitly derived. After discussing and solving the corresponding implementation aspects, both simulation and experimental validations are performed. The experimental validation is performed on a simplified problem, where only horizontal motion is possible. The simulation based validation is performed on a nonlinear two dimensional model of a quadcopter carrying a suspended payload.

中文翻译：

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通过枢轴底座的垂直运动来抑制缆索悬挂有效载荷摇摆的算法

摘要 提出了通过在垂直方向移动枢轴底座来解决悬吊有效载荷摇摆阻尼的案例研究问题。与用于在水平方向上移动基座的经典防摇控制问题不同，例如在起重机中实施，使用线性系统的控制反馈理论的直接解决方案是不可能的。一旦模型被线性化，它就变得无法控制。因此，需要推导非线性控制器来解决该任务。在这种情况下，提出了两种解决方案。第一种解决方案是基于有效载荷固有频率的两倍频率的基座的谐波运动。基座和有效载荷偏转角的同步通过比例延时控制器或比例微分无延时控制器完成。第二，Lyapunov 的第二种方法直接用于推导非线性控制器。对于这两种情况，为了平衡耗散能量，明确导出了确定等效阻尼的规则。在讨论和解决相应的实施方面之后，进行了模拟和实验验证。实验验证是在一个简化的问题上进行的，其中只能进行水平运动。基于仿真的验证是在携带悬挂有效载荷的四轴飞行器的非线性二维模型上执行的。进行了模拟和实验验证。实验验证是在一个简化的问题上进行的，其中只有水平运动是可能的。基于仿真的验证是在携带悬挂有效载荷的四轴飞行器的非线性二维模型上执行的。进行了模拟和实验验证。实验验证是在一个简化的问题上进行的，其中只有水平运动是可能的。基于仿真的验证是在携带悬挂有效载荷的四轴飞行器的非线性二维模型上执行的。