In this paper, a novel hybrid fractional-order control strategy for the PUMA-560 robot manipulator is developed and presented, which combines the derivative of Caputo–Fabrizio and the integral of Atangana–Baleanu, both in the Caputo sense. The fractional-order dynamic model of the system (FODM) is also considered which consists of two models, the robot manipulator model, and the model of the induction motors which are the actuators that drive their joints. The fractional model of the manipulator is obtained using the Euler–Lagrange formulation. On the other hand, for controlling each one of the induction motors, fractional-order controllers \({{\mathop{\mathrm{PI}}\nolimits } ^{\vartheta }}\) based on Atangana–Baleanu in the Caputo sense integral were developed. And for the trajectory tracking control, fractional-order controllers \({{\mathop{\mathrm{PD}}\nolimits } ^{\xi }}\) were developed based on the fractional derivative of Caputo–Fabrizio in the Caputo sense. Also, ordinary PI and PD controllers were developed for the PUMA robot control to compare their performance with the fractional-order controllers. The results obtained demonstrated that the fractional-order controllers have a better capability for tracking trajectory tasks than the integer-order controllers, even when changes of the desired trajectory and external disturbances are considered. Additionally, an end-effector trajectory tracking task for manufacturing applications is also considered. All numerical simulations were performed by using the same orders and gains, demonstrating that the proposed fractional-order \({{\mathop{\mathrm{PI}}\nolimits } ^{\vartheta }}\) and \({{\mathop{\mathrm{PD}}\nolimits } ^{\xi }}\) controllers are robust, under different operating conditions, for tracking trajectory tasks. The fractional-order controllers and the integer-order controllers were tuned applying the cuckoo search optimization algorithm where the root-mean-square error (RMSE) was chosen as the cost function to minimize.

本文提出并提出了一种新颖的PUMA-560机器人机械手混合分数阶控制策略，该策略结合了Caputo–Fabrizio的导数和Atangana–Baleanu的积分，两者在Caputo方面都是如此。还考虑了系统的分数阶动态模型（FODM），该模型包含两个模型，即机器人操纵器模型和感应电动机的模型，感应电动机模型是驱动其关节的致动器。使用欧拉-拉格朗日公式可以得到机械手的分数模型。另一方面，为了控制每个感应电动机，分数阶控制器\（{{\ mathop {\ mathrm {PI}} \ nolimits} ^ {\ vartheta}} \）在Caputo的Atangana–Baleanu的基础上开发了感官积分。对于轨迹跟踪控制，分数阶控制器\（{{\ mathop {\ mathrm {PD}} \ nolimits} ^ {\ xi}} \）基于Caputo的Caputo–Fabrizio的分数导数开发的。此外，还为PUMA机器人控制开发了普通PI和PD控制器，以将其性能与分数阶控制器进行比较。所得结果表明，即使考虑了所需轨迹的变化和外部干扰，分数阶控制器也比整数阶控制器具有更好的跟踪轨迹任务的能力。另外，还考虑了用于制造应用的末端执行器轨迹跟踪任务。所有数值模拟都是通过使用相同的阶数和增益执行的，表明拟议的分数阶\（{{\ mathop {\ mathrm {PI}} \ nolimits} ^ {\ vartheta}} \）和\（{{\ mathop {\ mathrm {PD}} \ nolimits} ^ {\ xi}} \）控制器在不同的操作条件下具有很强的跟踪轨迹任务的能力。使用布谷鸟搜索优化算法对分数阶控制器和整数阶控制器进行了调整，其中选择了均方根误差（RMSE）作为成本函数以使其最小。