It is known that the Proportional Integral and Derivative (PID) regulator with constant and symmetric positive definite gain matrices (Kp, Kv and Ki), in closed loop with robotic manipulators, guarantees semiglobal asymptotic stability of the equilibrium point. In this paper, a fresh approach for control of robots manipulators based on a class of PID regulators with variable gain matrices Kp and Kv, which guarantee global asymptotic stability, is proposed. This PID control scheme, proposed with PD variable gains and fixed integral gains, improves the performance of the transient response and the handling of constraints, such as the limits of the actuator torques. Based on the authors experience, our proposal is the first scheme of a nonlinear PID regulator for robot manipulators whose PD gains are variable and its stability proof is global asymptotic in the sense of Lyapunov. The PD variable gains are directly dependent on the joint position errors and are fine tuned by fuzzy logic methodology. Good results were obtained on an experimental direct-drive robot arm of two degrees of freedom, when it was tested in order to verify the effectiveness of the new controller.

众所周知，具有恒定和对称正定增益矩阵（Kp，Kv和Ki）的比例积分和微分（PID）调节器与机器人机械手成闭环，可以保证平衡点的半全局渐近稳定性。本文提出了一种新的机器人机械手控制方法，该方法基于一类具有可变增益矩阵Kp和Kv的PID调节器，可以保证全局渐近稳定性。提出的具有PID可变增益和固定积分增益的PID控制方案提高了瞬态响应的性能以及对约束条件（例如执行器转矩极限）的处理。根据作者的经验，我们的建议是针对机器人操纵器的非线性PID调节器的第一个方案，该机器人的PD增益是可变的，其稳定性证明在Lyapunov方面是全局渐近的。PD变量增益直接取决于关节位置误差，并通过模糊逻辑方法进行微调。为了验证新控制器的有效性，在两个自由度的实验性直接驱动机器人手臂上进行测试时均获得了良好的结果。