Abstract
Proportional-Derivative (PD) control is one of the most widely used controllers, especially for robot manipulators. When the robot presents gravitational terms, PD control cannot guarantee position convergence, therefore compensation is required such as PD with gravity compensation, PD+G. PD+G control requires knowledge of the gravitational term and there exist several results that prove global asymptotic stability. However, there is no method to tune the PD gains. In this work, a novel method to tune the PD+G controller is proposed. The tuning method is obtained using the global asymptotic stability result of the La Salle's theorem and robot dynamics properties. A comparison between previous works is realized via simulations and experiments to verify our approach. The results show fast and smooth convergence to the desired reference without overshoots.
Highlights
Proportional-Derivative (PD) control is one of the simplest controllers for robot manipulators control [1], [2]
When the robot is not affected by gravitational terms the PD controller guarantees global asymptotic stability (GAS) by choosing strictly positive gains [3], [4]
The previous stability analysis shows that the origin is GAS by means of the LaSalle’s invariance principle, there is no information about how the gains of the PD controller must be selected
Summary
Proportional-Derivative (PD) control is one of the simplest controllers for robot manipulators control [1], [2]. The most popular result is obtained from La Salle’s theorem, which guarantees global asymptotic stability of the closed-loop system but does not give any information of how the controller gains can be tuned and only meets the sufficient condition of choosing strictly positive gains [6]. One of the most popular controllers and wide used is the PID control [22]–[24] which has been used to develop different tuning methods [7], [25], [26] using robot dynamics bounds. The tuning method of the classical PD+G controller is still an open control problem In this paper it is proposed a novel and simple method to tune the PD+G controller that only requires the gravitational torques vector bound and the global asymptotic stability result using La Salle’s theorem.
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