Robustness of PID-controlled manipulators with respect to external disturbances

Abstract

We present a robustness analysis for PIDcontrolled robot manipulators. For robot manipulators under the influence of external disturbances we provide a proof, and a tuning procedure, to establish uniform semiglobal practical asymptotic stability. In particular, in contrasts to other works on robust stability of PIDs, we do not use La Salle's principle but provide a strict Lyapunov function. The perturbations that we consider include discontinuous functions of the state, such as Coulomb friction. As corollaries of our main results, one may conclude the same stability property for the case of motion control using linear PID.

Closed-loop identification and tracking control of Lagrangian systems under input constraints

“…In order to corroborate the effectiveness of the studied scheme, simulations where implemented using a two degree of freedom robot model appearing in [9], [10]. Using Property 5 the regression matrix and parameter vector of the considered dynamics can be written as The desired trajectory is given by…”

New Tuning Conditions for Semiglobal Exponential Stability of the Classical PID Regulator for Rigid Robots

“…We stress that the controller gains used in experiments reported by Chaillet et al . [10] have not been verified to satisfy the tuning conditions proposed in that paper to ensure semi-global exponential stability. The tuning procedure proposed in [10] is conservative mainly due to the fact that it is expressed in terms of the smallest and the largest eigenvalues (or norms) of both matrix controller gains and matrix robot parameters.…”

“…On the other hand, a similar situation exists for semi-global exponential stability, which has been claimed by Chaillet et al . [10]. However, in this case the problem still remains unsolved: the resulting tuning procedure is so conservative that no experimental test was reported.…”

“…[10] have not been verified to satisfy the tuning conditions proposed in that paper to ensure semi-global exponential stability. The tuning procedure proposed in [10] is conservative mainly due to the fact that it is expressed in terms of the smallest and the largest eigenvalues (or norms) of both matrix controller gains and matrix robot parameters. Although this feature allows us to write tuning procedures in terms of simple expressions, this also forces us to compute the controller gains under extreme operating conditions.…”

“…Although this feature allows us to write tuning procedures in terms of simple expressions, this also forces us to compute the controller gains under extreme operating conditions. For instance, a common condition establishes that the smallest proportional gain must dominate the gravity effect of the whole robot [10]. This results in excessively large proportional gains for most joints because the joints close to the robot tip are provided with low torque actuators since they do not need to deal with the gravitational effect of links placed close to the robot base.…”