Stability aspects in case of small delayed robot manipulators system

Abstract

There are analyzed the effects of the small delays in the feedback loop that inevitably lead the systems into an unstable situation. How small must be the delay in real conditions such that to preserve the system stability, will be studied and analyzed for a robot manipulator. The case of an adaptive controller is also developed for the robot system actuated by brushed direct current motors in the presence of external disturbances and parametric uncertainties. The control scheme requires the measurements of link position and armature current for feedback. These measurements are delayed due to the actuators unfasten response. The elaborated adaptive controller results in a closed-loop system locally stable while the all states and signals are bounded and the tracking error can be obtained as small as possible. The advantage of the presented algorithm consists in the number of parameter estimates equal to the number of unknown parameters throughout the entire mechanical system. In consequence, it is eliminated the overparametrization induced by employing the integrator backstepping technique in control of electrically driven robots. Finally, the performance of the proposed approach is illustrated in simulation examples