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A proportional-derivative-double derivative controller for robot manipulators

Feeding a controller with acceleration signal can improve system robustness and relative stability. However, neither measurements of acceleration signals nor velocity signals are available in most industrial robot manipulators. Inevitable estimation errors may lead to chattering phenomenon that can excite unmodeled high frequency plant dynamics yielding either severe vibrations in the arm or instability of the control system. This paper proposes a stochastic discrete-time multivariable proportional-derivative-double derivative (PDD) controller with the objective of possessing superior tracking capability in presence of unmodeled joint friction forces while only using joint position measurements. The proposed approach models the estimation errors of velocity and acceleration stochastically. Subsequently, the time-varying PDD gains are derived based on minimising the mean-square state error per-discrete-time instant. We show that the mean-square velocity error is inversely proportional to the square of the sample rate. We demonstrate the tracking superiority of the proposed control experimentally on a four-degree-of-freedom robot manipulator.