Equations of motion of a robot manipulator as described by the Euler-Lagrange model:
The proportional-derivative (PD) feedback control is a fairly famous method in the industrial context for the convergence of an output signal to a reference one. It is based on the use of two terms: P and D. The first one affects the system using proportional control on the error introducing a positive matrix
The full control scheme with the Proportional-Derivative control is shown in the following figure. The PD controller produces a command control that is given as input to the manipulator nominal model shown in Eq. 1. Inverting the Euler-Lagrange equation and substituting
From these computed quantities, the PD controller makes use of