Use of a Simple Mechanical Analogy to Analytically Tune the PD Controller of a Flexible Manipulator System

Figure 7

Predicted tip displacements: (a) the frequency responses from Equation (12) (dashed lines) and Equation (13) (solid) for three test cases: (upper pair), (middle), and (lower). The symbols, “+,” “ο,” and “∇” are indicated at the nominal natural frequency , the standard natural frequency , and the damped natural frequency in successive order. The dotted line indicates the command input signal. (b) The corresponding time responses to a step input.

(a)

(b)