A model of a flexible structure is given by where n is the natural frequency of the

A model of a flexible structure is given by

where ωn is the natural frequency of the flexible mode, and £ is the corresponding damping ratio. In general, it is difficult to know the structural damping precisely, while the natural frequency can be predicted more accurately using well-established modeling techniques. Assume the nominal values of ωn - 2 rad/s, f - 0.005, and* = 0.1.
(a) Design a lead compensator to meet the following specifications: (1) a closed-loop system response to a unit step input with a settling time (with a 2% criterion) less than 200 seconds and (2) an overshoot of less than 50%.
(b) With the controller from part (a), investigate the closed-loop system unit step response with ζ = 0, 0.005, 0.1, and 1. Co-plot the various unit step responses and discuss the results.
(c) From a control system point of view, is it preferable to have the actual flexible structure damping less than or greater than the design value? Explain. CP12.6 The industrial process.

Transcribed Image Text:

2 (1 + kw,?)s + 2%ws + wn G(s) + 25w,s + w,?) s?(s?