# Feedback Control Systems: Systems Specifications

Find a second order model to achieve the following response to a step output disturbance of height 0.5. Minimum value 0.05 after 0.1s. Make a rough sketch of the bode magnitude plot and the step response.

(Please see attachments for details.)

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#### Solution Preview

Posting 23525:

Ty/do is high-passing

Note from then class notes you attached:

Ty/di = P/(1+L), since P* = P

Ty/do = 1/(1+L), since P* = 1

and hence, Ty/do = [Ty/di]/P

Typically P(s) = k/(s+a)

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Now, we know from previous postings and the normalized curves,

Ty/di is of the form:

Ty/di = bs/[s^2 + cs +d ]

Now, Ty/do = [Ty/di]/P

= bs/[s^2 + cs +d ]/[k/(s+a)]

= (s+a)(bs)/[k{s^2 + cs +d}]

= (bs^2+abs)/[k{s^2 + cs +d}]

This is the general form ofn the TF.

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Find a second-order model:

Step output disturbance of height 0.5

Output: Minimum value: 0.05 after 0.1 Sec

If d is the damping coefficient and Wn is the undamped angular velocity (in rad/sec),

Transfer function from output disturbance to output:

Y(s)/Do(s) = s*(s+2dWn)/[s^2 + 2dWn*s + Wn^2]

do = 0.5U(t)

Do(s) = 0.5/s

Hence, Y(s) = ...

#### Solution Summary

In 560 words, this solution provides a step-by-step response which clearly indicates how to approach this feedback control system problem.