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Feedback Control Systems: Systems Specifications

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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.

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

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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)
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.

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) = ...

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