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(Solved): DESIGN PROJECT 1 LEAD COMPENSATOR For the figure below, \( G(s)=9 / s(s+0.5) ...
![to shift the poles at new locations of
\[
s_{1}=-4+j 4 \text { and } s_{2}=-4-j 4
\]
- Obtain new transfer function by calcul](https://media.cheggcdn.com/media/316/316b6e40-f7a0-49b5-9da5-969f06a818b2/phpWoL8Bg)
DESIGN PROJECT 1 LEAD COMPENSATOR For the figure below, \( G(s)=9 / s(s+0.5) \) a) For the compensator \( G_{c}(s)=1 \) Obtain - Calculate the characteristic equation's roots, locate them on the \( S \) plane and obtain the unit step response values of; rising time, peak time, maximum overshoot and settling time for the \( 5 \% \) criterium. Are you happy about the performance ? Explain Why? b) In order to improve the step responses, design a lead compensator \( \mathrm{G}_{c}(\mathrm{~s}) \) to shift the poles at new locations of \( s_{1}=-4+j 4 \) and \( s_{2}=-4-j 4 \) - Obtain new transfer function by calculating \( \mathrm{K}_{\mathrm{c}}, \alpha \) and \( \mathrm{G}_{\mathrm{c}}(\mathrm{s}) \), and calculate the unit step response values. What kind of improvements have you got? c) Draw rooth locus and unit step response curves for case (a) and (b) by using MATLAB . d) Obtain the steady state errors for the ramp input for case (a) and case (b).
to shift the poles at new locations of \[ s_{1}=-4+j 4 \text { and } s_{2}=-4-j 4 \] - Obtain new transfer function by calculating \( \mathrm{K}_{\mathrm{c}}, \alpha \) and \( \mathrm{G}_{\mathrm{c}}(\mathrm{s}) \), and calculate the unit step response values. What kind of improvements have you got? c) Draw rooth locus and unit step response curves for case (a) and (b) by using MATLAB . d) Obtain the steady state errors for the ramp input for case (a) and case (b).