Use the Simulink block diagram built in Example 10.10 to find the unit-step responses for \(k_{\mathrm{D}}=1,10\), and 50 . Set \(k_{\mathrm{p}}=250\) and \(k_{\mathrm{I}}=500\). Discuss the effects of the derivative term on the unit-step response.

Data From Example 10.10:

Consider the mass-damper-spring system in Example 10.9, \[G(s)=\frac{1}{s^{2}+8 s+40}\]
Use Simulink to build a block diagram for proportional feedback control. Find the unit-step responses for \(k_{\mathrm{p}}=25,250\), and 2000. Discuss the effects of the proportional feedback on the unit-step response.

Data From Example 10.9:

Consider a mass-damper-spring system \(G(s)=Y(s) / U(s)=1 /\left(m s^{2}+b s+k\right)\), where \(m=1 \mathrm{~kg}, b=8 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}\), and \(k=40 \mathrm{~N} / \mathrm{m}\).