Consider the closed-loop control system shown below: \text { where } C(s)=K D_{c}(s) \text { and } G(s)=\frac{1}{(s+1)\left(\frac{s}{2}+1\right)\left(\frac{s}{5}+1\right)} The design requirements are given below: \text { 1. Stcady-state requircment: }

K_{p} \geq 9 \text { ( } K_{p} \text { is a static position crror constant.) } 2. Transient requirement: phase margin > 45 deg Problem 1. (10 points) Assuming De(s) = 1, dctcrminc K such that you can achicve thesteady-state requirement. Then, provide the Bode plot of the open-loop with the stabilitymargins (use "margin" command in MATLAB).