\text { Consider a unity-gain feedback system with } G(s)=\frac{4}{s(s+0.5)} \cdot(10+10+10=30 \text { pts) } \text { Design (any way you want) a lead-lag controller } G_{c}(s) \text { such that ( } 6 \text { [lead] }+4[\mathrm{lag}]=10 \mathrm{pts} \text { ) } \text { (i) the damping ratio of the closed-loop system is } \delta \geq 0.8 \text {, } \text { (ii) the closed-loop undamped natural frequency is } \omega_{n}=25 \mathrm{rad} / \mathrm{s} \text {, and } \text { (iii) } \quad K_{\nabla} \geq 20 b) We want an op-amp based realization of this controller. Use lecture 13 to draw me an op-amp based realization, with the component (resistance and capacitance) values computed. c) Discretize the controller and show me simulations (1 plot) with the analog and digital implementations compared for 3 different values of the sampling period, as was done in the last figure of lecture 13. Make sure you send me any Simulink files, and add the code that you used for your plots as part of your solution.

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