# HW 7 problem 4

This problem focuses on frequency domain specifications and loop shaping. You should learn in fact how to shape the frequency response of a plant so that it will present some desired properties.

Following the paradigm showed in class (Lecture 8-1, slide 5), you should plot the Bode diagram for the plant considered and mark on such graph the performance specifications required.

Based on the specifications, you should find what type of controller you need: make sure you understand what yields to gain and phase changes for the overall system. You should not do this by trial and error, but reason in terms of what you need to "add" to the open loop system to have the required behavior; add only the controller terms that are necessary. Don't forget to verify that the new system L(s)=P(s)C(s) satisfies the specifications.

Finally, you need to plot step and frequency response for the closed loop system, using the known MATLAB commands, finding rise time, overshoot, settling time and steady state error.