Design a $$P$$ controller, such that the closed$-$loop system has a damping

ratio larger than $0\mathrm{.}6.$ Discuss the tradeoff among the rising time, peak

time, settling time, and steady$-$state error. Simulate the closed$-$loop

system $($and obtain its unit step response, and the corresponding

overshoot, rising time, peak time, settling time, steady$-$state error$).$

$(2)$ Design a $$PI$$ controller such that the closed$-$ loop system has an

overshoot smaller than $10\%.$ You have design freedom on choosing

different pairs of the controller parameters. Discuss the tradeoff among

the rising time, peak time, settling time, and steady$-$state error. Simulate

the closed$-$loop system $($and obtain its unit step response, and the

corresponding overshoot, rising time, peak time, settling time, steady$-$

state error$).$

$(3)$ Compare the two controllers and discuss their pros and cons.