F2. Controller design to meet time domain specifications (30 points) Consider a linear dynamic system with transfer function 250 G(s)= (s+5)(s+50) Design a feedback controller K(s) meeting the following specifications Asymptotic tracking of steps Maximum fractional overshoot Mp ≤ 0.1 A raise time that is less than 0.25s. a) Provide the expression of the controller. b) Provide the plot of the step response. Hint If the specifications are not exactly met because of inaccuracies in the empirical formulas of the second order prototype, typically a higher static proportional gain k in the controller K(s) makes the system "faster" and a lower k makes it more "damped." Tweaking k as a final step to fine tune the design is totally acceptable.