Here you will continue with the same system model as the previous problem and will again use simple pro- portional feedback control. Your goal is to design a proportional controller that meets the following step response specifications: tr 0.4 sec, Mp 50% (a) Determine a range of values for the damping ratio and natural frequency that would satisfy the given performance specifications. (b) Next, determine a proportional controller gain K for which the system is critically damped. (c) Plot the step response for the value of controllers K = 0.5, 1, 2, 5, 8 using the step() command in MATLAB. Explain how the overshoot and rise time change as the controller gain increases. (d) Determine the range of K for which the rise time meets the desired specification. (e) Determine the range of K for which the overshoot meets the desired specification. (f) Do the above ranges have a nonempty intersection? If yes, choose a value of K from the intersection and plot the step response. If no, then find the value of K whose maximum distance from the above two ranges is minimum and plot the corresponding step response. Make sure that you have met the specifications