If the transfer functions of the plant and controller are given as

Plant: P(s)=1/s, (e.g., a normalized description of car velocity with force as the input; this can represent a cruise control system.)

Controller:C(s)=K((s+z)/s) , where K and z are constants.

Design a controller (select values of K and z) such that the following specifications are met:

Target crossover frequency = 1 rad/s (approximately equal to the closed-loop bandwidth).

Target phase margin is 60.

Show all your work and demonstrate your design meets these specifications by the use of allmargin command on the open-loop transfer function L(s) = P(s)C(s). (hint: help allmargin in Matlab). Include MATLAB code and results.

Plot the closed-loop frequency and step responses from the reference input r to the output y. Show the achieved bandwidth by marking on the Bode plot with a data cursor. Comment on how different, if so, it is from the specified bandwidth. Include MATLAB code and plots. (Read http://www.mathworks.com/help/matlab/creating_plots/data-cursor-displaying-data-values-interactively.html on how to use the data cursor.)

Plot the closed-loop frequency and step responses from the disturbance d to the output y. Does the steady state error e become 0 when a step disturbance d is applied to this closed loop transfer function? Include MATLAB code and plots.