2. (35 points) You wish to design a controller for a DC motor position control system. (a) Consider the following transfer function consisting of a PD compensator in series with the DC motor. 1 Gpd(s) = 5(s + 4). s(s+2) Sketch a straight-line approximation of the Bode plot of the above transfer function by hand. Check your result with the MATLAB command bode. (b) Now consider the DC motor in series with what is referred to as a lead compensator. s+4 1 Glead(s) = 150 's + 30 s(s+2) Again sketch a straight-line approximation of the Bode plot and check with MATLAB. (c) Based on the limited knowledge we have from class so far, discuss what the magnitude plots from Part (a) and Part (b) mean for how the system will respond differently under lead compensation as compared to PD control. (d) Determine the stability margins of the system given in Part (b) based on the MATLAB generated Bode plot. Is it possible to achieve a phase margin of 45 degrees simply by adding a gain K to the compensator? Explain. If it is possible, determine the value of gain K that would be necessary