Question

3. Consider the unity-feedback system of Figure P9.1, with G(s)=\frac{K(s+5)}{(s+2)(s+3)(s+7)(s+10)} a. Draw the root locus. b. Find the location of the dominant poles when 3 = 0.8. c. Find the gain at which = 0.8. d. If the system is to be cascade-compensated to attain T3 = 1second and = 0.8, find the compensator pole if the compensator zero is at -4. e. Make an argument for the validity of your second-order approximation. Verify the validity of your design by simulating your system using MATLAB or any other computer program.

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