Consider a plant given by G(s) = 1 (s+2)(2s+1) in a unity feedback structure.

(a) Determine the system type and the steady state error with respect to a tracking polynomial reference input with a proportional controller, D(s) = 5.
(b) Verify your result using MATLAB by plotting unit step and ramp responses. Use the Matlab command lsim() for ramp input. Attach the code and the plots.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.