Given the following plant transfer function s2 +10s +20 g(o) - s'+12s +47s+60
(a) find the observable canonical state-space representation
(b) design a state-feedback controller to have a set of dominant closed-loop poles that achieve 10% overshoot and a 2% setting time of 1 second. if needed, place remaining pole(s) 5 times further from the imaginary axis than the dominant complex pole pair (i. e, the real part of the faster pole(s) is 5 times the real part of the dominant complex poles). do not forget to set the reference command gain to achieve closed-loop steady- state gain of 1.
(c) find the closed-loop transfer function

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.