1. A system has the transfer function: e 2s Gp(s) = $2 + 5 The system is controlled by a proportional-integral controller with t, = 0.5 minute. The sensor and final control element transfer function, Gm(s) and G (S) are assumed to equal 1. a) Use the Routh-Hurwitz criterion method to show the stability of the system. b) What is the value of Kc where the system becomes unstable? c) Determine the output response y(1) whence the process encountered with a load disturbance change or the input function of the unit step of 5/s in the Laplace domain. The system undergoes the disturbance transfer function of Gas) = 2s and PI control is also used with Kc= 2 and t; = 0.5 minute. 20 points Nitrogen gas enters an adiabatic turbine at 850 degree Celsius and 1.7 MPa at a rate of 850 kg/min and exhausts at 200 kPa. If the turbine efficiency is 0.75, calculate the power output (in kW) and the exhaust temperature of nitrogen (in degree Celsius)