A continuous stirred tank reactor (CSTR) is cooled with an externally installed jacket. The temperature in the CSTR is controlled by controlling the flow rate of coolant (regulating coolant valve) to the jacket Please consider the information about the different parts of the control system: The pressure drop across the valve is constant. It passes 10 kg/s if fully open. Its time constant is negligible; The transfer function Gr(s) of the jacket temperature to the coolant flow is a first order lag with a gain of 3.5 C / (kg/s) and a time constant of 2 min. The transfer function Grr(s) of the reactor temperature to the jacket temperature is a first order lag with a gain of 0.33C/C and a time constant of 9 min. The sensor/transmitter for the jacket temperature has a range of 55 to 100C and a time constant of 1.5 min The sensor/transmitter for the reactor temperature has a range of 0 to 100C and a negligible time constant A) Write the equations for the transfer functions of the valve (G(s)), the Gr(s), Ger(s) and the reactor and jacket temperature sensor/transmitters (17x(s) and Hy(s)) - 6 points B) Sketch a block diagram of the (single) feedback control system - 6 points C) Write down the characteristic equation of the feedback control loop. - 12 points a D) Change the system from a single feedback loop to a cascade control system. Sketch the jacketed reactor in your paper and add a sketch of the cascade control system to it - 6 points Sketch a block diagram of the cascade control system.- 6 points E) Consider that the slave controller used for controlling the jacket temperature is a proportional controller with a controller gain of 4.5 % CO% TO. Use the substitution method to calculate the ultimate gain and period of the cascade control loop. 24 points