Cоntrоl System Design fоr а Volаtile Reаctor-Gas Scrubber System A specialty chemical plant operates a continuous volatile polymerization reactor that releases a toxic gas by-product (NOx) as part of its process. The reactor is cooled using a chilled ethylene glycol jacket, and the NOx emissions are controlled by a gas scrubber system that injects caustic solution to neutralize the gas before release. Reactor Temperature Control The reactor’s temperature behavior with respect to coolant flow is characterized by a first-order transfer function: Where: T(s) the deviation of reactor temperature from nominal (°C), Q(s) is the deviation of coolant flow rate (L/min) from nominal (500 L/min), The temperature is measured by an Resistance Temperature Detector (RTD) with a first-order lag of 20 s, The valve controlling coolant has a time constant of 25 s and is normally 50% open. The transmitter outputs 0–10 V for 50–150 °C, and the controller outputs 0–10 V to the valve. NOx Scrubber Emission Control The scrubber has been tested and exhibits the following transfer function: where: CNOx(s) is the NOx concentration deviation (ppm) from nominal (200 ppm), FNaOH(s) is the flow rate of caustic solution (L/min) from nominal (150 L/min), The sensor has a measurement gain of 2.0 mV/ppm and no delay, The actuator (a dosing pump) has a gain of ±1.5 L/min/V and exhibits a 0.2 min time constant. The controller used is a PI controller with positive proportional gain, and the integral time constant is 0.6 min. 1. [SISO Design] For the reactor temperature control loop, identify: Controlled Variable (CV) Manipulated Variable (MV) Likely Disturbances (DVs) Then, sketch the instrument diagram and block diagram for the temperature control loop (take screen shot of your Simulink setup) 2. [Controller & Valve Action]Considering the reactor is exothermic and the process gain is negative, determine: The appropriate controller action (direct or reverse) The valve action (fail-open or fail-closed) 3. Sketch the instrument diagram and block diagram for the NOx control loop (take screen shot of your Simulink setup) Justify your answer. [Stability of NOx Control] For the NOx scrubber control system: Determine whether the actuator gain should be positive or negative, assuming the PI controller has a positive proportional gain. Justify based on the loop gain. [PI Controller Tuning: Stability Limit]For the NOx system, determine the range of proportional gain Kc that results in a stable closed-loop system with the given PI controller. Show your work. [Alternative Tuning: PD Controller]Suppose a PD controller with a derivative time constant of 0.6 min is used instead. What range of Kc ensures closed-loop stability? [Damping Design]If a damping ratio of 0.6 is desired for the NOx control loop, choose between PI or PD controller and estimate the value of Kc required. What is the corresponding natural frequency of the closed-loop system? [Realistic System Simulation]Now account for the measurement and actuator dynamics in the NOx system. Use your chosen controller from PI controller tunning (2) and PD Controller tuning (3) and simulate the response to a −15 ppm step decrease in NOx setpoint. Sketch or describe the expected system behavior. Please include the Simulink output for both cases and clearly indicate your tuning parameters [Controller Output Analysis]Based on your simulation (5), describe how the controller output (in volts) would behave initially and over time. Comment on whether there is an initial jump, a steady change, or overshoot in the controller signal.
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