Let's solve each part step by step: --- ### **a) Identify the control objectives for the operation of the two CSTRs.** **Control objectives:** - **Maintain desired product concentration/quality:** Ensure the concentration of product B at the outlet is at setpoint. - **Maintain reactor temperatures:** Since the reaction is endothermic, controlling temperature is critical for reaction rate and conversion. - **Ensure safe operation:** Avoid unsafe temperatures or pressures. - **Maintain stable operation:** Prevent oscillations or instability in the process. --- ### **b) Classify the variables of the system into inputs and outputs.** **Inputs:** - Flow rate of Reactant A - Flow rate of Catalyst - Flow rate of steam to each reactor (affects temperature) - Initial concentrations of A and catalyst **Outputs:** - Concentration of product B (final product) - Temperature in each reactor - Concentrations of A and B in each reactor --- ### **c) Classify the inputs and outputs further into disturbances and manipulated variables, and the outputs into measured and unmeasured.** #### **Inputs:** - **Manipulated Variables (MV):** - Steam flow rates to reactors (can be adjusted) - (Possibly) feed flow rates of A and catalyst - **Disturbances (D):** - Fluctuations in feed concentrations (A, catalyst) - Variations in steam supply pressure/temperature #### **Outputs:** - **Measured Outputs:** - Reactor temperatures (usually measured) - (Possibly) product flow rate - **Unmeasured Outputs:** - Product concentration (often not measured directly if analyzer is not available) - Intermediate concentrations --- ### **d) Is the system SISO or MIMO?** - **MIMO (Multiple-Input, Multiple-Output):** - There are multiple manipulated variables (steam flows, perhaps feeds) and multiple outputs (temperatures, concentrations). - The variables are often coupled (changing one affects others). --- ### **e) Develop a feedback system that satisfies your objectives.** **Feedback system:** - **Measure reactor temperatures** with sensors. - **Compare** measured values to setpoints for each reactor. - **Controller** (PID or similar) adjusts steam flow to each reactor to maintain setpoint temperature. - **If product concentration is measured**, feedback can also be used to adjust feed or steam to maintain product quality. --- ### **f) Develop an inferential control configuration that uses temperatures and flow rates only.** - Since analyzers are not available, **estimate (infer) product concentration** from temperature and flow rates: - Use a model (e.g., first-principles or empirical) to relate temperature/flow to conversion. - Control system uses reactor temperatures and flow rates as proxies for product quality. - Adjust steam and feed rates based on these inferred values. --- ### **g) Develop a feedforward control configuration.** - **Feedforward control** anticipates disturbances: - Measure disturbances (e.g., changes in feed concentration, steam supply). - Use a process model to calculate the required adjustment to steam or feed flow to compensate before the output is affected. - Combine with feedback for best performance. --- ### **h) Under what condition is a cascade control system required?** - **Cascade control** is used when: - There are **significant disturbances** (e.g., in steam supply pressure) that affect the inner loop variable (jacket temperature). - The inner loop (e.g., jacket temperature) responds faster than the primary variable (reactor temperature). - Improves disturbance rejection and overall control performance. --- ### **i) Sketch the cascade control system for the two tanks.** Here's a simple sketch description: ``` [Reactor 1] Setpoint (T1) ----> [Master Controller] ----> Setpoint (Jacket T1) ----> [Slave Controller] ----> Steam Valve 1 [Reactor 2] Setpoint (T2) ----> [Master Controller] ----> Setpoint (Jacket T2) ----> [Slave Controller] ----> Steam Valve 2 - Master Controller: Controls reactor temperature - Slave Controller: Controls jacket temperature (inner loop) - Each tank has its own cascade loop ``` --- ## **Summary Table** | Part | Answer | |------|--------| | a | Maintain product quality, reactor temperatures, safe and stable operation | | b | Inputs: Feed & steam flows; Outputs: Product conc., temp. | | c | MV: Steam, feeds; D: Disturbances in feed/steam; Outputs: Measured (temp), Unmeasured (conc.) | | d | MIMO system | | e | Feedback via temperature (and/or concentration) control | | f | Inferential control using temperature and flow as proxies | | g | Feedforward control using measured disturbances | | h | Cascade needed when inner loop variable (jacket T) is faster and disturbed | | i | Cascade: Reactor temp (outer) → Jacket temp (inner) → Steam valve (per tank) | --- If you need a detailed diagram for part (i), let me know!