CHEE 4703: Process Dynamics and Control

CHEE 4703: Process Dynamics and Control Fall 2024

Lab 3: Root Locus Diagram and Controller Tuning

Process Background Consider a blending process with two inlet streams and a single (overflow) outlet stream. Theschematic diagram of the process is shown in Figure 1, where x1, x2 and x represent the massfraction of component A and w1, w2 and w represents the overall mass flow rate. One of the inletstreams, stream 1, is made up of compound A (and the balance compound B). The mass fractionof A is a disturbance variable and has a steady state value of 20% (with a total steady state flowrate of 1 kg/min). The other inlet stream, stream 2, is made up of pure B, where the flow rate is a

manipulated variable. The outlet mass fraction of A is a controlled variable with a target of 10%.Assume that there is 10 kg of liquid in the tank (constant volume with a density similar to water).Figure 1.A blending process in a CSTR.Process Parameters The process operating conditions are as follows:𝐺𝑣= 𝑒−𝑎𝑠𝑠 ≈ 𝑠 − (𝑎𝑠 𝑎𝑠 + + 2 2 ) (1/1 𝑃𝑎𝑑é 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛)Figure 2.General representation of a closed loop process.Objectives

1. Determine the critical controller parameters using a root locus plot.
2. Evaluate the effect of delay on stability and critical controller parameter using root locus plots.
3. Apply the direct synthesis controller tuning method to the process and evaluate the responseto disturbance rejection.CHEE 4703: Process Dynamics and ControFall 2024Kathy Isaac, Stanislav SokolenkoPage 3 of 7Controller Setup

1. Implement a closed loop PI controller in Simulink to control the outlet mass fraction ofcomponent A by controlling the flow rate of stream 2 as illustrated in Figure 2.Use Transfer Fcn blocks to implement the process, Gp, disturbance, Gd, and the actuator,GvRefer to Prelab 2 to set up the appropriate controller in a closed loop process.

• Use Setpoint blocks for the setpoint and disturbance inputs and set the setpoint equal to aconstant value of 0 and the disturbance input to a constant value of 0.1.

Root Locus Diagram

2. Add a Pole-Zero Plot block and set the Disturbance input signal as the Input Perturbation anthe Process output signal as the Output Measurement. See the example provided at the end ofthis document for an example on setting up the root locus plot.

Questions

1. For the closed loop process with a PI controller with a delay of 1 s, set Kc = 1 and find thcritical τI. Make plots of the poles and zeros showing the transition from stable to unstable atthe critical τI. Include 3 代寫 CHEE 4703: Process Dynamics and Control plots: stable, critical and unstable. Repeat for delays of 3 and 5 s. Note:

Set the Setpoint block constant at 0 and the Disturbance Step block constant at 0.1

How does the critical τI change with increase in delay?

1. For the closed loop process with a PI controller with a delay of 1 s, set τI = 10 and find thecritical Kc.Make a plot of the poles and zeros showing the transition from stable to unstable atthe critical Kc. Include 3 plots: stable, critical and unstable. Repeat for delays of 3 and 5 s.Note: Set the Setpoint block constant at 0 and the Disturbance Step block constant at 0.1

How does the critical Kc change with increase in delay?CHEE 4703: Process Dynamics and ControFall 2024Kathy Isaac, Stanislav SokolenkoPage 4 of 7When there is no delay in the actuator, tune the PI controller using the direct synthesis methodand evaluate the response to a step change of 0.1 in the disturbance variable to different valuesof τc between 10 and 100. Note: set the initial value of the disturbance input to 0 and the final

value to 0.1.

1. How does τc affect the process response?
2. What τc should be chosen if the process must reject a step disturbance of 0.1 in unde60 seconds with no large oscillations.

Report Guidelines

1. Use the lab report template provided.
2. The report must seek to concisely answer the questions in the previous section.
3. The text of the report body must be within 1 page. It is recommended to use a 12-point font,1.5 spaced but please use 11-point font, single spaced at a minimum.

4. Do not break up the text. Add all the text to page 1 and refer to figures and tables on subsequent

pages to aid your discussion.Include a screenshot of your complete Simulink model for the PI controller set up in Question-

Pole-Zero Plot Example for the Heating Tank Process Set up the closed loop for the given process and controller. Set the Setpoint block constant at0 and the Disturbance Step block constant at 1. CHEE 4703: Process Dynamics and ControlFall 2024Kathy Isaac, Stanislav SokolenkoPage 5 of 7Add a Pole-Zero Plot block to the workspace

2. Double click on the Pole-Zero Plot block and click on the + symbol to add inputs and outputs
3. Click on the disturbance signal (highlighted in blue) and press the << symbol to add the

signal. Repeat for the Output signal.CHEE 4703: Process Dynamics and ControlFall 2024Kathy Isaac, Stanislav SokolenkoPage 6 of 7

5. Once added, change the Configuration of the input signal to Input Perturbation and theoutput to Output Measurement and click Apply. Change the snapshot time to 1.

6. Click on Show PlotCHEE 4703: Process Dynamics and ControlFall 2024Kathy Isaac, Stanislav Sokolenko

7. Click on the green Run button to display the poles and zeros. Poles are represented by x andzeros by o. Click on them to see their exact values

8. Change controller parameters and assess how the poles and zeros change.
9. a) Kc = 1, 𝜏