Lab 3: Relay (On-Off) Control#
Your Name:
In this lab assignment you will implement relay control for the Temperature Control Laboratory. The class website explains the Python interface to the TCLab in more detail.
Implement and test a relay control for the heater/sensor system
Implement and test a relay control to track a complex setpoint.
Spring 2025 TODO List:#
Rename from Lab 2 to Lab 3
Complete solutions for Exercise 0
Add a discussion question comparing Exercise 0 and Exercise 1 results
Excercise 0. Simulation#
This exercise is due BEFORE the start of lab. It is a pre-lab assignment. Your task:
Read the entire lab assigment. If you have a question, post to Canvas.
Create a plot showing the setpoints described in Excercise 1.
On paper (or a tablet), write down the system of differential equations for the TCLab with the simple relay controller described in Exercise 1. Include in your model the intial conditions for each state.
Using Python, numerically simulate the system of differential equations. Use the TCLab model parameters you estimated in Lab 2 for your personal TCLab hardware.
### Create a plot showing the setpoints described in Exercise 1
# modify these setpoints to change with time
def SP1(t):
"""Set point definition for T1
Arguments:
t: time (s)
Returns:
set point of T1
"""
return 40
def SP2(t):
"""Set point definition for T2
Arguments:
t: time (s)
Returns:
set point of T2
"""
return 35
# Add your solution here
### Simulate differential equations for the TCLab system plus relay controller
# Add your solution here
Exercise 1. Simple Relay Control for TC Lab#
Create a relay controller subject to the following requirements:
Simultaneous control of sensor temperatures T\(_1\) and T\(_2\) to setpoints 35 and 40 °C, respectively. The setpoints return to 25 °C at t = 300.
Use a tolerance value \(d\) of 0.5 °C.
Set the minimum and maximum values of the heater to 0 and 100%, respectively. lab.P1 and lab.P2 should be left at their default values.
Show the results of an experiment in which the setpoints are adjusted accordingly.
Some started code is include below.
# As a first step, let's verify the sample code runs
from tclab import TCLab, clock, Historian, Plotter, setup
TCLab = setup(connected=True)
# modify these setpoints to change with time
def SP1(t):
"""Set point definition for T1
Arguments:
t: time (s)
Returns:
set point of T1
"""
return 40
def SP2(t):
"""Set point definition for T2
Arguments:
t: time (s)
Returns:
set point of T2
"""
return 35
# relay controller
def relay(SP, d=1, Umin=0, Umax=100):
"""Relay controller definition
Arguments:
SP: set point function
d: set point tolerance
Umin: minimum heater output (%)
Umax: maximum heater output (%)
Returns:
none
"""
#start with the heater off
U = 0
#while the simulation is active (t<tfinal)
while True:
t, T = yield U
#When T is below the set point, turn on heater
if T < SP(t) - d/2:
U = Umax
#When T is above the set point, turn off heater
if T > SP(t) + d/2:
U = Umin
# create a single control loop for T1
controller1 = relay(SP1)
controller1.send(None)
#simulate with TCLab
t_final = 60 # change this to 500 seconds for the actual experiment
t_step = 1
with TCLab() as lab:
sources = [("T1", lambda: lab.T1), ("T2", lambda: lab.T2),
("SP1", lambda: SP1(t)), ("SP2", lambda: SP2(t)),
("Q1", lab.Q1), ("Q2", lab.Q2)]
#load historian
h = Historian(sources)
#load plotter
p = Plotter(h, t_final, layout=(("T1", "SP1"), ("T2", "SP2"), ("Q1", "Q2")))
#While time is less than tfinal
for t in clock(t_final, t_step):
# This starter code only manipulates U1 to control T1.
# Your specifications also give a setpoint for T2
T1 = lab.T1
#Send the controller time and T1 data
U1 = controller1.send([t, T1])
lab.Q1(U1)
#Read data and update plot
p.update()
# Verify your device has cooled back to ambient
tfinal = 30 #seconds
# perform experiment
with TCLab() as lab:
#Set power to 0
lab.U1 = 0
lab.U2 = 0
#load historian
h = Historian(lab.sources)
#Load plotter
p = Plotter(h, tfinal)
#While time is less than tfinal
for t in clock(tfinal):
#Read data and update plot
p.update(t)
# Copy the code from above and modify to match the specifications
# Add your solution here
Exercise 2. Tempering Chocolate#
We now want to create a rely controller that matches the temperature profile for tempering chocolate.
Temperature 1 specifications:
Start from ambient.
Reach 50 °C at 3 minutes, 27 °C at 7 minutes, return to 32 °C at 8 minutes, and hold until 10 minutes.
The goal is follow the linear ramp between setpoints as closely as possible.
Temperature 2 specifications:
Start from ambient, ramp, and then hold at 30 °C.
Hints:
Modify SP1 to linearly interpolate the set point as a function of time.
# Copy your code from above and modify to match the specifications
# Add your solution here
Discussion#
Write a 1 to 3 sentences to answer each of the following questions.
Describe the shape of the temperature profiles (time-series) for the excrise 1 experiment. Are these shapes expected?
Answer:
Speculate about why T1 overshoots the setpoint more than T2 in the excerise 1 experiment.
Answer:
In the cholcate tempering simulation, how many times does each heater transitions from (a) one to off and (b) off to on? Fill in the table below.
Sensor |
On to Off |
Off to On |
|---|---|---|
T1 |
||
T2 |
Answer:
Descibe the shape of the T1 and T2 timeseries for the excerise 2 experiment. How do the T1 and T2 profiles relate to the on/off and off/on transitions for Q1 and Q2?
Answer:
How can we reduce the oscillations in these experiments? Propose at least one idea and provide reasoning for why it could work.
Answer:
Consider the following feedback diagram from the first day of class:
Identify the variables in each of the categories for our temperature control lab.
Maninpulated Variable(s):
Answer:
Controlled Variable(s):
Answer:
Process/Measured Variable(s):
Answer:
Set Point Variable(s):
Answer:
Disturbance Variable(s):
Answer:
How can we reduce the oscillations in these experiments? Propose at least one idea and provide reasoning for why it could work.
Answer:
Common Mistakes#
Not using the correct kernel (for the controls environment with TCLab installed)
Not setting up controller #2 (This includes assigning T2 and Q2 in the simulation code)
When switching to
connected=Truemost got errors if they did not restart the kernel and clear all the cells outputTrying to create their own linear interpolation function, just use
np.interp
Declarations#
Collaboration: If you worked with any classmates, please give their names here. Describe the nature of the collaboration.
Generative AI: If you used any Generative AI tools, please elaborate here.
Reminder: The written discussions responses must be in your own words. Many of these questions ask about your specific results or are open-ended questions with many reasonable answers. Thus we expect unique responses, analyses, and ideas.
We may use writing analysis software to check for overly similar written responses. You are responsible for reviewing the colaboration policy outlined in the class syllabus to avoid violations of the honor code.