The following Python code creates a PID generator that can be use for feedback control. This the same generator we developed in class on Thursday, with an additional filter used for a more robust implementation of derivative action. In today's laboratory you will use this code to test several aspects of feedback control of the TCLab heater.
def PID(Kp, Ki, Kd, MV_bar=0, beta=1, gamma=0):
# initialize stored data
t_prev = -100
P = 0
I = 0
D = 0
S = 0
N = 10
# initial control
MV = MV_bar
while True:
# yield MV, wait for new t, SP, PV, TR
data = yield MV
# see if a tracking data is being supplied
if len(data) < 4:
t, SP, PV = data
else:
t, SP, PV, TR = data
I = TR - MV_bar - P - D
# PID calculations
P = Kp*(beta*SP - PV)
I = I + Ki*(SP - PV)*(t - t_prev)
eD = gamma*SP - PV
D = N*Kp*(Kd*eD - S)/(Kd + N*Kp*(t - t_prev))
MV = MV_bar + P + I + D
# Constrain MV to range 0 to 100 for anti-reset windup
MV = 0 if MV < 0 else 100 if MV > 100 else MV
I = MV - MV_bar - P - D
# update stored data for next iteration
S = D*(t - t_prev) + S
t_prev = t
The cell below is a starter code to implement feedback control. The code establishes a setpoint of 40°C, and for the first 30 seconds runs under manual control. The control then transfers to automatic. Do you observe bumpless transfer? Explain what you see.
%matplotlib inline
from tclab import clock, setup, Historian, Plotter
TCLab = setup(connected=True)
controller = PID(Kp=2, Ki=0.1, Kd=2, beta=0) # create pid control
controller.send(None) # initialize
tfinal = 600
SP = 40
with TCLab() as lab:
sources = [('SP', lambda: SP), ('T1', lambda: lab.T1), ('MV', lambda: MV), ('Q1', lab.Q1)]
h = Historian(sources)
p = Plotter(h, tfinal)
for t in clock(tfinal, 2):
PV = lab.T1 # get measurement
MV = controller.send([t, SP, PV, lab.U1]) # for bumpless transfer
if t < 100: # choice between manual and auto control
MV = 50
lab.U1 = MV # apply
p.update(t) # update information display
from tclab import diagnose
diagnose()
Looking for Arduino on ... NHduino found on port /dev/cu.wchusbserial1410 Testing TCLab object in debug mode ---------------------------------- TCLab version 0.4.6dev Sent: "Q1 0" Return: "" Sent: "Q1 0" Return: "0" Could not connect at high speed, but succeeded at low speed. This may be due to an old TCLab firmware. New Arduino TCLab firmware available at: https://github.com/jckantor/TCLab-sketch Sent: "VER" Return: "TCLab Firmware Version 1.2.1" NHduino connected on port /dev/cu.wchusbserial1410 at 9600 baud. TCLab Firmware Version 1.2.1. Sent: "Q2 0" Return: "0" Reading temperature Sent: "T1" Return: "27.02" 27.02 Sent: "Q1 0" Return: "0" Sent: "Q2 0" Return: "0" Sent: "X" Return: "X" TCLab disconnected successfully. Testing TCLab functions ----------------------- TCLab version 0.4.6dev Could not connect at high speed, but succeeded at low speed. This may be due to an old TCLab firmware. New Arduino TCLab firmware available at: https://github.com/jckantor/TCLab-sketch NHduino connected on port /dev/cu.wchusbserial1410 at 9600 baud. TCLab Firmware Version 1.2.1. Testing LED. Should turn on for 10 seconds. Countdown: 0 Reading temperatures T1 = 26.05 °C, T2 = 26.05 °C We will now turn on the heaters, wait 30 seconds and see if the temperatures have gone up. Countdown: 0 T1 started a 26.05 °C and went to 31.86 °C T2 started a 26.05 °C and went to 28.63 °C TCLab disconnected successfully. Diagnostics complete
Create a new experiment in the cell below. The new experiment should do the following:
Run the experiment for at least 800 seconds. How would describe the behavior at the point when the setpoint is changed?
from tclab import diagnose
diagnose()
Looking for Arduino on ... NHduino found on port /dev/cu.wchusbserial1410 Testing TCLab object in debug mode ---------------------------------- TCLab version 0.4.6dev Sent: "Q1 0" Return: "" Sent: "Q1 0" Return: "0" Could not connect at high speed, but succeeded at low speed. This may be due to an old TCLab firmware. New Arduino TCLab firmware available at: https://github.com/jckantor/TCLab-sketch Sent: "VER" Return: "TCLab Firmware Version 1.2.1" NHduino connected on port /dev/cu.wchusbserial1410 at 9600 baud. TCLab Firmware Version 1.2.1. Sent: "Q2 0" Return: "0" Reading temperature Sent: "T1" Return: "21.54" 21.54 Sent: "Q1 0" Return: "0" Sent: "Q2 0" Return: "0" Sent: "X" Return: "X" TCLab disconnected successfully. Testing TCLab functions ----------------------- TCLab version 0.4.6dev Could not connect at high speed, but succeeded at low speed. This may be due to an old TCLab firmware. New Arduino TCLab firmware available at: https://github.com/jckantor/TCLab-sketch NHduino connected on port /dev/cu.wchusbserial1410 at 9600 baud. TCLab Firmware Version 1.2.1. Testing LED. Should turn on for 10 seconds. Countdown: 0 Reading temperatures T1 = 22.19 °C, T2 = 22.51 °C We will now turn on the heaters, wait 30 seconds and see if the temperatures have gone up. Countdown: 5