In this section, we'll build a Python application to implement a PID controller. In general, our program flowchart can be described as follows:
We should not build a PID library from scratch. You can translate the PID controller formula into Python code easily. For implementation, I'm using the PID class from https://github.com/ivmech/ivPID. The following the PID.py file:
import time
class PID:
"""PID Controller
"""
def __init__(self, P=0.2, I=0.0, D=0.0):
self.Kp = P
self.Ki = I
self.Kd = D
self.sample_time = 0.00
self.current_time = time.time()
self.last_time = self.current_time
self.clear()
def clear(self):
"""Clears PID computations and coefficients"""
self.SetPoint = 0.0
self.PTerm = 0.0
self.ITerm = 0.0
self.DTerm = 0.0
self.last_error = 0.0
# Windup Guard
self.int_error = 0.0
self.windup_guard = 20.0
self.output = 0.0
def update(self, feedback_value):
"""Calculates PID value for given reference feedback
.. math::
u(t) = K_p e(t) + K_i int_{0}^{t} e(t)dt + K_d {de}/{dt}
.. figure:: images/pid_1.png
:align: center
Test PID with Kp=1.2, Ki=1, Kd=0.001 (test_pid.py)
""
error = self.SetPoint - feedback_value
self.current_time = time.time()
delta_time = self.current_time - self.last_time
delta_error = error - self.last_error
if (delta_time >= self.sample_time):
self.PTerm = self.Kp * error
self.ITerm += error * delta_time
if (self.ITerm < -self.windup_guard):
self.ITerm = -self.windup_guard
elif (self.ITerm > self.windup_guard):
self.ITerm = self.windup_guard
self.DTerm = 0.0
if delta_time > 0:
self.DTerm = delta_error / delta_time
# Remember last time and last error for next calculation
self.last_time = self.current_time
self.last_error = error
self.output = self.PTerm + (self.Ki * self.ITerm) + (self.Kd * self.DTerm)
def setKp(self, proportional_gain):
"""Determines how aggressively the PID reacts to the current error with setting Proportional Gain"""
self.Kp = proportional_gain
def setKi(self, integral_gain):
"""Determines how aggressively the PID reacts to the current error with setting Integral Gain"""
self.Ki = integral_gain
def setKd(self, derivative_gain):
"""Determines how aggressively the PID reacts to the current error with setting Derivative Gain"""
self.Kd = derivative_gain
def setWindup(self, windup):
"""Integral windup, also known as integrator windup or reset windup,
refers to the situation in a PID feedback controller where
a large change in setpoint occurs (say a positive change)
and the integral terms accumulates a significant error during the rise (windup), thus overshooting and continuing
to increase as this accumulated error is unwound
(offset by errors in the other direction).
The specific problem is the excess overshooting.
"""
self.windup_guard = windup
def setSampleTime(self, sample_time):
"""PID that should be updated at a regular interval.
Based on a pre-determined sample time, the PID decides if it should compute or return immediately.
"""
self.sample_time = sample_time
For testing, we'll create a simple program for simulation. We need libraries such as numpy, scipy, pandas, patsy, and matplotlib. Firstly, you should install python-dev for Python development. Type these commands on a Raspberry Pi terminal:
$ sudo apt-get update
$ sudo apt-get install python-dev
Now you can install the numpy, scipy, pandas, and patsy libraries. Open a Raspberry Pi terminal and type these commands:
$ sudo apt-get install python-scipy
$ pip install numpy scipy pandas patsy
The last step is to install the matplotlib library from the source code. Type these commands into the Raspberry Pi terminal:
$ git clone https://github.com/matplotlib/matplotlib
$ cd matplotlib
$ python setup.py build
$ sudo python setup.py install
After the required libraries are installed, we can test our PID.py code. Create a script with the following contents:
import matplotlib
matplotlib.use('Agg')
import PID
import time
import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import spline
P = 1.4
I = 1
D = 0.001
pid = PID.PID(P, I, D)
pid.SetPoint = 0.0
pid.setSampleTime(0.01)
total_sampling = 100
feedback = 0
feedback_list = []
time_list = []
setpoint_list = []
print("simulating....")
for i in range(1, total_sampling):
pid.update(feedback)
output = pid.output
if pid.SetPoint > 0:
feedback += (output - (1 / i))
if 20 < i < 60:
pid.SetPoint = 1
if 60 <= i < 80:
pid.SetPoint = 0.5
if i >= 80:
pid.SetPoint = 1.3
time.sleep(0.02)
feedback_list.append(feedback)
setpoint_list.append(pid.SetPoint)
time_list.append(i)
time_sm = np.array(time_list)
time_smooth = np.linspace(time_sm.min(), time_sm.max(), 300)
feedback_smooth = spline(time_list, feedback_list, time_smooth)
fig1 = plt.gcf()
fig1.subplots_adjust(bottom=0.15)
plt.plot(time_smooth, feedback_smooth, color='red')
plt.plot(time_list, setpoint_list, color='blue')
plt.xlim((0, total_sampling))
plt.ylim((min(feedback_list) - 0.5, max(feedback_list) + 0.5))
plt.xlabel('time (s)')
plt.ylabel('PID (PV)')
plt.title('TEST PID')
plt.grid(True)
print("saving...")
fig1.savefig('result.png', dpi=100)
Save this program into a file called test_pid.py. Then run it:
$ python test_pid.py
This program will generate result.png as a result of the PID process. A sample output is shown in the following screenshot. You can see that the blue line has the desired values and the red line is the output of the PID:
