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: