Implementing a PID controller in Python

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: