Gene Expression Control using PID Control

# Gene Expression Control using PID Control
# Yong-Jun Shin (2020)

import numpy as np
import matplotlib.pyplot as plt

N = 100                       # total number of data points
n = np.arange(0, N, 1)        # [0,..., N-1] (vector)
x = np.empty(N)               # protein x concentration in uM (vector)
r = np.empty(N)               # reference concentration in uM (vector)
r.fill(10)                    # constant reference concentration (= 10 uM)
c = np.empty(N)               # control light effect on concentration in uM (vector)
                              # red light (positive values) enhances protein production
                              # blue light (negative values) enhances protein degradation
e = np.empty(N)               # error(r - x) in uM (vector)
sum_e = np.empty(N)           # error sum in uM (vector)
diff_e = np.empty(N)          # error difference (current error - previous error) in uM (vector)
d = np.empty(N)               # disturbance in uM (vector)
angle = np.arange(0, 2*np.pi, 2*np.pi/N)  # angle from 0 to 2pi in radian (N data points)
d = 2*np.sin(angle)           # sine wave disturbance (1 cycle) 
x[0] = 12                     # initial protein x concentration in uM
e[0] = r[0] - x[0]            # initial error(r - x)
sum_e[0] = e[0]               # initial error sum
diff_e[0] = 0                 # initial error difference (current error - previous error)
Kp = 0                        # proportional gain 
Ki = 0                        # integral gain 
Kd = 0                        # derivative gain 
Px = 0.9                      # degradation parameter

for i in range (1, N):                                         # discrete-time index i
    c[i-1] = 0                                                 # control light effect update equation  
    x[i] = c[i-1] + Px*x[i-1] + d[i]                           # protein x concentration update equation
    if x[i] < 0:                                               # if protein x concentration is lower than 0
      x[i] = 0                                                 # protein x concentration becomes 0
    e[i] = 0                                                   # error update equation 
    sum_e[i] = 0                                               # error sum update equation 
    diff_e[i] = 0                                              # error difference update equation 

plt.plot(n,r,'blue',label = 'reference')      # plot reference concentration 
plt.plot(n,x,'cyan',label = 'x protein')      # plot x concentration 
plt.plot(n,d,'red',label = 'disturbance')     # plot disturbance 
plt.plot(n[1:N-1],c[1:N-1],'green',label = 'control')   # plot control light effect(positive or negative)
plt.xlabel('time (n)')
plt.ylabel('concentrtion (uM) & light effect (arbitrary unit)')
plt.legend(loc='upper right')
plt.ylim(-5, 20)
plt.title('Gene Expression Control using PID Control')
plt.grid(True)
plt.show()
plt.show