Controllo PID

Simulazione PID

!pip install slycot
!pip install control

Collecting slycot
Installing collected packages: slycot
Successfully installed slycot-0.2.0
Collecting control
  Using cached control-0.7.0-py2.py3-none-any.whl
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Installing collected packages: control
Successfully installed control-0.7.0

import numpy as np
import matplotlib.pyplot as plt
import control.matlab as control

# control constants
Kc = 0.85
tauI = 10000

# control transfer function
Gc = Kc*control.tf([tauI,1],[tauI,0])

# model transfer functions
Gp = control.tf([0.31],[16,1])*control.tf([1],[135,1])

t = np.linspace(0,1000)
y,t = control.step(Gp,t)
plt.plot(t,50*y + 22)

# control constants
Kc = 2
tauI = 60

# control transfer function
Gc = Kc*control.tf([tauI,1],[tauI,0])

t = np.linspace(0,1000)

H = Gp*Gc/(1+Gp*Gc)
y,t = control.step(H,t)
plt.plot(t,y)

Implementazione PID

Condizioni di riferimento

Uno dei problemi di implementazione del controllo PID del Laboratorio di Controllo della Temperatura è la scelta delle condizioni di riferimento. Uno dei motivi è che la linearizzazione su cui si basa l’analisi PID è valida solo in alcune “vicinanze” di una condizione operativa nominale. Ma forse una situazione più tipica e più pratica

import sys
sys.path.append('..')
from TCLab import TCLab, clock, pid

# ambient and reference values
Tamb = 20
Tref = 50
uref = (Tref - Tamb)/0.85

# control parameters
b = 1              # setpoint weighting
kp = 0.8          # proportional control gain
ki = kp/60

# sampling period
tf = 1200           # experiment length (sec.)
h = 1               # sample time (sec.)

# setpoint function
def Tset(t):
    if t <= 900:
        return 50
    else:
        return 35


bi = ki*h

r = Tset(0) - Tref
y = Tamb - Tref

P = kp*(b*r - y)
I = 0

uref,P,I,r

(35.294117647058826, 24.0, 0, 0)

# device initialization
with TCLab() as a:
    a.initplot(tf)
    for t in clock(tf,h):
        r = Tset(t) - Tref
        y = a.T1 - Tref
    
        P = kp*(b*r - y)
        v = P + I
    
        u = max(0,min(200,v + uref))
        I += bi*(r-y)
    
        a.Q1 = u
        a.updateplot()

TCLab disconnected successfully.