import matplotlib.pyplot as plt

class PIDRegler:
    def __init__(self, kp, ki, kd):
        self.kp = kp
        self.ki = ki
        self.kd = kd
        self.prev_error = 0
        self.integral = 0

    def regeln(self, setpoint, ist_temperatur):
        error = setpoint - ist_temperatur
        P = self.kp * error
        self.integral += error
        I = self.ki * self.integral
        D = self.kd * (error - self.prev_error)
        self.prev_error = error
        return P + I + D

# Define the PID parameters
kp = 0.5
ki = 0.005
kd = 0.1

# Create the PID regulator
regler = PIDRegler(kp, ki, kd)

# Define the setpoint
setpoint = 22.0 # 22 degrees Celsius

# Simulate the heating system
ist_temperatur = 15.0 # Initial temperature
temperature_over_time = []
for i in range(500): # Runtime: 200 time units
    regelung = regler.regeln(setpoint, ist_temperatur)
    ist_temperatur += regelung * 0.05 # Adjustment factor
    temperature_over_time.append(ist_temperatur)

# Plot the temperature over time
plt.plot(range(500), temperature_over_time)
plt.xlabel('Time')
plt.ylabel('Temperature (Celsius)')
plt.title('Temperature Over Time')
plt.grid(True)
plt.show()