Proportional-Integral-Derivative (PID) Control of a Tank Level with Anti-Windup
Proportional-Integral-Derivative (PID) Control of a Tank Level with Anti-Windup
The dynamic behavior of a tank of height (in meters) is governed by the following ODE:
h
A=-
dh
dt
F
0
F
1
A=1
2
m
F
0
F
1
3
m
The discharge flow is given by =maxKe+edt,0≥0, where is the valve constant expressed in /s, is the error, is the proportional gain, and is the integral time constants. The setpoint for the tank height is chosen to be 3 meters.
F
1
h
-K
p
1
τ
i
K=0.5
3
m
1/2
m
e=(3-h)
K
p
τ
i
The inlet flow rate is =1.4/s.
F
0
3
m
The red and blue curves correspond to a controller with and without anti-windup. Anti-windup is important because it is possible that the discharge flow rate has a maximum value (taken here to be 1.5 /s) corresponding to a fully open flow control valve. Computationally, this is achieved by setting =minmaxKe+edt,01.5. When reaches the maximal value of 1.5 /s, the rate of change of the tank's height is constant and negative (equal to ) and the height decreases linearly versus time, as can be seen in snapshot 2.
3
m
F
1
h
-K
p
1
τ
i
F
1
3
m
-0.1/s
3
m