There are many situations where you need to control the level of liquid
in a tank. Here is a situation in which you can control the rate
of flow into the tank while liquid flows out of a pipe at the bottom of
the tank. You can apply a voltage to a pump to control the rate of
flow, and the outflow rate is proportional to the height. We have
the following.
Rate of flow in:
Flow Rate In = K1Vp
Rate of flow out:
Flow Rate Out = K2h
Then, the rate of accumulation
is:
Rate of Accumulation =
dV/dt
= Adh/dt = Flow Rate In
- Flow Rate Out
dh/dt = -C1h
+ C2Vp, or, putting this into a standard
form.
dh/dt = -h/t
+ (Gdc/t)Vp
The differential equation
is implemented in the simulator below, which simulated this closed loop
system.
G(s) is the liquid
level system described by the differential equation above. Here is
the simulator for the closed loop system. In this simulator you can
do the following.
You can change the parameters
of the system, i.e. the time constant and the DC gain.
You can change the desired
height.
You can change the controller
gain.
Note the following
for this system
In the steady state
There is a non-zero error.
The output equals the
inflow, and the inflow is non-zero.
Determine the following:
When the system's open loop time constant is 20 seconds,
and the gains are as shown in the pre-loaded values, what is the predicted
error?
What is the error at the end of the simulation?
Compare that to the predicted error.
What is the error (predicted and simulated value)
when the gain is doubled from the pre-loaded value - i.e. changed from
5 to 10?
