Advanced Control: Tank Level Control

[Peter Nachtwey]

This video shows the things I think about on page 1.
I use Laplace transforms a lot. Laplace transforms allow one to express differential equations as simple lgebra



The pump has a gain with units of flow/% control output. This must be more than the maximum inflow or the level cannot be controlled. The tank itself has a gain which is 1/area. It should make sense that the larger the surface are of the tank the slower the level will change. It is also better to think in terms of the tank gain being 1/surface are because the surface area may change as a function of level.
I show how to compute the formulas for the controller gain and the integrator time constant. It is pretty easy.


The next part is the simulation. A PLC person wouldn't care about this because he is stuck with the system before him. "It is what it is". I hate that. Engineers would need to know how tall to make the tank by doing simulations like I show. At the end I show what happens when the in-flow exceeds the pump capacity. The closed loop time constants need to be fast enough to react to the changes in the in-flow.
At the end I make the time constants too short. 0.05 minutes is 3 seconds and the sample time is 1 second.

https://deltamotion.com/peter/Videos/tank level control outflow.mp4

 

[kamenges]

Peter, you make the comment in your video that an integral gain is required in order for the actual level to reach setpoint. That really isn't true in an integrating system, at least not the way it is in a non-integrating system. In the simulation case the only reason you need an integrator is that you are introducing an unmodeled disturbance. If that didn't exist a change in setpoint (at least from high to low) could be fully accomplished with proportional gain. Granted, system with a controller that experiences no disturbances is a pretty useless thing in the real world.

Contrast this with a non-integrating system, where disturbances or not, a proportional term will not be able to drive the actual to the setpoint on its own. A non-integrating system really does need an integrator unconditionally.

But that gets into an odd philosophical discussion about non-integrating systems. Are non-integrating systems more often than not just integrating systems with systemic, immutable losses?

Keith

 

[Peter Nachtwey]

Peter, you make the comment in your video that an integral gain is required in order for the actual level to reach setpoint. That really isn't true in an integrating system, at least not the way it is in a non-integrating system. In the simulation case the only reason you need an integrator is that you are introducing an unmodeled disturbance. If that didn't exist a change in setpoint (at least from high to low) could be fully accomplished with proportional gain. Granted, system with a controller that experiences no disturbances is a pretty useless thing in the real world.

Contrast this with a non-integrating system, where disturbances or not, a proportional term will not be able to drive the actual to the setpoint on its own. A non-integrating system really does need an integrator unconditionally.

But that gets into an odd philosophical discussion about non-integrating systems. Are non-integrating systems more often than not just integrating systems with systemic, immutable losses?

Keith

If there wasn't an inflow you are correct in theory but we know that position motion control is also an integrating system but we still use an integrator gain.


Tank level control is a true integrating system in that the net inflow and out flow is integrated. Look at the formula for the new level. It is integrating the net flow. How else would it work? You could call the inflow a disturbance. If the integrator is not used then there is only a proportional band where the outflow will be (level-min_level)/(max_level-min_level)*100% control output. Add limits at 0 to100% control output. Now the level will be somewhere between min and max level but not at any set point unless you call the min_level the set point.


Two non-integrating systems are velocity and temperature.
Yes, they have loses. They require energy to keep from reaching a quiescent or ambient state. Position control suffers from the same loses as velocity control. The only difference is that when doing position control and power is off the actuator doesn't return to the initial position whereas velocity returns to 0 unless acted on by another force.