Ok...did I get this right


Thread Starter


Take for example a tank with an inlet valve and a 4-40mA actuator controlled by a Proportional only controller with a A 4-20mA level gage.

The flow out of the tank increases, the tank level begins to decrease due to the imbalance between inflow and outflow. While the tank level decreases the error as reported by the gage (SP – Tank Level) increases our proportional controller (PV - Inflow) increases the controller output proportional to this error. Consequently, the valve controlling the flow into the tank opens wider and more water flows into the tank. As the level continues to decrease, the valve continues to open until it gets to a point where the inflow matches the outflow. At this point the tank level remains constant, and so does the error (it has reached a steady-state ess). Then, because the error remains constant the P controller will keep its output constant and the controlled inlet valve will maintain its position. The system now remains ‘balanced’ with the tank level remaining below than its set point. This residual error is called Offset. Close the valve at any other rate than you opened it and shut off valve will respond to the constant Kc without being able to factor time and the tank will retain some level of the offset.

Is it that simple?

Robert Scott

Your example has a little complication that makes it not quite a pure proportional control situation. If the inflow is directly related to the inlet valve position, which is in turn directly proportional to the error in tank level, then the inflow itself is integrated by the tank, making the level dependent on the integral of the error rather than purely proportional. That would imply that even the smallest change in the inlet valve position would eventually raise the tank level to any desired setpoint, and there would be no offset (which is typical of integral control).

However, we must assume that the outflow is also somewhat dependent on the tank level. Therefore the steady-state tank level is dependent on a term that is proportion to the inflow valve position. So we have a combination of integral and proportional control.

-Robert Scott
Real-Time Specialties

Embedded Systems Consulting

Fred Thomasson

I thought you "had it" until I read your last sentence. It doesn't make sense to me.The valve output position is always:VO=Kc(level_error).The response will be as fast as the outlet flow changes.

You need to recognize that tight level control is not desirable in most cases. Tight level control allows a downstream flow disturbance to transfer to the upstream part of the process. Let the level fall as the downstream flow increases. This doesn't hurt anything as long as you turn it around before it gets too low.

First, set the proportional gain based on how much you are willing to let the level fall in a worst case situation(eg. 30% for a setpoint = 50%). If the proportional gain is 2.0, the Valve Output would increase by 60%[ Delta VO=2*30 ]. Start with a very low value of integral gain(eg Ki=0.05 repeats per minute). The value depends on the holdup time of the tank[Volume/(Max.Flow Rate)]. Increase the integral gain if the level droops too much or the time it takes to return to setpoint is too long. If you have access to Lambda tuning procedures you can do a bump test and calculate these tuning values.

Allowing the level to droop temporarily attenuates the flow disturbance to the upstream process. Sudden flow changes bothers many proceses. The tank is used as a buffer.

Many people mistakingly think you should use proportional only level control on a tank because the tank is an integrator. What you really need is mostly proportional gain and a little integral gain. The integral gain may be small but it is so important.

The integral gain is important only if you want the level to eventually return to its set point.

For a tank used entirely for surge control, it may be desirable for the level to not stay at its setpoint. Take for example a storage tank on a sewer main going into the treatment plant. The flow in is uncontrolled, the flow out is manipulated to control level. If we use proportional only control, when the flow into the tank is very low the level is low. This provides a large amount of unused space that can be filled when a sudden rain storm adds a tremendous amount of water for a short period of time. The surge handling capacity is higher for P only than for PI control.

Also, with PI control, after the sudden increase in flow in, the flow out will have to exceed the flow in for a period of time to bring the level back to the setpoint.

John Shaw

Johan Bengtsson

I think you got it right, I am used to somewhat different names for some parts so there might be some small error somewhere I missed.

With proporional only control you will get an error (except for exactly one load) as a steady state. This is in many cases completely ok and don't need anything more. If you however need the level to return to the setpoint you need to use a PI controller.

/Johan Bengtsson

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Your Understanding of the offset is alright.But The main question on this topic is trivial for a control engineer.that is why there is an error.and the job of any controller wheather a feed back or feed forward are auto tuning or ultimately a robust controller is to understand the error correctly in time and in phase or any other related parameter of the plant for whose transfer function the controller is calulating and decides its out puts.this is the stsrting point of the entire subject of control theory.
very good question indeed.I observe cooly the response to this question.and answers are interesting and various according to applications.
good job-keep it up!!!