How to linearize a command signal?

[agarb]

We commonly use proportional pressure relief valves to control hydraulic system pressure. These valves are driven by an analog output card in our PLC rack. Now, most proportional relief valves that I've used are pretty non-linear, especially at the lower end. Something like this:

What are some ways that one could use to linearize the control in the logic? For this example, let's assume we are using a SLC 5/03 and it is totally open loop control, with no pressure feedback.

The best I've been able to come up with is multiple SCP instructions, each preceeded with a comparsion that only allows one SCP to be active at a time. See attached.

Anybody have a better way to do this?

(In real life, I wouldn't typically hard-code all the values and would instead use values from a populated data table. For clarity in this example, I didn't do that...)

Aaron

 

[WireGuy1950]

I do something like this in our system to program and select various pressures. We use a proportional relief valve and I can enter a pressure from the OIT in real numbers and get an acceptable output from the system.

Initially, I plotted quite a few points and eventually devised a formula which gave me a pretty close approxamation of the pressure I wanted. Generally my range is from about 1000 to 2500 psi.

Putting this into a compute statment in our SLC 5/04 it looks something like this: ((desired pressure in psi)* 82)+ 7400.

Seems I needed a constant to offset the non-linearity of the valve.

Hope this helps.

 

[Tom Jenkins]

You can plot the data in Excell, chart it, and add a trendline to the chart with the option set to display the equation. This will give you a single equation that will closely approximate the data. You can pick from several equation types to find the best one.

As an aside, if you are routinely operating in the non-linear area below 10% command perhaps your valve selection should be re-examined.

 

[Peter Nachtwey]

Not so simple

It looks like this function needs two sections. There is a curved section when the command is < 10% but the rest looks linear. I would use two functions or segments to approximate this response is there is more that hasn't been mentioned. You need to have the over all linear gain. This case is simple because the over all linear gain is 1.

(PressMax-PressureMin)
---------------------- = 1
(CommandMax-CommandMin)

To linearize your system you need to

Compensated command = Gain*Command/fn(Command)

where fn(Command) is your approximation. Dividing by the approximation linearizes the response.