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I got a position error measured by a linear encoder like in the picture below.

Position error graph

Could anyone explain some possible reasons for this kind of shape to occur in control theory?

My system looks like table with four legs.

The four legs move up and down by using motors and have a linear encoder as control reference.

The table should stay in its position after moving up.

The four servo motors actuating the four legs control the position by using linear encoder signals, respectively.

But after moving the table up around 10 mm ~ 20 mm, a strange symptom has happened. One or two encoder signals look like square waves (sometimes one encoder signal, sometimes two, sometimes none).

A simple setup diagram is as below.

Diagram of table

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    $\begingroup$ Having a pure square wave superimposed on the data suggests that it may be external interference affecting the sensor output. Are you by any chance using a square wave as a time reference ? $\endgroup$ Mar 23 '16 at 8:29
  • $\begingroup$ I am afraid the plot is not real measured data. Real data is not perfect square wave, but almost square. $\endgroup$
    – KKS
    Mar 23 '16 at 8:53
  • $\begingroup$ You mean time clock could be a source? But the frequency of square shape is 0.1~0.2Hz. It's very far from time clock freq. $\endgroup$
    – KKS
    Mar 23 '16 at 8:56
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    $\begingroup$ What is the resolution of the control system? It looks like there's some sort of quantization going on, and the system is "hunting" between two thresholds. $\endgroup$
    – Dave Tweed
    Mar 23 '16 at 12:03
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    $\begingroup$ Please provide the name& model of your encoder, and the best possible diagram of your setup. $\endgroup$ Mar 23 '16 at 13:11
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Your system is not reaching the target value. Possibly this is due to static friction in the actuator mechanism, which causes it not to move until the force exceeds some threshold.

Assuming you are using a PID controller, the residual error will cause the I error term to accumulate slowly. This will cause the actuator force to increase until it is enough to cause actual movement. It seems that this movement will cause a small jerk, which will move the table further than intended and cause opposite error value.

The way you can test this is to change the target height in small steps (e.g. 1 µm) and see what is the smallest distance you can reliably move. You can then either choose to improve the actuator, or to set this as the deadband value in your controller.

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