Re: Bound control system

On Aug 30, 8:28 am, Vladimir Vassilevsky <antispam_bo...@xxxxxxxxxxx>
wrote:
The classic closed loop system tries to minimize the error wrt some
criteria.  But what if the requirement is to limit the error to the
bounds (-E,+E) ? So as long as the error is within the bounds, the
control signal should be zero.

Consider the PID controller and just the upper bound of error E.
Initially, the error is below the bound, so the control signal is set to
0 and the controller state is set to zero also. Then the error drifts
up, and when it crosses the bound E, the controller is enabled and it
tries to keep the error at E. So far so good.

Eventually the error goes down below E. At this moment, the controller
output is disabled, the integrator state is frozen, the differentiator
memory is updated normally. When the error goes above E again, the
controller is enabled again.

The problem is what to do with the integrator. Since the error is always
non negative, the integrator will grow up indefinitely. If the
integrator is set to zero every time when the error goes below E, then
the control is not going to be optimal. A solution could be multiplying
the integrator by a factor of A (less then unity) when crossing E on the
way down. Then what should be the rational way for determining A.

I am sure that the problem is not unusual, so there should be a good
solution for it. Can you suggest an idea or a book with the treatment of
that sort of problem?

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultanthttp://www.abvolt.com

I am surprised that no one has asked what you are truly controlling.
Is it the torque or the velocity loop or just the position loop. This
makes a big difference. If just controlling the position loop then
just a little error will cause the inner loops to wind up and zeroing
the outer loops does not limit or zero the control output of the inner
loops. Even if you force the output of the position and velocity loop
to 0 there may be a inner torque loop that maintains a current due to
its integrator. It appears like you need to get down to what controls
the current and zero or limit that.

Peter Nachtwey

.

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