Re: Bound control system

On Aug 31, 3:28 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

If you want to minimize the maximum value of the error then you will
need H infinity control theory.

.

Relevant Pages

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    ... 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. ... 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. ... The problem is what to do with the integrator. ...
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