Re: Bound control system

Vladimir Vassilevsky 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.

No. You wrote above that the integrator state is frozen. That's all you need to do.

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?

Phelan?

Jerry
--
Engineering is the art of making what you want from things you can get.
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Relevant Pages

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