Balance scales and integral action. Part II

In a previous post we discussed how the principles of operation of a balance scale could be understood as a feedback loop with integral action. We left off after analyzing the impact of measurement disturbances in the loop and mentioned that input disturbances could be used to model “operator errors.”

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Let your inputs go!

As one learns more about feedback and control systems, at some point, comes an important realization that a variety of distinct problems can be answered if we know how to answer the question: “is some closed-loop system asymptotically stable?” Indeed, the study of stability dominates Chapters 6 and 7, arguably the densest chapters in the book. Many students, when asked what they remember from their undergraduate control class, will quickly point at the root-locus or at the Nyquist stability criterion. Yet, in the beginning, it might seem that stability is a side dish and not the main attraction.

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To disturb or not to disturb?

So here is a recurrent question. You have some model that has a constant showing up on the differential equation and you’re not sure how to handle it. For example, your model looks like:


where $c$ is a constant. There are multiple ways you can handle this situation.

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