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@@ -22,16 +22,16 @@ In order to implement anti-windup, the integrator usually has to be **explicit**
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This is one of the reasons why the PID controller is so useful: the integral action is clearly separated from the other terms.
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### Anti-windup strategies {#anti-windup-strategies}
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## Anti-windup strategies {#anti-windup-strategies}
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#### Conditional integration (integrator clamping) {#conditional-integration--integrator-clamping}
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### Conditional integration (integrator clamping) {#conditional-integration--integrator-clamping}
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The integrator is simply stopped (or reset) when the actuator is saturated.
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For instance, the integration is frozen as long as \\(u \neq \text{sat}(u)\\), possibly only if the error would further increase the saturation (i.e. same sign of \\(u\\) and \\(e\\)).
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#### Back-calculation {#back-calculation}
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### Back-calculation {#back-calculation}
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The difference between the saturated and the requested control signal, \\(e\_s = \text{sat}(u) - u\\), is fed back to the integrator input through a gain \\(1/T\_t\\):
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@@ -42,9 +42,3 @@ The difference between the saturated and the requested control signal, \\(e\_s =
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When there is no saturation, \\(e\_s = 0\\) and the controller behaves as usual.
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When saturated, the integrator state is driven so that \\(u\\) tracks the saturation limit.
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The tracking time constant \\(T\_t\\) sets how fast the integrator is unwound (a common choice is \\(T\_t = \sqrt{T\_i T\_d}\\) or \\(T\_t = T\_i\\)).
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## Bibliography {#bibliography}
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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</div>
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