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lines changed Original file line number Diff line number Diff line change @@ -135,10 +135,15 @@ LinModel with a sample time Ts = 0.1 s:
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state-space representation.
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It is assumed that ``\m athbf{D_u=0}`` (or `sys` is strictly proper) since otherwise the
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- resulting discrete controller is acausal by definition. Indeed, all discrete controllers
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- (1) sample an output ``\m athbf{y}(k)`` from the plant, (2) computes an action
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- ``\m athbf{u}(k)`` and (3) apply the action on the plant. There is a causality paradox
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- if ``\m athbf{u}(k)`` impacts ``\m athbf{y}(k)`` even before computing it.
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+ resulting discrete controller would be acausal in its implementation (≠ mathematical
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+ causality). Indeed, at each sampling instant `k`, the predictive controller will:
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+
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+ 1. sample an output ``\m athbf{y}(k)`` from the plant
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+ 2. computes an action ``\m athbf{u}(k)`` and
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+ 3. apply the action on the plant.
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+
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+ There is a causality paradox if ``\m athbf{u}(k)`` impacts ``\m athbf{y}(k)`` even before
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+ computing it.
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"""
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function LinModel (
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sys:: StateSpace{E, NT} ,
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