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Merge pull request #83 from JuliaControl/doc_correction
doc: change nomenclature EMPC
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docs/src/manual/nonlinmpc.md

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@@ -153,17 +153,17 @@ See [`sim!`](@ref) documentation for details on the possible simulation scenario
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## Economic Model Predictive Controller
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Economic MPC can achieve the same objective but with lower economical costs. For this case
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study, the controller will aim to reduce the energy consumed by the motor. The power (W)
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study, the controller will aim to reduce the energy consumed by the motor. The power in watt
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transmitted by the motor to the pendulum is:
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```math
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(t) = τ(t) ω(t)
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P(t) = τ(t) ω(t)
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```
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Thus, the work (J) done by the motor from ``t = t_0`` to ``t_{end}`` is:
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Thus, the work in joule done by the motor from ``t = t_0`` to ``t_{end}`` is:
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```math
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W = \int_{t_0}^{t_{end}} (t) \mathrm{d}t = \int_{t_0}^{t_{end}} τ(t) ω(t) \mathrm{d}t
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W = \int_{t_0}^{t_{end}} P(t) \mathrm{d}t = \int_{t_0}^{t_{end}} τ(t) ω(t) \mathrm{d}t
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```
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With the sampling time ``T_s`` in s, the prediction horizon ``H_p``, the limits defined as

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