@@ -182,15 +182,15 @@ savefig(ans, "plot2_LinMPC.svg"); nothing # hide
182182The [ ` SteadyKalmanFilter ` ] ( @ref ) is a simple observer but it is not able to handle
183183constraints at estimation. The [ ` MovingHorizonEstimator ` ] ( @ref ) (MHE) can improve the
184184accuracy of the state estimate `` \mathbf{x̂} `` . It solves a quadratic optimization problem
185- under a past time window `` \mathbf{ H_e} `` , and bounds on the estimated plant state
186- `` \mathbf{x̂ } `` , estimated process noise `` \mathbf{ŵ } `` and estimated sensor noise
187- `` \mathbf{v̂} `` can be included in the problem. This can be useful to include physical
188- knowledge in the soft sensor, without adding new physical sensors (e.g. a strictly positive
189- concentration). The closed-loop performance of a predictive controller depends on the
190- accuracy of the plant state estimate.
191-
192- For the CSTR, we will bound the innovation term `` \mathbf{\mathbf{y}(k)- \mathbf{ŷ}(k)} `` ,
193- and increase `` \mathbf{Q}_{int_u} `` to accelerate the estimation of the load
185+ under a past time window `` H_e `` . Bounds on the estimated plant state `` \mathbf{x̂} `` ,
186+ estimated process noise `` \mathbf{ŵ } `` and estimated sensor noise `` \mathbf{v̂ } `` can be
187+ included in the problem. This can be useful to add physical knowledge in the soft sensor,
188+ without adding new physical sensors (e.g. a strictly positive concentration). The
189+ closed-loop performance of a predictive controller depends on the accuracy of the plant
190+ state estimate.
191+
192+ For the CSTR, we will bound the innovation term ``\mathbf{\mathbf{y}(k) - \mathbf{ŷ}(k)} =
193+ \mathbf{v̂} `` , and increase `` \mathbf{Q}_ {int_u}`` to accelerate the estimation of the load
194194disturbance. The rejection is slightly faster:
195195
196196``` @example 1
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