From 5cd67f9b6a0688ae6b9e40f27c99392477de7980 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 17 Aug 2020 22:55:14 +0200 Subject: [PATCH] Change export bibliography links --- content/article/bibel92_guidel_h.md | 28 +++++++++++++++------------- 1 file changed, 15 insertions(+), 13 deletions(-) diff --git a/content/article/bibel92_guidel_h.md b/content/article/bibel92_guidel_h.md index 760a667..48b7dc9 100644 --- a/content/article/bibel92_guidel_h.md +++ b/content/article/bibel92_guidel_h.md @@ -8,7 +8,7 @@ Tags : [H Infinity Control]({{< relref "h_infinity_control" >}}) Reference -: (Bibel \& Malyevac, 1992) +: ([Bibel and Malyevac 1992](#org47391fd)) Author(s) : Bibel, J. E., & Malyevac, D. S. @@ -19,11 +19,11 @@ Year ## Properties of feedback control {#properties-of-feedback-control} - + {{< figure src="/ox-hugo/bibel92_control_diag.png" caption="Figure 1: Control System Diagram" >}} -From the figure [1](#org5999225), we have: +From the figure [1](#org55b0783), we have: \begin{align\*} y(s) &= T(s) r(s) + S(s) d(s) - T(s) n(s)\\\\\\ @@ -77,11 +77,11 @@ Usually, reference signals and disturbances occur at low frequencies, while nois - + {{< figure src="/ox-hugo/bibel92_general_plant.png" caption="Figure 2: \\(\mathcal{H}\_\infty\\) control framework" >}} -New design framework (figure [2](#org4e0009c)): \\(P(s)\\) is the **generalized plant** transfer function matrix: +New design framework (figure [2](#orgbbca2ea)): \\(P(s)\\) is the **generalized plant** transfer function matrix: - \\(w\\): exogenous inputs - \\(z\\): regulated performance output @@ -108,9 +108,9 @@ The \\(H\_\infty\\) control problem is to find a controller that minimizes \\(\\ ## Weights for inputs/outputs signals {#weights-for-inputs-outputs-signals} -Since \\(S\\) and \\(T\\) cannot be minimized together at all frequency, **weights are introduced to shape the solutions**. Not only can \\(S\\) and \\(T\\) be weighted, but other regulated performance variables and inputs (figure [3](#orgdd8fae0)). +Since \\(S\\) and \\(T\\) cannot be minimized together at all frequency, **weights are introduced to shape the solutions**. Not only can \\(S\\) and \\(T\\) be weighted, but other regulated performance variables and inputs (figure [3](#org75a0ac3)). - + {{< figure src="/ox-hugo/bibel92_hinf_weights.png" caption="Figure 3: Input and Output weights in \\(\mathcal{H}\_\infty\\) framework" >}} @@ -154,15 +154,15 @@ When using both \\(W\_S\\) and \\(W\_T\\), it is important to make sure that the ## Unmodeled dynamics weighting function {#unmodeled-dynamics-weighting-function} -Another method of limiting the controller bandwidth and providing high frequency gain attenuation is to use a high pass weight on an **unmodeled dynamics uncertainty block** that may be added from the plant input to the plant output (figure [4](#org0d13a20)). +Another method of limiting the controller bandwidth and providing high frequency gain attenuation is to use a high pass weight on an **unmodeled dynamics uncertainty block** that may be added from the plant input to the plant output (figure [4](#orgd3e0294)). - + {{< figure src="/ox-hugo/bibel92_unmodeled_dynamics.png" caption="Figure 4: Unmodeled dynamics model" >}} -The weight is chosen to cover the expected worst case magnitude of the unmodeled dynamics. A typical unmodeled dynamics weighting function is shown figure [5](#org45b0983). +The weight is chosen to cover the expected worst case magnitude of the unmodeled dynamics. A typical unmodeled dynamics weighting function is shown figure [5](#org6d5884c). - + {{< figure src="/ox-hugo/bibel92_weight_dynamics.png" caption="Figure 5: Example of unmodeled dynamics weight" >}} @@ -181,5 +181,7 @@ Typically actuator input weights are constant over frequency and set at the inve **The order of the weights should be kept reasonably low** to reduce the order of th resulting optimal compensator and avoid potential convergence problems in the DK interactions. -# Bibliography -Bibel, J. E., & Malyevac, D. S., *Guidelines for the selection of weighting functions for h-infinity control* (1992). [↩](#5b41da575e27e6e86f1a1410a0170836) + +## Bibliography {#bibliography} + +Bibel, John E, and D Stephen Malyevac. 1992. “Guidelines for the Selection of Weighting Functions for H-Infinity Control.” NAVAL SURFACE WARFARE CENTER DAHLGREN DIV VA.