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dev/.documenter-siteinfo.json

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{"documenter":{"julia_version":"1.12.1","generation_timestamp":"2025-10-26T21:43:11","documenter_version":"1.15.0"}}
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{"documenter":{"julia_version":"1.12.1","generation_timestamp":"2025-11-02T01:31:30","documenter_version":"1.15.0"}}

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dev/manual/linmpc/index.html

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u, y, d = model.uop, model(), mpc_d.estim.model.dop
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initstate!(mpc_d, u, y, d)
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u_data, y_data, ry_data = test_mpc_d(mpc_d, model)
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plot_data(t_data, u_data, y_data, ry_data)</code></pre><p><img src="../plot4_LinMPC.svg" alt="plot4_LinMPC"/></p><p>Note that measured disturbances are assumed constant in the future by default but custom <span>$\mathbf{D̂}$</span> predictions are possible. The same applies for the setpoint predictions <span>$\mathbf{R̂_y}$</span>.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>As an alternative to state observer, we could have use an <a href="../../public/state_estim/#InternalModel"><code>InternalModel</code></a> structure with <code>mpc = LinMPC(InternalModel(model), Hp=15, Hc=2, Mwt=[1, 1], Nwt=[0.1, 0.1])</code>. It was tested on the example of this page and it gave similar results.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../installation/">« Installation</a><a class="docs-footer-nextpage" href="../nonlinmpc/">Nonlinear Design »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Sunday 26 October 2025 21:43">Sunday 26 October 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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plot_data(t_data, u_data, y_data, ry_data)</code></pre><p><img src="../plot4_LinMPC.svg" alt="plot4_LinMPC"/></p><p>Note that measured disturbances are assumed constant in the future by default but custom <span>$\mathbf{D̂}$</span> predictions are possible. The same applies for the setpoint predictions <span>$\mathbf{R̂_y}$</span>.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>As an alternative to state observer, we could have use an <a href="../../public/state_estim/#InternalModel"><code>InternalModel</code></a> structure with <code>mpc = LinMPC(InternalModel(model), Hp=15, Hc=2, Mwt=[1, 1], Nwt=[0.1, 0.1])</code>. It was tested on the example of this page and it gave similar results.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../installation/">« Installation</a><a class="docs-footer-nextpage" href="../nonlinmpc/">Nonlinear Design »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Sunday 2 November 2025 01:31">Sunday 2 November 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/manual/mtk/index.html

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res_ry = sim!(nmpc, N, [180.0], plant=plant, x_0=[0, 0], x̂_0=[0, 0, 0])
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plot(res_ry)</code></pre><p><img src="../plot1_MTK.svg" alt="plot1_MTK"/></p><p>and also the output disturbance rejection:</p><pre><code class="language-julia hljs">res_yd = sim!(nmpc, N, [180.0], plant=plant, x_0=[0, π], x̂_0=[0, π, 0], y_step=[10])
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plot(res_yd)</code></pre><p><img src="../plot2_MTK.svg" alt="plot2_MTK"/></p><h2 id="Acknowledgement"><a class="docs-heading-anchor" href="#Acknowledgement">Acknowledgement</a><a id="Acknowledgement-1"></a><a class="docs-heading-anchor-permalink" href="#Acknowledgement" title="Permalink"></a></h2><p>Authored by <code>1-Bart-1</code> and <code>baggepinnen</code>, thanks for the contribution.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nonlinmpc/">« Nonlinear Design</a><a class="docs-footer-nextpage" href="../../public/sim_model/">Plant Models »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Sunday 26 October 2025 21:43">Sunday 26 October 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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plot(res_yd)</code></pre><p><img src="../plot2_MTK.svg" alt="plot2_MTK"/></p><h2 id="Acknowledgement"><a class="docs-heading-anchor" href="#Acknowledgement">Acknowledgement</a><a id="Acknowledgement-1"></a><a class="docs-heading-anchor-permalink" href="#Acknowledgement" title="Permalink"></a></h2><p>Authored by <code>1-Bart-1</code> and <code>baggepinnen</code>, thanks for the contribution.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nonlinmpc/">« Nonlinear Design</a><a class="docs-footer-nextpage" href="../../public/sim_model/">Plant Models »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Sunday 2 November 2025 01:31">Sunday 2 November 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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res_slin = sim_adapt!(mpc3, model, N, ry, plant, x_0, x̂_0)
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plot(res_slin)</code></pre><p><img src="../plot12_NonLinMPC.svg" alt="plot12_NonLinMPC"/></p><p>and the 10° step disturbance:</p><pre><code class="language-julia hljs">x_0 = [π, 0]; x̂_0 = [π, 0, 0]; y_step = [10]
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res_slin = sim_adapt!(mpc3, model, N, ry, plant, x_0, x̂_0, y_step)
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plot(res_slin)</code></pre><p><img src="../plot13_NonLinMPC.svg" alt="plot13_NonLinMPC"/></p><p>The computations of the successive linearization MPC are about 75 times faster than the nonlinear MPC on average, an impressive gain for similar closed-loop performances!</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Arnström, D., Bemporad, A., and Axehill, D. (2022). A dual active-set solver for embedded quadratic programming using recursive LDLᵀ updates. IEEE Trans. Autom. Contr., 67(8). <a href="https://doi.org/doi:10.1109/TAC.2022.3176430">https://doi.org/doi:10.1109/TAC.2022.3176430</a>.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linmpc/">« Linear Design</a><a class="docs-footer-nextpage" href="../mtk/">ModelingToolkit »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Sunday 26 October 2025 21:43">Sunday 26 October 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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plot(res_slin)</code></pre><p><img src="../plot13_NonLinMPC.svg" alt="plot13_NonLinMPC"/></p><p>The computations of the successive linearization MPC are about 75 times faster than the nonlinear MPC on average, an impressive gain for similar closed-loop performances!</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Arnström, D., Bemporad, A., and Axehill, D. (2022). A dual active-set solver for embedded quadratic programming using recursive LDLᵀ updates. IEEE Trans. Autom. Contr., 67(8). <a href="https://doi.org/doi:10.1109/TAC.2022.3176430">https://doi.org/doi:10.1109/TAC.2022.3176430</a>.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linmpc/">« Linear Design</a><a class="docs-footer-nextpage" href="../mtk/">ModelingToolkit »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.15.0 on <span class="colophon-date" title="Sunday 2 November 2025 01:31">Sunday 2 November 2025</span>. Using Julia version 1.12.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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