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{"documenter":{"documenter_version":"1.17.0","generation_timestamp":"2026-06-08T17:17:52","julia_version":"1.12.6"}}
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{"documenter":{"documenter_version":"1.17.0","generation_timestamp":"2026-06-09T22:32:04","julia_version":"1.12.6"}}

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dev/manual/mtk/index.html

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N = 35
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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 1.17.0 on <span class="colophon-date" title="Monday 8 June 2026 17:17">Monday 8 June 2026</span>. Using Julia version 1.12.6.</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 1.17.0 on <span class="colophon-date" title="Tuesday 9 June 2026 22:32">Tuesday 9 June 2026</span>. Using Julia version 1.12.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/manual/nonlinmpc/index.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 1.17.0 on <span class="colophon-date" title="Monday 8 June 2026 17:17">Monday 8 June 2026</span>. Using Julia version 1.12.6.</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 1.17.0 on <span class="colophon-date" title="Tuesday 9 June 2026 22:32">Tuesday 9 June 2026</span>. Using Julia version 1.12.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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