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Documenter.jl committed Oct 15, 2023
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{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-06T03:50:54","documenter_version":"1.1.0"}}
{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-15T18:25:32","documenter_version":"1.1.1"}}
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u, y, d = model.uop, model(), mpc_ff.estim.model.dop
initstate!(mpc_ff, u, y, d)
u_data, y_data, ry_data = test_mpc_ff(mpc_ff, model)
plot_data(t_data, u_data, y_data, ry_data)</code></pre><p><img src="../plot3_LinMPC.svg" alt="plot3_LinMPC"/></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/#ModelPredictiveControl.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 gives 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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Friday 6 October 2023 03:50">Friday 6 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
plot_data(t_data, u_data, y_data, ry_data)</code></pre><p><img src="../plot3_LinMPC.svg" alt="plot3_LinMPC"/></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/#ModelPredictiveControl.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 gives 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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Sunday 15 October 2023 18:25">Sunday 15 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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0 unmeasured outputs yu
0 measured disturbances d</code></pre><p>We test <code>mpc</code> performance on <code>plant</code> by imposing an angular setpoint of 180° (inverted position):</p><pre><code class="language-julia hljs">res = sim!(mpc, 60, [180.0], plant=plant, x0=zeros(plant.nx), x̂0=zeros(mpc.estim.nx̂))
plot(res)</code></pre><p><img src="../plot3_NonLinMPC.svg" alt="plot3_NonLinMPC"/></p><p>The controller seems robust enough to variations on <span>$K$</span> coefficient. Starting from this inverted position, the closed-loop response to a step disturbances of 10° is also satisfactory:</p><pre><code class="language-julia hljs">res = sim!(mpc, 60, [180.0], plant=plant, x0=[π, 0], x̂0=[π, 0, 0], y_step=[10])
plot(res)</code></pre><p><img src="../plot4_NonLinMPC.svg" alt="plot4_NonLinMPC"/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linmpc/">« Linear 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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Friday 6 October 2023 03:50">Friday 6 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
plot(res)</code></pre><p><img src="../plot4_NonLinMPC.svg" alt="plot4_NonLinMPC"/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../linmpc/">« Linear 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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Sunday 15 October 2023 18:25">Sunday 15 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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