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Author: Documenter.jl

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-{"documenter":{"julia_version":"1.11.6","generation_timestamp":"2025-09-06T23:18:28","documenter_version":"1.14.1"}}
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dev/func_index/index.html

@@ -74,31 +74,44 @@
 inputs, outputs = [mtk_model.τ], [mtk_model.y]
 f!, h!, p, nu, nx, ny, vx = generate_f_h(mtk_model, inputs, outputs)
 Ts = 0.1
-vu, vy = [&quot;\$τ\$ (Nm)&quot;], [&quot;\$θ\$ (°)&quot;]</code></pre><p>A <a href="../../public/sim_model/#NonLinModel"><code>NonLinModel</code></a> can now be constructed:</p><pre><code class="language-julia hljs">model = setname!(NonLinModel(f!, h!, Ts, nu, nx, ny; p); u=vu, x=vx, y=vy)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">NonLinModel with a sample time Ts = 0.1 s, RungeKutta(4) solver and:
- 1 manipulated inputs u
- 2 states x
- 1 outputs y
- 0 measured disturbances d</code></pre><p>We also instantiate a plant model with a 25 % larger friction coefficient <span>$K$</span>:</p><pre><code class="language-julia hljs">mtk_model.K = defaults(mtk_model)[mtk_model.K] * 1.25
+vu, vy = [&quot;\$τ\$ (Nm)&quot;], [&quot;\$θ\$ (°)&quot;]</code></pre><p>A <a href="../../public/sim_model/#NonLinModel"><code>NonLinModel</code></a> can now be constructed:</p><pre><code class="language-julia hljs">model = setname!(NonLinModel(f!, h!, Ts, nu, nx, ny; p); u=vu, x=vx, y=vy)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">NonLinModel with a sample time Ts = 0.1 s:
+├ solver: RungeKutta(4)
+├ jacobian: AutoForwardDiff
+└ dimensions:
+  ├ 1 manipulated inputs u
+  ├ 2 states x
+  ├ 1 outputs y
+  └ 0 measured disturbances d</code></pre><p>We also instantiate a plant model with a 25 % larger friction coefficient <span>$K$</span>:</p><pre><code class="language-julia hljs">mtk_model.K = defaults(mtk_model)[mtk_model.K] * 1.25
 f_plant, h_plant, p = generate_f_h(mtk_model, inputs, outputs)
-plant = setname!(NonLinModel(f_plant, h_plant, Ts, nu, nx, ny; p); u=vu, x=vx, y=vy)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">NonLinModel with a sample time Ts = 0.1 s, RungeKutta(4) solver and:
- 1 manipulated inputs u
- 2 states x
- 1 outputs y
- 0 measured disturbances d</code></pre><h2 id="Controller-Design"><a class="docs-heading-anchor" href="#Controller-Design">Controller Design</a><a id="Controller-Design-1"></a><a class="docs-heading-anchor-permalink" href="#Controller-Design" title="Permalink"></a></h2><p>We can than reproduce the Kalman filter and the controller design of the <a href="../nonlinmpc/#man_nonlin">last section</a>:</p><pre><code class="language-julia hljs">α=0.01; σQ=[0.1, 1.0]; σR=[5.0]; nint_u=[1]; σQint_u=[0.1]
+plant = setname!(NonLinModel(f_plant, h_plant, Ts, nu, nx, ny; p); u=vu, x=vx, y=vy)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">NonLinModel with a sample time Ts = 0.1 s:
+├ solver: RungeKutta(4)
+├ jacobian: AutoForwardDiff
+└ dimensions:
+  ├ 1 manipulated inputs u
+  ├ 2 states x
+  ├ 1 outputs y
+  └ 0 measured disturbances d</code></pre><h2 id="Controller-Design"><a class="docs-heading-anchor" href="#Controller-Design">Controller Design</a><a id="Controller-Design-1"></a><a class="docs-heading-anchor-permalink" href="#Controller-Design" title="Permalink"></a></h2><p>We can than reproduce the Kalman filter and the controller design of the <a href="../nonlinmpc/#man_nonlin">last section</a>:</p><pre><code class="language-julia hljs">α=0.01; σQ=[0.1, 1.0]; σR=[5.0]; nint_u=[1]; σQint_u=[0.1]
 estim = UnscentedKalmanFilter(model; α, σQ, σR, nint_u, σQint_u)
 Hp, Hc, Mwt, Nwt = 20, 2, [0.5], [2.5]
 nmpc = NonLinMPC(estim; Hp, Hc, Mwt, Nwt, Cwt=Inf)
 umin, umax = [-1.5], [+1.5]
-nmpc = setconstraint!(nmpc; umin, umax)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">NonLinMPC controller with a sample time Ts = 0.1 s, Ipopt optimizer, SingleShooting transcription, UnscentedKalmanFilter estimator and:
- 20 prediction steps Hp
-  2 control steps Hc
-  0 slack variable ϵ (control constraints)
-  1 manipulated inputs u (1 integrating states)
-  3 estimated states x̂
-  1 measured outputs ym (0 integrating states)
-  0 unmeasured outputs yu
-  0 measured disturbances d</code></pre><p>The 180° setpoint response is identical:</p><pre><code class="language-julia hljs">using Plots
+nmpc = setconstraint!(nmpc; umin, umax)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">NonLinMPC controller with a sample time Ts = 0.1 s:
+├ estimator: UnscentedKalmanFilter
+├ model: NonLinModel
+├ optimizer: Ipopt 
+├ transcription: SingleShooting
+├ gradient: AutoForwardDiff
+├ jacobian: AutoForwardDiff
+└ dimensions:
+  ├ 20 prediction steps Hp
+  ├  2 control steps Hc
+  ├  0 slack variable ϵ (control constraints)
+  ├  1 manipulated inputs u (1 integrating states)
+  ├  3 estimated states x̂
+  ├  1 measured outputs ym (0 integrating states)
+  ├  0 unmeasured outputs yu
+  └  0 measured disturbances d</code></pre><p>The 180° setpoint response is identical:</p><pre><code class="language-julia hljs">using Plots
 N = 35
 res_ry = sim!(nmpc, N, [180.0], plant=plant, x_0=[0, 0], x̂_0=[0, 0, 0])
 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=[π, 0], x̂_0=[π, 0, 0], y_step=[10])
-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 1.14.1 on <span class="colophon-date" title="Saturday 6 September 2025 23:18">Saturday 6 September 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+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 1.14.1 on <span class="colophon-date" title="Sunday 7 September 2025 21:22">Sunday 7 September 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>