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Diff for: notebooks/3-dev/PyomoDAE_TCLab.ipynb

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"source": [
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"# Pyomo.DAE Example: Temperature Control Lab\n",
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"\n",
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"This page is [adapted from our process control class](https://github.com/ndcbe/controls/blob/main/notebooks/06.02-Simulation-and-Open-Loop-Optimal-Control.ipynb) at Notre Dame; it was developed by Prof. Jeff Kantor."
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"This page is [adapted from our process control class](https://github.com/ndcbe/controls/blob/main/notebooks/6/Simulation-and-Open-Loop-Optimal-Control.ipynb) at Notre Dame; it was developed by Prof. Jeff Kantor."
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Diff for: notebooks/3-dev/PyomoDAE_car.ipynb

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"Mathematically, you want to solve the following optimal control problem:\n",
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"\n",
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"$$\\begin{align*}\n",
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"\\min_{u} \\quad & t_f \\\\\n",
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"\\min_{u,t_f} \\quad & t_f \\\\\n",
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"\\mathrm{s.t.} \\quad & \\frac{dx}{dt} = v \\\\\n",
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"& \\frac{dv}{dt} = u - R v^2 \\\\\n",
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"& x(t=0) = 0, ~~ x(t=t_f) = L \\\\\n",
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"& v(t=0) = 0, ~~ v(t=t_f) = 0 \\\\\n",
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"& -3 \\leq u \\leq 1\n",
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"\\end{align*}$$\n",
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"\n",
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"where $a$ is the acceleration/braking (your control variable) and $R$ is the drag coefficient (parameter)."
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"where $u$ is the acceleration/braking (your control variable) and $R$ is the drag coefficient (parameter)."
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"Let $t = \\tau \\cdot t_f$ where $\\tau \\in [0,1]$. Thus $dt = t_f d\\tau$. The optimal control problem becomes:\n",
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"\n",
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"$$\\begin{align*}\n",
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"\\min_{u} \\quad & t_f \\\\\n",
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"\\min_{u,t_f} \\quad & t_f \\\\\n",
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"\\mathrm{s.t.} \\quad & \\frac{dx}{d\\tau} = t_f v \\\\\n",
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"& \\frac{dv}{d\\tau} = t_f (u - R v^2) \\\\\n",
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"& x(\\tau = 0) = 0, ~~ x(\\tau = 1) = L \\\\\n",
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"provenance": []
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"kernelspec": {
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"display_name": "Python 3",
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"display_name": "summer2024",
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"language": "python",
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"name": "python3"
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},

Diff for: notebooks/3-dev/PyomoDAE_example.ipynb

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"provenance": []
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"kernelspec": {
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"display_name": "Python 3",
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"display_name": "summer2024",
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"language": "python",
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"name": "python3"
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