notebooks/tclab_model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TCLab Mathematical Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the TCLab as a motivating example for this workshop.\n",
    "\n",
    "The code below sets default font sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "SMALL_SIZE = 14\n",
    "MEDIUM_SIZE = 16\n",
    "BIGGER_SIZE = 18\n",
    "\n",
    "plt.rc('font', size=SMALL_SIZE)  # controls default text sizes\n",
    "plt.rc('axes', titlesize=SMALL_SIZE)  # fontsize of the axes title\n",
    "plt.rc('axes', labelsize=MEDIUM_SIZE)  # fontsize of the x and y labels\n",
    "plt.rc('xtick', labelsize=SMALL_SIZE)  # fontsize of the tick labels\n",
    "plt.rc('ytick', labelsize=SMALL_SIZE)  # fontsize of the tick labels\n",
    "plt.rc('legend', fontsize=SMALL_SIZE)  # legend fontsize\n",
    "plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title\n",
    "plt.rc('lines', linewidth=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Temperature control lab\n",
    "\n",
    "The [temperature control lab](http://apmonitor.com/pdc/index.php/Main/ArduinoTemperatureControl) is an Arduino-based hands-on experiment for teaching dynamic modeling and process control developed by Prof. John Hedengren. At Notre Dame, we restructured our core [undergraduate process control class](https://ndcbe.github.io/controls/Readme.html) around six hands-on laboratory assignments with the TCLab.\n",
    "\n",
    "The TCLab board contains two heater plus temperature sensor assemblies. Using Python (or MATLAB), students can independently maninputate the electrical power to the heaters and measure the temperatures.\n",
    "\n",
    "![TC Lab hardware](https://ndcbe.github.io/controls/_images/TCLab_labelled.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## System identification data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the TCLab, we performed two system identification tests: step test and sine wave test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step test\n",
    "\n",
    "We will start by loading the data using `pandas`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>T1</th>\n",
       "      <th>T2</th>\n",
       "      <th>Q1</th>\n",
       "      <th>Q2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>22.84</td>\n",
       "      <td>22.84</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.00</td>\n",
       "      <td>22.84</td>\n",
       "      <td>22.84</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.01</td>\n",
       "      <td>23.16</td>\n",
       "      <td>22.84</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.02</td>\n",
       "      <td>22.84</td>\n",
       "      <td>22.84</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.01</td>\n",
       "      <td>22.84</td>\n",
       "      <td>22.84</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Time     T1     T2    Q1   Q2\n",
       "0  0.00  22.84  22.84  50.0  0.0\n",
       "1  1.00  22.84  22.84  50.0  0.0\n",
       "2  2.01  23.16  22.84  50.0  0.0\n",
       "3  3.02  22.84  22.84  50.0  0.0\n",
       "4  4.01  22.84  22.84  50.0  0.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "\n",
    "on_colab = \"google.colab\" in sys.modules\n",
    "if on_colab:\n",
    "    file = \"https://raw.githubusercontent.com/dowlinglab/pyomo-doe/main/data/tclab_step_test.csv\"\n",
    "else:\n",
    "    file = '../data/tclab_step_test.csv'\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(file)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by plotting the heater data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df.plot(x='Time', y=['Q1', 'Q2'], xlabel='Time (s)', ylabel='Heater Power (%)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this step test, heater 1 was set to 50% power and heater 2 was off. Let's see the resulting temperature profiles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "ax = df.plot(x='Time', y=['T1', 'T2'], xlabel='Time (s)', ylabel='Temperature (°C)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, temperature 1 rises as expected for a (near) linear system. The experimentation noise is noticeable once the device approaches steady-state after 600 seconds. As expected, temperature 2 gradually rises in response to heater assembly 1 heating up. On the device, the two heater assembles are separated by ~1 cm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sine test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>T1</th>\n",
       "      <th>T2</th>\n",
       "      <th>Q1</th>\n",
       "      <th>Q2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>22.2</td>\n",
       "      <td>22.2</td>\n",
       "      <td>50</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.01</td>\n",
       "      <td>22.2</td>\n",
       "      <td>22.2</td>\n",
       "      <td>51</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.01</td>\n",
       "      <td>22.2</td>\n",
       "      <td>22.2</td>\n",
       "      <td>52</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.00</td>\n",
       "      <td>22.2</td>\n",
       "      <td>22.2</td>\n",
       "      <td>53</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.01</td>\n",
       "      <td>22.2</td>\n",
       "      <td>22.2</td>\n",
       "      <td>54</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Time    T1    T2  Q1  Q2\n",
       "0  0.00  22.2  22.2  50   0\n",
       "1  1.01  22.2  22.2  51   0\n",
       "2  2.01  22.2  22.2  52   0\n",
       "3  3.00  22.2  22.2  53   0\n",
       "4  4.01  22.2  22.2  54   0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if on_colab:\n",
    "    file = \"https://raw.githubusercontent.com/dowlinglab/pyomo-doe/main/data/tclab_sine_test_5min_period.csv\"\n",
    "else:\n",
    "    file = '../data/tclab_sine_test_5min_period.csv'\n",
    "\n",
    "df2 = pd.read_csv(file)\n",
    "df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df2.plot(x='Time', y=['T1', 'T2'], xlabel='Time (s)', ylabel='Temperature (°C)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two-state mathematical model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using these data, we want to develop a science-based mathematical model for the TCLab. For simplicity, we will develop a mathemical single heater and temperature sensor assembly. However, this workshop example also supports modeling both assemblies.\n",
    "\n",
    "![TCLab schematic](../images/tclab_schematic2.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will define two **states**:\n",
    "* $T_{H,1}$ is the temperature of the heater/fin assembly (°C)\n",
    "* $T_{S,1}$ is the temperature of the sensor (°C)\n",
    "\n",
    "Assumptions:\n",
    "* The two bodies are uniform temperature, i.e., we are neglecting any temperature gradients in the fin.\n",
    "* The sensor exchanges heat only with the heater, and heat transfer to the surroundings is dominated by the heat sink attached to the heater.]\n",
    "* Heat capacities $C_p$ are constant.\n",
    "* Radiative heat transfer is negligible.\n",
    "\n",
    "We define the **manipulated variable**:\n",
    "* $u_1$ is the power sent to the heater (% of max)\n",
    "\n",
    "This motivates the following model:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "C^H_p\\frac{dT_{H,1}}{dt} & = U_a(T_{amb} - T_{H,1}) + U_b(T_{S,1} - T_{H,1}) + \\alpha P_1u_1\\\\\n",
    "C^S_p\\frac{dT_{S,1}}{dt} & = U_b(T_{H,1} - T_{S,1}) \n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The model has the following **unknown parameters**:\n",
    "* $C^H_p$ is the heat capacity of the heater/fin assembly (J / °C)\n",
    "* $C^S_p$ is the heat capacity of the sensor (J / °C)\n",
    "* $U_a$ is the heat transfer coefficient from the heater/fin to ambient (W / °C)\n",
    "* $U_b$ is the heat transfer coefficient from the heater/fin to the sensor (W / °C)\n",
    "\n",
    "And the following **known parameters**:\n",
    "* $\\alpha P_1$ are constants for the TCLab (W / %)\n",
    "* $T_{amb}$ is the ambient temperature (°C)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State space model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although not essential for this tutorial, we can write this model a a state space linear system.\n",
    "\n",
    "The initial steady state is $T_{amb}$. So let's write the dependent variables as excursions from the ambient temperature.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "C^H_p\\frac{d(T_{H,1} - T_{amb})}{dt} & = U_a(T_{amb} - T_{H,1}) + U_b((T_{S,1} - T_{amb}) - (T_{H,1} - T_{amb})) + \\alpha P_1u_1\\\\\n",
    "C^S_p\\frac{d(T_{S,1} - T_{amb})}{dt} & = U_b((T_{H,1} - T_{amb}) - (T_{S,1} - T_{amb}))\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Then divide by the heat capacities.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{d(T_{H,1} - T_{amb})}{dt} & = -\\frac{U_a+U_b}{C^H_p}(T_{H,1} - T_{amb}) + \\frac{U_b}{C^H_p}(T_{S,1} - T_{amb}) + \\frac{\\alpha P_1}{C^H_p}u_1 \\\\\n",
    "\\frac{d(T_{S,1} - T_{amb})}{dt} & = \\frac{U_b}{C^S_p}((T_{H,1} - T_{amb}) - (T_{S,1} - T_{amb})) \n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The two-state model can be rewritten using vectors to collect the states, inputs, measurable outputs, and arrays to collect the coefficients of the differential equations. \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{d}{dt}\\underbrace{\\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix}}_\\mathbf{x} & = \n",
    "\\underbrace{\\begin{bmatrix} -\\frac{U_a+U_b}{C^H_p} & \\frac{U_b}{C^H_p} \\\\ \\frac{U_b}{C^S_p} & - \\frac{U_b}{C^S_p}\\end{bmatrix}}_\\mathbf{A} \n",
    "\\underbrace{\\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix}}_\\mathbf{x} + \n",
    "\\underbrace{\\begin{bmatrix} \\frac{\\alpha P_1}{C^H_p} \\\\ 0 \\end{bmatrix}}_\\mathbf{B} \n",
    "\\underbrace{\\begin{bmatrix} u_1 \\end{bmatrix}}_\\mathbf{u} \\\\\n",
    "\\\\\n",
    "\\underbrace{\\begin{bmatrix} T_{S,1} - T_{amb} \\end{bmatrix}}_\\mathbf{y} & = \n",
    "\\underbrace{\\begin{bmatrix}0 & 1 \\end{bmatrix}}_\\mathbf{C} \n",
    "\\underbrace{\\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix}}_\\mathbf{x}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "In other words, we can write the temperature control lab model as a **state-space model**\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{d\\mathbf{x}}{dt} & = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u} \\\\\n",
    "\\mathbf{y} & = \\mathbf{C} \\mathbf{x}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where the state space variables are the deviations of temperature from the ambient $T_{amb}$:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathbf{u} & = \\begin{bmatrix} u_1 \\end{bmatrix} && \\text{inputs} \\\\\n",
    "\\\\\n",
    "\\mathbf{x} & = \\begin{bmatrix} T_{H,1} - T_{amb} \\\\ T_{S,1} - T_{amb} \\end{bmatrix} && \\text{states} \\\\\n",
    "\\\\\n",
    "\\mathbf{y} & = \\begin{bmatrix} T_{S,1} - T_{amb} \\end{bmatrix} && \\text{measurements} \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "and the parameters are embedded in the matrices:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathbf{A} = \\begin{bmatrix} -\\frac{U_a+U_b}{C^H_p} & \\frac{U_b}{C^H_p} \\\\ \\frac{U_b}{C^S_p} & - \\frac{U_b}{C^S_p}\\end{bmatrix}\n",
    "\\quad\n",
    "\\mathbf{B} = \\begin{bmatrix} \\frac{\\alpha P_1}{C^H_p} \\\\ 0 \\end{bmatrix} \n",
    "\\quad\n",
    "\\mathbf{C} = \\begin{bmatrix}0 & 1 \\end{bmatrix} \\\\\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}