![\"drawing\"](\"../images/mass_spring_damper.png\")
\n",
"\n",
"$$\n",
"\\begin{align}\n",
"& \\dot{x_1} = x_2 \\\\\n",
"& \\dot{x_2} = \\frac{1}{m} (u - k x_1 - d x_2) \\\\\n",
"\\end{align}\n",
"$$\n",
"\n",
"Therein, the state $x_1$ is the displacement of the mass $m$, the state $x_2$ is the velocity of the mass, the input $u$ is the applied force, $k$ is the spring constant and $d$ is the damping factor.\n",
"\n",
"We assume that the states can be measured perfectly, i.e., we will not define a separate output equation.\n",
"\n",
"One sampling period takes $15~\\text{ms}$. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Add HILO-MPC to path. NOT NECESSARY if it was installed via pip.\n",
"import sys\n",
"sys.path.append('../../../')\n",
"\n",
"import numpy as np\n",
"\n",
"from hilo_mpc import Model, NMPC, SimpleControlLoop, ANN, Layer"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"system = Model(plot_backend='bokeh', name='Linear SMD')\n",
"\n",
"# Set states and inputs\n",
"system.set_dynamical_states('x', 2)\n",
"system.set_inputs('u')\n",
"\n",
"# Add dynamics equations to model\n",
"system.set_dynamical_equations(['x_1', 'u - 2 * x_0 - 0.8 * x_1'])\n",
"\n",
"# Sampling time\n",
"Ts = 0.015 # Ts = 15 ms\n",
"\n",
"# Set-up\n",
"system.setup(dt=Ts)\n",
"\n",
"# Initialize system\n",
"x_0 = [12.5, 0]\n",
"system.set_initial_conditions(x_0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generate data \n",
"We start defining the MPC we want to learn as follows. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\Bruno\\Documents\\GitHub\\hilo-mpc\\hilo_mpc\\modules\\base.py:2174: UserWarning: Plots are disabled, since no backend was selected.\n",
" warnings.warn(\"Plots are disabled, since no backend was selected.\")\n"
]
}
],
"source": [
"# Make controller\n",
"nmpc = NMPC(system)\n",
"\n",
"# Set horizon\n",
"nmpc.horizon = 15\n",
"\n",
"# Set cost function\n",
"nmpc.quad_stage_cost.add_states(names=['x_0', 'x_1'], weights=[100, 100], ref=[1, 0])\n",
"nmpc.quad_stage_cost.add_inputs(names=['u'], weights=[10], ref=[2])\n",
"nmpc.quad_terminal_cost.add_states(names=['x_0', 'x_1'], weights=np.array([[8358.1, 1161.7], [1161.7, 2022.9]]),\n",
" ref=[1, 0])\n",
"nmpc.set_box_constraints(u_ub=[15], u_lb=[-20])\n",
"\n",
"# Set-up controller\n",
"nmpc.setup(options={'print_level': 0})\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Manuall closed-loop data generation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The data can be generated manually, by running the system as follows"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Vector of simulation time points\n",
"Tf = 10 # Final time\n",
"t = np.arange(0, Tf, Ts)\n",
"n_steps = int(Tf / Ts)\n",
"scl = SimpleControlLoop(system, nmpc)\n",
"scl.run(n_steps)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
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