TVC_do_mpc.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "220263f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sys\n",
    "from casadi import *\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "# Import do_mpc package:\n",
    "import do_mpc\n",
    "T=1000\n",
    "r=np.array([0,0,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "6a17d881",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_type = 'continuous' # either 'discrete' or 'continuous'\n",
    "model = do_mpc.model.Model(model_type)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "30079292",
   "metadata": {},
   "outputs": [],
   "source": [
    "r=model.set_variable('_x','linear',(3))\n",
    "v=model.set_variable('_x','dlinear',(3))\n",
    "m=model.set_variable('_x','mass',(1))\n",
    "q=model.set_variable('_x','attitude',(4))\n",
    "omega=model.set_variable('_x','omega',(3))\n",
    "g=np.array([0,0,-9.81])\n",
    "d=model.set_variable('_u','tvc',(3))\n",
    "F_B=d*T\n",
    "F_N=SX.sym('force_in',3)\n",
    "x,y,z=vertsplit(F_B)\n",
    "F_N=SX.sym('force_in',3)\n",
    "qw,qx,qy,qz=vertsplit(q)\n",
    "F_N[0] = x*(qx*qx+qw*qw-qy*qy- qz*qz) + y*(2*qx*qy- 2*qw*qz) + z*(2*qx*qz+ 2*qw*qy)\n",
    "F_N[1] = x*(2*qw*qz + 2*qx*qy) + y*(qw*qw - qx*qx+ qy*qy - qz*qz)+ z*(-2*qw*qx+ 2*qy*qz)\n",
    "F_N[2] = x*(-2*qw*qy+ 2*qx*qz) + y*(2*qw*qx+ 2*qy*qz)+ z*(qw*qw - qx*qx- qy*qy+ qz*qz)\n",
    "J = SX.sym('moi', 3, 3)\n",
    "J[0, 0] = 10\n",
    "J[0, 1] = 0\n",
    "J[0, 2] = 0\n",
    "J[1, 0] = 0\n",
    "J[1, 1] = 10\n",
    "J[1, 2] = 0\n",
    "J[2,0]=0\n",
    "J[2, 1] = 0\n",
    "J[2, 2] = 10\n",
    "op=SX.sym('op',3,3)\n",
    "op[0,0]=0\n",
    "op[0,1]=-omega[2]\n",
    "op[0,2]=omega[1]\n",
    "op[1,0]=omega[2]\n",
    "op[1,1]=0\n",
    "op[1,2]=-omega[0]\n",
    "op[2,0]=-omega[1]\n",
    "op[2,1]=omega[0]\n",
    "op[2,2]=0\n",
    "L_B=cross(r,F_B)\n",
    "oh=SX.sym('oh',4,4)\n",
    "oh[0,0]=0\n",
    "oh[0,1]=-omega[0]\n",
    "oh[0,2]=-omega[1]\n",
    "oh[0,3]=-omega[2]\n",
    "oh[1,0]=omega[0]\n",
    "oh[1,1]=0\n",
    "oh[1,2]=omega[2]\n",
    "oh[1,3]=-omega[1]\n",
    "oh[2,0]=omega[1]\n",
    "oh[2,1]=-omega[2]\n",
    "oh[2,2]=0\n",
    "oh[2,3]=omega[0]\n",
    "oh[3,0]=omega[2]\n",
    "oh[3,1]=omega[1]\n",
    "oh[3,2]=-omega[0]\n",
    "oh[3,3]=0\n",
    "oh\n",
    "J_inv=inv(J)\n",
    "domega=-J_inv@op@J@omega+L_B\n",
    "dq=(oh@q)/2\n",
    "dv=(F_N/m)+g\n",
    "dm=(sqrt(F_B[0]**2+F_B[1]**2+F_B[2]**2))/100 # 100 is I_sp*g_ref"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "f74750b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# M = 1 #Mach Number\n",
    "# N = 1 #number of Fins \n",
    "# At = 1 #Planform area of one exposed fin \n",
    "# Ar = 1 #reference Area \n",
    "# S = 1 #fin semi span\n",
    "# rl = 1 #fin leading edge radius \n",
    "# tl = 1 #leading edge sweep angle \n",
    "# Abf = 1 #base area of one fin \n",
    "# lc = 1 #midchord line sweep angle\n",
    "# cr = 1 #fin root chord\n",
    "# hr = 1 #root fin trailing edge thickness \n",
    "# tr = 1 #root fin thickness \n",
    "# Awb = 1 #wetted area of body\n",
    "# fb = 1 #body and nose fineness ratio \n",
    "# Ab = 1 #base area at tail \n",
    "# Aw = 1 #total wetted area \n",
    "# Re=1 #Unknown\n",
    "# Abn = 1 #Nosecone Base Area\n",
    "\n",
    "# Af = 1 #total area of one fin \n",
    "# ar = 1 #aspect ratio\n",
    "# rt = 1 #body radius at tail \n",
    "# s = 1 #exposed fin semi span \n",
    "# lc = 1 #midchord line sweep angle  \n",
    "\n",
    "# ## Calculation for DragCoeff   \n",
    "# Cf = 1.328/((Re)**0.5)\n",
    "# Cfc = Cf*(1-(0.12*M*M))\n",
    "# Cfb = 2*Cf*(cr/hr)\n",
    "# Kdbt = ((1+((18*Cfc*(tr/hr)**2)/(N*(1-0.52)*(Abf/Ar)))) * ((0.135*N*(Abf/Ar))/(Cfc**(1/3)))) + ((math.cos(lc))**2)\n",
    "# del_Cd = ((1-(M**2))**-0.417)-1\n",
    "# Kdp = 1 + (((6.82*Awb*Cfc*((fn+0.7)**1.29))/((fb**3)*Ar))**(5/3))\n",
    "# Kdbb = 1 +  (1/((6.38 + 39.7*(hr/cr))(Cfc*(Aw/Ab))))\n",
    "# CDft = 2*N*Cfc*(At/Ar)\n",
    "# CDlt = (2*N*S*rl*(math.cos(tl)**2)*del_Cd)/Ar\n",
    "# CDbt = (0.135*N*Abf)/(Ar*(Cfb**(1/3))*(Kdbt-M*M*(math.cos(lc))**2)**0.5)\n",
    "# CDtt = (4*N*Cfc) * (At/At) * ((tr/cr)*(math.cos(lc)**2) + ((30 * (tr/cr)**4 * math.cos(lc)**2) / ((K - M*M*(math.cos(lc)**2))**1.5)))       \n",
    "# Cdtt = CDft + CDlt + CDbt + CDtt\n",
    "# CDp = (6*Awb*Cfc) / (((fb)**3) * Ar * ((Kdp-(M**2))**0.6))\n",
    "# CDbb = (0.29*(Ab / Ar)) / ((Cfc*(Aw/Ab)*(Kdbb-(M**2)))**0.5)\n",
    "# Cdtb = CDp + CDbb\n",
    "# Cd = Cdtt + Cdtb \n",
    "\n",
    "# ##Calculation for Normal Coeff\n",
    "# B = (1-(M**2))**0.5\n",
    "# pi = 3.141592\n",
    "# tou = (s + rt)/rt\n",
    "# Cnab = 2 * (Abn / Ar)\n",
    "# Cnat = (N*pi*ar*(Af/Ar))/(2+(4+((B*ar)/(math.cos(lc)))**2)**0.5)\n",
    "# Ktb = (2/(pi*((1-(1/tou))**2)))*(((1+(1/(tou**2)))*(0.5*m.atan(0.5*(tou-(1/tou)))))-((1/(tou**2))*(tou - (t/tou)+ 2*m.atan(1/tou))))\n",
    "# Cnatb = Cnat * Ktb \n",
    "# Kbt = (((1-(1/(tou**2)))/(1-(t/tou)))**2) - Ktb \n",
    "# Cnabt = Cnat * Kbt \n",
    "# Cna = Cnab + Cnatb + Cnabt "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "d04921d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "model.set_rhs('attitude',dq)\n",
    "model.set_rhs('omega',domega)\n",
    "model.set_rhs('dlinear',dv)\n",
    "model.set_rhs('linear',v)\n",
    "model.set_rhs('mass',dm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "41501f70",
   "metadata": {},
   "outputs": [],
   "source": [
    "model.setup()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "1b141972",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = do_mpc.simulator.Simulator(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "e686499b",
   "metadata": {},
   "outputs": [],
   "source": [
    "params_simulator = {\n",
    "    'integration_tool': 'cvodes',\n",
    "    'abstol': 1e-10,\n",
    "    'reltol': 1e-10,\n",
    "    't_step': 0.005\n",
    "}\n",
    "\n",
    "simulator.set_param(**params_simulator)\n",
    "simulator.setup()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "5f20bc1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "estimator = do_mpc.estimator.StateFeedback(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "8c659a27",
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=np.array([0,0,0,0,0,0,10,0,0,0,1,0,0,0]).reshape(-1,1)\n",
    "simulator.x0 = x0\n",
    "estimator.x0 = x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "1a6b99c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "data=[]\n",
    "time=[]\n",
    "for k in range(500):\n",
    "    u0=np.array([[0],[0],[1]])\n",
    "    y_next = simulator.make_step(u0)\n",
    "    x0 = estimator.make_step(y_next)\n",
    "    data.append(x0)\n",
    "    time.append(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "dd7e2678",
   "metadata": {},
   "outputs": [
    {
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