{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "***Note: this is the fECR.ipynb notebook. The\n", "PDF version \"Enzyme-catalysed reaction: analysis as a feedback control\n", "actuator\"\n", "is available [here](fECR.pdf).***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "Using the methods of control theory to examine and reexamine the behaviour of living systems is well-established\n", "(Craik, 1947)\n", "(Weiner, 1961)\n", "(Bayliss, 1966)\n", "(Savageau, 1976)\n", "(Jagacinski and Flach, 2003)\n", "(Inglesias and Ingalls, 2010)\n", "(Wellstead et al, 2008)\n", "(Drion et al, 2015)\n", "(Del Veccio, 2013).\n", "This notebook examines the enzyme-catalysed reaction as a control actuator and its behavior within a feedback loop controlling product concentration.\n", "\n", "\n", "As discussed by (Gawthrop and Crampin, 2016):\n", "\"The bond graph approach gives the set of *nonlinear* ordinary\n", "differential equations describing the biomolecular system being modelled.\n", "Linearisation of non-linear systems is a standard technique in control\n", "engineering: as discussed by \n", "(Goodwin, Graebe and Salgado), \n", "\"The incentive to\n", "try to approximate a nonlinear system by a linear model is that the\n", "science and art of linear control is vastly more complete and simpler\n", "than they are for the nonlinear case.\". Nevertheless, it is important\n", "to realise that conclusions drawn from linearisation can only be\n", "verified using the full *nonlinear* equations.\"\n", "\n", "Linearisation *per se* is discussed in the notebook [Linearisation](https://github.com/gawthrop/BondGraphTools-Biomolecular/blob/master/Linearisation.ipynb).\n", "In particular, linearisation of a dynamic system $\\dot x = f(x,v)$ is with reference to a steady state defined by constant states $x=x_{ss}$ and constant flows $v=v_{ss}$ such that $f(x_{ss},v_{ss})=0$. In general, determination of steady-states is a difficult problem and can only be determined numerically; this is the approach taken here.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import some python code\n", "The bond graph analysis uses a number of Python modules:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "## Some useful imports\n", "import BondGraphTools as bgt\n", "import numpy as np\n", "import sympy as sym\n", "import matplotlib.pyplot as plt\n", "import IPython.display as disp\n", "\n", "## Stoichiometric analysis\n", "import stoich as st\n", "\n", "## SVG bg representation conversion\n", "import svgBondGraph as sbg\n", "\n", "## Control systems package\n", "import control as con\n", "\n", "## Set quiet=False for verbose output\n", "quiet = True\n", "\n", "## Set slycot=True if slycot is installed (see control module)\n", "slycot=True\n", "\n", "## For reimporting: use imp.reload(module)\n", "import importlib as imp\n", "\n", "## Printing options\n", "np.set_printoptions(precision=3)\n", "fmt = '{:5.3f}'\n", "\n", "## Allow output from within functions\n", "from IPython.core.interactiveshell import InteractiveShell\n", "InteractiveShell.ast_node_interactivity = \"all\"\n", "\n", "## Product removal\n", "productRemoval = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feedback control\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "kfb\n", "\n", "kact\n", "\n", "ksys\n", "\n", "kd\n", "\n", "+\n", "\n", "+\n", "\n", "+\n", "\n", "-\n", "\n", "kw\n", "\n", "w=xE0\n", "\n", "y=xB\n", "\n", "d=xB0\n", "\n", "u=v\n", "\n", "" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "disp.SVG('feedback.svg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure shows a feedback control loop. In terms of control theory, $k_{fb}$, $k_{act}$, $k_{sys}$, $k_d$ and $k_w$ are the feedback, actuator, system, disturbance and setpoint gains respectively; $u$,$y$ and $w$ are the control signal, system output and setpoint respectively. The blocks can be intepreted as static gains (for steady-state analysis) or as transfer functions for dynamic analysis.\n", "\n", "As discussed below this diagram has a systems biology interpretation for the particular example considered here; in particular: $k_{fb}$ and $k_w$ are associated with a linearised feedback inhibition, $k_{act}$ with an enzyme-catalysed reaction and $k_{sys}$ and $k_{sys}$ and $k_d$ with product removal.\n", "\n", "Defining the loop-gain $L = k_{fb}k_{act}k_{sys}$, it follows that:\n", "\\begin{align}\n", "y &= \\frac{L}{1+L} k_w w + \\frac{1}{1+L}k_d d\n", "\\end{align}\n", "Thus a large loop gain $L$ leads to:\n", "\\begin{align}\n", "y &\\approx k_w w \n", "\\end{align}\n", "The disturbance is eliminated whilst the system output follows $k_w w$.\n", "\n", "It is important to emphasise that the actuator requires power to operate in the correct manner." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analysis functions\n", "The folowing functions are used to analyse the various systems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Stoichiometry\n", "This function returns the bond graph stoichiometry without chemostats **s**, with chemostats **sc** and with flowstats **sf** using the [stoich](https://github.com/gawthrop/BondGraphTools-Biomolecular/blob/master/stoich.ipynb) package and [BondGraphTools](https://pypi.org/project/BondGraphTools/)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def stoichiometry(abg,chemostats=[],flowstats=[]):\n", " s = st.stoich(abg.model(),quiet=quiet)\n", " sc = st.statify(s,chemostats=chemostats)\n", " \n", " if len(flowstats) is 0:\n", " sf = None\n", " else:\n", " sf = st.statify(s,flowstats=flowstats)\n", " \n", " return s,sc,sf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linearise about the steady-state\n", "The bond graph model in stoichiometric form is symbolically linearised and combined with numerical parameters to give a linear system in numerical state-space form. The [Python Control Systems Library](https://pypi.org/project/control/) is used to convert the state-space systems into transfer functions and to give the steady-state (DC) gain." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def plot(t_step,vv,KK_F,title,ylabel='$v$'):\n", " \"\"\"Plot step responses of linearised systems\"\"\"\n", " plt.plot(t_step,vv.T) \n", " plt.title(title)\n", " Legend = ['K_F='+str(K_F) for K_F in KK_F]\n", " plt.legend(Legend)\n", " plt.grid()\n", " plt.xlabel('$t$')\n", " plt.ylabel(ylabel)\n", " plt.show()\n", " \n", "def linearise(s,sc,sf=None,i_r=2,dist='B',t_step_max=10,KK_F=[10,100,1000]):\n", " \"\"\"Linearise systems, generate transfer functions, plot step responses\"\"\"\n", " useFlowstat = sf is not None\n", " productRemoval = 'B0' in s['species'] \n", " \n", " ## Steady state via long simulation\n", " ##Time\n", " t_max = int(1e3)\n", " t = np.linspace(0,t_max,1000)\n", " t_step = np.linspace(0,t_step_max,1000)\n", " \n", " if useFlowstat:\n", " ## Flowstat\n", " f0 = 0\n", " V_flow = {'r0':str(f0)}\n", " #print(V_flow)\n", " stats = sc['chemostats']+sf['flowstats']\n", " #print(stats)\n", " inp = 'r0'\n", " else:\n", " stats = sc['chemostats']\n", " inp = 'E0'\n", " \n", " ## index of input\n", " i_in = stats.index(inp)\n", " ##print('i_in',i_in)\n", "\n", " ## index of disturbance\n", " i_dist = stats.index(dist)\n", " #print('i_dist',i_dist)\n", " \n", " for K_F in KK_F:\n", " parameter['K_F'] = K_F\n", " parameter['K_G'] = 1/K_F\n", " print('\\n==========================')\n", " print('K_F =',K_F)\n", " print('==========================')\n", "\n", " ## Simulate to get the steady state\n", " if useFlowstat:\n", " ssdat = st.sim(s,sc=sc,t=t,parameter=parameter,V_flow=V_flow,quiet=quiet)\n", " else:\n", " ssdat = st.sim(s,sc=sc,t=t,parameter=parameter,quiet=quiet)\n", "\n", " ## Use the final value as the steady-state\n", " x_ss = ssdat['X'][-1,:]\n", "# print(s['species'])\n", "# print('x_ss =', x_ss)\n", " v_ss = ssdat['V'][-1,:]\n", "# print('v_ss =', v_ss)\n", "\n", "\n", " ## Linearise: Sys is the linearised system in control toolbox form\n", " ## Flow output\n", " Sys = st.lin(s,sc,sf=sf,x_ss=x_ss,parameter=parameter,outvar='V',quiet=quiet)\n", " ## Potential output\n", " SysX = st.lin(s,sc,sf=sf,x_ss=x_ss,parameter=parameter,outvar='X',quiet=quiet)\n", " \n", " #con.ss2tf(Sys)\n", " tf = con.ss2tf(Sys)\n", " tfPhi = con.ss2tf(SysX)\n", " \n", " if useFlowstat:\n", " deriv = con.tf([1,0],[1])\n", " tf_f_in = con.minreal(con.series(deriv,tf[i_r,i_in]))\n", " tf_f_dist = con.minreal(tf[i_r,i_dist])\n", " inName = 'f_0'\n", " else:\n", " tf_f_in = con.minreal(tf[i_r,i_in])\n", " tf_f_dist = con.minreal(tf[i_r,i_dist])\n", " inName = 'x_E0'\n", " \n", " if productRemoval:\n", " ## Compute transfer functions to B\n", " i_B = s['species'].index('B')\n", " print('i_B',i_B,'i_dist',i_dist)\n", "\n", " tf_X_in = tfPhi[i_B,i_in]\n", " print('\\nTransfer function: phi_B/input',tf_X_in)\n", " in_gain_X = con.dcgain(tf_X_in)\n", " print('\\tgain:',fmt.format(in_gain_X))\n", " print('\\tpoles:', con.pole(tf_X_in))\n", " \n", " tf_X_dist = tfPhi[i_B,i_dist]\n", " print('\\nTransfer function: phi_B/phi_B0',tf_X_dist)\n", " dist_gain_X = con.dcgain(tf_X_dist)\n", " print('\\tgain:',fmt.format(dist_gain_X))\n", " \n", " tf_in = tf_X_in\n", " \n", " else:\n", " dist_gain_X = None\n", " in_gain_X= None\n", " print('\\nTransfer function: f_2/'+inName,tf_f_in)\n", " in_gain = con.dcgain(tf_f_in)\n", " print('\\tgain:',fmt.format(in_gain))\n", " print('\\tpoles:', con.pole(tf_f_in))\n", " \n", " print('\\nTransfer function: f_2/x_B',tf_f_dist)\n", " dist_gain = con.dcgain(tf_f_dist)\n", " print('\\tgain:',fmt.format(dist_gain))\n", " \n", " tf_in = tf_f_in\n", " \n", " ## Step responses\n", " if productRemoval:\n", " t,p = con.step_response(tf_X_in,T=t_step)\n", " t,pd = con.step_response(tf_X_dist,T=t_step)\n", " else:\n", " t,v = con.step_response(tf_f_in,T=t_step)\n", " t,vd = con.step_response(tf_f_dist,T=t_step)\n", " \n", " if K_F is KK_F[0]:\n", " if productRemoval:\n", " pp = p\n", " ppd = pd\n", " else:\n", " vv = v\n", " vvd = vd \n", " else:\n", "\n", " if productRemoval:\n", " pp = np.vstack((pp,p))\n", " ppd = np.vstack((ppd,pd))\n", " else:\n", " vv = np.vstack((vv,v))\n", " vvd = np.vstack((vvd,vd))\n", "\n", " if productRemoval:\n", " plot(t_step,pp,KK_F,'Control response -- X',ylabel='$X$') \n", " plot(t_step,ppd,KK_F,'Disturbance response -- X',ylabel='$X$') \n", " else:\n", " plot(t_step,vv,KK_F,'Control response -- flow',ylabel='$v$') \n", " plot(t_step,vvd,KK_F,'Disturbance response -- flow',ylabel='$v$') \n", " \n", " return Sys,SysX,x_ss,v_ss,dist_gain_X,in_gain_X,tf_in\n", "\n", "def extractSS(s,x_ss,species):\n", " code = ''\n", " for spec in species:\n", " ss = x_ss[s['species'].index(spec)]\n", " name = 'x_ss_'+spec\n", " print(name+' =',fmt.format(ss))\n", " #exec(name+' = '+str(ss))\n", " code += name+' = '+str(ss)+'\\n'\n", " #print(code)\n", " return code\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Pumped enzyme-catalysed reaction: analysis as a control actuator\n", "The bond graph representation of the (reversible) enzyme-catalysed reaction is given by\n", "(Gawthrop and Crampin, 2014) and is discussed in the tutorial [ECR](ECR.ipynb).\n", "\n", "The additional species $E0$ represents a reservoir of enzyme coupled to the ECR via the reaction $r0$. \n", "$E0$ is used as a chemostat to adjust the total amount of enzyme associated with the ECR.\n", "The additional species F and G act as a *pump* -- the idea is that a high potential of F and a low potential of G will drive the reaction $A \\leftrightarrow B$ strongly towards B and thus endow the reaction with desirable actuator properties.\n", "\n", "Following (Gawthrop and Crampin, 2014), the steady-state flow $v$ through r1 and r2 is:\n", "\\begin{align}\n", " v &= \\bar{\\kappa} \\frac{K_C e_0}{\\frac{K_C}{K_E} + \\sigma_v} \\delta_v\\\\\n", " \\text{where }\n", " \\delta_v &= v_o^+ - v_o^-\\\\\n", " \\sigma_v &= \\frac{\\kappa_1 v_o^+ + \\kappa_2 v_o^-}{\\kappa_1 +\n", " \\kappa_2}\\\\\n", " \\text{and, in this case }\n", " v_o^+ &= K_A K_F x_A x_F \\; , v_o^- = K_B K_G x_A x_G\n", "\\end{align}\n", "Further\n", "\\begin{align}\n", " e_0 &= (1 + \\frac{K_E}{K_C} \\sigma_v) x_E = (1 + \\frac{K_e}{K_c} \\sigma_v) \\frac{K_{E0}}{K_E}x_{E0}\n", "\\end{align}\n", "Now, as discussed above $K_F$ is large and $K_G$ small hence:\n", "\\begin{align}\n", "v &\\approx k_{act} x_E = k_{act} \\frac{K_{E0}}{K_E} x_{E0} \\label{eq:v_act}\\\\\n", "\\text{where }\n", "k_{act} &=\n", "\\bar{\\kappa} \\sigma_v K_E x_E\n", "\\end{align}\n", "In the particular case where $\\kappa_1=\\kappa_2=\\kappa$\n", "\n", "\\begin{align}\n", "k_{act} &= \\frac{\\kappa}{2} K_A K_F x_A x_F K_E \n", "\\end{align}\n", "\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "1\n", "\n", "\n", "Re:r0\n", "\n", "Ce:E0\n", "\n", "0\n", "\n", "Ce:A\n", "\n", "Ce:F\n", "\n", "Ce:G\n", "\n", "1\n", "\n", "0\n", "\n", "Ce:C\n", "\n", "Ce:B\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "\n", "Re:r1\n", "\n", "\n", "Re:r2\n", "\n", "Ce:E\n", "\n", "0\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sbg.model('pRE_abg.svg')\n", "import pRE_abg\n", "abg = pRE_abg\n", "disp.SVG('pRE_abg.svg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Parameters" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'X0_A': 2, 'K_E0': 1, 'X0_E0': 1, 'K_A': 1, 'K_B': 10, 'K_C': 1, 'K_E': 1, 'K_F': 100, 'K_G': 0.01, 'kappa_r0': 1, 'kappa_r1': 10, 'kappa_r2': 10}\n" ] } ], "source": [ "## Parameters\n", "X0_A = 2\n", "K_A = 1\n", "X0_E0 = 1\n", "K_B = 10\n", "K_E0 = 1\n", "K_C = 1\n", "K_E = 1\n", "K_F = 100\n", "KK_F = [10,100]\n", "K_G = 1/K_F\n", "kappa_r0 = 1\n", "\n", "kappa = 10\n", "kappa_r1 = kappa\n", "kappa_r2 = kappa\n", "\n", "pars = ['X0_A','K_E0','X0_E0','K_A','K_B','K_C','K_E','K_F','K_G','kappa_r0','kappa_r1','kappa_r2']\n", "parameter = {}\n", "for par in pars:\n", " parameter[par] = eval(par)\n", "print(parameter)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyse" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "None\n", "Reactions:\n" ] }, { "data": { "text/latex": [ "\\begin{align}\n", "E &\\Leftrightarrow E0 \\\\\n", "A + E + F &\\Leftrightarrow C \\\\\n", "C &\\Leftrightarrow B + E + G \n", "\\end{align}\n" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Pathway reaction:\n" ] }, { "data": { "text/latex": [ "\\begin{align}\n", "A + F &\\Leftrightarrow B + G \n", "\\end{align}\n" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "==========================\n", "K_F = 10\n", "==========================\n", "0 states have been removed from the model\n", "0 states have been removed from the model\n", "\n", "Transfer function: f_2/x_E0 \n", " -10 s + 1900\n", "----------------\n", "s^2 + 231 s + 20\n", "\n", "\tgain: 95.000\n", "\tpoles: [-2.309e+02 -8.661e-02]\n", "\n", "Transfer function: f_2/x_B \n", "-10 s^2 - 2110 s - 100\n", "----------------------\n", " s^2 + 231 s + 20\n", "\n", "\tgain: -5.000\n", "\n", "==========================\n", "K_F = 100\n", "==========================\n", "0 states have been removed from the model\n", "0 states have been removed from the model\n", "\n", "Transfer function: f_2/x_E0 \n", " -s + 1.999e+04\n", "-----------------\n", "s^2 + 2022 s + 20\n", "\n", "\tgain: 999.500\n", "\tpoles: [-2.022e+03 -9.891e-03]\n", "\n", "Transfer function: f_2/x_B \n", "-0.993 s^2 - 1997 s - 9.93\n", "--------------------------\n", " s^2 + 2022 s + 20\n", "\n", "\tgain: -0.497\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "x_ss_A = 2.000\n", "x_ss_F = 1.000\n", "k_act = 1000.0\n" ] } ], "source": [ "chemostats=['E0','A','B','F','G']\n", "# flowstats = []\n", "s,sc,sf = stoichiometry(abg,chemostats=chemostats)\n", "print(sf)\n", "print('Reactions:')\n", "disp.Latex(st.sprintrl(s))\n", "sp = st.path(s,sc)\n", "print('Pathway reaction:')\n", "disp.Latex(st.sprintrl(sp))\n", "Sys,SysX,x_ss,v_ss,dist_gain_X,in_gain_X,tf_in_act = linearise(s,sc,i_r=2,dist='B',KK_F=KK_F,t_step_max=500)\n", "\n", "## Actuator gain\n", "exec(extractSS(s,x_ss,['A','F']))\n", "k_act = (kappa/2)*K_A*K_E*K_F*x_ss_A*x_ss_F\n", "print('k_act =', k_act)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion.\n", "\n", "- With the values given in the Parameters section, the theoretical steady-state flow $v$ is $1000 x_{E0}$.\n", "- This agrees with the final value (1000) of the unit step response to $x_{E0}$ \n", "- This also agrees with the final value (~0) of the unit step response to $x_{B}$ \n", "- As there are two non-chemostated **Ce** components, the transfer function is second-order. \n", "- There are two real poles at about $s=-0.01$ and $s=-2000$. The slow pole (timeconstant about 100) corresponds to the approximate conserved moiety.\n", "- Thus the ECR acts a nearly ideal actuator: the flow $v$ depends on $E0$ only in a linear fashion.\n", "- However, the use of F and G to pump the actuator consumes energy - this is a typical performance/energy tradeoff in control systems.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Product removal.\n", "The additional reaction **Re:R3** and species **Ce_BO** is added to the bond graph so that product B is removed. \n", "In the steady-state this means that $v = \\kappa_3 (K_B x_B - K_{B0} x_{B0})$, hence:\n", "\\begin{align}\n", "x_B &= k_{sys} v + k_{d}x_{B0}\\\\\n", "\\text{where }\n", "k_{sys} &= \\frac{1}{\\kappa_3 K_B}\\\\\n", "\\text{and }\n", "k_d &= \\frac{K_{B0}}{K_B}\n", "\\end{align}\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "1\n", "\n", "\n", "Re:r0\n", "\n", "Ce:E0\n", "\n", "0\n", "\n", "Ce:A\n", "\n", "Ce:F\n", "\n", "Ce:G\n", "\n", "1\n", "\n", "0\n", "\n", "Ce:C\n", "\n", "Ce:B\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "\n", "Re:r1\n", "\n", "\n", "Re:r2\n", "\n", "Ce:E\n", "\n", "0\n", "\n", "\n", "Re:r3\n", "\n", "Ce:B0\n", "\n", "0\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sbg.model('pREpr_abg.svg')\n", "import pREpr_abg\n", "abg = pREpr_abg\n", "disp.SVG('pREpr_abg.svg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Parameters" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": true }, "outputs": [], "source": [ "## Parameters\n", "K_B0 = 1\n", "X0_B0 = 1e-6\n", "kappa_r3 = 1\n", "\n", "pars = ['K_B0','X0_B0','kappa_r3']\n", "for par in pars:\n", " parameter[par] = eval(par)\n", "#print(parameter)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyse" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "==========================\n", "K_F = 10\n", "==========================\n", "0 states have been removed from the model\n", "0 states have been removed from the model\n", "i_B 1 i_dist 2\n", "\n", "Transfer function: phi_B/input \n", "3.331e-16 s^2 - 66.67 s + 1333\n", "------------------------------\n", "s^3 + 307.7 s^2 + 5007 s + 300\n", "\n", "\tgain: 4.444\n", "\tpoles: [-2.904e+02 -1.718e+01 -6.014e-02]\n", "\n", "Transfer function: phi_B/phi_B0 \n", " s^2 + 287.7 s + 20\n", "------------------------------\n", "s^3 + 307.7 s^2 + 5007 s + 300\n", "\n", "\tgain: 0.067\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/peterg/.local/lib/python3.6/site-packages/scipy/signal/filter_design.py:1619: BadCoefficients: Badly conditioned filter coefficients (numerator): the results may be meaningless\n", " \"results may be meaningless\", BadCoefficients)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "==========================\n", "K_F = 100\n", "==========================\n", "0 states have been removed from the model\n", "1 states have been removed from the model\n", "i_B 1 i_dist 2\n", "\n", "Transfer function: phi_B/input \n", "-1.11e-16 s^2 - 95.23 s + 1.905e+04\n", "-----------------------------------\n", "s^3 + 2127 s^2 + 2.319e+04 s + 210\n", "\n", "\tgain: 90.704\n", "\tpoles: [-2.116e+03 -1.095e+01 -9.062e-03]\n", "\n", "Transfer function: phi_B/phi_B0 \n", " s^2 + 2116 s + 20\n", "----------------------------------\n", "s^3 + 2127 s^2 + 2.319e+04 s + 210\n", "\n", "\tgain: 0.095\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "chemostats=['E0','A','B0','F','G']\n", "s,sc,sf = stoichiometry(abg,chemostats=chemostats)\n", "#print(sf)\n", "Sys,SysX,x_ss,v_ss,dist_gain_X,in_gain_X,tf_in_pr = linearise(s,sc,i_r=3,dist='B0',t_step_max=1000,KK_F=KK_F)\n", "#con.ss2tf(Sys)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Computed steady-state values:\n", "x_ss_A = 2.000\n", "x_ss_F = 1.000\n", "x_ss_B = 95.229\n", "x_ss_B0 = 0.000\n", "\n", "The control system gains:\n", "k_sys = 0.100\n", "k_dist = 0.100\n", "Setpoint gain: Theory = 100.0 , Linearised= 90.704\n", "Disturbance gain: Theory = 0.1 , Linearised= 0.095\n" ] } ], "source": [ "print('\\nComputed steady-state values:')\n", "exec(extractSS(s,x_ss,['A','F','B','B0']))\n", "\n", "print('\\nThe control system gains:')\n", "k_sys = 1/(kappa_r3*K_B)\n", "k_dist = K_B0/K_B\n", "print('k_sys =', fmt.format(k_sys))\n", "print('k_dist =', fmt.format(k_dist))\n", "\n", "print('Setpoint gain: Theory =', k_act*k_sys, ', Linearised=',fmt.format(in_gain_X ))\n", "print('Disturbance gain: Theory =',k_dist, ', Linearised=',fmt.format(dist_gain_X ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion\n", "\n", "- As there are three non-chemostated **Ce** components, the transfer function is third-order. \n", "- There are three real poles. The two at about $s=-0.01$ and $s=-2000$ corespond to the actuator, the third at about $s=-10$ corresponds to the product removal.\n", "- If isolated, the product removal pole would be at $s = -\\kappa_{r3}K_B=-10$. The degree of isolation depends on $K_F$ ($K_G=1/K_F$); large values of $K_F$ do indeed give a pole close to $s=-10$.\n", "- The high gains and the lack of feedback lead to an ill-defined response and numerical issues\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Feedback Control\n", "\n", "Feedback is added using the red bonds in the Figure. The reaction relating E and E0 now contains B:\n", "\\ch{E + N B <> [ r0 ] E0} where $N=5$.\n", "In the steady state, this implies that:\n", "\\begin{align}\n", " K_E K_B^N x_E x_B^N = K_{E0} x_{E0}\n", "\\end{align}\n", "For a given steady state this can be linearised to give:\n", "\\begin{align}\n", " K_E K_B^N (\\bar{x}_B^N\\tilde{x}_E + \\bar{x}_E N \\bar{x}_B^{N-1} \\tilde{x}_B) = K_{E0} \\tilde{x}_{E0}\n", "\\end{align}\n", "This can be rewritten as:\n", "\\begin{align}\n", "\\tilde{x}_E &= k_{fb} (k_{w}\\tilde{x}_{E0} - \\tilde{x}_B) \\label{eq:fb}\\\\\n", "\\text{where }\n", "k_{fb} &= N\\frac{\\bar{x}_E}{\\bar{x}_B}\\\\\n", "\\text{and }\n", "k_{w} &= \\frac{1}{k_{fb}}\\frac{K_{E0}}{ K_E K_B^N \\bar{x}_B^{N} }\n", "\\end{align}\n", "\n", "Equation \\ref{eq:fb} represents negative feedback where:\n", "\n", "- $k_b$ is the feedback gain\n", "- $\\tilde{x}_B$ is the controllled output and\n", "- $k_{w}\\tilde{x}_{E0}$ is the setpoint.\n", "\n", "In system biology terms, this is an example of *feedback inhibition* with multiple binding sites." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "1\n", "\n", "\n", "Re:r0\n", "\n", "Ce:E0\n", "\n", "0\n", "\n", "Ce:A\n", "\n", "Ce:F\n", "\n", "Ce:G\n", "\n", "1\n", "\n", "0\n", "\n", "Ce:C\n", "\n", "Ce:B\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "\n", "Re:r1\n", "\n", "\n", "Re:r2\n", "\n", "Ce:E\n", "\n", "0\n", "\n", "\n", "Re:r3\n", "\n", "Ce:B0\n", "\n", "0\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sbg.model('fREpr_abg.svg')\n", "import fREpr_abg\n", "imp.reload(fREpr_abg)\n", "abg = fREpr_abg\n", "disp.SVG('fREpr_abg.svg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Parameters" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "## Number of feedback bonds\n", "N=5\n", "K_E0 = K_B**N\n", "parameter['K_E0'] = K_E0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyse" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "==========================\n", "K_F = 10\n", "==========================\n", "0 states have been removed from the model\n", "1 states have been removed from the model\n", "i_B 1 i_dist 2\n", "\n", "Transfer function: phi_B/input \n", " 5e+05 s^2 + 1.158e+08 s + 1.855e+08\n", "---------------------------------------------\n", "s^3 + 2.365e+06 s^2 + 4.146e+08 s + 7.779e+08\n", "\n", "\tgain: 0.238\n", "\tpoles: [-2.365e+06 -1.734e+02 -1.897e+00]\n", "\n", "Transfer function: phi_B/phi_B0 \n", " s^2 + 6.401e+05 s + 1.28e+07\n", "---------------------------------------------\n", "s^3 + 2.365e+06 s^2 + 4.146e+08 s + 7.779e+08\n", "\n", "\tgain: 0.016\n", "\n", "==========================\n", "K_F = 100\n", "==========================\n", "0 states have been removed from the model\n", "1 states have been removed from the model\n", "i_B 1 i_dist 2\n", "\n", "Transfer function: phi_B/input \n", " 5e+05 s^2 + 1.011e+09 s + 1.998e+09\n", "-------------------------------------------\n", "s^3 + 5.8e+06 s^2 + 2.485e+09 s + 5.566e+09\n", "\n", "\tgain: 0.359\n", "\tpoles: [-5.800e+06 -4.263e+02 -2.251e+00]\n", "\n", "Transfer function: phi_B/phi_B0 \n", " s^2 + 4.639e+06 s + 9.275e+07\n", "-------------------------------------------\n", "s^3 + 5.8e+06 s^2 + 2.485e+09 s + 5.566e+09\n", "\n", "\tgain: 0.017\n" ] }, { "data": { "image/png": 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\n", 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D2LHEWRIcEQWDJsLUW2HIdBhyhjNv0k6HK6rZvOcwWQUlZO8vY3vhEbbvL6PwcGV9nsgIYXDvONJ69+TcUf2pLtnH2ZPGktanB2l9epCSFEe0BQ9jWsQCjQmdQ3mQ9QZseg12uw+e6zUEJlwHGRfB8HPaPfxVcrSadbuK2VRQyqaCErIKSsktKq/fnxQXxcgBCZw7uj8j+ycwsn88IwckMKRvzwaBJDMzkxmnp7WrLsaEKws0JrgqSmHjq7D+H5C/ykkbOAEu+AWMucKZX2njRLOqsuPAEdbsLGbtrmLW7Czmy31l9fuH9O3JuMFJfOO0NMalJjF2UC9SkmK77cS2MZ2FBRrjPVVnzmXNPMh6HarLYcBYJ7iMnQnJI9tcdGFpBUuzD7B02wGWZh+oH/5KiovitKF9+NqEwZw2tA+npPUiKS5417AYY46xQGO846t2hsY++3/OMuSYRGdY7LTvwuDT2tRzqa1V1uUV8/6mfSzeWljfY+nTM5qzMvpx5sh+TBnWh5H9E4iIsJ6KMZ2BBRrT8arKYfUzsPzPUJrvrBS74nGYcL1zhXwrVdb4+Gx7Ee9v2ssHWYUcKKskOlKYOrwvXz8tjbMz+jF2UJIFFmM6KQs0puPUVMKaZ+GT38GRQhh6Nnz19zDqYoho3QotVWXtrmL+tXY3b32xh5Kj1cTHRDJjzAAuGTeQGSf1t6EwY7oICzSm/Wpr4fMXYfFvnB7M0LPhuudg6PRWF7W3pIKXVuXxr3X57CwqJy46govHDuSqSYM5K6MfsVGRHjTAGOMlCzSmffLXwDv/5VxUmXo6zHzSuaCyFfMvqsqynCKeX7aT97P2UavK9BHJ3HV+BpeOH0ii9VyM6dIs0Ji2OVoM7/8c1j3v3IDy6r86czCtCDBVNbW8ti6fpz/dwbbCMnr3jOb7Zw/n29OGMiS5p4eVN8YEU1ACjYhcCjwBRAJPq+ojjfbHAs8BpwNFwPWqmisiycACYArwrKre5XdMJjAIOOomXayqhU2V5WHzwk7ygZXw1A+c2+qfeTec99+turCyvKqGF1fs4ulPd7C3tIJxg5P4v2sm8LVTBxMXbUNjxnQ3ngcaEYkEngIuAvKBVSKyUFWz/LLdAhSraoaIzAIeBa4HKoCfA+PdV2PfVtXVjdKaKsu019FieOd/OGXjS85NLL/9snO/sRaqqPbx7Ge5/HXJdorLqzljRF9+e80EzhnVzy6aNKYbC0aPZiqQrao5ACIyH5gJ+AeamcAD7vYC4EkREVU9AiwVkYxWnK+psjrg4RxhLH8NvHITHC4gd+j1DLvhSecpkS1Q46vl1bX5PP7BNvaWVnDe6P7cfcEoTh/ax9s6G2M6hWAEmlQgz+9zPjCtqTyqWiMiJUAycKCZsv8uIj7gVeAhN5i0qCwRuQ24DSAlJYXMzMzWtwwoKytr87Fdgipp+W8yImceVTF92TTx1+yJSCV36WctOnzD/hr+uaWKgiPKiF4R3Ds1jjF9yzm843Myd3hc9w7U7f+dA7A2h4dgtLkrLwb4tqruFpFEnEBzA87cTIuo6hxgDsDkyZO1rU9PzMzM9OTJi51C9VF4407Y/iqcdDlxM5/i9J59W9TmgkNH+dVbWbyzcS/D+8Xzl6vHcMm4lC47RNat/52bYG0OD8FoczACzW4g3e9zmpsWKE++iEQBvXAm8pukqrvd98Mi8iLOEN1zbSnLBHB4L8z/lvPAsQt+AWfPbtGKshpfLU8v3cETH25DUf7rkpP4/jnD7foXY8JYMALNKmCUiAzHCQKzgG81yrMQuBFYBlwDfHyiORU3gPRW1QMiEg1cAXzYlrJMAHs3wovXOZP/178AJ1/RosOyC8v4ySuf83neIS4am8IvvjaWtD62TNmYcOd5oHHnSe4C3sNZ3vyMqm4SkQeB1aq6EJgLPC8i2cBBnGAEgIjkAklAjIhcBVwM7ATec4NMJE6Q+Zt7SJNlmRbYtQL+ca1zT7Kb34NBE5o9xFer/P3fO/i/97bSMyaSJ781iSsmDA5CZY0xXUFQ5mhUdRGwqFHa/X7bFcC1TRw7rIliT28if5NlmWZs/xjmfxsSB8F334De6c0eUlhawQ/nr2dZThEXnpzCr78+ngGJcUGorDGmq+jKiwFMR9qyCF65EfqNhhteg4QBzR7yWfYB7p6/nrLKan77jQlcOzmty072G2O8Y4HGQPZHTpAZeAp851XoceLrW2pVeeLDbfzhoy8Z0S+ef3x/GicNbN8jl40x3ZcFmnC38zNnuKzfSS0KMkerfPxpfSWr933JVRMH8/DVpxAfa/8ZGWOaZr8Q4Wz3WvjHdc5czA2vNRtk9pZUcOtzq9m4z8dPLz+Z758z3IbKjDHNskATrop3OkuYe/ZxJv4T+p8we1ZBKd97diVlFTX88LRYbj13RJAqaozp6lr32EPTPVSUOEHGVwXffhWSTrwUeVXuQa6fs4wIERbccSYTB9jfJ8aYlrNAE2581fDyjVCUDdc9D/1HnzD74q2F3DB3Bf0TYllwx5mcPCgpSBU1xnQX9qdpuPngfshZDDOfghHnnTDr21/s4Yfz13HSwETm3TyVfgmxQaqkMaY7sUATTja9Bsv/BNNuh0nfOWHWdzbs4e756zhtSG/m3jSFJHucsjGmjSzQhIv9X8Ibd0HaVLjoVyfM+kHWPv7zn+uYmN6bZ7831ZYvG2PaxeZowkFVObx8A0TFwrXPnvCBZZlbC7nzH2sZNziJv39vigUZY0y72a9IOPjg57B/i3OtTK/UJrOtzzvEHS+sJWNAAs/dPM2Gy4wxHcJ6NN3dtg9g1dNwxp0w8itNZss9cIRbnl1Fv8QY5t08lV49LcgYYzqGBZru7EiR84TMAWPhgvubzFZUVslNf19JrSrPfm8q/RNtdZkxpuPY0Fl39vZs5+Fl33kVogPfur+yxsetz61mT0kFL956BiP7JwS5ksaY7s56NN3V5rcg6w2Yca9zV+YAVJX7X9/E2l2HeOy6iZw+9MT3OjPGmLawQNMdVZTCov+ClPFw5t1NZnthxS5eWp3HXedn8NUJg4JYQWNMOLGhs+7o44fg8B64/nmIDDypv3LHQX65cBNfGTOA2Red+DY0xhjTHtaj6W7y18DKOTD1VkibHDDL/sOV3PniWob07cnj108kMsJu9W+M8Y71aLqT2lpY9BNIHAhf+XkTWZSfvPI5pUeref6WqfTqYcuYjTHeCkqPRkQuFZGtIpItIvcG2B8rIi+5+1eIyDA3PVlEFotImYg86Ze/p4i8LSJbRGSTiDzit+8mEdkvIuvd1/eD0cZO4YuXoGAdXPhLiAt8l+Wnl+bwyZf7+dkVYxkz0O7EbIzxnueBRkQigaeAy4CxwDdFZGyjbLcAxaqaATwOPOqmVwA/B+4JUPTvVHUMMAk4S0Qu89v3kqpOdF9Pd2BzOq+qI/DRLyH1dDjl2oBZ1ucd4rfvbuXScQP5zrQhQa6gMSZcBaNHMxXIVtUcVa0C5gMzG+WZCcxztxcAF4iIqOoRVV2KE3DqqWq5qi52t6uAtUCal43o9P79hLMA4JLfQMTx/6zlVTX8cP46UpLiePQbE+wRzMaYoAlGoEkF8vw+57tpAfOoag1QAiS3pHAR6Q18DfjIL/kbIvKFiCwQkfS2VrzLKMmHf/8Rxn8DhkwLmOW3725lZ1E5v7/uVLu9jDEmqLr0YgARiQL+CfxRVXPc5DeBf6pqpYj8AKendNxNvkTkNuA2gJSUFDIzM9tUh7KysjYf21FGb32Sgb5qViRcSmWAumw56OPZlRVcOCSKil0byNzVvvN1hjYHm7U5PFibPaKqnr6A6cB7fp/vA+5rlOc9YLq7HQUcAMRv/03AkwHKfgYnyDR17kigpLk6nn766dpWixcvbvOxHeJAtuoDfVQX/XfA3Ucqq/WcRz/Wcx79WI9UVnfIKUPe5hCwNocHa3PrAKu1BXEgGENnq4BRIjJcRGKAWcDCRnkWAje629cAH7uNaJKIPAT0An7UKN3/Evcrgc3tqHvnt+S3EBkDZ/844O7fvruVXQfL+e01E+gZ06U7sMaYLsrzXx5VrRGRu3B6LZHAM6q6SUQexImGC4G5wPMikg0cxAlGAIhILpAExIjIVcDFQCnwU2ALsNad2H5SnRVmd4vIlUCNW9ZNXrcxZAq3OEuaz/xPSEw5bvfneYeYtyyX704fyhkjWjTlZYwxHS4of+Kq6iJgUaO0+/22K4CAa3JVdVgTxQZcNqWq9+EMz3V/mb+BmHg460fH7fLVKj97fSP9EmK555KTQlA5Y4xx2C1ouqrCzZD1OpxxB8Qf31t5ceUuNuwu4WdfPdmelGmMCSkLNF3Vv5+A6J5wxn8ct+tAWSX/9+4Wpo9I5spTB4egcsYYc4wFmq7oUB5seAVO+y707Hvc7kfe2UJ5lY8HZ46zCzONMSFngaYrWv4n5336ncft+iL/EAvW5HPL2cMZlZIY5IoZY8zxLNB0NeUHYc08GH8N9G54vzJV5deLNtM3PoY7v5IRogoaY0xDFmi6mlVPQ/UROOuHx+36aHMhy3MO8qMLR9kCAGNMp2GBpiupqXQeajbqYkhpeAPsGl8tv3lnMyP6xfPNqXZnZmNM52GBpivJegOO7Idptx+3a/6qPLbvP8K9l40hOtL+WY0xnYf9InUlK/8GfUfCiPMbJFdU+3jio21MHdaXi8Yef4cAY4wJJQs0XUXBOshfCVNvPe55My8s38n+w5X8+OLRtpzZGNPpWKDpKlY+7Vygeeo3GySXV9XwlyXbOSsj2e5nZozplOx2vl1B+UHYuMAJMj16N9j1/LKdHCir4i8Xjg5R5Ywx5sSsR9MVrHsBaiqcYTM/ZZVOb+bc0f2ZPOz4OwQYY0xnYIGms1OFtc9B+jRIGddg1/PLdlJcXs3sC0eFqHLGGNM8CzSdXf4qKNoGk25okFxR7WPu0h2cM6ofk4b0CVHljDGmeRZoOrt1zzuLAMZd1SD5X2t3c6CskjvOGxmiihljTMtYoOnMqo7Axn/BuKsh9tgNMn21ypxPtjMhrRfTR9pKM2NM52aBpjPLegOqymDSdxokv7txL7lF5dxx3ki7bsYY0+lZoOnM1v0D+o6AIdPrk1SVPy/JZni/eC4eNzCElTPGmJaxQNNZFe+EnUth4rfAr9eyLKeIjbtLue3cEURGWG/GGNP5WaDprDa+6ryfcm2D5Gf/nUvf+BiunpQagkoZY0zrBSXQiMilIrJVRLJF5N4A+2NF5CV3/woRGeamJ4vIYhEpE5EnGx1zuohscI/5o7iTFSLSV0Q+EJFt7nvXXPu78VVImwJ9htUn5R0s58PN+5g1JZ246MjQ1c0YY1rB80AjIpHAU8BlwFjgmyIytlG2W4BiVc0AHgceddMrgJ8D9wQo+s/ArcAo93Wpm34v8JGqjgI+cj93LYVbYN/G43ozLyzfiYjwnTOGhqhixhjTesHo0UwFslU1R1WrgPnAzEZ5ZgLz3O0FwAUiIqp6RFWX4gSceiIyCEhS1eWqqsBzwFUByprnl951bFwAEuEsa3YdrfIxf1Uel44byODePUJYOWOMaZ1g3FQzFcjz+5wPTGsqj6rWiEgJkAwcOEGZ+Y3KrJu0SFHVPe72XiDgA1pE5DbgNoCUlBQyMzNb0pbjlJWVtfnYgFSZtvJ5jvY+hS9WZwFZAGTmVVNytJoJPYo79nxt0OFt7gKszeHB2uyNbn33ZlVVEdEm9s0B5gBMnjxZZ8yY0aZzZGZm0tZjA8pfA0v20uPinzHjNKdcVeWRJz5l7KA4brv67JBfO9Phbe4CrM3hwdrsjWAMne0G0v0+p7lpAfOISBTQCyhqpsy0Jsrc5w6t1Q2xFba55qGQ9RpERMPJX6tPWrvrEFv2Hua704eGPMgYY0xrBSPQrAJGichwEYkBZgELG+VZCNzobl8DfOzOvQTkDo2VisgZ7mqz7wJvBCjrRr/0zk8VNr8JI2Y0eO7M/JW7iI+J5GunDg5Z1Ywxpq08Hzpz51zuAt4DIoFnVHWTiDwIrFbVhcBc4HkRyQYO4gQjAEQkF0gCYkTkKuBiVc0C/gN4FugBvOO+AB4BXhaRW4CdwHVet7HD7NsIxblw9uz6pMMV1bz1xR6Iy8hzAAAagElEQVRmThxMfGy3Huk0xnRTQfnlUtVFwKJGaff7bVcA1zY+zt03rIn01cD4AOlFwAXtqG7obH4LEDjpq/VJCz8v4Gi1j1lTh4SuXsYY0w52Z4DOZPObMPRMSOhfnzR/ZR5jBiZyalqvEFbMGGPazgJNZ1G0HQo3NVgEsHF3CRt2lzBrSrotAjDGdFkWaDqLLW8572OODZu9vDqP2KgIrp6U1sRBxhjT+Vmg6Sw2vwmDJkJvZy6mqqaWhZ8XcMm4gfTqGR3iyhljTNtZoOkMyvZD/uoGvZnMrYUcKq/m6tPsLs3GmK7NAk1nkP0hoDDq4vqk19btpl9CDOdk9AtdvYwxpgNYoOkMtr0PCSkwcAIAJUer+WhzIV87dTBRkfZPZIzp2uxXLNR8NbD9Ixh1EUQ4/xyLNuyhyldrDzczxnQLFmhCLX8lVJQcN2w2on88p6TatTPGmK7PAk2offkeRETBiPMByC8uZ+WOg3x9UqpdO2OM6RYs0ITatvdhyHSISwKcW84AzJxow2bGmO7BAk0oHcqDwiwYfUl90qINe5iY3pv0vj1DWDFjjOk4FmhCaftHznvGRQDsKipn4+5SLj9lYAgrZYwxHavZQCMi89znyJiOlpMJiYOg/0kAvL3BeQL1ZeMHhbBSxhjTsVrSo8kDlonIMP9EEZkgIs94UamwUFsLOUucRQDupP+iDXs4Na2XDZsZY7qVZp9Ho6o/E5HlwIci8kMgGvgRkAg84XH9uq99G+DoQedpmkDewXI27C7hvsvGhLRaxhjT0Vr64LNPgHeBN4FC4DpV/cSzWoWDnEznfcR5gNObAbj8FBs2M8Z0Ly2Zo/kTsAEoA04GPgbuFhEb32mP7Yuh/8mQ6Ez8L9qwh1NSbdjMGNP9tGSO5nNgjKreq6pbVfVbwDJguYiM9rZ63VR1BexaVj9sll9czuf5JdabMcZ0Sy2Zo/lrgLTfi8g6YBGQ4UXFurW8FVBTUR9oPszaB8Al41JCVydjjPFIm6+jUdWPgfM7sC7hIyfTue3MsLMA+HBzISP7xzOif0Jo62WMMR5o1wWbqprXknwicqmIbBWRbBG5N8D+WBF5yd2/wn8ptYjc56ZvFZFL3LSTRGS936tURH7k7ntARHb77bu8PW30xI4lkDoZYhMprahmeU4RF4613owxpntq6aqzNhORSOAp4CIgH1glIgtVNcsv2y1AsapmiMgs4FHgehEZC8wCxgGDcZZYj1bVrcBEv/J3A6/5lfe4qv7O67a1SWUZFKyHs2cDsGTrfmpqlYtOtkBjjOmegnELmqlAtqrmqGoVMB+Y2SjPTGCeu70AuECcWxfPBOaraqWq7gCy3fL8XQBsV9WdnrWgI+WvBPXB0DMB+GjzPvrGxzBpSJ8QV8wYY7zheY8GSMW5u0CdfGBaU3lUtUZESoBkN315o2Mb39Z4FvDPRml3ich3gdXAT1S1uHGlROQ24DaAlJQUMjMzW9GkY8rKylp17PCcFxlCBEtzK6nctZj3N5ZzWkoUn36ypE3nD4XWtrk7sDaHB2uzN4IRaDzj3oPtSuA+v+Q/A78C1H3/PXBz42NVdQ4wB2Dy5Mk6Y8aMNtUhMzOTVh2b8ygMnsg5F17Osu1FlNcs5zvnn8qM8V3nRpqtbnM3YG0OD9ZmbwRj6Gw3kO73Oc1NC5hHRKKAXkBRC469DFirqvvqElR1n6r6VLUW+BvHD7WFTnUF7F7tt9psHzFREZwzql+IK2aMMd4JRqBZBYwSkeFuD2QWsLBRnoXAje72NcDHqqpu+ix3VdpwYBSw0u+4b9Jo2ExE/K96vBrY2GEtaa/da8BXBUPPQlX5cPM+zhqZTHxsl+5YGmPMCXn+C+fOudwFvAdEAs+o6iYReRBYraoLgbnA8yKSDRzECUa4+V4GsoAa4E5V9QGISDzOSrYfNDrlb0VkIs7QWW6A/aGz89+AwJAzyC0qZ2dRObecPTzUtTLGGE8F5U9pVV2EcxcB/7T7/bYrgGubOPZh4OEA6UdwFgw0Tr+hvfX1zM5/Q8p46NGHT9blAnDe6P6hrZMxxnjMnrAZLL5qyFtZv6x5yZf7GZrck6HJ8SGumDHGeMsCTbDs+QKqy2HodCprfCzbXmS9GWNMWLBAEyx5K5z39Gmszi3maLWPc0dZoDHGdH8WaIIlfyUkpUHSYD75cj/RkcL0kcdNMRljTLdjgSZY8lZB+hTAmZ+ZPLSvLWs2xoQFCzTBUFoApfmQNpV9pRVs2XuY806yYTNjTHiwQBMM+auc9/SpLPlyP2DLmo0x4cMCTTDkrYTIWBg4gU+3HaB/YixjBiaGulbGGBMUFmiCIX8VDJ6IRkazbPsBzs7oh/MUBGOM6f4s0Hitpsp50FnaFLYVlnGgrIrpI2y1mTEmfFig8dreL8BXCelT+Sz7AIAtazbGhBULNF7Lc282nTaFZTlFpPftQXrfnqGtkzHGBJEFGq/lr4KkVHwJg1iec9CGzYwxYccCjdcK1kHqaWzeU0rJ0WrOHGkPOTPGhBcLNF46WgzFO2DwJJZtLwJsfsYYE34s0HipYL3zPngSn20/wIj+8aQkxYW2TsYYE2QWaLxUsA6A6pRTWbnjIGdab8YYE4Ys0HipYB30Gc6GgxEcqfIxfYTNzxhjwo8FGi8VrIfBk1ie48zPnDGib4grZIwxwWeBxitHDkDJLhg8idW5xYzsH09yQmyoa2WMMUEXlEAjIpeKyFYRyRaRewPsjxWRl9z9K0RkmN+++9z0rSJyiV96rohsEJH1IrLaL72viHwgItvc9z5ety8gdyFA7aCJrM49yNTh1psxxoQnzwONiEQCTwGXAWOBb4rI2EbZbgGKVTUDeBx41D12LDALGAdcCvzJLa/O+ao6UVUn+6XdC3ykqqOAj9zPwecuBMiOGklpRQ2Th1qgMcaEp2D0aKYC2aqao6pVwHxgZqM8M4F57vYC4AJxbm88E5ivqpWqugPIdss7Ef+y5gFXdUAbWq9gHSSPYkVBDQBThlmgMcaEp2AEmlQgz+9zvpsWMI+q1gAlQHIzxyrwvoisEZHb/PKkqOoed3svkNIRjWi1gnXu/MxBUpJiSe/bIyTVMMaYUOvKD60/W1V3i8gA4AMR2aKqn/hnUFUVEQ10sBucbgNISUkhMzOzTZUoKys77tjoqkOcdbiA7PIElm7fw8jeESxZsqRN5XdGgdrc3Vmbw4O12RvBCDS7gXS/z2luWqA8+SISBfQCik50rKrWvReKyGs4Q2qfAPtEZJCq7hGRQUBhoEqp6hxgDsDkyZN1xowZbWpcZmYmxx2b/SF8Br0mfpWiTZX855STmHHW8DaV3xkFbHM3Z20OD9ZmbwRj6GwVMEpEhotIDM7k/sJGeRYCN7rb1wAfq6q66bPcVWnDgVHAShGJF5FEABGJBy4GNgYo60bgDY/a1bS9TlVWHR0MwGSbnzHGhDHPezSqWiMidwHvAZHAM6q6SUQeBFar6kJgLvC8iGQDB3GCEW6+l4EsoAa4U1V9IpICvOY+DjkKeFFV33VP+QjwsojcAuwErvO6jcfZuwF6pfNZgY+E2ChOHpQU9CoYY0xnEZQ5GlVdBCxqlHa/33YFcG0Txz4MPNwoLQc4tYn8RcAF7axy++zbCCnjWZ1bzGlD+xAZISGtjjHGhJLdGaCjVR+FA19SkTyWrfsOM2VoaK4XNcaYzsICTUcr3Axay/bI4ajC6RZojDFhzgJNR9vnLARYeXQwIjAhvXeIK2SMMaHVla+j6Zz2boCYBD7ZH8/oAdEkxNpXbIwJb9aj6Wh7N6Ip41iXX8pE680YY4wFmg6lCvs2crj3GA6VVzNpiAUaY4yxQNORDu2EylK2RwwDYKIFGmOMsUDTofZuAGDl0TTiYyIZNSAxxBUyxpjQs5nqjrRvEyB8UNSXCWkJdqGmMcZgPZqOVZhFbZ/hrN9TZcNmxhjjskDTkQo3U5KYQU2t2oozY4xxWaDpKDWVULSd3IghAEyyQGOMMYAFmo5zYBuoj/UVg0jt3YMBSXGhrpExxnQKFmg6yv4tACwuTrZhM2OM8WOBpqMUZqESyfKSPpyS1ivUtTHGmE7DAk1HKdxCeeIwqojmlFQLNMYYU8cCTUcpzGJPzDAAxg+2QGOMMXUs0HSEqnIozmVLbRpD+vakV8/oUNfIGGM6DQs0HeHAVkBZXjbAhs2MMaYRCzQdodBZcbbs8ADGW6AxxpgGLNB0hMIsaiNi2Kkp1qMxxphGghJoRORSEdkqItkicm+A/bEi8pK7f4WIDPPbd5+bvlVELnHT0kVksYhkicgmEfmhX/4HRGS3iKx3X5d73sD9WyjuMYQaohifmuT56Ywxpivx/O7NIhIJPAVcBOQDq0Rkoapm+WW7BShW1QwRmQU8ClwvImOBWcA4YDDwoYiMBmqAn6jqWhFJBNaIyAd+ZT6uqr/zum31CjeTI6NI79uD3j1jgnZaY4zpCoLRo5kKZKtqjqpWAfOBmY3yzATmudsLgAtERNz0+apaqao7gGxgqqruUdW1AKp6GNgMpAahLceJ8FVASR6fV6bYsmZjjAkgGM+jSQXy/D7nA9OayqOqNSJSAiS76csbHdsgoLjDbJOAFX7Jd4nId4HVOD2f4saVEpHbgNsAUlJSyMzMbGWzHBFF2QCsO9Kf+MqiNpfTlZSVlYVFO/1Zm7s2ESE+Pp7IyMgT5ktKSmLdunVBqlXn0JI2+3w+jhw5gqq26Rxd+sFnIpIAvAr8SFVL3eQ/A78C1H3/PXBz42NVdQ4wB2Dy5Mk6Y8aMNtVh08tLAcjRQdx3ziTOHd2/TeV0JZmZmbT1++qqrM1d244dO0hMTCQ5ORlnsCSww4cPk5gYXk/Gba7NqkpRURGHDx9m+PDhbTpHMIbOdgPpfp/T3LSAeUQkCugFFJ3oWBGJxgky/1DVf9VlUNV9qupT1VrgbzhDd57pWe40JVdTGDvYFgIY0xlVVFQ0G2RMYCJCcnIyFRUVbS4jGIFmFTBKRIaLSAzO5P7CRnkWAje629cAH6vTR1sIzHJXpQ0HRgEr3fmbucBmVX3MvyARGeT38WpgY4e3yE/P8t0cih5AfEIS/RJivTyVMaYdLMi0XXu/O8+Hztw5l7uA94BI4BlV3SQiDwKrVXUhTtB4XkSygYM4wQg338tAFs5KsztV1SciZwM3ABtEZL17qv9V1UXAb0VkIs7QWS7wAy/b1+NoATkMZnRKeHW3jTGmpYIyR+MGgEWN0u73264Arm3i2IeBhxulLQUChlhVvaG99W2N2MoicqpSLdAYY0wT7M4A7RRVXcZ+XzwnDbRAY4xpWkJCQv32okWLGD16NDt37gyY94EHHiA1NZWJEycyceJE7r33uOvcA9qyZQvTp08nNjaW3/2u4aWE7777LieddBIZGRk88sgjbW9IG3TpVWchV1VOpFZxSBOZ1D+h+fzGmJD75ZubyCooDbjP5/M1uwQ6kLGDk/jF18a1KO9HH33E3XffzXvvvcfQoUObzDd79mzuueeeVtWjb9++/PGPf+T1119vkO7z+bjzzjv54IMPSEtLY8qUKVx55ZWMHTu2VeW3lfVo2uPoQQCKSWBQr7gQV8YY09l98skn3Hrrrbz11luMHDmyw8sfMGAAU6ZMITq64aNKVq5cSUZGBiNGjCAmJoZZs2bxxhtvdPj5m2I9mvaoOgLAEY0jJckCjTFdwYl6Hl5eR1NZWclVV11FZmYmY8aMaTb/448/zgsvvADAo48+yiWXXMLs2bNZvHjxcXlnzZp1wuG13bt3k55+7EqRtLQ0VqxY0WT+jmaBpj1qawDoERdLTJR1Do0xTYuOjubMM89k7ty5PPHEE83mDzR09vjjj3tVPU/Zr2N7uIEmsaf1ZowxJxYREcHLL7/MypUr+fWvf92mMmbPnl2/QMD/1dzkfmpqKnl5x+4Elp+fT2pq8G4PaT2a9qj1AZDUs0eIK2KM6Qp69uzJ22+/zTnnnENKSgq33HJLq45va49mypQpbNu2jR07dpCamsr8+fN58cUX21RWW1igaQ830PSMszsCGGNapm/fvrz77ruce+659O/fnyuvvLLDyt67dy+TJ0+mtLSUiIgI/vCHP5CVlUVSUhJPPvkkl1xyCT6fj5tvvplx41q2Sq4jWKBpD3foLDYmupmMxphwV1ZWVr+dnp7Ojh07msz7wAMPtOkcAwcOJD8/P+C+yy+/nMsv9/45kIHYHE07aG01AHGx9rAzY4xpivVo2qGyqpo4ICbGAo0xpvUefvhhXnnllQZp1157LT/96U9DVCNvWKBph4rKKuKAuBibozHGtN5Pf/rTbhdUArGhs3Y4WlkJQGyszdEYY0xTLNC0Q02NM0cTE2WBxhhjmmKBph18Nc6qs6hoCzTGGNMUCzTtUNejsUBjjDFNs0DTDvU9Ghs6M8Y0o7M+jyY3N5dp06aRkZHB9ddfT1VVVRtad2K26qwdfHU9Ggs0xnQd79wLezcE3NXDVwORbfhZHHgKXNayh4l1tufR/OIXv2D27NnMmjWL22+/nblz53LHHXe06rzNsR5NO/h81qMxxrRcZ3sejaqyZMkSrrnmGgBuvPHG44JUR7AeTTvU9Wga/6MaYzqxE/Q8jobZ82iKioro1asXUVFR9em7d+9ubdOaZYGmHdTt0UTbnQGMMc2w59F4TEQuFZGtIpItIseFXRGJFZGX3P0rRGSY37773PStInJJc2WKyHC3jGy3TM+igM9X16OxeG2MObHO+Dya5ORkSkpKqHEXNnn1nBrPfyFFJBJ4CrgIyAdWichCVc3yy3YLUKyqGSIyC3gUuF5ExgKzgHHAYOBDERntHtNUmY8Cj6vqfBH5i1v2n71oW12PJibKejTGmOZ1tufRiAjnnnsuCxYsYNasWcybN4+ZM2e26RwnEowezVQgW1VzVLUKmA80bslMYJ67vQC4QETETZ+vqpWqugPIdssLWKZ7zFfcMnDLvMqrhvl8zvNoou0xAcaYFqp7Hs1DDz3EwoULO7TsvXv3kpaWxmOPPcZDDz1EWloapaWlREVF1T+P5uSTT+a6666rfx7NL3/5Sx577DEyMjIoKipqdfBrCVHVDi+0wQlErgEuVdXvu59vAKap6l1+eTa6efLdz9uBacADwHJVfcFNnwu84x52XJl++TPc9HTgHVUdH6BetwG3AaSkpJw+f/78VretJPsz+u1ZTMX0/yIyjHo1ZWVlDa4JCAfW5q6tV69eZGRkNJvP5/MRGRkZhBp1Hi1tc3Z2NiUlJQ3Szj///DWqOrm5Y8N2ckFV5wBzACZPnqwzZsxofSEzZpCZeSYXtOXYLiwzM5M2fV9dmLW5a9u8eXOLVpMd9nDVWWfV0jbHxcUxadKkNp0jGIFmN5Du9znNTQuUJ19EooBeQFEzxwZKLwJ6i0iUqtY0cS5jjOkU7Hk0HWcVMEpEhuP86M8CvtUoz0LgRmAZcA3wsaqqiCwEXhSRx3AWA4wCVgISqEz3mMVuGfPdMt/wuoHGmM5PVXGmcTuPrvI8mvZOsXi+GMDtWdwFvAdsBl5W1U0i8qCIXOlmmwski0g28GPgXvfYTcDLQBbwLnCnqvqaKtMt63+AH7tlJbtlG2PCWFxcHEVFRe3+wQxHqkpRURFxcXFtLiMoczSqughY1Cjtfr/tCuDaJo59GHi4JWW66Tk4q9KMMQZwrnjPz89n//79J8xXUVHRrh/UrqglbY6LiyMtLa3N5wjbxQDGmPARHR3N8OHDm82XmZnZ5gnvrioYbbabahpjjPGUBRpjjDGeskBjjDHGU57fGaArEJH9QOBH3TWvH3CgA6vTFVibw4O1OTy0p81DVbV/c5ks0LSTiKxuyS0YuhNrc3iwNoeHYLTZhs6MMcZ4ygKNMcYYT1mgab85oa5ACFibw4O1OTx43mabozHGGOMp69EYY4zxlAUaY4wxnrJA0w4icqmIbBWRbBG5N9T18ZqIPCMihe4TUcOCiKSLyGIRyRKRTSLyw1DXyWsiEiciK0Xkc7fNvwx1nYJBRCJFZJ2IvBXqugSDiOSKyAYRWS8iqz09l83RtI2IRAJfAhcB+TjP3fmmqmaFtGIeEpFzgTLguUCPx+6ORGQQMEhV14pIIrAGuKqb/zsLEK+qZSISDSwFfqiqy0NcNU+JyI+ByUCSql4R6vp4TURygcmq6vkFqtajabupQLaq5qhqFc6D1maGuE6eUtVPgIOhrkcwqeoeVV3rbh/Gef5Ramhr5S11lLkfo91Xt/6LVETSgK8CT4e6Lt2RBZq2SwXy/D7n081/gMKdiAwDJgErQlsT77nDSOuBQuADVe3ubf4D8N9AbagrEkQKvC8ia0TkNi9PZIHGmBYQkQTgVeBHqloa6vp4zX2S7UQgDZgqIt12qFRErgAKVXVNqOsSZGer6mnAZcCd7tC4JyzQtN1uIN3vc5qbZroZd57iVeAfqvqvUNcnmFT1ELAYuDTUdfHQWcCV7pzFfOArIvJCaKvkPVXd7b4XAq/h4ZOJLdC03SpglIgMF5EYYBawMMR1Mh3MnRifC2xW1cdCXZ9gEJH+ItLb3e6Bs+BlS2hr5R1VvU9V01R1GM7/xx+r6ndCXC1PiUi8u7gFEYkHLgY8W01qgaaNVLUGuAt4D2eC+GVV3RTaWnlLRP4JLANOEpF8Ebkl1HUKgrOAG3D+yl3vvi4PdaU8NghYLCJf4PxB9YGqhsWS3zCSAiwVkc+BlcDbqvquVyez5c3GGGM8ZT0aY4wxnrJAY4wxxlMWaIwxxnjKAo0xxhhPWaAxxhjjKQs0xhhjPGWBxhhjjKcs0BjTSYlImohcH+p6GNNeFmiM6bwuAE4LdSWMaS+7M4AxnZCInA28ARwCDgNfV9Wc0NbKmLaxQGNMJyUi7wL3qGrYPDrbdE82dGZM53US3fiuySZ8WKAxphMSkX5AiXuXcGO6NAs0xnROw4CCUFfCmI5ggcaYzmkL0E9ENorImaGujDHtYYsBjDHGeMp6NMYYYzxlgcYYY4ynLNAYY4zxlAUaY4wxnrJAY4wxxlMWaIwxxnjKAo0xxhhP/X9qVJj6fjC3fwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s,sc,sf = stoichiometry(abg,chemostats=chemostats)\n", "Sys,SysX,x_ss,v_ss,dist_gain_X,in_gain_X,tf_in_fb = linearise(s,sc,sf=None,i_r=3,dist='B0',t_step_max=5,KK_F=KK_F)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Control system analysis" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Computed steady-state values:\n", "x_ss_A = 2.000\n", "x_ss_B = 2.154\n", "x_ss_E = 0.022\n", "x_ss_C = 2.159\n", "x_ss_F = 1.000\n", "\n", "The control system gains:\n", "k_act = 1000.000\n", "k_fb = 0.050\n", "k_sys = 0.100\n", "\n", "Feedback loop analysis:\n", "L = 5.005\n", "L/(1+L) = 0.833\n", "Disturbance gain. Theory: 0.017 , Linearised: 0.017\n", "Setpoint gain. Theory: 0.359 , Linearised: 0.359\n" ] } ], "source": [ "print('\\nComputed steady-state values:')\n", "species = ['A','B','E','C','F']\n", "exec(extractSS(s,x_ss,species))\n", "print('\\nThe control system gains:')\n", "k_act = (kappa/2)*K_A*K_E*K_F*x_ss_A*x_ss_F\n", "print('k_act =', fmt.format(k_act))\n", "k_fb = N*(x_ss_E/x_ss_B)\n", "print('k_fb =', fmt.format(k_fb))\n", "k_sys = 1/(kappa_r3*K_B)\n", "k_dist = K_B0/K_B\n", "k_w = ((K_E0/K_E)/(K_B*x_ss_B)**N)/k_fb\n", "print('k_sys =', fmt.format(k_sys))\n", "\n", "print('\\nFeedback loop analysis:')\n", "L = k_act*k_fb*k_sys\n", "print('L =', fmt.format(L))\n", "print('L/(1+L) =', fmt.format(L/(1+L)))\n", "print('Disturbance gain. Theory:',fmt.format(k_dist/(1+L)), ', Linearised:',fmt.format(dist_gain_X))\n", "print('Setpoint gain. Theory:',fmt.format(k_w*L/(1+L)), ', Linearised:', fmt.format(in_gain_X))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion\n", "\n", "- The system output $x_B$ has a well-defined response to both setpoint $w=x_{E0}$ and disturbance $d=x_{B0}$.\n", "- The linear response steady-state gain is as predicted by the theory for the given parameters.\n", "- The dynamic reponse is simple as the system dynamics are simple. If the product removal 'system' were replace by a long chain of reactions, the dynamic response would be more complicated.\n", "- As there are three non-chemostated **Ce** components, the transfer function is third-order.\n", "- Compared to the open-loop case, the feedback has moved the poles. In particular the slowest pole, which dominates the response, is now at about $s = -2.25$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Nonlinear simulation" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NON-LINEAR SIMULATION\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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vP6zHXzqU+B4PwHteP5vn9xzhX+59jjs37uL02bXMmVLN+MoyxpWXUZ4yBubXgTfMvqr2A8vl4aG5L70UfTsDNC06gaUn10V+3mLy4v4jbNzZyt62Ttq7eunNOJmMB/8P6GzH1cZxeumlbt54bi8TxuU3NRRS4plDsEpCnxbgTcOVcfdeMzsM1IX71w06dk74eqT3BMDMVgGrAGbMmEFzc/NxV+DfHu5g26E0vPj8cR87VmdMK8sq5lxob2/P2bnPLIevLq3iwZ297Gg9zP/sOURPBrrTTnrAh8IfDcYNGpnz4b+UO+6Rt3M6A/c8+QJfXlod6Xn75LKd47CjLcOPNnbx/OFXr5BhBEtOWd8GxNLGsXNn2W9/x6TK/P4hW0iJJ1bufgNwA0BjY6M3NTUd93s0NUFzczPZHJtk+ajzR3L6brkXRzt/6j8eY9PLrbH9fCX5Z3v7viNcft2DVJZX8Pfvmc/Sk6cyq7aamqpyysyGvAE7yfXNVlR1LqTEsxOYO2C7Ptw3VJkWMysHaoH9Ixw70nuKJMLUCZUcONoddxiJ9JW1T+PAz//6zcydqnvf41YwkwuAR4GFZjYvXA17BbB2UJm1wGXh6w8A97m7h/tXhLPe5gELgUdG+Z4iiTBlfCWHO3ro1WKqx2XrnnYeeG4vn/jf85V0CkTB9HjCazafAu4GyoCb3f1pM7sSWO/ua4GbgH8NJw8cIEgkhOVuI5g00At80t3TAEO9Z9R1E8mFKeMrcIfDHT3UhY8Ml5GtffJlUgYfapw7cmGJRMEkHgB3v5NBqyG4+1cGvO4EPjjMsVcBV43mPUWSaMqE4LFYB48q8RyPh57fxxlzajmhRt+zQlFIQ20i8hqm9iceXecZrc6eNE/sOMTS+ZqCXkiUeEQSYsr4IPHsb1fiGa2te9rpSTtn1k+OOxQZQIlHJCGmh0NFe9s6Y44kOZ7f2w7AgukTY45EBlLiEUmIaRPHUVmWouVQx8iFBYAtu9spSxkNdXrAYCFR4hFJiFTKmDOlmpaDSjyjtW1fOydNHU9luT7qColaQyRB5kyuZqcSz6jtOtzJrMlVcYchgyjxiCRIvXo8x2X34U5mTFLiKTRKPCIJMm/aBPa1d3HwiGa2jSSTcfa0dTFTiafgKPGIJMhps2sB2LSrNeZICt/+I930Zlw9ngKkxCOSIKfNngTAxp2HY46k8O1uDaadK/EUHiUekQSZMqGSk+rGs27b/rhDKXh727sAtFROAVLiEUmY806Zzu+f38/R7t64QylorR3B49NrqwtqSUpBiUckcd59xiy6ezP87DE9Wuq1tHUGibmmqiLmSGQwJR6RhGk8aQpvOHEy197zHK8c1vI5w2nv6ks86vEUGrWISMKYGVe///W87zu/573XPchH3tzA2SdN4YSacdSMKyeVsuBxzmakUkH5Vz/Y+fh19jpHupIzvHfwSDdlKaO6oizuUGQQJR6RBHrdjBpu/8Sb+dqvnuYf7342uhPfc3d058qBqRMqMctF2pVcKojEY2ZTgZ8ADcB24EPufnCIcpcBXw43/6+7rwn3nw38CKgmeOjbp93dzeyDwNeAU4Fz3H19XisiEqHFsydx21+ey962LjbvauXg0W5aO3txdzIZJ+0Er91zcr7nn9/G/Pkn5+S9onLKzElxhyBDKIjEA6wG7nX3q81sdbj9xYEFwuT0VaARcGCDma0NE9R3gY8DDxMknmXAfwEbgT8Dvh9VRUSidkLNOE6oOSHv52nO7KDpbfPzfh4pfoUyuWA5sCZ8vQZ43xBl3gX8xt0PhMnmN8AyM5sFTHL3de7uwC19x7v7ZnePcBxCRERGUiiJZ4a77wpfvwLMGKLMHGDHgO2WcN+c8PXg/SIiUoAiG2ozs3uAmUN86e8GboTXZnIzKH0czGwVsCrcbDezbHtK04B9uYkqMVTn0lBqdS61+sLY63zSaApFlnjc/Z3Dfc3MdpvZLHffFQ6d7Rmi2E6gacB2PdAc7q8ftP+476xz9xuAG473uMHMbL27N471fZJEdS4NpVbnUqsvRFfnQhlqWwtcFr6+DPjlEGXuBv7EzKaY2RTgT4C7wyG6VjNbasG8yUuHOV5ERApAoSSeq4HzzWwL8M5wGzNrNLMbAdz9APAN4NHw35XhPoC/Bm4EtgLPE8xow8z+1MxagHOBX5tZsm5CEBEpQuY5muMvATNbFQ7blQzVuTSUWp1Lrb4QXZ2VeEREJFKFMtQmIiIlQolHREQipcSTI2a2zMyeNbOt4bI/RcfM5prZ/Wa2ycyeNrNPh/unmtlvzGxL+P+UuGPNNTMrM7PHzew/w+15ZvZw2N4/MbPKuGPMJTObbGa3m9kzZrbZzM4t9nY2s8+GP9cbzezHZlZVbO1sZjeb2R4z2zhg35DtaoFvh3X/g5m9IVdxKPHkgJmVAd8BLgAWA5eY2eJ4o8qLXuBz7r4YWAp8Mqxn31p7C4F7w+1i82lg84Dta4BvufsC4CCwMpao8uda4C53PwU4k6DuRdvOZjYHuBxodPfTgTJgBcXXzj8iWMtyoOHa9QJgYfhvFcGamDmhxJMb5wBb3X2bu3cDtxKsP1dU3H2Xuz8Wvm4j+DCaw+jW2kssM6sHLiSYsk94v9h5wO1hkaKqs5nVAm8DbgJw9253P0SRtzPBDfXVZlYOjAd2UWTt7O4PAAcG7R6uXZcDt3hgHTA5vMF/zJR4cmO4deSKlpk1AEsIVgQfzVp7SfYvwBeATLhdBxxy976nohVbe88D9gI/DIcXbzSzCRRxO7v7TuCfgJcIEs5hYAPF3c59hmvXvH2uKfHIcTOzicDPgM+4e+vAr4UrhBfNHH0zew+wx903xB1LhMqBNwDfdfclwBEGDasVYTtPIfgLfx4wG5jAq4ekil5U7arEkxs7gbkDtrNaLy4JzKyCIOn8u7vfEe7e3dcFf4219pLqLcBFZradYAj1PILrH5PDIRkovvZuAVrc/eFw+3aCRFTM7fxO4AV33+vuPcAdBG1fzO3cZ7h2zdvnmhJPbjwKLAxnwFQSXJRcG3NMORde27gJ2Ozu3xzwpdGstZdI7n6Fu9e7ewNBu97n7n8B3A98ICxWbHV+BdhhZovCXe8ANlHE7UwwxLbUzMaHP+d9dS7adh5guHZdC1wazm5bChweMCQ3Jlq5IEfM7N0E1wLKgJvd/aqYQ8o5M3sr8DvgKY5d7/gSwXWe24ATgRcJHl0++AJm4plZE/B5d3+PmZ1M0AOaCjwOfNjdu+KML5fM7CyCyRSVwDbgowR/qBZtO5vZ14GLCWZvPg58jOCaRtG0s5n9mGCV/2nAboKnOv+CIdo1TMDXEQw5HgU+6u7rcxKHEo+IiEQp0UNtI920aWYfMbO9ZvZE+O9jccQpIiLHRPYguFwbcNPm+QQXQx81s7XuvmlQ0Z+4+6ciD1BERIaU5B5PSdy0KSJSbBLb42Hom5veNES595vZ24DngM+6+44hymBmqwiWhaC6uvrsuXPnDlVsRJlMhlQqyfn8+KnOpaHU6lxq9YWx1/m5557b5+4njFQuyYlnNH4F/Njdu8zsLwmWgzhvqILhw49uAGhsbPT167ObvNHc3ExTU1N20SaU6lwaSq3OpVZfGHudzezF0ZRLcjof8eYmd98/YOrjjcDZEcUmIiLDSHLiGfGmzUEL2l3EH68uLDFr7ezh5UMdcYchIhFL7FCbu/ea2aeAuzl20+bTZnYlsN7d1wKXm9lFBDeEHQA+ElvA8ioXfvt37DjQwfarL4w7FBGJUGITD4C73wncOWjfVwa8vgK4Iuq4ZHR2HFBvR0pbT08PLS0tdHZ2xh0KALW1tWzePPLAUFVVFfX19VRUVGR1nkQnHikO7k6wOodIaWlpaaGmpoaGhoaC+B1oa2ujpqbmNcu4O/v376elpYV58+ZldZ4kX+ORItHZkxm5kEgR6uzspK6uriCSzmiZGXV1dWPqpSnxSOzau3pHLiRSpJKUdPqMNWYlHondESUekYKxYcMGzjjjDBYsWMDll19OPhaSVuKR2JSlgr+a1OMRKQzuzl/91V/xgx/8gC1btrBlyxbuuuuunJ9HiUdiM76iDFCPRyRO27dvZ9GiRVx66aWceeaZ7N27l6VLl2JmXHrppfziF7/I+Tk1q01iU11ZRltXr3o8IsDXf/U0m15uzel7Lp49ia++97QRy23ZsoU1a9awcuVKvvGNb/Tvr6+vZ+fO3D/tWz0eiU11ZdDjUeIRiddJJ53E0qVLIzufejwSm+r+obZ0zJGIxG80PZN8mTBhAgCzZ8+mpaWlf39LSwtz5szJ+fnU45HYjK/UNR6RQjJz5kwmTZrEunXrcHduueUWli/P/WPOlHgkNn1DbW2dPTFHIiJ9rr/+ej72sY+xYMEC5s+fzwUXXJDzc2ioTWLTd3vAwaNKPCJxaWhoYOPGjf3bjY2Nf7SdD+rxSGwyYeY5cKQ75khEJEpKPBKbTLhEmxKPSGlR4pHYqMcjUpqUeCQ2/YnnqBKPlK58rIWWb2ONWYlHYpPum1xwpDuRv3wiY1VVVcX+/fsT9fPf9zyeqqqqrN9Ds9okNn2/bL0Zp7Wjl9rx2T3NUCSp6uvraWlpYe/evXGHAgTPBxpNQul7Amm2lHgkNpkBf+XtbutU4hnB3U+/wpfueIrfrz6PqnDVB0m2ioqKrJ/imQ/Nzc0sWbIk7+fRUJvEJp2BaRMrAdh5sCPmaArfP979LPuPdPPCviNxhyIyJko8Eht3Z+7U8QC0HDwaczSFb1ZtMASy67CStCSbEo/EJp1xpteMo7I8RYt6PCOaOSlIPOodStIp8UhsMu6Up1LUT65mh3o8I5ocXgPbocQjCafEI7FxBzOYP30iz77SFnc4Ba83E0zG2La3PeZIRMZGiUdik3anLGWcPruWbfuO6PEII+hJB2sM/aHlcMyRiIyNEo/EJuNOyozT50zCHTbtyu1jf4tNT2/Q49nT1sUrhztjjkYke0o8EptMJhhqO2vuZMzgwS374g6poHWHPR6Addv2xxiJyNgo8UhsMu6UmVE3cRxnnziF/960O1FLh0StO53h5GkTmDFpHHdtfCXucESyltfEY2YPmNmk8PUnzOwzZlaZ43MsM7NnzWyrma0e4uvjzOwn4dcfNrOGXJ5fstc31Aaw/KzZbN7VyrptB2KOqnD19GaoLE9x4RmzufeZ3ew4oJmAkkz57vHUunurmZ0NfByYAvwgV29uZmXAd4ALgMXAJWa2eFCxlcBBd18AfAu4Jlfnl7FJZyCVChLPBxvnMnNSFV/6+VMc1GMShtSTDhLPx982j5QZX7j9Dxzt1oQMSZ58r9XWY2blwKXANe5+m5mtz+H7nwNsdfdtAGZ2K7Ac2DSgzHLga+Hr24HrzMw8D2M6m15u5bmDaSZsj/6v9pOmjmf6pKEX99vT2klvxjl4tJtMJuhppN1xdzI5+C5kW+fu3jRh3qGqooxvX7KED33/IZZ84zd8eOmJnDprEpOrK5kwrozKsvBvJAMjOMgMDDA7th2VONp5/5FuKspSzKqt5h/+9Aw+f/uTnP/NB3jnqdM5fU4tE8eVU1td8arvUZ+B355svmdx/WyPxdwp45lZ+8e/F5mMc6ijhwNHuujsyQS/DxknM+j3IYn1HavnDqZ5SzpDRVl++yT5TjzfBp4EqoC+YbCJOXz/OcCOAdstwJuGK+PuvWZ2GKgDcn4l+0s/f4ondnTCww/l+q1HtGhGDXd/9m3920e7e7nhgW38/PGdvLg/giGZLOs8serYj+A586b2v/7Zhp109Lw05rDyKoZ2Pu+U6QC8/+x6ZtZW8b3fPs9PN7Sw5qEXowkghjqPxYlTx/PAF94OwHO72/j2vVv43ZZ9HO7oGd0bJKy+ufD+83uomzgur+fIa+Jx91vM7A4g7e4dZrYAKMiWNLNVwCqAGTNm0NzcfNzvcdGcNG+tdaqrqnMc3Wv7r+09vHy4vT/mzl7n6kc62d6a4fRpZbxxZhlza1LMnpCiLBX85Zsywt6GMdaOQkdnR1Z1NoOTK16huXl3/74r31yFA3NrUhzsdDp6g/qkHZzgptM+AztrUc9JyLbOYzW3pv2PfjZXzofL5o1jf4fT1u30+tDfi6G+PcdxZwBUAAALnElEQVT7PYurztm6b0cPm/Yfpbm5mYd39XLjU12Up+CNM8uZO7GSmkqjouzY70KKoCfY9/uQtPrmQkdnB48/8j+Up/I8fODhkEu+/wHnhf/PAspy9J7nAncP2L4CuGJQmbuBc8PX5QQ9HXut9z377LM9W/fff3/Wx2brb3/6hL/pqnv6t//+F095w+r/9P9++pVIzh9HneOmOhe+f/j1Jn/d393p+9u7/HV/d6e/61u/9b1tnaM+Pmn1zYWx1hlY76P47I5yOvUyM6sHvkdwkT8XHgUWmtm8cLbcCmDtoDJrgcvC1x8A7gu/QUXDMDz8m3ZPaye3PrKDFW88kfMXz4g5MpH4VJan6ElnuH3DDrp6M1y7YgnT8jyEJKOTl8RjZqcOsXsy8EXgC0BObrt2917gUwS9ms3Abe7+tJldaWYXhcVuAurMbCvwNxy71lQ0UqljwyZ3PrWL7nSGlW8tnIdLicShoixFxuGOx3Zy5tzJLJpZE3dIEsrXNZ5fm9lvga+6e98V4iuBU9z9WTPLvMaxx8Xd7wTuHLTvKwNedwIfzNX5CpP1z8a595k9nHzCBBZMz+UcDpHkqSwP/q5+5pU2vnzhUH8LS1zyNdR2CvAY8Fszu9bMTnD3Fne/B8Ddi67XEadgSqzzVMthfrdlH2+ZPy3ukERiN3BK8DtO1bBzIclL4nH3bnf/f8CpBFOZHzGzb/StYiC5lbJgqG3lmkcBGFeulZBE+no848pTNNSNjzkaGSivn1Du3unu/wScDnQAG8zs8/k8ZykyjIw7S06cDMBlb26INyCRAlBZFkwJPqlufP8Ns1IY8r1WW4OZLQM+BpwItAH/kM9zliKz4D6N3rSzeNYk5k7VX3cifT2e6TVDr+gh8cnL5AIz+wPBigEvAc8QzDi7F7gOeC4f5yxlKTMyGWffkW7qJuZ0DVaRxOpJBzNuptdoCnWhydestvcBLxTb/TKFzIEDR7qYp7FsEQD2tnUBcIIST8HJS+LxcNFOiUYqHGvb396d9zWWRJJi/gkTAHjzAs3yLDT5XiRUImAGR3vSpDPO1AkaahMBWHb6LB784tupn6JRgEKjebdFwIB0eAfpNF3jEemnpFOYIkk8ZvbeKM5TqlIDVpKdOkFDbSJS2KLq8VwV0XlK0sA7FDSrTUQKXVSJR3dv5dOA726drvGISIGLKvFoWnUepQbclT15vBKPiBQ2TS4oAgO7kxPHaaKiiBQ2JZ4i0NfjqRlXTlm+H1krIjJGUSWe3RGdpyT1jbRNqq6INxARkVGIJPG4+/lRnKdU9fVxaqo0zCYihS/KR19LnvQt+a7EIyJJkK8ez6/N7IdmdmKe3l8G6Btqq6nSUJuIFL7IHn2dp/MIwYPgQDPaRCQZ9OjrItA3kW2ihtpEJAH06OsiUqMej4gkgB59XQTChakZV67bskSk8OnR10XA+1YkMt08KiKFT4++LgJ9PR4tWiAiSaBHXxeDML+bFgEXkQTQRYEi0Net1EibiCSBEk8RyIQ9Hg21iUgSJDbxmNlUM/uNmW0J/58yTLm0mT0R/lsbdZxR8P65Bco8IlL4Ept4gNXAve6+kGDG3OphynW4+1nhv4uiCy86msEhIkmS5MSzHFgTvl5DMJOuJPUNtanDIyJJkOTEM8Pdd4WvXwFmDFOuyszWm9k6MyvO5NQ31KZZbSKSAFbIt9qY2T3AzCG+9HfAGnefPKDsQXd/1XUeM5vj7jvN7GTgPuAd7v78EOVWAasAZsyYcfatt96aVczt7e1MnDgxq2Ozdesz3dy1vYcPLarg3fMqIz03xFPnuKnOxa/U6gtjr/Pb3/72De7eOFK5gl7cy93fOdzXzGy3mc1y911mNgvYM8x77Az/32ZmzcAS4FWJx91vAG4AaGxs9Kampqxibm5uJttjs/Vg+ybY/gIL5s+n6W3zIz03xFPnuKnOxa/U6gvR1TnJQ21rgcvC15cBvxxcwMymmNm48PU04C3ApsgijEj/fTwaahORBEhy4rkaON/MtgDvDLcxs0YzuzEscyqw3syeBO4Hrnb34ks8WqpNRBKkoIfaXou77wfeMcT+9QSrYePu/wOcEXFokTs2q02ZR0QKX5J7PDKI0o6IJIESTxFw3ccjIgmixFMEjk0uEBEpfEo8RaB/kVCtEioiCaDEUwT6Z7XFG4aIyKgo8RSB/rUndJFHRBJAiacIuB59LSIJosRTBFyPvhaRBFHiKQJauUBEkkSJpwg4fT0eEZHCp8RTBI5d41HqEZHCp8RTBDK6g1REEkSJpwhoqE1EkkSJpxhoqE1EEkSJpwhcdNZsAN5w0que/C0iUnAS+zweOaZp0XS2X31h3GGIiIyKejwiIhIpJR4REYmUEo+IiETK+tb5kmPMbC/wYpaHTwP25TCcJFCdS0Op1bnU6gtjr/NJ7n7CSIWUeHLMzNa7e2PccURJdS4NpVbnUqsvRFdnDbWJiEiklHhERCRSSjy5d0PcAcRAdS4NpVbnUqsvRFRnXeMREZFIqccjIiKRUuLJETNbZmbPmtlWM1sddzz5YGZzzex+M9tkZk+b2afD/VPN7DdmtiX8v+gWjTOzMjN73Mz+M9yeZ2YPh+39EzOrjDvGXDKzyWZ2u5k9Y2abzezcYm9nM/ts+HO90cx+bGZVxdbOZnazme0xs40D9g3Zrhb4dlj3P5jZG3IVhxJPDphZGfAd4AJgMXCJmS2ON6q86AU+5+6LgaXAJ8N6rgbudfeFwL3hdrH5NLB5wPY1wLfcfQFwEFgZS1T5cy1wl7ufApxJUPeibWczmwNcDjS6++lAGbCC4mvnHwHLBu0brl0vABaG/1YB381VEEo8uXEOsNXdt7l7N3ArsDzmmHLO3Xe5+2Ph6zaCD6M5BHVdExZbA7wvngjzw8zqgQuBG8NtA84Dbg+LFFWdzawWeBtwE4C7d7v7IYq8nQkWTa42s3JgPLCLImtnd38AODBo93Dtuhy4xQPrgMlmNisXcSjx5MYcYMeA7ZZwX9EyswZgCfAwMMPdd4VfegWYEVNY+fIvwBeATLhdBxxy995wu9jaex6wF/hhOLx4o5lNoIjb2d13Av8EvESQcA4DGyjudu4zXLvm7XNNiUeOm5lNBH4GfMbdWwd+zYNpkkUzVdLM3gPscfcNcccSoXLgDcB33X0JcIRBw2pF2M5TCP7CnwfMBibw6iGpohdVuyrx5MZOYO6A7fpwX9ExswqCpPPv7n5HuHt3Xxc8/H9PXPHlwVuAi8xsO8EQ6nkE1z8mh0MyUHzt3QK0uPvD4fbtBImomNv5ncAL7r7X3XuAOwjavpjbuc9w7Zq3zzUlntx4FFgYzoCpJLgouTbmmHIuvLZxE7DZ3b854EtrgcvC15cBv4w6tnxx9yvcvd7dGwja9T53/wvgfuADYbFiq/MrwA4zWxTuegewiSJuZ4IhtqVmNj78Oe+rc9G28wDDteta4NJwdttS4PCAIbkx0Q2kOWJm7ya4FlAG3OzuV8UcUs6Z2VuB3wFPcex6x5cIrvPcBpxIsKr3h9x98AXMxDOzJuDz7v4eMzuZoAc0FXgc+LC7d8UZXy6Z2VkEkykqgW3ARwn+UC3adjazrwMXE8zefBz4GME1jaJpZzP7MdBEsAr1buCrwC8Yol3DBHwdwZDjUeCj7r4+J3Eo8YiISJQ01CYiIpFS4hERkUgp8YiISKSUeEREJFJKPCIiEiklHhERiZQSj4iIREqJRyQhzKzezC6OOw6RsVLiEUmOdxCsmSaSaFq5QCQBwuWKfgkcAtqAP3P3bfFGJZIdJR6RhDCzuwjWits4YmGRAqahNpHkWAQ8E3cQImOlxCOSAGY2jWBZ+t4RC4sUOCUekWRoAF6OOwiRXFDiEUmGZ4BpZrbRzN4cdzAiY6HJBSIiEin1eEREJFJKPCIiEiklHhERiZQSj4iIREqJR0REIqXEIyIikVLiERGRSCnxiIhIpP4/Dv+N6vqQaG0AAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "##Time\n", "t_max = int(100)\n", "t = np.linspace(0,t_max,1000)\n", "t_0_0 = 10\n", "t_1_0 = 25\n", "t_0_d = 50\n", "t_1_d = 75\n", "\n", "step_0 = 1\n", "step_d = 1\n", "print('NON-LINEAR SIMULATION')\n", "## Chemostat\n", "chemo = '({0}+{1}*(np.heaviside(t-{2},1)-np.heaviside(t-{3},1)))'\n", "x_chemo_0 = chemo.format(parameter['X0_E0'],str(step_0),str(t_0_0),str(t_1_0))\n", "x_chemo_b = chemo.format(parameter['X0_B0'],str(step_d),str(t_0_d),str(t_1_d))\n", "\n", "## Simulate\n", "X_chemo = {'B0':x_chemo_b,'E0':x_chemo_0}\n", "ndat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=x_ss,X_chemo=X_chemo,quiet=quiet)\n", "\n", "\n", "##Plot\n", "st.plot(s,ndat,species=['B'],reaction=['r3'],x_ss=x_ss,v_ss=v_ss)\n", "st.plot(s,ndat,species=['E'],reaction=['r0'],x_ss=x_ss,v_ss=v_ss)\n", "\n", "X = ndat['X']\n", "X_E = X[:,s['species'].index('E')]\n", "X_C = X[:,s['species'].index('C')]\n", "e0 = X_E + X_C\n", "plt.plot(t,e0)\n", "plt.grid()\n", "plt.xlabel('$t$')\n", "plt.ylabel('$e_0$')\n", "plt.show()\n", "\n", "print('LINEAR SIMULATION')\n", "## Chemostat\n", "x_chemo_0 = chemo.format('1e-6',str(step_0),str(t_0_0),str(t_1_0))\n", "x_chemo_b = chemo.format('1e-6',str(step_d),str(t_0_d),str(t_1_d))\n", "X_chemo = {'B0':x_chemo_b,'E0':x_chemo_0}\n", "ldat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=x_ss,X_chemo=X_chemo,linear=True,V0=v_ss,quiet=quiet)\n", "st.plot(s,ldat,species=['B'],reaction=['r3'],x_ss=x_ss,v_ss=v_ss)\n", "st.plot(s,ndat,species=['E'],reaction=['r0'],x_ss=x_ss,v_ss=v_ss)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion\n", "\n", "- The non linear response has similar behaviour to the linear case although the values are different for a non-infinitesimal step.\n", "- The net enzyme $e_0 = x_E+x_C$ is directly manipulated by the feedback system to adjust product flow driven by the actuator. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusion\n", "\n", "- A control-theoretical appoach via linearisation has been used to give insight into the behavior of a simple biomolecular system with product inhibition.\n", "\n", "- Although linearisation is used to provide insights, the full non-linear system is still available for further analysis and simulation. In particular, energy flows are still available in the non-linear bond graph model.\n", "\n", "- The role of *pumping* to endow the 'actuator' with desirable decoupling properties is emphasised.\n", "\n", "- the feedback system has five chemostats: E0, F, G, A, B0. These can become ports to interact with the wider system. \n", "\n", "- it would be interesting to look at a real enzyme such as PFK.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.9" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }