Categories
Dynamic Modeling Integration Methods Kotlin Stiff Models TornadoFX User Interface

A Humidification Column GUI

Introduction

Previously I showed how straightforward it is to build a user interface with TornadoFX and how expedient it is to re-use modules from a well-designed MVC application. In this post I capitalize on these facts and build a Humidification Column App.

The Humidification column is described in detail in ref. 1. It consists of a packed column where warm water from the top is contacted with dry, warm air from the bottom. The water is cooled on its way down the column from evaporative cooling while the moisture content in the air increases. A PI-controller senses the water exit temperature and adjusts the incoming air rate in order to hold the water temperature at setpoint. The column is modelled by three partial differential equations plus the PI controller and valve equation.

These equations are easily implemented in Kotlin. Here I just show the code for calculating the derivatives. Please note that I have not followed strict Kotlin conventions in naming my variables. This is because I have translated the original FORTRAN code almost verbatim.

    override fun updateDerivativeVector(derivativeVector: DoubleArray, time: Double): DoubleArray {

        val dydt = derivativeVector.copyOf()

        val e = tl[0] - TLSET
        x = XSS + KC * (e + EI / TI)
        if (x < 0) {
            x = 0.0
        }
        if (x > 1) {
            x = 1.0
        }
        V = CVDP * x
        val P1 = V / (G * S)

        val ep = tg.copyOf()
        val ys = tg.copyOf()
        for (I in 0 until N) {
            tg[I] = (ev[I] - y[I] * DHVAP) / (CVA + y[I] * CVV)
            ep[I] = CPA * tg[I] + y[I] * (CPV * tg[I] + DHVAP)
            val exponent = 7.96681 - 3002.4 / (378.4 + 1.8 * tl[I] + 32.0)
            val P = pow(10.0, exponent)
            ys[I] = P / (760.0 - P)
            if (ys[I] < 0) {
                ys[I] = 0.0
            }
        }

        y[0] = 0.01
        tl[N-1] = 43.33
        tg[0] = 43.33
        ep[0] = CPA * tg[0] + y[0] * (CPV * tg[0] + DHVAP)

        val yz = derivativesAtGridpoints(xL = 0.0, xU = ZL, n = N, u = y).b
        val epz = derivativesAtGridpoints(xL = 0.0, xU = ZL, n = N, u = ep).b
        val tlz = derivativesAtGridpoints(xL = 0.0, xU = ZL, n = N, u = tl).b

        var index = 0
        for (I in 0 until N) {
            dydt[index] = -P1 * yz[I] + P2 * (ys[I] - y[I])
            index += 1
        }
        for (I in 0 until N) {
            val P7 = CVV * tg[I] + DHVAP
            dydt[index] = -P1 * epz[I] + P3 * (tl[I] - tg[I]) + P2 * (ys[I] - y[I]) * P7
            index += 1
        }
        for (I in 0 until N) {
            val P7 = CVV * tg[I] + DHVAP
            dydt[index] = P4 * tlz[I] - P5 * (tl[I] - tg[I]) - P6 * (ys[I] - y[I]) * P7
            index += 1
        }
        dydt[index++] = e
        dydt[index] = (x - valveLag) / tau

        dydt[0] = 0.0
        dydt[N] = 0.0
        dydt[3 * N - 1] = 0.0

        return dydt
    }

The User Interface

The user interface will consist of a few controls and a couple of plots to show the controlled temperature and the air rate as computed by the PI-controller. It should be possible to make one run after the other while changing the chosen integration method and the number of grid points. Here are screenshots of the final interface.

This interface was almost trivial to construct especially since I copied most of it directly from other models. Here is the TornadoFX code for the interface.

import controller.ViewController
import javafx.geometry.Pos
import javafx.scene.chart.NumberAxis
import tornadofx.*

var viewController = find(ViewController::class)

class MainView: View() {
    override val root = borderpane {
        left = vbox {
            alignment = Pos.CENTER_LEFT
            button("Run Simulation") {
                action {
                    viewController.runSimulation()
                }
            }
            button("Pause Simulation") {
                action {
                    viewController.pauseSimulation()
                }
            }
            button("Resume Simulation") {
                action {
                    viewController.resumeSimulation()
                }
            }
            combobox(viewController.selectedIntMethod, viewController.intMethods)
            combobox(viewController.selectedDiscretizer, viewController.dicretizers)
            combobox(viewController.selectedHpMethod, viewController.hpMethods)
            label("  Initial StepSize:")
            textfield(viewController.initStepSize)
            label("  Number of grid points:")
            textfield(viewController.nGridPoints)
            label("  UI update delay (ms):")
            label("1000=Slow updates, 1=Fast")
            textfield(viewController.simulator.sliderValue)
            slider(min=1, max=1000, value = viewController.simulator.sliderValue.value) {
                bind(viewController.simulator.sliderValue)
            }
        }
        center = tabpane {
            tab("Liquid Temperature") {
                linechart("Exit temperature", NumberAxis(), NumberAxis()) {
                    xAxis.isAutoRanging = false
                    val xa = xAxis as NumberAxis
                    xa.lowerBound = 0.0
                    xa.upperBound = 2.0
                    xa.label = "Time, h"
                    yAxis.isAutoRanging = false
                    val ya = yAxis as NumberAxis
                    ya.lowerBound = 30.0
                    ya.upperBound = 38.0
                    ya.label = "Temperature, oC"
                    series("liqTemp") {
                        data = viewController.liqTempData
                    }
                }
            }
            tab("Vapor Rate") {
                linechart("Vapor Rate", NumberAxis(), NumberAxis()) {
                    xAxis.isAutoRanging = false
                    val xa = xAxis as NumberAxis
                    xa.lowerBound = 0.0
                    xa.upperBound = 2.0
                    xa.label = "Time, h"
                    yAxis.isAutoRanging = false
                    val ya = yAxis as NumberAxis
                    ya.lowerBound = 0.0
                    ya.upperBound = 25000.0
                    ya.tickUnit = 5000.0
                    ya.label = "Vapor Rate"
                    series("vapRate") {
                        data = viewController.vapFlowData
                    }
                }
            }
        }
    }
}

The view depends heavily on the (View-)controller for its behavior. The view-controller code is not complicated either and it makes good use of JavaFX’s collection classes. Recall that these are observable objects meaning that they automatically update as changes in the interface are detected.

import Notification.IObserver
import javafx.beans.property.SimpleDoubleProperty
import javafx.beans.property.SimpleIntegerProperty
import javafx.beans.property.SimpleStringProperty
import javafx.collections.FXCollections
import javafx.scene.chart.XYChart
import model.HumidificationColumn
import model.Simulator
import tornadofx.*


class ViewController: Controller(), IObserver {

    var model = HumidificationColumn(21)
    var endTime = 2.0
    var simulator = Simulator(model)

    var liqTempData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()
    var vapFlowData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()



    val dicretizers = FXCollections.observableArrayList("Euler", "RungeKutta", "RKFehlberg")
    val intMethods = FXCollections.observableArrayList("SingleStep", "HpMethods")
    val selectedDiscretizer = SimpleStringProperty("Euler")
    val selectedIntMethod = SimpleStringProperty("SingleStep")
    val hpMethods = FXCollections.observableArrayList("Eulex", "Eulsim")
    val selectedHpMethod = SimpleStringProperty("Eulex")
    val initStepSize = SimpleDoubleProperty(0.001)
    val nGridPoints = SimpleIntegerProperty(model.N)


    init {
        simulator.addIObserver(this)
    }

    fun runSimulation() {
        model = HumidificationColumn(nGridPoints.value)
        simulator.ode = model
        simulator.discretizer = selectedDiscretizer.value
        simulator.intMethod = selectedIntMethod.value
        simulator.hpMethod = selectedHpMethod.value
        simulator.initialStepSize = initStepSize.value
        simulator.runSimulation()
    }

    fun pauseSimulation() {
        simulator.pauseSimulation()
    }

    fun resumeSimulation() {
        simulator.resumeSimulation()
    }


    override fun update(theObserved: Any?, changeCode: Any?) {
        val code = changeCode as String
        when (code) {
            "reset" -> {
                if (liqTempData.size > 0) {
                    liqTempData.remove(0, liqTempData.size)
                    vapFlowData.remove(0, vapFlowData.size)
                }
            }
            "update" -> {
                val time = model.time
                liqTempData.add(XYChart.Data(time, model.tl[0]))
                vapFlowData.add(XYChart.Data(time, model.V))
                if (time > 0.333) {
                    model.TLSET = 36.0
                }
                if (time > 0.67) {
                    model.TLSET = 32.0
                }
                if (time > 1.67) {
                    model.TLSET = 36.0
                }
            }
            else -> {}
        }
    }
}

Stiff Problems

In all my previous posts I have used dynamic models that are non-stiff, meaning that the separation of time constants (inverse of eigenvalues) is not large. If we define the largest time constant as the time-scale of the problem then the smallest time constant is the inverse of the numerically largest eigenvalue of the Jacobian matrix. The ratio of the largest time constant to the smallest is called the stiffness ratio.

Why do we care about the stiffness ratio? The reason is that the maximum allowable step size for an explicit integrator like Euler and Runge-Kutta is limited by the smallest time constant of the problem. Thus, the integrator has to evaluate the derivatives roughly as many times as the magnitude of the stiffness ratio. For stiffness ratios < 10^4 we usually don’t notice any performance degradation in using an explicit integrator but as the stiffness ratio grows we start noticing a problem.

Let me illustrate with the Humidification column. Stiffness increases with the number of grid points, N, chosen for the spatial derivative approximations. With the default value of N = 21, the explicit integrator RKFehlberg requires a step size of h = 0.00012 h (= 0.4 seconds) for stability. The time to complete 2 h of process time is roughly 2.2 seconds on my computer. That’s plenty fast.

However, when I double the number of grid points to N = 41, I have to lower the fixed step size to h = 0.00006 to retain numerical stability. The time for 2 h integration triples to 6.6 seconds even though the number of derivative evaluations only doubled. The reason is the nonlinearities in the derivative evaluations. The execution speed is no longer fast but tolerable.

The situation becomes problematic when we double the number of grid points one more time to N = 81. Predictably, the stable step size is h = 0.00003 h (= 0.1 second) but the execution speed is now 23.5 seconds! That’s impracticably slow for evaluating multiple scenarios on a model.

Extrapolation Methods

The general idea of an extrapolation method is to have an integrator that tries to take long time steps, H, by extrapolating the results of several sub-steps, p, within the long step. The long step and the number of sub-steps are adjusted by a step controller to give a desired accuracy of integration. These methods are sometimes referred to as Hp-methods. Here I will not go into details of extrapolation methods but merely refer to a couple of relevant references (2, 3).

The Hp methods come in two flavors, an explicit integrator called Eulex and a semi-implicit version called Eulsim. Eulex has similar stability properties to Euler, Runge-Kutta and RKFehlberg and is not expected to do any better than those. In fact, because of the extra sub-steps involved in an Hp method, we would expect Eulex to do slightly worse than a fixed-step Euler using its largest, stable step size. However, Eulex has the advantage over a fixed-step Euler that the step controller will automatically find a stable step size for a given accuracy.

In contrast to the explicit methods, a semi-implicit method like Eulsim, has a much wider stability region for the step size and should be expected to do better for stiff problems.

The following table summarizes the results of a few runs with the model and its interactive interface. It is pretty clear that for stiff problems the choice of integrator becomes important.

# Grid pointsRKFehlberg, secondsEulex, secondsEulsim, seconds
212.22.71.1
416.68.41.2
8123.533.23.8
CPU time for integrating the Humidification column with various methods

The boldface entries in the table are visualized in a short video that also demonstrates the use of the interface.

Short demonstration of the Humidification column interface.

Summary

I have covered a few different topics in this post. First, I showed once more how easy it is to construct a user interface with TornadoFX and Kotlin. Second, I demonstrated the power of MVC when it comes to re-use of view- and controller modules for entirely different models. Finally, the concepts of stiff problems and implicit integrators were discussed.

References

  1. Silebi, C.A. and Schiesser, W.E. Dynamic Modeling of Transport Process Systems, Academic Press, Inc., San Diego, CA, 1992
  2. Deuflhard, P. “Order and Stepsize Control in Extrapolation Methods”, Numer. Math., 41, 1983, pp 399-422.
  3. Deuflhard, P., “Recent Progress in Extrapolation Methods”, SIAM Rev. vol 27, 1985, pp. 505-535.
Categories
Dynamic Modeling Kotlin Model-View-Controller TornadoFX User Interface

Building an Interactive Process Simulator from Scratch

Introduction

In previous posts I have introduced dynamic integration techniques, MVC designs, Kotlin and TornadoFX. It is now time to put all the pieces together in a free-standing app with a responsive user interface. The final result will look like these two screen shots.

Figure 1. User interface with time dependent velocity profiles shown.
Figure 2. Tab 2 of the UI showing the fluid velocity as a function of time at three different x-positions.

Let’s get started putting this app together piece by piece.

Create the Project Template

In previous posts I have shown how to do this so I will move quickly through this section.

Step 1. Make a new project with JetBrains IntelliJ.

Figure 3. The new project screen. Use Kotlin, Gradle, Groovy and JDK 1.8

Step 2. Link the project to any local, supporting projects you might have (in my case SyMods), assign dependencies in build.gradle and finally provide empty folders (packages) for the “app”, “model”, “view” and the “controller” as in MVC.

Figure 4. Model structure ready for source files.

Since the build.gradle is such an important part of the project I show the script more clearly here:

plugins {
    id 'org.jetbrains.kotlin.jvm' version '1.7.10'
}

group = 'org.example'
version = '1.0-SNAPSHOT'

repositories {
    mavenCentral()
}

dependencies {
    testImplementation 'org.jetbrains.kotlin:kotlin-test'
    implementation 'org.example:SyMods'
    implementation 'no.tornado:tornadofx:1.7.20'
    implementation "org.jetbrains.kotlinx:kotlinx-coroutines-core:1.6.4"
    implementation "org.jetbrains.kotlinx:kotlinx-coroutines-javafx:1.6.4"
}

test {
    useJUnitPlatform()
}

compileKotlin {
    kotlinOptions.jvmTarget = '1.8'
}

compileTestKotlin {
    kotlinOptions.jvmTarget = '1.8'
}

The Model

In most versions of MVC designs, the model is the only part that is completely independent of the other pieces. In other words, the model has no knowledge of either the view or the (view-) controller. The only contract the model has with the outside world is that it implements the Integratable interface. That way the same model, without substantial modifications, can be used with a completely different user interface implementation (e.g. Java/Swing or Swift/Cocoa).

The model I have chosen for this example is borrowed from the field of fluid dynamics. Such systems are described by a set of nonlinear partial differential equations expressing the conservation of mass and momentum for incompressible Newtonian fluids. The fluid velocity in three dimensions is captured in the Navier Stokes equation of fluid dynamics (see Ref. 1 for a complete derivation).

If we limit the flow model to the fluid velocity component in one dimension, and neglect pressure and gravitational effects, we obtain the one-dimensional Burgers’ equation.

Figure 5. Model of the one-dimensional velocity component, u, for a viscous fluid.

We can think of this equation as representing the velocity in the x-direction as the fluid is moving freely along a path. Note that the fluid is viscous as captured by the kinematic viscosity, v (m^2/s).

According to Ref. 1, Burgers’ equation is a standard test problem for numerical methods for two reasons (1) It is a nonlinear equation with known analytical solutions, (2) It can be made increasingly more difficult to solve numerically as the viscosity decreases.

The equation is first order in time and second order in space. Thus, it requires one initial condition and two boundary conditions. The initial condition is taken from the analytical solution at time = 0. The boundary conditions are shown above. They state that the spatial velocity derivative is zero at both ends of the flow path at all times.

Numerical techniques for solving partial differential equations like this typically involve breaking up the x-direction in a large number (N-1) of small segments, dx, flanked by N grid points to help with the approximation of the spatial derivatives. This way we end up with a set of N ordinary differential equations that can be solved with standard integrators such as Euler or Runge-Kutta.

For this example I’m choosing to use a Spline Collocation Method to approximate the first and second order spatial derivatives (See Ref. 2 for details of this method). The complete code for the model is shown here:

package model

import integrators.Integratable
import utilities.derivativesAtGridpoints
import kotlin.math.exp

class BurgersEquation(var nGridPoints: Int): Integratable {

    val length = 1.0
    var dx = length / (nGridPoints - 1)
    var time = 0.0
    var vis = 0.003
    var x = DoubleArray(nGridPoints) { it * dx }
    var u = DoubleArray(nGridPoints) { phi(x[it], time) }

    override fun initialConditionsUsingArray(xin: DoubleArray): DoubleArray {
        x = DoubleArray(nGridPoints) { it * dx }
        val u0 = xin.copyOf()
        for (i in 0 until nGridPoints) {
            u0[i] = phi(this.x[i], time)
        }
        return u0
    }

    override fun updateStatesFromStateVector(x: DoubleArray, time: Double) {
        this.time = time
        u = x
    }

    override fun updateDerivativeVector(df: DoubleArray, time: Double): DoubleArray {
        val ux = derivativesAtGridpoints(xL=0.0, xU=length, n=nGridPoints, u=u).b
        ux[0] = 0.0
        ux[nGridPoints-1] = 0.0
        val uxx = derivativesAtGridpoints(xL=0.0, xU=length, n=nGridPoints, u=ux).b
        val ut = df.copyOf()
        for (i in 0 until nGridPoints) {
            ut[i] = vis * uxx[i] - u[i] * ux[i]
        }
        return ut
    }

    override fun dimension(): Int {
        return nGridPoints
    }

    override fun stiff(): Boolean {
        return false
    }

    fun phi(x: Double, t: Double): Double {
        //
        // Function phi computes the exact solution of Burgers' equation
        // for comparison with the numerical solution.  It is also used to
        // define the initial and boundary conditions for the numerical
        // solution.
        //
        // Analytical solution
        val a = (0.05 / vis) * (x - 0.5 + 4.95 * t)
        val b = (0.25 / vis) * (x - 0.5 + 0.75 * t)
        val c = (0.5 / vis) * (x - 0.375)
        val ea = exp(-a)
        val eb = exp(-b)
        val ec = exp(-c)
        return (0.1 * ea + 0.5 * eb + ec) / (ea + eb + ec)
    }
}

The View

Next to the model, the view is similarly isolated from the other software components. In particular, it has no direct knowledge of the model implementation. This is important from a code reuse point of view. For example, it would be quite easy to use this view for another model by just changing a few text labels.

I’m using TornadoFX to build the interface. Without further explanations of the code, I think you can see how the declarative statements below result in the interfaces shown in Figures 1 and 2.

package view

import controller.ViewController
import javafx.geometry.Pos
import javafx.scene.chart.NumberAxis
import tornadofx.*

var viewController = find(ViewController::class)

class MainView: View() {
    override val root = borderpane {
        left = vbox {
            alignment = Pos.CENTER_LEFT
            button("Run Simulation") {
                action {
                    viewController.runSimulation()
                }
            }
            button("Pause Simulation") {
                action {
                    viewController.pauseSimulation()
                }
            }
            button("Resume Simulation") {
                action {
                    viewController.resumeSimulation()
                }
            }
            combobox(viewController.selectedDiscretizer, viewController.dicretizers)
            combobox(viewController.selectedStepController, viewController.stepControllers)
            label("  Initial StepSize:")
            textfield(viewController.initStepSize)
            label("  Number of grid points:")
            textfield(viewController.nGridPoints)
            label("  Model Parameter, viscosity:")
            textfield(viewController.viscosity)
            label("  UI update delay (ms):")
            label("1000=Slow updates, 1=Fast")
            textfield(viewController.simulator.sliderValue)
            slider(min=1, max=1000, value = viewController.simulator.sliderValue.value) {
                bind(viewController.simulator.sliderValue)
            }
        }
        center = tabpane {
            tab("Profile Chart 1") {
                scatterchart("Burgers' Equation", NumberAxis(), NumberAxis()) {
                    xAxis.isAutoRanging = false
                    val xa = xAxis as NumberAxis
                    xa.lowerBound = 0.0
                    xa.upperBound = 1.0
                    xa.label = "x"
                    yAxis.isAutoRanging = false
                    val ya = yAxis as NumberAxis
                    ya.lowerBound = 0.0
                    ya.upperBound = 1.2
                    ya.label = "u(x,t)"
                    series("uSeries") {
                        data = viewController.uSeriesData
                    }
                    series("uAnalSeries") {
                        data = viewController.uAnalSeriesData
                    }
                }
            }
            tab("Profile Chart 2") {
                linechart("Burgers' Equation", NumberAxis(), NumberAxis()) {
                    xAxis.isAutoRanging = false
                    val xa = xAxis as NumberAxis
                    xa.lowerBound = 0.0
                    xa.upperBound = 1.0
                    xa.label = "Time, t"
                    yAxis.isAutoRanging = false
                    val ya = yAxis as NumberAxis
                    ya.lowerBound = 0.0
                    ya.upperBound = 1.2
                    ya.label = "u(t)"
                    series("midGridpoint") {
                        data = viewController.midGridpointData
                    }
                    series("lowGridpoint") {
                        data = viewController.lowGridpointData
                    }
                    series("hiGridpoint") {
                        data = viewController.hiGridpointData
                    }
                }
            }
        }
    }
}

A couple of important comments on the view code:

  • There is no explicit mention of any of the UI classes like Button, Label, TextField etc.. Instead, these are created implicitly from TornadoFX’s builder functions.
  • There is no procedural code in the view, only configuration statements.
  • Values in and out of the interface go through the viewController. The controller is injected into the view by the statement var viewController = find(ViewController::class)
  • The view component values and the viewController variables are connected through bindings. Bindings allow for automatic transfer of updated information without having to write code to detect changes and transfer new values from one object to another.

Anyone who has worked with Java/Swing or Java/JavaFX will appreciate how simple it is to build an interface with Kotlin/TornadoFX.

View – Styling

While it is possible to provide styling code directly into the view functions I find that view code becomes less clear. An alternative that I like is to list the styling attributes in a separate Stylesheet class. This is what I used for the example application:

package app

import javafx.scene.paint.Color
import javafx.scene.text.FontWeight
import tornadofx.*

class Styles : Stylesheet() {
    init {
        button {
            padding = box(10.px)
            textFill = c("green")
            and(hover) {
                backgroundColor += Color.AQUAMARINE
            }
        }

        label {
            padding = box(5.px)
            fontSize = 14.px
            fontWeight = FontWeight.BOLD
            textFill = c("blue")
        }
    }
}

I have only done the most basic of what you can achieve with these Stylesheets. For example, I specify how much padding the buttons should have and their text color. I also specify the desired color change when the mouse “hovers” over them. Similar decorations for the labels are also shown.

The Controller

The controller usually takes a very central position in most MVC designs. In my version it owns the model and it is injected into the view as I mentioned above. The controller is also an Observer of the Simulator (see below). As such it implements the IObserver‘s update(…) function. This function is called from the Simulator when changes in the model’s data have taken place and need to be displayed. Recall that the model does not know about the view and therefore has no direct way of communicating with it. All communication between the model and the view must pass through the controller.

The controller implements a few JavaFX and TornadoFX data structures that are observable to view items through bindings. For example, take the uSeriesData in the controller. It holds data for one of the series in the view’s Profile Chart 1. This is how we use it in the view:

series("uSeries") {
      data = viewController.uSeriesData
}

In the controller this variable is a special ArrayList and is declared as follows:

var uSeriesData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()

When the Simulator sends the controller an update(…) request, the uSeriesData array is updated based on information it finds in the model.

if (updateCounter > updateFrequency || updateCounter == 0) {
      for (i in 0 until model.nGridPoints) {
           val xValue = model.x[i]
           uSeriesData.add(XYChart.Data(xValue, model.u[i]))
       }
       updateCounter = 1
 }

The neat feature about these data structures is that they are “observable” in the sense that the chart updates automatically as soon as the controller makes new data available in the uSeriesData array. Similarly, when data items are removed from the array, the display changes accordingly. In other words, there is no need to explicitly “refresh” the charts with user code. Ref 3. is a good source to learn about these data structures and their use in JavaFX/TornadoFX applications.

package controller

import utilities.IObserver
import javafx.beans.property.SimpleDoubleProperty
import javafx.beans.property.SimpleIntegerProperty
import javafx.beans.property.SimpleStringProperty
import javafx.collections.FXCollections
import javafx.scene.chart.XYChart
import model.BurgersEquation
import model.Simulator
import tornadofx.*


class ViewController: Controller(), IObserver {

    var model = BurgersEquation(201)
    var endTime = 1.0
    var simulator = Simulator(model)

    var uSeriesData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()
    var uAnalSeriesData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()
    var midGridpointData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()
    var lowGridpointData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()
    var hiGridpointData = FXCollections.observableArrayList<XYChart.Data<Number, Number>>()



    val dicretizers = FXCollections.observableArrayList("Euler", "RungeKutta", "RKFehlberg")
    val stepControllers = FXCollections.observableArrayList("FixedStep", "VariableStep")
    val selectedDiscretizer = SimpleStringProperty("Euler")
    val selectedStepController = SimpleStringProperty("FixedStep")
    val initStepSize = SimpleDoubleProperty(0.001)
    val nGridPoints = SimpleIntegerProperty(model.nGridPoints)
    val viscosity = SimpleDoubleProperty(model.vis)

    var updateCounter = 0
    val updateFrequency = 4

    init {
        simulator.addIObserver(this)
    }

    fun runSimulation() {
        model = BurgersEquation(nGridPoints.value)
        model.vis = viscosity.value
        simulator.ode = model
        simulator.discretizer = selectedDiscretizer.value
        simulator.stepSizeType = selectedStepController.value
        simulator.initialStepSize = initStepSize.value
        simulator.runSimulation()
    }

    fun pauseSimulation() {
        simulator.pauseSimulation()
    }

    fun resumeSimulation() {
        simulator.resumeSimulation()
    }

    override fun update(theObserved: Any?, changeCode: Any?) {
        val code = changeCode as String
        when (code) {
            "reset" -> {
                if (uSeriesData.size > 1) {
                    uSeriesData.remove(0, uSeriesData.size)
                    uAnalSeriesData.remove(0, uAnalSeriesData.size)
                    midGridpointData.remove(0, midGridpointData.size)
                    lowGridpointData.remove(0, lowGridpointData.size)
                    hiGridpointData.remove(0, hiGridpointData.size)
                }
            }
            else -> {
                val time = model.time
                if (updateCounter > updateFrequency || updateCounter == 0) {
                    for (i in 0 until model.nGridPoints) {
                        val xValue = model.x[i]
                        uSeriesData.add(XYChart.Data(xValue, model.u[i]))
                        uAnalSeriesData.add(XYChart.Data(xValue, model.phi(x = xValue, t = time)))
                    }
                    updateCounter = 1
                }
                updateCounter += 1
                val midGridpoint = model.nGridPoints / 2
                val lowGridpoint = midGridpoint - 20 * model.nGridPoints / 201
                val hiGridpoint = midGridpoint + 20 * model.nGridPoints / 201
                midGridpointData.add(XYChart.Data(time, model.u[midGridpoint]))
                lowGridpointData.add(XYChart.Data(time, model.u[lowGridpoint]))
                hiGridpointData.add(XYChart.Data(time, model.u[hiGridpoint]))
            }
        }
    }
}

There are a few more modules we have to discuss before the app is complete. One of these is the Simulator.

The Simulator

This module is most closely characterized as a model but it is generic enough that it can be treated separately. The simulator is responsible for the numerical integration and for notifying the controller when is time to sample the model for new data to display.

The simulator is generic in the sense that it can integrate any model as long as the model implements the Integratable interface. The simulator itself implements the interface IObservable which means that it can keep track of, and notify, observing objects (e.g. the controller).

An important task for the simulator is to start the integration and run it to completion without blocking the user from working with the UI. Traditionally this is done by starting a low priority background Thread. However, threads can be tricky to work with, especially around shared data. Instead I have opted to use Kotlin’s Coroutine package. Ref. 4 is the perfect source to learn about coroutines. Here I will only highlight the features I have used.

Coroutines are launched in a CoroutineScope. For UI applications it is quite useful to derive a private scope from the general CoroutineScope() but specify that we want the coroutine to be dispatched on the JavaFx UI thread.

import kotlinx.coroutines.*
import kotlinx.coroutines.javafx.JavaFx


class Simulator(var ode: Integratable) : IObservable {

    private var job = Job()
    private val myScope: CoroutineScope =     CoroutineScope(Dispatchers.JavaFx + job)
                :
                :
                :
}

We use the private scope to launch a coroutine with code provided in the trailing lambda.

        myScope.launch {
            while (time <= endTime) {
                time = integrator.currentTime
                integrator.startTime = time
                integrator.endTime = time + dt
                integrator.continueCalculations()
                            :
                            :
                            :
            }
        }

You can easily identify these code snippets in their complete context of the Simulator code below. The coroutines are quite nice for dynamic simulations like this because we can implement start, stop, pause, resume, etc. without freezing the UI or making it sluggish.

package model

import integrators.DiscretizationModel
import integrators.Integratable
import integrators.IntegrationServer
import integrators.StepSizeControlModel
import javafx.beans.property.SimpleDoubleProperty
import utilities.IObservable
import utilities.IObserver
import utilities.ObservableComponent
import kotlinx.coroutines.*
import kotlinx.coroutines.javafx.JavaFx


class Simulator(var ode: Integratable) : IObservable {
    private val myObservableComponent: ObservableComponent = ObservableComponent()
    private var job = Job()
    private val myScope: CoroutineScope = CoroutineScope(Dispatchers.JavaFx + job)

    val sliderValue = SimpleDoubleProperty(200.0)
    var sliderValueInt: Long = 200

    lateinit var integrator: IntegrationServer
    var discretizer = "Euler"
    var stepSizeType = "FixedStep"
    lateinit var discretizationType: DiscretizationModel
    lateinit var stepSizeControlType: StepSizeControlModel
    var time = 0.0
    var endTime = 1.0
    var reportingInterval = 0.1
    var dt = reportingInterval / 10
    var dt0 = dt
    var initialStepSize = 0.001
    var simulationPaused = false
    var endSimulation = false
    private var reportTimer = 0.0
    var x: DoubleArray

    init {
        val dim = ode.dimension()
        x = DoubleArray(dim)
        System.arraycopy(ode.initialConditionsUsingArray(x), 0, x, 0, dim)
    }

    fun reset() {
        discretizationType = when(discretizer) {
            "RungeKutta" -> DiscretizationModel.ClassicalRK
            "RKFehlberg" -> DiscretizationModel.RKFehlberg
            else -> DiscretizationModel.ModifiedEuler
        }
        stepSizeControlType = when(stepSizeType) {
            "VariableStep" -> StepSizeControlModel.VariableStepController
            else -> StepSizeControlModel.FixedStepController
        }
        x = DoubleArray(ode.dimension())
        System.arraycopy(ode.initialConditionsUsingArray(x), 0, x, 0, ode.dimension())
        integrator = IntegrationServer(discretizationType, stepSizeControlType);
        integrator.ode = ode

        integrator.initialStepSize = initialStepSize
        integrator.accuracy = 1.0e-5
        reportingInterval = 0.03
        dt = reportingInterval / 2
        dt0 = dt

        time = 0.0
        reportTimer = 0.0
        integrator.startTime = 0.0
        integrator.start(x)
    }

    fun pauseSimulation() {
        simulationPaused = true
    }

    fun resumeSimulation() {
        simulationPaused = false
    }

    fun endSimulation() {
        endSimulation = true
    }


    fun runSimulation() {
        reset()
        endSimulation = false
        simulationPaused = false
        myScope.launch {
            myObservableComponent.notifyIObservers(this, "reset")
            while (time <= endTime) {
                time = integrator.currentTime
                integrator.startTime = time
                integrator.endTime = time + dt
                integrator.continueCalculations()
                time = integrator.currentTime
                x = integrator.currentValues()

                reportTimer += dt
                dt = if (simulationPaused) {
                    delay(500L)
                    0.0
                } else {
                    dt0
                }
                if (reportTimer >= reportingInterval) {
                    sliderValueInt = sliderValue.value.toLong()
                    delay(sliderValueInt)
                    myObservableComponent.notifyIObservers(this, "update")
                    reportTimer = 0.0
                }
                if (time >= endTime || endSimulation) {
                    myObservableComponent.notifyIObservers(this, "done")
                }
            }
        }
    }

    override fun addIObserver(anIObserver: IObserver?) {
        myObservableComponent.addIObserver(anIObserver)
    }

    override fun deleteIObserver(anIObserver: IObserver?) {
        myObservableComponent.deleteIObserver(anIObserver)
    }

    override fun deleteIObservers() {
        myObservableComponent.deleteIObservers()
    }
}

The App

We now have all the pieces ready for the App itself. It is trivially simple as you can see from the code below:

package app

import javafx.stage.Stage
import tornadofx.*
import view.MainView

class MyApp: App(MainView::class, Styles::class) {
    override fun start(stage: Stage) {
        with(stage) {
            width = 1000.0
            height = 600.0
        }
        super.start(stage)
    }
}

Let’s review what happens here.

  1. The Application is instantiated along with the View and Styles classes.
  2. We set the size of the stage (=application window) and start the UI Thread.
  3. The View instantiates the ViewController, which in turn instantiates a copy of the Model and the Simulator.

At that point all the actors are on stage, so to speak, and the application is ready for user input. In the short video below I show how the app is used.

Conclusions

Kotlin is a perfect tool for dynamic simulations because it multi-platform (by virtue of running on the JVM) and fast. TornadoFX, a domain specific language written in Kotlin for use with JavaFX, is also quite attractive in constructing a user interface quickly and with minimal code.

References

  1. W. E. Schiesser, Computational Mathematics in Engineering and Applied Science, CRC Press, 1994.
  2. W. E. Schiesser, Spline Collocation Methods for Partial Differential Equations, John Wiley & Sons, 2017.
  3. K. Sharan and P. Späth, Learn JavaFX 17 2nd ed., Apress Media LLC, 2022.
  4. M. Moskala, Kotlin Coroutines, Kt. Academy, 2022
Categories
Distillation control Dynamic Modeling Kotlin Model-View-Controller Process Control

A Column Simulation Model

Introduction

In my previous post I introduced the use of the build system Gradle and showed how it can be used to build Kotlin applications. As an example, I created a new project, “ColumnSimulation”, aimed at simulating a distillation column with a realistic control system. The column with its controls are shown in the picture below.

Binary distillation column separating methanol and water.

This is a conventional distillation column separating a 50/50 mixture of methanol and water. It has a total of 40 trays with 75% tray efficiency. Feed enters on tray 6 and the temperature on tray 3 is measured and controlled.

The system has 7 controllers where two are operated in a cascade arrangement (the Tray TC and the Vapor FC).

Object-Oriented Modeling

I use an object-oriented approach to modeling in order to retain maximum flexibility and code reusability. Thus, all units you see in the picture are represented by software classes stored in my SyMods library. In other words, the tray section, the reboiler, the condenser, the feed system, and the controllers are all units that can be configured for the application at hand. I’ve even combined the tray section, the reboiler and the condenser into a composite class called a “ColumnWtotalCondenser”. This saves me a bit of configuration effort every time I need a column of that type.

Given that I have all the pieces to the simulation pre-made, what remains to be done? I need to instantiate the classes into objects, configure them and make the connections corresponding to the process diagram. During this effort it is useful to do further grouping such as collecting all the controllers into another composite class called DCS (short for distributed control system). Notice that I use the Builder pattern to configure my controllers. There are other ways of doing this in Kotlin but the builder pattern is generic and works well in situations with many parameters. Also please note that the code type says “Swift” and not Kotlin. At this point Kotlin was not an option and Swift is sufficiently close in its syntax not to confuse the keywords of Kotlin too much.

class DCS: DCSUnit() {
    val feedFlowController = PIDController.Builder().
        gain(0.2).
        resetTime(0.002).
        directActing(false).
        pvMax(3000.0).
        sp(1634.0).
        output(0.25).
        build()
    val trayTemperatureController = PIDController.Builder().
        gain(0.75).
        resetTime(0.3).
        analyzerTime(0.025).
        pvMax(150.0).
        sp(92.0).
        directActing(false).
        output(0.5).
        build()
    val boilupFlowController = PIDController.Builder().
        gain(0.2).
        resetTime(0.01).
        analyzerTime(0.0).
        pvMax(2000.0).
        sp(1319.0).
        directActing(false).
        output(0.33).
        build()
    val reboilerLevelController = PIDController.Builder().
        resetTime(0.5).
        output(0.5).
        build()
    val condenserLevelController = PIDController.Builder().
        resetTime(0.5).
        pvMax(110.0).
        output(0.25).
        build()
    val condenserPressureController = PIDController.Builder().
        resetTime(0.1).
        output(0.5).
        pvMax(2.0).
        sp(1.0).
        build()
    val refluxFlowController = PIDController.Builder().
        gain(0.2).
        resetTime(0.002).
        analyzerTime(0.0).
        directActing(false).
        pvMax(3200.0).
        sp(831.0).
        output(0.25).
        build()
    init {
        with(controllers) {
            add(feedFlowController)
            add(trayTemperatureController)
            add(boilupFlowController)
            add(reboilerLevelController)
            add(condenserLevelController)
            add(condenserPressureController)
            add(refluxFlowController)
        }
    }
}

This took care of the control system setup. Next I configure the rest of the process by creating two reference fluid objects and instantiating the two process objects (Feeder and Column). The so-called reference fluids (refVapor and refLiq) are made in two steps. The first step is to instantiate a local dictionary object, factory, from a component file I’ve created using publicly available databases. In the second step I call a member function on the factory object with the names of the components I wish to include. The function searches a hard coded dictionary of Wilson activity parameters and creates an ideal vapor phase and a non-ideal liquid phase. These fluids are used as templates in all objects that require them. Finally, I connect the controllers to the process. All of that is part of the model class below.

class ProcessModel(var dcsUnit: DCS) {
    val ode = ODEManager()
    val factory = FluidFactoryFrom("/Users/bjorntyreus/component_file2.csv")
    val vl = factory.makeFluidsFromComponentList(listOf("Methanol", "Water"))
    val refVapor = vl?.vapor ?: throw IllegalStateException("Did not get a vapor")
    val refLiq = vl?.liquid ?: throw IllegalStateException("Did not get a liquid")

    val feed = Feeder(identifier = "Feed",
        composition = listOf(0.5, 0.5),
        initialFlow = 1600.0,
        minFlow = 0.0,
        maxFlow = 2000.0,
        operatingTemperature = 100.0,
        maxTemperature = 100.0,
        operatingPressure = 1.2,
        maxPressure = 3.0,
        refVapor = refVapor,
        refLiquid = refLiq)
    val column = ColumnWtotalCondenser(identifier = "column",
        numberOfTrays = numberOfTrays,
        feedRate = 1600.0,
        distillateRate = 800.0,
        refluxRatio = 1.0,
        topPressure = 1.0,
        trayDP = 0.005,
        trayEfficiency = 0.75,
        coolantInletTemperature = 25.0,
        trayDiameter = 3.0,
        lightKey = "Methanol",
        heavyKey = "Water",
        refVapor = refVapor,
        refLiq = refLiq)
    init {
        with(ode.units) {
            add(feed)
            add(column)
            add(dcsUnit)
        }
        column.trays[feedTrayLocation].liquidFeed = feed.liquidOutlet

        with(dcsUnit) {
            trayTemperatureController.pvSignal = column.trays[temperatureTrayLocation].temperatureTT
            trayTemperatureController.outSignal = boilupFlowController.exSpSignal
            trayTemperatureController.efSignal = boilupFlowController.normPvSignal
            boilupFlowController.slave = true

            boilupFlowController.pvSignal = column.reboiler.vaporBoilupFT
            boilupFlowController.outSignal = column.reboiler.heatInputAC
            boilupFlowController.efSignal = column.reboiler.heatInputAC
            column.reboiler.heatInputAC.useProcessInput = false

            reboilerLevelController.pvSignal = column.reboiler.levelLT
            reboilerLevelController.outSignal = column.reboiler.outletValveAC
            reboilerLevelController.efSignal = column.reboiler.outletValveAC
            column.reboiler.outletValveAC.useProcessInput = false

            feedFlowController.pvSignal = feed.feedRateFT
            feedFlowController.outSignal = feed.feedValveAC
            feedFlowController.efSignal = feed.feedValveAC
            feed.feedValveAC.useProcessInput = false

            condenserLevelController.pvSignal = column.condenser.levelLT
            condenserLevelController.outSignal = column.condenser.outletValveBAC
            condenserLevelController.efSignal = column.condenser.outletValveBAC
            column.condenser.outletValveBAC.useProcessInput = false

            condenserPressureController.pvSignal = column.condenser.pressurePT
            condenserPressureController.outSignal = column.condenser.coolantValveAC
            condenserPressureController.efSignal = column.condenser.coolantValveAC
            column.condenser.coolantValveAC.useProcessInput = false

            refluxFlowController.pvSignal = column.condenser.liquidOutletAFT
            refluxFlowController.outSignal = column.condenser.outletValveAAC
            refluxFlowController.efSignal = column.condenser.outletValveAAC
            column.condenser.outletValveAAC.useProcessInput = false
        }

    }
}

Notice how each controller connection requires four actions: 1) The controlled signal needs to be connected (pvSignal). 2) The output from the controller needs to be connected (outSignal). 3) The external feedback signal is then connected (efSignal). Often this signal is the same as the final control element except in cascade arrangements. 4) We have to make sure that the final control element responds to the attached control signal as opposed to retaining whatever process value that is given to it (e.g. during initialization).

We now have a process with its control system attached. Time to subject these to the integration system, prepare for data collection and design a test suite. This is done in the columnSimulation function below. Notice in particular how transparent it is to specify the timing for various tests by using Kotlin’s when expression in conjunction with ranges. It should be pretty clear from the code that during the span of 16 hours we are subjecting the process to the following changes:

  • Boilup controller switching from Auto to Cascade
  • Tray TC switching from Auto to Manual
  • ATV test on Tray TC
  • Tray TC back to Auto
  • Tray TC setpoint change 92 -> 85 oC
  • Applied results from ATV test and changed setpoint back to 92 oC
  • Feed composition change from 50/50 to 40/60 methanol/water
  • Feed flow increase by roughly 10%
fun columnSimulation(discr: DiscretizationModel, control: StepSizeControlModel): List<Plot> {
    // Prepare process for integration
    val dcsUnit = DCS()
    val model = ProcessModel(dcsUnit)
    val ode = model.ode
    
    // Instantiate, configure and start integrator
    val ig = IntegrationServer(discr, control)
    val dim = ode.dimension()
    val x = DoubleArray(dim)
    val endTime = 16.0
    ig.ode = ode
    ig.initialStepSize = 1.0e-3
    val reportingInterval = 0.05
    val dt = reportingInterval / 2.0
    var localTime = 0.0
    var reportTimer = 0.0
    ig.startTime = 0.0
    ig.start(ode.initialConditionsUsingArray(x))
    
    // Create lists to hold the dynamic data from a run
    val timeList = mutableListOf<Double>()
    val tempList = mutableListOf<Double>()
    val pressureList = mutableListOf<Double>()
    val tcOutList = mutableListOf<Double>()
    val boilupList = mutableListOf<Double>()
    val reboilLevelList = mutableListOf<Double>()
    val condenserLevelList = mutableListOf<Double>()
    val h20OHList = mutableListOf<Double>()
    val meohBtmsList = mutableListOf<Double>()
    val btmsFlowList = mutableListOf<Double>()
    val distList = mutableListOf<Double>()
    val feedRateList = mutableListOf<Double>()
    val feedCmpList = mutableListOf<Double>()
    val plotList = mutableListOf<Plot>()
    var atvGain = dcsUnit.trayTemperatureController.gainATV
    var atvReset = dcsUnit.trayTemperatureController.resetTimeATV
    var reductFactor = dcsUnit.trayTemperatureController.resetReductionFactor

    // Simulate and collect data
    while (localTime <= endTime) {
        localTime = ig.currentTime
        ig.startTime = localTime
        ig.endTime = localTime + dt
        ig.continueCalculations()
        localTime = ig.currentTime
        reportTimer += dt
        if (reportTimer > reportingInterval) {
            reportTimer = 0.0
            //println("time= $localTime, Tank temp = ${model.tank.tankTemperatureTT.processValue}")
            timeList.add(localTime)
            tempList.add(model.column.trays[temperatureTrayLocation].temperatureTT.processValue)
            pressureList.add(model.column.condenser.pressurePT.processValue)
            val tcOut = model.dcsUnit.trayTemperatureController.outSignal?.signalValue ?: 0.0
            tcOutList.add(tcOut * 100.0)
            boilupList.add(model.column.reboiler.vaporBoilupFT.processValue)
            reboilLevelList.add(model.column.reboiler.levelLT.processValue)
            condenserLevelList.add(model.column.condenser.levelLT.processValue)
            h20OHList.add(model.column.condenser.liquidHoldup.weightFractions[1] * 1.0e6)
            meohBtmsList.add(model.column.reboiler.reboilerHoldup.weightFractions[0] * 1.0e6)
            btmsFlowList.add(model.column.reboiler.outletFlowFT.processValue)
            distList.add(model.column.condenser.liquidOutletBFT.processValue)
            feedRateList.add(model.feed.feedRateFT.processValue)
            feedCmpList.add(model.feed.feedComposition[0] * 100.0)

            // Perform test on the system at specified time points
            val wholeHours = localTime.toInt()
            with (dcsUnit) {
                when (wholeHours) {
                    in 1..3 -> boilupFlowController.controllerMode = ControlMode.cascade
                    in 3..4 -> {
                        trayTemperatureController.controllerMode = ControlMode.manual
                        trayTemperatureController.output = 0.92
                    }
                    in 4..6 -> {
                        trayTemperatureController.h = 0.10
                        trayTemperatureController.controllerMode = ControlMode.autoTune
                        atvGain = trayTemperatureController.gainATV
                        atvReset = trayTemperatureController.resetTimeATV
                        reductFactor = trayTemperatureController.resetReductionFactor
                    }
                    in 6..7 -> {
                        trayTemperatureController.controllerMode = ControlMode.automatic
                        trayTemperatureController.sp = 92.0
                    }
                    in 7..8 -> {
                        trayTemperatureController.controllerMode = ControlMode.automatic
                        trayTemperatureController.sp = 85.0
                    }
                    in 8..9 -> {
                        trayTemperatureController.gain = atvGain / 2.0
                        trayTemperatureController.resetTime = atvReset
                        trayTemperatureController.sp = 92.0
                    }
                    in 10..12 -> {
                        model.feed.currentComposition = listOf(0.4, 0.6)
                    }
                    in 12..14 -> feedFlowController.sp = 1800.0
                }
            }
        }
    }

The actual start of the program is trivially simple. In the main function I call the columnSimulation function and get a list of plots back. Six of these I display in one figure and the other six go to the second figure. The whole operation of simulating the 40 tray column for 16 hours takes 1.6 seconds on a 2014 vintage MacBook Pro. Kotlin is fast!

fun main(args: Array<String>) {
    val timeInMillis = measureTimeMillis {

        val plotGroup = columnSimulation(DiscretizationModel.ModifiedEuler, StepSizeControlModel.FixedStepController)

        val group1 = plotGroup.take(6)
        val group2 = plotGroup.drop(6)
        gggrid(group1, ncol = 2, cellWidth = 470, cellHeight = 300).show()
        gggrid(group2, ncol = 2, cellWidth = 470, cellHeight = 300).show()

    }
    println("(The operation took $timeInMillis ms)")
}

Below I show the results of the simulation run described in the code.

Performance of control system for the 40 tray column. Pay particular attention to the Tray Temperature Controller behavior (upper left). It is activated (cascade with Boilup) after 1 hour of operation but responds slowly due to poor tuning. After the ATV test the old tuning parameters remain for one setpoint change (at hour 7). The new tuning parameters are set at hour 8 just before a final setpoint change to 92 oC. After that both feed composition and feed rate change in steps of 10%. Temperature is held close to setpoint in the face of these disturbances.
This figure shows how the important composition variables behave in the face of temperature setpoint changes and external disturbances. Notice that the ATV test itself causes only minor deviations in the compositions. The control system is also quite robust against feed rate and composition changes.

MVC

An important concept in software engineering is the separation of a Model from its View and the software Controller used to manipulate both the view and the model. The Model-View-Controller (MVC) concept is important because it enables software reuse, provides flexibility in the choice of views and controllers and it facilitates trouble shooting and debugging.

While this post is primarily aimed at demonstrating modeling with Kotlin and Let’s plot, it also provides me with an opportunity to dwell a bit on MVC.

In the example above it should be clear that the model in my MVC is the class “ProcessModel”. It consists of the column, the feeder and the feedback control system. But the model does nothing by itself, it needs to be driven by an integrator and be told about changes to its environment. That’s the job of the controller.

Furthermore, the model has no built-in display capabilities or views. The reason is that you should be able to choose the view independently from the model. Only the controller will know about the view and will be feeding it with information from the model.

In my example the function columnSimulation(…) is the controller. It owns the model and the integrator and knows how to collect information to feed the plotting program Let’s plot. But we could have chosen another method to display the result. For example, the controller could have exported data to a text file that could have been used to display graphs in Excel. I have used that method many times.

To further drive home the flexibility of a well designed MVC I share an example simulation of the same distillation column on an iPad. Here the model is the same as above but implemented in Swift instead of Kotlin. However, the views and controllers are quite different. Instead of collecting data for static plots I update strip charts live as the simulation progresses. I also provide views and dedicated controllers for the PID controllers so the user can interact with them and provide tuning parameters while the simulation is running. This mode of operation is called interactive dynamic simulation and mimics running a real plant.

I’m currently exploring a user interface system (controllers and views) called TornadoFX. It has a set of Kotlin API’s for user interfaces and is built upon a well established UI system called JavaFX. I’m hoping to report progress on my findings in a future post.

Categories
Dynamic Modeling Kotlin Modeling Languages

Kotlin and Gradle

Introduction

As I mentioned in my previous post, my new favorite programming language is Kotlin. I particularly like it because it has much of Python’s flexibility but the speed of Java, an awesome combination. I’ve done a few execution speed comparisons and find that for dynamic simulations of my chemical engineering models, Kotlin is 10-15 times faster than Python.

Now, execution speed is not everything. Python’s ease of use and rich library of readily available packages account for a great deal of this language’s popularity. I described in a previous blog post how one can create virtual environments and use pip to safely download packages and manage their dependencies. This is a big deal and a huge advantage for Python. In particular the numerical package numpy and the plotting package matplotlib are hard to beat.

So the purpose of today’s post is to ask what are the Kotlin equivalents to virtual environments, pip, numpy and matplotlib? The short answer is Gradle and Lets-Plot. I elaborate below.

Gradle

Gradle is an open-source build automation tool (https://gradle.org). You can download Gradle separately and use it to build almost any software project. Personally I use the plug-in provided in JetBrains IntelliJ IDEA tool. Since it took me a bit of research and tinkering before I figured out how to use Gradle, I decided to share my findings here and perhaps help others who are new to Kotlin and Gradle.

The first step in the process is to create a new Gradle project from IntelliJ. This looks as follows:

The New Project window in IntelliJ IDEA. Make note of all the selected and checked fields

The next step is to give the project a name. I call this ColumnSimulation since I will be constructing a dynamic simulation of a distillation column with PID controllers.

After clicking “Finish” I have a ready-made Gradle project that I can start populating with source code. But before I do that I’d like to link this new project to another Gradle project where I have most of my reusable process and instrument models. This other project I’ve named SyMods. This is how I link the two together.

First click on the little icon at the bottom left corner of the IntelliJ IDE. From the pop-up, select Gradle as in the picture below.

Pop-up window from clicking the lower left icon on IntelliJ IDEA.

This opens the Gradle window on the right hand side of the IDE. The ‘+’ sign at the top of the Gradle window allows you to add another Gradle project to be linked with the first. By selecting the “build.gradle.kts” within the SyMods project, I can now add this project as a companion project to my newly created ColumnSimulation project.

Find the second Gradle project in the file system and click on the build.gradle.kts file to include it.

Both projects then show up in the Gradle window. By right-clicking on the ColumnSimulation project I can tell the build system that I want a “Composite Build Configuration”. Both projects are then built together.

Gradle window showing two projects. Right-click the first and select Composite Build

I close the Gradle window and focus on the Project window on the left side of the IDE. It looks like the picture below where I have the “build.gradle.kts” file open for the ColumnSimulation project. I now add some dependencies particularly for plotting.

Gradle window closed and focus is on the two projects.

Lets-Plot and Other Dependencies

One of the beauties of Gradle is that it manages external libraries and dependencies for you. All you have to do is find the URL to the particular library you want to include and add this to the dependency section of the build.gradle.kts file. Below I show how I have added the appropriate links for JetBrains’ Lets-plot library. I also added a library for working with csv files and finally told the ColumnSimulation project that I will be importing models from my own project SyMods (that I previously linked and will be built along with my ColumnSimulation project).

Dependencies added to the gradle.build file. Notice the little Gradle icon in the upper right corner of this picture. To update the build configuration, this icon should be clicked after changes have been made to the build file.

We are now ready to write some application code. Notice that by having my “library” project, SyMods, available as a linked project I can make changes in the library as if I were working on it separately. This is very useful since I often discover some features in the application that could be reused and thus belong in the library.

Summary

Kotlin has proven to be an effective language in writing dynamic simulation models. To manage projects with Kotlin and to provide external libraries and dependencies, Gradle is the preferred tool. I have shown how to make a Gradle project, link it to other projects and include external dependencies for reading csv-files and plotting.

Categories
Dynamic Modeling

Integrators for Simulation

Dynamic simulations have long been of great interest to me. Not for their own sake but to help solve real business problems. There are many components required for a complete and interactive process simulation. One important ingredient is the method by which the differential equations are integrated. In the imbedded ‘Jupyter’ notebook below I share my experience of what works along with some code and one simple example.