OMNotebook with DrModelica and DrControl

This chapter covers the OpenModelica electronic notebook subsystem, called OMNotebook, together with the DrModelica tutoring system for teaching Modelica, and DrControl for teaching control together with Modelica. Both are using such notebooks.

Interactive Notebooks with Literate Programming

Interactive Electronic Notebooks are active documents that may contain technical computations and text, as well as graphics. Hence, these documents are suitable to be used for teaching and experimentation, simulation scripting, model documentation and storage, etc.

Mathematica Notebooks

Literate Programming [Knu84] is a form of programming where programs are integrated with documentation in the same document. Mathematica notebooks [Wol96] is one of the first WYSIWYG systems that support Literate Programming. Such notebooks are used, e.g., in the MathModelica modeling and simulation environment, see e.g. Figure 56 below and Chapter 19 in [Fri04].

OMNotebook

The OMNotebook software [Axe05][Fernstrom06] is a new open source free software that gives an interactive WYSIWYG realization of Literate Programming, a form of programming where programs are integrated with documentation in the same document.

The OMNotebook facility is actually an interactive WYSIWYG realization of Literate Programming, a form of programming where programs are integrated with documentation in the same document. OMNotebook is a simple open-source software tool for an electronic notebook supporting Modelica.

A more advanced electronic notebook tool, also supporting mathematical typesetting and many other facilities, is provided by Mathematica notebooks in the MathModelica environment, see Figure 56.

_images/mathematica-notebooks.svg

Figure 56 Examples of Mathematica notebooks in the MathModelica modeling and simulation environment.

Traditional documents, e.g. books and reports, essentially always have a hierarchical structure. They are divided into sections, subsections, paragraphs, etc. Both the document itself and its sections usually have headings as labels for easier navigation. This kind of structure is also reflected in electronic notebooks. Every notebook corresponds to one document (one file) and contains a tree structure of cells. A cell can have different kinds of contents, and can even contain other cells. The notebook hierarchy of cells thus reflects the hierarchy of sections and subsections in a traditional document such as a book.

DrModelica Tutoring System – an Application of OMNotebook

Understanding programs is hard, especially code written by someone else. For educational purposes it is essential to be able to show the source code and to give an explanation of it at the same time.

Moreover, it is important to show the result of the source code’s execution. In modeling and simulation it is also important to have the source code, the documentation about the source code, the execution results of the simulation model, and the documentation of the simulation results in the same document. The reason is that the problem solving process in computational simulation is an iterative process that often requires a modification of the original mathematical model and its software implementation after the interpretation and validation of the computed results corresponding to an initial model.

Most of the environments associated with equation-based modeling languages focus more on providing efficient numerical algorithms rather than giving attention to the aspects that should facilitate the learning and teaching of the language. There is a need for an environment facilitating the learning and understanding of Modelica. These are the reasons for developing the DrModelica teaching material for Modelica and for teaching modeling and simulation.

An earlier version of DrModelica was developed using the MathModelica (now Wolfram SystemModeler) environment. The rest of this chapter is concerned with the OMNotebook version of DrModelica and on the OMNotebook tool itself.

DrModelica has a hierarchical structure represented as notebooks. The front-page notebook is similar to a table of contents that holds all other notebooks together by providing links to them. This particular notebook is the first page the user will see (Figure 57).

_images/omnotebook-drmodelica.png

Figure 57 The front-page notebook of the OMNotebook version of the DrModelica tutoring system.

In each chapter of DrModelica the user is presented a short summary of the corresponding chapter of the Modelica book [Fri04]. The summary introduces some keywords, being hyperlinks that will lead the user to other notebooks describing the keywords in detail.

_images/omnotebook-helloworld.png

Figure 58 The HelloWorld class simulated and plotted using the OMNotebook version of DrModelica.

Now, let us consider that the link “HelloWorld” in DrModelica Section is clicked by the user. The new HelloWorld notebook (see Figure 58), to which the user is being linked, is not only a textual description but also contains one or more examples explaining the specific keyword. In this class, HelloWorld, a differential equation is specified.

No information in a notebook is fixed, which implies that the user can add, change, or remove anything in a notebook. Alternatively, the user can create an entirely new notebook in order to write his/her own programs or copy examples from other notebooks. This new notebook can be linked from existing notebooks.

_images/omnotebook-drmodelica-ch9.png

Figure 59 DrModelica Chapter on Algorithms and Functions in the main page of the OMNotebook version of DrModelica.

When a class has been successfully evaluated the user can simulate and plot the result, as previously depicted in Figure 58 for the simple HelloWorld example model.

After reading a chapter in DrModelica the user can immediately practice the newly acquired information by doing the exercises that concern the specific chapter. Exercises have been written in order to elucidate language constructs step by step based on the pedagogical assumption that a student learns better “using the strategy of learning by doing”. The exercises consist of either theoretical questions or practical programming assignments. All exercises provide answers in order to give the user immediate feedback.

Figure 59 shows part of Chapter 9 of the DrModelica teaching material. Here the user can read about language constructs, like algorithm sections, when-statements, and reinit equations, and then practice these constructs by solving the exercises corresponding to the recently studied section.

_images/omnotebook-drmodelica-ex1.png

Figure 60 Exercise 1 in Chapter 9 of DrModelica.

Exercise 1 from Chapter 9 is shown in Figure 60. In this exercise the user has the opportunity to practice different language constructs and then compare the solution to the answer for the exercise. Notice that the answer is not visible until the Answer section is expanded. The answer is shown in Figure 61.

_images/omnotebook-drmodelica-ex1-answer.png

Figure 61 The answer section to Exercise 1 in Chapter 9 of DrModelica.

DrControl Tutorial for Teaching Control Theory

DrControl is an interactive OMNotebook document aimed at teaching control theory. It is included in the OpenModelica distribution and appears under the directory:

>>> getInstallationDirectoryPath() + "/share/omnotebook/drcontrol"
"«OPENMODELICAHOME»/share/omnotebook/drcontrol"

The front-page of DrControl resembles a linked table of content that can be used as a navigation center. The content list contains topics like:

  • Getting started

  • The control problem in ordinary life

  • Feedback loop

  • Mathematical modeling

  • Transfer function

  • Stability

  • Example of controlling a DC-motor

  • Feedforward compensation

  • State-space form

  • State observation

  • Closed loop control system.

  • Reconstructed system

  • Linear quadratic optimization

  • Linearization

Each entry in this list leads to a new notebook page where either the theory is explained with Modelica examples or an exercise with a solution is provided to illustrate the background theory. Below we show a few sections of DrControl.

Feedback Loop

One of the basic concepts of control theory is using feedback loops either for neutralizing the disturbances from the surroundings or a desire for a smoother output.

In Figure 62, control of a simple car model is illustrated where the car velocity on a road is controlled, first with an open loop control, and then compared to a closed loop system with a feedback loop. The car has a mass m, velocity y, and aerodynamic coefficient α. The θ is the road slope, which in this case can be regarded as noise.

_images/omnotebook-feedback.png

Figure 62 Feedback loop.

Lets look at the Modelica model for the open loop controlled car:

m \dot y = u - \alpha y - m g * sin(\theta)

model noFeedback
  import SI = Modelica.SIunits;
  SI.Velocity y;                              // output signal without noise, theta = 0 -> v(t) = 0
  SI.Velocity yNoise;                         // output signal with noise,    theta <> 0 -> v(t) <> 0
  parameter SI.Mass m = 1500;
  parameter Real alpha = 200;
  parameter SI.Angle theta = 5*3.141592/180;
  parameter SI.Acceleration g = 9.82;
  SI.Force u;
  SI.Velocity r=20;
equation
  m*der(y)=u-alpha*y;                          // signal without noise
  m*der(yNoise)=u-alpha*yNoise-m*g*sin(theta); // with noise
  u = 250*r;
end noFeedback;

By applying a road slope angle different from zero the car velocity is influenced which can be regarded as noise in this model. The output signal in omnotebook-open-loop is stable but an overshoot can be observed compared to the reference signal. Naturally the overshoot is not desired and the student will in the next exercise learn how to get rid of this undesired behavior of the system.

>>> loadModel(Modelica)
false
>>> simulate(noFeedback, stopTime=100)
record SimulationResult
    resultFile = "",
    simulationOptions = "startTime = 0.0, stopTime = 100.0, numberOfIntervals = 500, tolerance = 1e-06, method = 'dassl', fileNamePrefix = 'noFeedback', options = '', outputFormat = 'mat', variableFilter = '.*', cflags = '', simflags = ''",
    messages = "Failed to build model: noFeedback",
    timeFrontend = 0.010830817,
    timeBackend = 0.0,
    timeSimCode = 0.0,
    timeTemplates = 0.0,
    timeCompile = 0.0,
    timeSimulation = 0.0,
    timeTotal = 0.010872154
end SimulationResult;

Error

[<interactive>:3:3-3:16:writable] Error: Class SI.Velocity not found in scope noFeedback.

Error: Error occurred while flattening model noFeedback

Error

Unable to execute gnuplot directive

Expected {quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]}) | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")}) | Group:({Suppress:("{") [Forward: None [, Forward: None]...] Suppress:("}")}) | Group:({Suppress:("(") [Forward: None [, Forward: None]...] Suppress:(")")}) | {Suppress:("SOME") Suppress:("(") Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]})} | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")})} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})} Suppress:(")")} | "true" | "false" | {"NONE" Suppress:("(") Suppress:(")")} | Combine:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} (at char 1), (line:2, col:1) Traceback (most recent call last): File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3235, in parseImpl result = instring[loc] == self.firstQuoteChar and self.re.match(instring,loc) or None IndexError: string index out of range During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/var/lib/jenkins/ws/OpenModelica_beta1/doc/UsersGuide/source/sphinxcontribopenmodelica.py", line 173, in run filename = os.path.abspath(self.options.get('filename') or omc.sendExpression("currentSimulationResult")) File "/usr/local/lib/python3.6/dist-packages/OMPython/__init__.py", line 606, in sendExpression answer = OMTypedParser.parseString(result) File "/usr/local/lib/python3.6/dist-packages/OMPython/OMTypedParser.py", line 120, in parseString return omcGrammar.parseString(string)[0] File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1828, in parseString raise exc File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1818, in parseString loc, tokens = self._parse( instring, 0 ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3735, in parseImpl loc, resultlist = self.exprs[0]._parse( instring, loc, doActions, callPreParse=False ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 4098, in parseImpl return self.expr._parse( instring, loc, doActions, callPreParse=False ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3917, in parseImpl raise maxException File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3902, in parseImpl ret = e._parse( instring, loc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1564, in _parseNoCache raise ParseException( instring, len(instring), self.errmsg, self ) pyparsing.ParseException: Expected {quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]}) | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")}) | Group:({Suppress:("{") [Forward: None [, Forward: None]...] Suppress:("}")}) | Group:({Suppress:("(") [Forward: None [, Forward: None]...] Suppress:(")")}) | {Suppress:("SOME") Suppress:("(") Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]})} | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")})} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})} Suppress:(")")} | "true" | "false" | {"NONE" Suppress:("(") Suppress:(")")} | Combine:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} (at char 1), (line:2, col:1)

The closed car model with a proportional regulator is shown below:

u = K*(r-y)

model withFeedback
  import SI = Modelica.SIunits;
  SI.Velocity y;                                // output signal with feedback link and without noise, theta = 0 -> v(t) = 0
  SI.Velocity yNoise;                           // output signal with feedback link and noise,    theta <> 0 -> v(t) <> 0
  parameter SI.Mass m = 1500;
  parameter Real alpha = 250;
  parameter SI.Angle theta = 5*3.141592/180;
  parameter SI.Acceleration g = 9.82;
  SI.Force u;
  SI.Force uNoise;
  SI.Velocity r=20;
equation
  m*der(y)=u-alpha*y;
  m*der(yNoise)=uNoise-alpha*yNoise-m*g*sin(theta);
  u = 5000*(r-y);
  uNoise = 5000*(r-yNoise);
end withFeedback;

Error

[<interactive>:1:1-1:0:writable] Error: Variable currentSimulationResult not found in scope <global scope>.

By using the information about the current level of the output signal and re-tune the regulator the output quantity can be controlled towards the reference signal smoothly and without an overshoot, as shown in omnotebook-closed-loop.

In the above simple example the flat modeling approach was adopted since it was the fastest one to quickly obtain a working model. However, one could use the object oriented approach and encapsulate the car and regulator models in separate classes with the Modelica connector mechanism in between.

>>> loadModel(Modelica)
false
>>> simulate(withFeedback, stopTime=10)
record SimulationResult
    resultFile = "",
    simulationOptions = "startTime = 0.0, stopTime = 10.0, numberOfIntervals = 500, tolerance = 1e-06, method = 'dassl', fileNamePrefix = 'withFeedback', options = '', outputFormat = 'mat', variableFilter = '.*', cflags = '', simflags = ''",
    messages = "Failed to build model: withFeedback",
    timeFrontend = 0.009166772,
    timeBackend = 0.0,
    timeSimCode = 0.0,
    timeTemplates = 0.0,
    timeCompile = 0.0,
    timeSimulation = 0.0,
    timeTotal = 0.009181029
end SimulationResult;

Error

[<interactive>:3:3-3:16:writable] Error: Class SI.Velocity not found in scope withFeedback.

Error: Error occurred while flattening model withFeedback

Error

Unable to execute gnuplot directive

Expected {quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]}) | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")}) | Group:({Suppress:("{") [Forward: None [, Forward: None]...] Suppress:("}")}) | Group:({Suppress:("(") [Forward: None [, Forward: None]...] Suppress:(")")}) | {Suppress:("SOME") Suppress:("(") Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]})} | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")})} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})} Suppress:(")")} | "true" | "false" | {"NONE" Suppress:("(") Suppress:(")")} | Combine:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} (at char 1), (line:2, col:1) Traceback (most recent call last): File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3235, in parseImpl result = instring[loc] == self.firstQuoteChar and self.re.match(instring,loc) or None IndexError: string index out of range During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/var/lib/jenkins/ws/OpenModelica_beta1/doc/UsersGuide/source/sphinxcontribopenmodelica.py", line 173, in run filename = os.path.abspath(self.options.get('filename') or omc.sendExpression("currentSimulationResult")) File "/usr/local/lib/python3.6/dist-packages/OMPython/__init__.py", line 606, in sendExpression answer = OMTypedParser.parseString(result) File "/usr/local/lib/python3.6/dist-packages/OMPython/OMTypedParser.py", line 120, in parseString return omcGrammar.parseString(string)[0] File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1828, in parseString raise exc File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1818, in parseString loc, tokens = self._parse( instring, 0 ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3735, in parseImpl loc, resultlist = self.exprs[0]._parse( instring, loc, doActions, callPreParse=False ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 4098, in parseImpl return self.expr._parse( instring, loc, doActions, callPreParse=False ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1562, in _parseNoCache loc,tokens = self.parseImpl( instring, preloc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3917, in parseImpl raise maxException File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 3902, in parseImpl ret = e._parse( instring, loc, doActions ) File "/usr/local/lib/python3.6/dist-packages/pyparsing.py", line 1564, in _parseNoCache raise ParseException( instring, len(instring), self.errmsg, self ) pyparsing.ParseException: Expected {quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]}) | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")}) | Group:({Suppress:("{") [Forward: None [, Forward: None]...] Suppress:("}")}) | Group:({Suppress:("(") [Forward: None [, Forward: None]...] Suppress:(")")}) | {Suppress:("SOME") Suppress:("(") Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({["-"] {"0" | W:(1234...,0123...)} [{"." W:(0123...)}] [{W:(eE) W:(0123...,0123...)}]})} | Forward: Group:({{{{{Suppress:("record") Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Dict:(Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}}) [, Group:({{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} Suppress:("=")} Forward: {{{{{{{{{quoted string, starting with " ending with " | Combine:({{{["-"] {"0" | W:(1234...,0123...)}} [{"." W:(0123...)}]} [{W:(eE) W:(0123...,0123...)}]})} | Forward: None} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})}})]...)} Suppress:("end")} Suppress:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} Suppress:(";")})} | Group:({{Suppress:("{") [Forward: None [, Forward: None]...]} Suppress:("}")})} | Group:({{Suppress:("(") [Forward: None [, Forward: None]...]} Suppress:(")")})} | {{{Suppress:("SOME") Suppress:("(")} Forward: ...} Suppress:(")")}} | "true"} | "false"} | {{"NONE" Suppress:("(")} Suppress:(")")}} | Combine:(Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: {{{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "."} Forward: ...} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}}} | {W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '}})} Suppress:(")")} | "true" | "false" | {"NONE" Suppress:("(") Suppress:(")")} | Combine:(Forward: {{{W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '} "." Forward: ...} | W:(ABCD...,ABCD...) | quoted string, starting with ' ending with '})} (at char 1), (line:2, col:1)

Mathematical Modeling with Characteristic Equations

In most systems the relation between the inputs and outputs can be described by a linear differential equation. Tearing apart the solution of the differential equation into homogenous and particular parts is an important technique taught to the students in engineering courses, also illustrated in Figure 63.

{{\partial ^{n}y}\over{\partial t^n}} + a_1 {{\partial ^{n-1}y}\over{\partial t^{n-1}}} + \ldots + a_n y = b_0 {{\partial ^{m}u} \over {\partial t^m}} + \ldots + b_{m-1} {{\partial u}\over{\partial t}} + b_m u

Now let us examine a second order system:

\ddot y + a_1 \dot y + a_2 y = 1

model NegRoots
  Real y;
  Real der_y;
  parameter Real a1 = 3;
  parameter Real a2 = 2;
equation
  der_y = der(y);
  der(der_y) + a1*der_y + a2*y = 1;
end NegRoots;

Error

[<interactive>:1:1-1:0:writable] Error: Variable currentSimulationResult not found in scope <global scope>.

Choosing different values for a1 and a2 leads to different behavior as shown in Figure 64 and Figure 65.

_images/omnotebook-mathematical-modeling-with-characteristic-equation.png

Figure 63 Mathematical modeling with characteristic equation.

In the first example the values of a1 and a2 are chosen in such way that the characteristic equation has negative real roots and thereby a stable output response, see Figure 64.

>>> simulate(NegRoots, stopTime=10)
record SimulationResult
    resultFile = "«DOCHOME»/NegRoots_res.mat",
    simulationOptions = "startTime = 0.0, stopTime = 10.0, numberOfIntervals = 500, tolerance = 1e-06, method = 'dassl', fileNamePrefix = 'NegRoots', options = '', outputFormat = 'mat', variableFilter = '.*', cflags = '', simflags = ''",
    messages = "LOG_SUCCESS       | info    | The initialization finished successfully without homotopy method.
LOG_SUCCESS       | info    | The simulation finished successfully.
",
    timeFrontend = 0.012835571,
    timeBackend = 0.002000597,
    timeSimCode = 0.0006527260000000001,
    timeTemplates = 0.003667727,
    timeCompile = 0.4295577239999999,
    timeSimulation = 0.01893283,
    timeTotal = 0.46776259
end SimulationResult;

Warning

Warning: The initial conditions are not fully specified. For more information set -d=initialization. In OMEdit Tools->Options->Simulation->OMCFlags, in OMNotebook call setCommandLineOptions("-d=initialization").

_images/omnotebook-drcontrol-negroots.svg

Figure 64 Characteristic equation with real negative roots.

The importance of the sign of the roots in the characteristic equation is illustrated in Figure 64 and Figure 65, e.g., a stable system with negative real roots and an unstable system with positive imaginary roots resulting in oscillations.

model ImgPosRoots
  Real y;
  Real der_y;
  parameter Real a1 = -2;
  parameter Real a2 = 10;
equation
  der_y = der(y);
  der(der_y) + a1*der_y + a2*y = 1;
end ImgPosRoots;

>>> simulate(ImgPosRoots, stopTime=10)
record SimulationResult
    resultFile = "«DOCHOME»/ImgPosRoots_res.mat",
    simulationOptions = "startTime = 0.0, stopTime = 10.0, numberOfIntervals = 500, tolerance = 1e-06, method = 'dassl', fileNamePrefix = 'ImgPosRoots', options = '', outputFormat = 'mat', variableFilter = '.*', cflags = '', simflags = ''",
    messages = "LOG_SUCCESS       | info    | The initialization finished successfully without homotopy method.
LOG_SUCCESS       | info    | The simulation finished successfully.
",
    timeFrontend = 0.011291521,
    timeBackend = 0.001425857,
    timeSimCode = 0.0004676080000000001,
    timeTemplates = 0.003352515,
    timeCompile = 0.403037057,
    timeSimulation = 0.018573645,
    timeTotal = 0.438253401
end SimulationResult;

Warning

Warning: The initial conditions are not fully specified. For more information set -d=initialization. In OMEdit Tools->Options->Simulation->OMCFlags, in OMNotebook call setCommandLineOptions("-d=initialization").

_images/omnotebook-drcontrol-imgposroots.svg

Figure 65 Characteristic equation with imaginary roots with positive real part.

_images/omnotebook-step-pulse.png

Figure 66 Step and pulse (weight function) response.

The theory and application of Kalman filters is also explained in the interactive course material.

_images/omnotebook-theory-kalman.png

Figure 67 Theory background about Kalman filter.

In reality noise is present in almost every physical system under study and therefore the concept of noise is also introduced in the course material, which is purely Modelica based.

_images/omnotebook-kalman-noisy-feedback.png

Figure 68 Comparison of a noisy system with feedback link in DrControl.

OpenModelica Notebook Commands

OMNotebook currently supports the commands and concepts that are described in this section.

Cells

Everything inside an OMNotebook document is made out of cells. A cell basically contains a chunk of data. That data can be text, images, or other cells. OMNotebook has four types of cells: headercell, textcell, inputcell, and groupcell. Cells are ordered in a tree structure, where one cell can be a parent to one or more additional cells. A tree view is available close to the right border in the notebook window to display the relation between the cells.

  • Textcell – This cell type is used to display ordinary text and

    images. Each textcell has a style that specifies how text is displayed. The cell´s style can be changed in the menu Format->Styles, example of different styles are: Text, Title, and Subtitle. The Textcell type also has support for following links to other notebook documents.

  • Inputcell – This cell type has support for syntax highlighting and

    evaluation. It is intended to be used for writing program code, e.g. Modelica code. Evaluation is done by pressing the key combination Shift+Return or Shift+Enter. All the text in the cell is sent to OMC (OpenModelica Compiler/interpreter), where the text is evaluated and the result is displayed below the inputcell. By double-clicking on the cell marker in the tree view, the inputcell can be collapsed causing the result to be hidden.

  • Latexcell – This cell type has support for evaluation of latex scripts.

    It is intended to be mainly used for writing mathematical equations and formulas for advanced documentation in OMNotebook. Each Latexcell supports a maximum of one page document output.To evaluate this cell, latex must be installed in your system.The users can copy and paste the latex scripts and start the evaluation.Evaluation is done by pressing the key combination Shift+Return or Shift+Enter or the green color eval button present in the toolbar. The script in the cell is sent to latex compiler, where it is evaluated and the output is displayed hiding the latex source. By double-clicking on the cell marker in the tree view,the latex source is displayed for further modification.

  • Groupcell – This cell type is used to group together other cell. A

    groupcell can be opened or closed. When a groupcell is opened all the cells inside the groupcell are visible, but when the groupcell is closed only the first cell inside the groupcell is visible. The state of the groupcell is changed by the user double-clicking on the cell marker in the tree view. When the groupcell is closed the marker is changed and the marker has an arrow at the bottom.

Cursors

An OMNotebook document contains cells which in turn contain text. Thus, two kinds of cursors are needed for positioning, text cursor and cell cursor:

  • Textcursor – A cursor between characters in a cell, appearing as a

    small vertical line. Position the cursor by clicking on the text or using the arrow buttons.

  • Cellcursor – This cursor shows which cell currently has the input

    focus. It consists of two parts. The main cellcursor is basically just a thin black horizontal line below the cell with input focus. The cellcursor is positioned by clicking on a cell, clicking between cells, or using the menu item Cell->Next Cell or Cell->Previous Cell. The cursor can also be moved with the key combination Ctrl+Up or Ctrl+Down. The dynamic cellcursor is a short blinking horizontal line. To make this visible, you must click once more on the main cellcursor (the long horizontal line). NOTE: In order to paste cells at the cellcursor, the dynamic cellcursor must be made active by clicking on the main cellcursor (the horizontal line).

Selection of Text or Cells

To perform operations on text or cells we often need to select a range of characters or cells.

  • Select characters – There are several ways of selecting characters,

    e.g. double-clicking on a word, clicking and dragging the mouse, or click followed by a shift-click at an adjacent positioin selects the text between the previous click and the position of the most recent shift-click.

  • Select cells – Cells can be selected by clicking on them. Holding

    down Ctrl and clicking on the cell markers in the tree view allows several cells to be selected, one at a time. Several cells can be selected at once in the tree view by holding down the Shift key. Holding down Shift selects all cells between last selected cell and the cell clicked on. This only works if both cells belong to the same groupcell.

File Menu

The following file related operations are available in the file menu:

  • Create a new notebook – A new notebook can be created using the

    menu File->New or the key combination Ctrl+N. A new document window will then open, with a new document inside.

  • Open a notebook – To open a notebook use File->Open in the menu or

    the key combination Ctrl+O. Only files of the type .onb or .nb can be opened. If a file does not follow the OMNotebook format or the FullForm Mathematica Notebook format, a message box is displayed telling the user what is wrong. Mathematica Notebooks must be converted to fullform before they can be opened in OMNotebook.

  • Save a notebook – To save a notebook use the menu item File->Save

    or File->Save As. If the notebook has not been saved before the save as dialog is shown and a filename can be selected. OMNotebook can only save in xml format and the saved file is not compatible with Mathematica. Key combination for save is Ctrl+S and for save as Ctrl+Shift+S. The saved file by default obtains the file extension .onb.

  • Print – Printing a document to a printer is done by pressing the

    key combination Ctrl+P or using the menu item File->Print. A normal print dialog is displayed where the usually properties can be changed.

  • Import old document – Old documents, saved with the old version of

    OMNotebook where a different file format was used, can be opened using the menu item File->Import->Old OMNotebook file. Old documents have the extension .xml.

  • Export text – The text inside a document can be exported to a text

    document. The text is exported to this document without almost any structure saved. The only structure that is saved is the cell structure. Each paragraph in the text document will contain text from one cell. To use the export function, use menu item File->Export->Pure Text.

  • Close a notebook window – A notebook window can be closed using the

    menu item File->Close or the key combination Ctrl+F4. Any unsaved changes in the document are lost when the notebook window is closed.

  • Quitting OMNotebook – To quit OMNotebook, use menu item File->Quit

    or the key combination Crtl+Q. This closes all notebook windows; users will have the option of closing OMC also. OMC will not automatically shutdown because other programs may still use it. Evaluating the command quit() has the same result as exiting OMNotebook.

Edit Menu

  • Editing cell text – Cells have a set of of basic editing functions.

    The key combination for these are: Undo (Ctrl+Z), Redo (Ctrl+Y), Cut (Ctrl+X), Copy (Ctrl+C) and Paste (Ctrl+V). These functions can also be accessed from the edit menu; Undo (Edit->Undo), Redo (Edit->Redo), Cut (Edit->Cut), Copy (Edit->Copy) and Paste (Edit->Paste). Selection of text is done in the usual way by double-clicking, triple-clicking (select a paragraph), dragging the mouse, or using (Ctrl+A) to select all text within the cell.

  • Cut cell – Cells can be cut from a document with the menu item

    Edit->Cut or the key combination Ctrl+X. The cut function will always cut cells if cells have been selected in the tree view, otherwise the cut function cuts text.

  • Copy cell – Cells can be copied from a document with the menu item

    Edit->Copy or the key combination Ctrl+C. The copy function will always copy cells if cells have been selected in the tree view, otherwise the copy function copy text.

  • Paste cell – To paste copied or cut cells the cell cursor must be

    selected in the location where the cells should be pasted. This is done by clicking on the cell cursor. Pasteing cells is done from the menu Edit->Paste or the key combination Ctrl+V. If the cell cursor is selected the paste function will always paste cells. OMNotebook share the same application-wide clipboard. Therefore cells that have been copied from one document can be pasted into another document. Only pointers to the copied or cut cells are added to the clipboard, thus the cell that should be pasted must still exist. Consequently a cell can not be pasted from a document that has been closed.

  • Find – Find text string in the current notebook, with the options

    match full word, match cell, search within closed cells. Short command Ctrl+F.

  • Replace – Find and replace text string in the current notebook,

    with the options match full word, match cell, search+replace within closed cells. Short command Ctrl+H.

  • View expression – Text in a cell is stored internally as a subset

    of HTML code and the menu item Edit->View Expression let the user switch between viewing the text or the internal HTML representation. Changes made to the HTML code will affect how the text is displayed.

Cell Menu

  • Add textcell – A new textcell is added with the menu item Cell->Add

    Cell (previous cell style) or the key combination Alt+Enter. The new textcell gets the same style as the previous selected cell had.

  • Add inputcell – A new inputcell is added with the menu item

    Cell->Add Inputcell or the key combination Ctrl+Shift+I.

  • Add latexcell – A new latexcell is added with the menu item

    Cell->Add Latexcell or the key combination Ctrl+Shift+E.

  • Add groupcell – A new groupcell is inserted with the menu item

    Cell->Groupcell or the key combination Ctrl+Shift+G. The selected cell will then become the first cell inside the groupcell.

  • Ungroup groupcell – A groupcell can be ungrouped by selecting it in

    the tree view and using the menu item Cell->Ungroup Groupcell or by using the key combination Ctrl+Shift+U. Only one groupcell at a time can be ungrouped.

  • Split cell – Spliting a cell is done with the menu item Cell->Split

    cell or the key combination Ctrl+Shift+P. The cell is splited at the position of the text cursor.

  • Delete cell – The menu item Cell->Delete Cell will delete all cells

    that have been selected in the tree view. If no cell is selected this action will delete the cell that have been selected by the cellcursor. This action can also be called with the key combination Ctrl+Shift+D or the key Del (only works when cells have been selected in the tree view).

  • Cellcursor – This cell type is a special type that shows which cell

    that currently has the focus. The cell is basically just a thin black line. The cellcursor is moved by clicking on a cell or using the menu item Cell->Next Cell or Cell->Previous Cell. The cursor can also be moved with the key combination Ctrl+Up or Ctrl+Down.

Format Menu

  • Textcell – This cell type is used to display ordinary text and

    images. Each textcell has a style that specifies how text is displayed. The cells style can be changed in the menu Format->Styles, examples of different styles are: Text, Title, and Subtitle. The Textcell type also have support for following links to other notebook documents.

  • Text manipulation – There are a number of different text

    manipulations that can be done to change the appearance of the text. These manipulations include operations like: changing font, changing color and make text bold, but also operations like: changing the alignment of the text and the margin inside the cell. All text manipulations inside a cell can be done on single letters, words or the entire text. Text settings are found in the Format menu. The following text manipulations are available in OMNotebook:

> Font family

> Font face (Plain, Bold, Italic, Underline)

> Font size

> Font stretch

> Font color

> Text horizontal alignment

> Text vertical alignment

> Border thickness

> Margin (outside the border)

> Padding (inside the border)

Insert Menu

  • Insert image – Images are added to a document with the menu item

    Insert->Image or the key combination Ctrl+Shift+M. After an image has been selected a dialog appears, where the size of the image can be chosen. The images actual size is the default value of the image. OMNotebook stretches the image accordantly to the selected size. All images are saved in the same file as the rest of the document.

  • Insert link – A document can contain links to other OMNotebook file

    or Mathematica notebook and to add a new link a piece of text must first be selected. The selected text make up the part of the link that the user can click on. Inserting a link is done from the menu Insert->Link or with the key combination Ctrl+Shift+L. A dialog window, much like the one used to open documents, allows the user to choose the file that the link refers to. All links are saved in the document with a relative file path so documents that belong together easily can be moved from one place to another without the links failing.

Window Menu

  • Change window – Each opened document has its own document window.

    To switch between those use the Window menu. The window menu lists all titles of the open documents, in the same order as they were opened. To switch to another document, simple click on the title of that document.

Help Menu

  • About OMNotebook – Accessing the about message box for OMNotebook

    is done from the menu Help->About OMNotebook.

  • About Qt – To access the message box for Qt, use the menu

    Help->About Qt.

  • Help Text – Opening the help text (document OMNotebookHelp.onb) for

    OMNotebook can be done in the same way as any OMNotebook document is opened or with the menu Help->Help Text. The menu item can also be triggered with the key F1.

Additional Features

  • Links – By clicking on a link, OMNotebook will open the document

    that is referred to in the link.

  • Update link – All links are stored with relative file path.

    Therefore OMNotebook has functions that automatically updating links if a document is resaved in another folder. Every time a document is saved, OMNotebook checks if the document is saved in the same folder as last time. If the folder has changed, the links are updated.

  • Evaluate whole Notebook – All the cells present in the Notebook can

    be evaluated in one step by pressing the red color evalall button in the toolbar. The cells are evaluated in the same order as they are in the Notebook.However the latexcells cannot be evaluated by this feature.

  • Evaluate several cells – Several inputcells can be evaluated at

    the same time by selecting them in the treeview and then pressing the key combination Shift+Enter or Shift+Return. The cells are evaluated in the same order as they have been selected. If a groupcell is selected all inputcells in that groupcell are evaluated, in the order they are located in the groupcell.

  • Moving and Reordering cells in a Notebook – It is possible to shift cells

    to a new position and change the hierarchical order of the document.This can be done by clicking the cell and press the Up and Down arrow button in the tool bar to move either Up or Down. The cells are moved one cell above or below.It is also possible to move a cell directly to a new position with one single click by pressing the red color bidirectional UpDown arrow button in the toolbar. To do this the user has to place the cell cursor to a position where the selected cells must be moved. After selecting the cell cursor position, select the cells you want to shift and press the bidirectional UpDown arrow button. The cells are shifted in the same order as they are selected.This is especially very useful when shifting a group cell.

  • Command completion – Inputcells have command completion support,

    which checks if the user is typing a command (or any keyword defined in the file commands.xml) and finish the command. If the user types the first two or three letters in a command, the command completion function fills in the rest. To use command completion, press the key combination Ctrl+Space or Shift+Tab. The first command that matches the letters written will then appear. Holding down Shift and pressing Tab (alternative holding down Ctrl and pressing Space) again will display the second command that matches. Repeated request to use command completion will loop through all commands that match the letters written. When a command is displayed by the command completion functionality any field inside the command that should be edited by the user is automatically selected. Some commands can have several of these fields and by pressing the key combination Ctrl+Tab, the next field will be selected inside the command. > Active Command completion: Ctrl+Space / Shift+Tab > Next command: Ctrl+Space / Shift+Tab > Next field in command: Ctrl+Tab’

  • Generated plot – When plotting a simulation result, OMC uses the

    program Ptplot to create a plot. From Ptplot OMNotebook gets an image of the plot and automatically adds that image to the output part of an inputcell. Like all other images in a document, the plot is saved in the document file when the document is saved.

  • Stylesheet –OMNotebook follows the style settings defined in

    stylesheet.xml and the correct style is applied to a cell when the cell is created.

  • Automatic Chapter Numbering – OMNotebook automatically numbers

    different chapter, subchapter, section and other styles. The user can specify which styles should have chapter numbers and which level the style should have. This is done in the stylesheet.xml file. Every style can have a <chapterLevel> tag that specifies the chapter level. Level 0 or no tag at all, means that the style should not have any chapter numbering.

  • Scrollarea – Scrolling through a document can be done by using the

    mouse wheel. A document can also be scrolled by moving the cell cursor up or down.

  • Syntax highlighter – The syntax highlighter runs in a separated

    thread which speeds up the loading of large document that contains many Modelica code cells. The syntax highlighter only highlights when letters are added, not when they are removed. The color settings for the different types of keywords are stored in the file modelicacolors.xml. Besides defining the text color and background color of keywords, whether or not the keywords should be bold or/and italic can be defined.

  • Change indicator – A star (*) will appear behind the filename in

    the title of notebook window if the document has been changed and needs saving. When the user closes a document that has some unsaved change, OMNotebook asks the user if he/she wants to save the document before closing. If the document never has been saved before, the save-as dialog appears so that a filename can be choosen for the new document.

  • Update menus – All menus are constantly updated so that only menu

    items that are linked to actions that can be performed on the currently selected cell is enabled. All other menu items will be disabled. When a textcell is selected the Format menu is updated so that it indicates the text settings for the text, in the current cursor position.

References

Todo

Add these into extrarefs.bib and cite them somewhere

Eric Allen, Robert Cartwright, Brian Stoler. DrJava: A lightweight pedagogic environment for Java. In Proceedings of the 33rd ACM Technical Symposium on Computer Science Education (SIGCSE 2002) (Northern Kentucky – The Southern Side of Cincinnati, USA, February 27 – March 3, 2002).

Anders Fernström, Ingemar Axelsson, Peter Fritzson, Anders Sandholm, Adrian Pop. OMNotebook – Interactive WYSIWYG Book Software for Teaching Programming. In Proc. of the Workshop on Developing Computer Science Education – How Can It Be Done?. Linköping University, Dept. Computer & Inf. Science, Linköping, Sweden, March 10, 2006.

Eva-Lena Lengquist-Sandelin, Susanna Monemar, Peter Fritzson, and Peter Bunus. DrModelica – A Web-Based Teaching Environment for Modelica. In Proceedings of the 44th Scandinavian Conference on Simulation and Modeling (SIMS’2003), available at www.scan-sims.org. Västerås, Sweden. September 18-19, 2003.

Axe05

Ingemar Axelsson. OpenModelica Notebook for interactive structured Modelica documents. Master's thesis, Linköping University, Department of Computer and Information Science, October 2005. LITH-IDA-EX–05/080–SE.

Fernstrom06

Anders Fernström. Extending OpenModelica Notebook – an interactive notebook for structured Modelica documents. Master's thesis, Linköping University, Department of Computer and Information Science, September 2006. LITH-IDA-EX–06/057—SE.

Fri04(1,2)

Peter Fritzson. Principles of Ob­ject-Ori­ent­ed Modeling and Simulation with Modelica 2.1. Wiley-IEEE Press, February 2004. ISBN 0-471-471631.

Knu84

Donald E. Knuth. Literate programming. The Computer Journal, 27:97–111, 1984.

Wol96

Stephen Wolfram. The Mathematica Book. Wolfram Media/Cambridge University Press, third edition, 1996.