MATLAB graphs

MATLAB is a mathematical programme developed by the company called The MathWorks Inc. Examples in this chapter have been tested on MATLAB versions between 201 la and 2015b. It is expected that most of the commands presented will work with some earlier versions, as well as most later versions. It will be assumed that the reader has a basic understanding of MATLAB, can write MATLAB statements, understands basic MATLAB commands, and can plot a simple MATLAB graph. This chapter will examine in detail additional features, such as the different toolboxes and formatting features. In order to clearly distinguish between the code required for the MATLAB function and text, all MATLAB commands and variables are shown in bold Courier New. 

Construet, on log-linear graph paper, using asymptotes, and validate using MATLAB or a similar tool, the Bode diagrams for... 

In the next two examples, we illustrate how state space models can handle a multiple-input multiple output (MIMO) problem. We ll show, with a simple example, how to translate information in a block diagram into a state space model. Some texts rely on signal-flow graphs, but we do not need them with simple systems. Moreover, we can handle complex problems easily with MATLAB. Go over MATLAB Session 4 before reading Example 4.7A. 

The graphs are designed to be simple but instructive. They do not make use of the richness of the Matlab graphics routines. We did not include any graphical user-interfaces (GUIs) in order to avoid difficulties with different versions of Matlab. Matlab versions starting from 5.3 should be compatible with all programs in this book. 

However, here we leave all numerical procedures and MATLAB coding as exercises to the students and readers. For each problem, all the necessary modeling and data is included, as well as samples of numerical results in the form of tables and graphs. Our readers should now be able to use the models and the given parameters to develop their own MATLAB codes along the lines of what has been practiced before. Then the students should be try to solve the exercises given at the end of each section and finally the general exercises at the end of the chapter. 

MATLAB is a very simple language for computations. Its lines of numerical code are often few and short. By comparison, the visual output and the proper texting of graphs created in MATLAB may take much more effort than the numerics. 

The MATLAB function adiabNisoplot.m finds the zero crossings of the graph of / in (3.4) graphically. Graphs are generally very helpful when trying to solve equations since they help us visualize the points of intersection of the function / in question with the... 

Exercise your command of MATLAB by trying to replicate the three graphs in Figure 3.15. Learn about the subplot, xlabel, ylabel, and title MATLAB commands and how to use them. 

This equation poses no problem at all for MATLAB s root-finder fzero, since F s zeros are always simple and the graph of F intersects the horizontal axis sufficiently steeply. Here is our MATLAB code colebrookplotsolve.m, which adapts itself automatically... 

It is advisable to graph and inspect the reaction more closely at the entrance of the reactor. After a few experiments with Vend = 0.1, 0.04, and 0.01, we have set the desired final volume to Vend = 0.01 m3 in Figure 4.4, which is drawn by the MATLAB command fixedbedreactf.003,160,1200,1030,.01,15,0,1) . ... 

The MATLAB program threeCSTR.m contains a few lines of numerical calculations at its top that generate the numerical solution for the IVP in equation (6.144), followed by more than two pages of plotting and graph annotation code, and it finishes with the right-hand side DE equation evaluator for the nine DEs collected in the equations (6.135) to (6.143). 

In threeCSTR.m, please note the use of the subplot MATLAB command that draws six separate graphs in our code, namely two for each tank. 

There are a large number of different types of graph available in Matlab. Below we discuss a few methods that can be used to produce diagrams of the type employed in this text. The enthusiast will soon discover further approaches. Matlab is a very powerful tool for data visualisation. 

Usir MATLAB, create a table that shows the viscosity of vrater as a function of temperature in the range of0°C (273.15 K) to 100°C (373.15 K) in increments of 5°C. Also, create a graph showing the value of viscosity as a function of temperature. 

MatLab is used to obtain graphs of the step response of this closed loop system. The transfer function of BF... 

These operations can be hardly manually performed, even for models of small size. However, a bond graph preprocessor such as CAMPG [11] can automatically derive the equations from the original as well as from the incremental bond graph. MATLAB [12] or Scilab [13] script files can then generate the matrices F and F in symbolic form and can perform the multiplication of a row of F by the factor F j8j for each requested parameter sensitivity of an ARR residual. 

Due to the simplicity of this model the state and output equations are derived by hand and transferred into MATLAB [21]. This step could have been done using a bond graph modeling environment (e.g., 20-Sim [22], CAMP-G [23]) to generate the time responses needed for the Analyze Activity step of MORA (see Fig. 2.2). The dynamic equations are numerically integrated to first produce the time response of the state variables and then the required set of outputs as defined in (2.3). 

In any case, software such as CAMP-G/MATLAB in cooperation with the Symbolic Math Toolbox can set up the matrices needed for establishing both transfer matrices in symbolic form from both bond graphs. 

Existing software such as CAMP-G/MATLAB supported by the Symbolic Math Toolbox can derive equations from the bond graph and from its associated incremental bond graph and can build the matrices of the state space equations and the output equations for both bond graphs in symbolic form. 

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