MATLAB functions M-file

We note that fzerotryl is a MATLAB function m file that is stored in its folder with the extension. m as fzerotryl.m. Our program code is annotated with comments following the % symbol. Anything that follows after a % symbol on a line of code is not executed in MATLAB. More on MATLAB files, their storage, creation, etc. is given in Section 1.2.5. Specific built-in MATLAB functions and their use, such as fzero in the code below, should always be scrutinized by our students for their input/output syntax etc. using the built-in help MATLAB command help fzero for example. 

The code above is a MATLAB function m file with two inputs xstaxt and k and one output X. Its first code line... 

Modify the MATLAB function m file newtonpoly9.m on p. 30 to print out three columns of iterates with their iteration indices for all values of k. 

Creates a function handle, so that functions can be passed to MATLAB function m files as variables are. 

Note that almost all calling sequences of MATLAB function m files start with the function s name, such as runsolveadiabxy above, followed by a list of parameters in parentheses (. .. ). Our particular call runsolveadiabxy(285,305,1,8.5) uses the interval limits 285 and 305 for a as its first two parameters, followed by the values of / and 7 for a specific chemical reaction. In our m files the list of possible parameters is always explained in the first comment lines of code. Often one or several of the parameters are optional. If they are not specified in the calling sequence, they are internally set to default values inside the program, such as n and anno are here. 

Our CD also contains the MATLAB function m file runNadiabNisokccurve. m. A call of runNadiabNisokccurve (180000,1,15,1,100,. 001, .7,1.2), for example, plots only the bifurcation curve with respect to Kc in Figure 3.16, i.e., it repeats the bottom plot in Figure 3.14. 

The Wegstein method is a secant method applied to g(x) = x - Fix). In Microsoft Excel, roots are found by using Goal Seek or Solver. Assign one cell to be x, put the equation for/(x) in another cell, and let Goal Seek or Solver find the value of x that makes the equation cell zero. In MATLAB, the process is similar except that a function (m-file) is defined and the command fzeroCf .xO) provides the solution x, starting from the initial guess xO. 

A script m file in MATLAB does not start with a function. . . declaration as the function m file fzerotryl. m does. A script m file rather consists only of MATLAB commands. See Section 1.2.5 for more details on these two types of m files in MATLAB. 

If this function m file is stored as f unct. m in the current desktop working directory, it can be called and executed in MATLAB by typing funct(3,5,17) or x=3 z=5 k=17 [yy.sign] = f unct (x, z, k) for example. These calls will create the following sequence of outputs. 

The reader should study our earlier MATLAB m files now, such as the script m file poly9. m on p. 28 and the function m file fzerotryl. m on p. 27 and look for their differences. 

Step 1 The MATLAB program requires you to write a function (m-file) that calculates the right-hand side of Eq. (8.24), given the input, z, X, and T, which are the axial location in the reactor and the conversion and temperature at that axial location, respectively. Thus, (1) to solve the problem you use the variables... 

MATLAB easily handles these kinds of problems. Basically you call a routine to integrate the ordinary differential equations (e.g., ode45). You construct a right-hand side function (m-file) to evaluate the right-hand side. The input variables are z and the three concentrations, and the output variables are the three derivatives. Take Ca and solve Eq. (8.46) using either fzero or fsolve. Then you have Ca,s at this location, z. You can evaluate the rates of reaction in Eq. (8.45) and put them in the output from the m-file. 

MATLAB provides main categories of functions. Some of MATLAB s functions are built into the interpreter, while others take the form of M-files. The M-file functions, and in the case of the built-in functions, M-files containing only help text, are organized into directories, each containing the files associated with a category. The MATLAB command help displays an online table of these main categories. 

MATLAB search path is an ordered list of directories that MATLAB searches to find script and function M-files stored on disk. The MATLAB s path is defined from the File menu via clicking on the Set Path sub-menu, as shown in Figs. 3.1 and 3.2a. 

The following suggestions are either necessary or highly recommended for the effective use of MATLAB script and function M-files ... 

Figure 5.5 The creation of the function M-file (importfile.m) by MATLAB, which can be exploited later to do the same procedure, but perhaps this time with another file name.

Use the MATLAB ode45 solver to solve Problem 7.3. First, define the derivative using the function M-file named Pr7 4.m. Second, write the calling code (main code) that defines the initial value of y, the time interval, calls the MATLAB ode45 solver, defines the exact... 

MATLAB does not even bother wit a Routh function. Such an M-file is provided on our Web... 

Note 2 The iterative solution in solving the ultimate frequency is tricky. The equation has poor numerical properties—arising from the fact that tan9 "jumps" from infinity at 9 = (ir/2) to negative infinity at 9 = (ir/2)+. To better see why, use MATLAB to make a plot of the function (LHS of the equation) with 9 < co < 1. With MATLAB, we can solve the equation with the f zero () function. Create an M-file named f. m, and enter these two statements in it ... 

It can be synthesized with the MATLAB function feedback (). As an illustration, we will use a simple first order function for Gp and Gm, and a PI controller for Gc. When all is done, we test the dynamic response with a unit step change in the reference. To make the reading easier, we break the task up into steps. Generally, we would put the transfer function statements inside an M-file and define the values of the gains and time constants outside in the workspace. 

MATLAB m and Other Files and Built-in MATLAB Functions... 

In the previous sections we have used MATLAB commands that were typed in on the desktop command line, as well as MATLAB commands that invoke special stored MATLAB files, called m files. When starting to work with MATLAB, we advise our users to create a special folder for their personal MATLAB m files once and to continue to use this folder to store personal m files. To access the stored m files from the MATLAB desktop, the user has to point the small desktop window called Current Directory to the personal m file folder. Then all stored m files, as well as all built in MATLAB functions can be accessed, called upon, and used from the command line. All stored personal... 

MATLAB m files can contain any number of MATLAB commands. They are handy for long sets of MATLAB instructions or data and afford easy repeated use and easy modification. There are two kinds of MATLAB m files function and script m files. Script m files such as poly9. m on p. 28 use the data that is defined inside of them and any undefined data is taken from the data (with the proper name) that is currently active on the workspace look at the top left window commonly displayed on the MATLAB desktop for a list of defined variables and their type. Script files overwrite the workspace data as instructed in their code. 

The fundamental difficulty in solving DEs explicitly via finite formulas is tied to the fact that antiderivatives are known for only very few functions / M —> M. One can always differentiate (via the product, quotient, or chain rule) an explicitly given function f(x) quite easily, but finding an antiderivative function F with F x) = f(x) is impossible for all except very few functions /. Numerical approximations of antiderivatives can, however, be found in the form of a table of values (rather than a functional expression) numerically by a multitude of integration methods such as collected in the ode... m file suite inside MATLAB. Some of these numerical methods have been used for several centuries, while the algorithms for stiff DEs are just a few decades old. These codes are... 

Using the MATLAB function called re anal.m, calculate values for each column shown in Table 4.1. Use the sample data file called pea dat . Use the results to make and interpret plots of the eigenvalues and Malinowski s RE and REV functions. 

The feval function causes MATLAB to compute the value of y (the output defined in specvol) using the m-file named specvol when v = 0.2. The output you get is ... 

Step 3 When using the global command, you must be sure to use the global command in the command window (or a run program that runs in the command window), set the variables after the global statement, and then repeat the global statement in the function. If you do not follow these mles, MATLAB will inform you that it was asked for an undefined variable or function, and give you the m-file and line number where it appears. 

In MATLAB the fminsearch function is used to find the minimum of a function of several variables. You first create an m-file that calculates the function, and then invoke the fminsearch function to minimize it. 

Step 2 Check the function as you did before. In fact, because you already checked the m-file prob2.m you only have to check that y2 is calculated correctly from fi anAf2. The command is invoked by first setting the initial guess (this also sets the length of the vector of independent variables, i.e. it tells MATLAB how many parameters it has to adjust) ... 

In MATLAB, you define the problem by means of a function, called an m-file. You then... 

Step 1 To integrate these equations using MATLAB, you need an m-file to compute the right-hand side, and then an m-file to call ode45 . The right-hand side function is... 

This means that q is either an undefined function or an undefined variable. If q is a function or m-file, then MATLAB cannot find it. Check the working directory or use set path and make sure that the path is set to the folder where you stored the m-file and that you have added that path to the list. Do not forget to save your pathlist so that it is there the next time you use MATLAB. If q is a variable, it has not been set or was not transferred correctly. 

The m-file will be called many times by the ode45 function. However, you only have to check the calculation once. Check the m-file by giving it t and all the y(t) compute what you expect the right-hand sides to be and see that the computer gives those values. This is the only way to ensure that MATLAB is solving the problem you want solved. 

Here the variables xldot, x2dot, x3dot, and x4dot correspond to the derivatives of the state variables, in this case positions and velocities for the two masses. The expressions for this variable represent the four first-order differential equations of the system. These are integrated and the solution calculated using the ODE45 function in MATLAB. The values of the initial conditions and physical parameters need to be entered into another. m file to initialize the simulation in MATLAB and to enter... 

SIMULINK and MATLAB share the same workspace. The state space matrices can be initialized with values using simple (.m) files, which when executed transfers the values in the workspace to SIMULINK state space blocks. The campgnum.m generated the transfer functions, which are also initialized on the SIMULINK transfer function block. 

Apart from performing operations, MATLAB is a programming language. Its operation is based on the use of. m files that can be divided in two classes, scripts and functions. A script is basically a number of operations that we want to perform in a certain sequence. It is required that they are in order so that the variables and parameters are already defined. We can use them as executables and within them, we can also call other subrogate scripts that contain other operations... 

It is also of interest to determine the LU factorization of this A matrix. The MATLAB file lua.m (Figure 2.7) can be run after running the file lin2-2.m to determine its triangular factorization. Note that we have first used the help facility to learn specific details on the MATLAB function lu. 

MATLAB has the function fzero which performs this bisection algorithm. The M-file bisec.m (Figure 2.11) uses fzero to calculate the root for this heat capacity example. 

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