MATLAB command function

This tutorial looks at how MATLAB commands are used to convert transfer functions into state-space vector matrix representation, and back again. The discrete-time response of a multivariable system is undertaken. Also the controllability and observability of multivariable systems is considered, together with pole placement design techniques for both controllers and observers. The problems in Chapter 8 are used as design examples. 

The very first step is to find the ultimate gain. With the given third order process transfer function, we use the following MATLAB commands,... 

The LTI Viewer runs in its own workspace, which is separate from the MATLAB workspace. The Viewer also works with only LTI objects generated by functions such as tf () and zpk (), and after Chapter 4, state space objects, ss (). So let s generate a couple of objects in the MATLAB command window first ... 

Simulink shares the main MATLAB workspace. When we enter information into, say, the transfer function block, we can use a variable symbol instead of a number. We then define the variable and assign values to it in the MATLAB command window. This allows for a much quicker route to do parametric studies than changing the numbers within the Simulink icons and dialog boxes. 

In this book we shall use MATLAB codes and explain more involved features of MAT-LAB as we encounter them. MATLAB has a built-in help menu typing help format at the prompt, or help, for example, will show the syntax and variations of these two commands format and backslash . Whenever a student encounters a MATLAB command that is not self explanatory, we suggest using this built-in help function of MATLAB. 

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. 

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. 

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 last part of this section lists a few standard MATLAB operations, functions, and commands, collected into groups, together with short descriptions. This may help our readers to more easily find and use built-in MATLAB functions in their own MATLAB program codes. Please note that our MATLAB function descriptions below are very few and very short by necessity. The user should use the help. . . command to find the full length MATLAB reference guide entry for each MATLAB function when the need arises. This will help our readers use the full power and functionality of MATLAB commands and will enable them to browse for and find related built-in MATLAB functions. 

The last two codes contain many intricate and useful plotting and contour commands that are self-explanatory when one uses the MATLAB help. .. function for the MAT-LAB graphics commands meshgrid, surface, contour3, xlabel, ylabel, title, colormap, etc. Students should study these graphics commands of MATLAB in order to be learn how to display the easily computed numerical data well. Please refer to MATLAB help. ... 

Now let s say that we want to plot the volume as a function of x. We then simply type die MATLAB commands that are shown in Figiire 15.24. The resulting plot is shoVm in Figure 15.25. 

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 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. 

NOTE Variable names in MATLAB must start with a letter and can be up to 31 characters long. The trailing characters can be numbers, letters, or underscores. (Some other characters are also available, but in this text we shall stick to these.) Hyphen (-), percent sign (%), and other such characters are not allowed in variable names. Also, reserved names should not be used as variable names. For example, pi, i, j, and e are reserved. Similarly, the names of functions and MATLAB commands should also be avoided. 

Using the MATLAB Command Window and its built-in library functions (see Table I.IL evaluate the following expressions ... 

Do not give a script file the same name as a MATLAB command or function. You can check to see whether a function already exists by using the which command. For example, to see whether qroots already exists, type... 

Fortunately, we do not have to perform tedious evaluations of expressions such as (6-102) and (6-103) by hand. State-space models can be converted to transfer function form using the MATLAB command ss2tf... 

A MATLAB code, or m-file, is a collection of commands that are executed sequentially. Commands can be mathematical operations, function calls, flow control statements, and calls to the functions and scripts described in Section C.1.4. m-files are written using the MATLAB editor and have names such as my file. m. They are executed from the MATLAB command window by typing the name of the m-file (without the. m). Saving an m-file will avoid many hours of retyping the same commands. 

To obtain the unit impulse response of a single transfer function, use the function impulse from the MATLAB command window. 

A script is simply a series of MATLAB commands that could have been entered in the workspace. When typing the name of the script, the commands will be executed in their sequential order as if they were individually typed in the workspace. For example, let us calculate the volume of an ideal gas as a function of pressure and temperature. Type the following commands in the editor and save it as myscript.m ... 

For each session, we put the most important functions in a table for easy reference or review. The first one is on the basic commands and plotting. Try the commands as you read. You do not have to enter any text after the "%" sign. Any text behind a "%" is considered a comment and is ignored. We will save some paper and omit the results generated by MATLAB. If you need to see that for help, they are provided on our Web Support. There is also where we post any new MATLAB changes and upgrades. Features in our tutorial sessions are based on MATLAB Version 6.1, and Control System Toolbox 5.1. 

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. 

The normal probability distribution function can be obtained in Microsoft Excel by using the NORMDIST function and supplying the desired mean and standard deviation. The cumulative value can also be determined. In MATLAB, the corresponding command is randn. 

Alternatively, Matlab s built-in function norm can be used to determine normalisation coefficients and perform the same task. An example for column-wise normalisation of a matrix X with orthogonal columns is given below. It is worthwhile to compare X with equation (2.15) the subspace command can be used to determine the angle between the vectors (in rad) and reconfirm orthogonality. ... 

The function NewtonRaphson. m is written in a very compact manner, taking full advantage of Matlab s vectorised commands. Sometimes this makes the lines difficult to read — a few additional remarks are appropriate. 

These indicate the limit of our successful numerical BVP integrations near the bifurcation points. In between the x and o marks on the middle branch, the curve is drawn using interpolation of our successful BVP solutions data, while in between two adjacent x or two adjacent o marks, the curve is drawn by extrapolating nearby computed function data. This is done automatically by MATLAB s plot commands. 

Step 3 To find the value of x that makes/(x) = 0 in MATLAB, use the fzero function. In the command window, issue the following command ... 

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. 

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) ... 

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