User manual MATLAB SYMBOLIC MATH TOOLBOX 5

[. . . ] Symbolic Math ToolboxTM 5 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Symbolic Math ToolboxTM User's Guide © COPYRIGHT 1993­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] For example, convert the following differential equation to a Simscape equation. Also, here you explicitly specify the left and the right sides of the equation by using the syntax simscapeEquation(LHS, RHS): syms a; x = sym('x(t)'); simscapeEquation(diff(x), -a^2*x) ans = x. der == -a^2*x simscapeEquation also translates piecewise expressions to the Simscape language. For example, the result of the following Fourier transform is a piecewise function: syms v u; syms x real; f = exp(-x^2*abs(v))*sin(v)/v; s = fourier(f, v, u) s= piecewise([x <> 0, atan((u + 1)/x^2) - atan(1/x^2*(u - 1))]) From this symbolic piecewise equation, simscapeEquation generates valid code for the equation section of a Simscape component file: simscapeEquation(s) ans = s == if x ~= 0, atan((u + 1)/x^2) - atan((u - 1)/x^2) end Clear the assumption that x is real: 3-140 Generating Code from Symbolic Expressions syms x clear Converting MuPAD Equations If you perform symbolic computations in the MuPAD Notebook Interface and want to convert the results to Simscape equations, follow these steps: 1 Open the notebook you want to use: · If you already have a notebook with the computations that you want to use, open that notebook file using the following syntax. You can replace mphandle by any variable name: mphandle = mupad(file_name); · If you want to create a new notebook, use the following syntax: mphandle = mupad; 2 Find all equations that you want to convert to the Simscape language. Assign each equation to a variable. 3 Switch to the MATLAB Command Window. Use the getVar function to copy the symbolic variables in a MuPAD notebook to the variables in the MATLAB workspace: f = getVar(mphandle, 'MuPAD_Variable') 4 Continue working in the MATLAB Command Window. Use simscapeEquation to generate Simscape equations from the variables that you created in the MATLAB workspace: simscapeEquation(f) Limitations The equation section of a Simscape component file supports a limited number of functions. If a symbolic equation contains the functions that the equation section of a Simscape component file does not support. simscapeEquation cannot correctly convert these equations to Simscape equations. The following types of expressions are prone to invalid conversion: 3-141 3 Using Symbolic Math ToolboxTM Software · Special functions · Expressions with infinities · MuPAD code. When converting a MuPAD expression or function that is not on the MATLAB vs. · Expressions returned by evalin and feval. 3-142 4 MuPAD in Symbolic Math Toolbox · "Understanding MuPAD" on page 4-2 · "MuPAD for MATLAB Users" on page 4-10 · "Integration of MuPAD and MATLAB" on page 4-25 4 MuPAD® in Symbolic Math ToolboxTM Understanding MuPAD In this section. . . "Introduction to MuPAD" on page 4-2 "The MATLAB Workspace and MuPAD Engines" on page 4-2 "Introductory Example Using a MuPAD Notebook from MATLAB" on page 4-3 Introduction to MuPAD Version 5 of Symbolic Math Toolbox is powered by the MuPAD symbolic engine. · Nearly all Symbolic Math Toolbox functions work the same way as in previous versions. To read about the differences with the new engine, see the transition Release Notes. · MuPAD notebooks provide a new interface for performing symbolic calculations, variable-precision calculations, plotting, and animations. "Introductory Example Using a MuPAD Notebook from MATLAB" on page 4-3 contains an introductory example of how to use this interface. · Symbolic Math Toolbox functions allow you to copy variables and expressions between the MATLAB workspace and MuPAD notebooks. For more information, see "Copying Variables and Expressions Between the MATLAB Workspace and MuPAD Notebooks" on page 4-25. · You can call MuPAD functions and procedures from the MATLAB environment. For more information, see "Calling MuPAD Functions at the MATLAB Command Line" on page 4-28. The MATLAB Workspace and MuPAD Engines A MuPAD engine is a separate process that runs on your computer in addition to a MATLAB process. A MuPAD engine starts when you first call a function that needs a symbolic engine, such as syms. Symbolic Math Toolbox functions that use the symbolic engine use standard MATLAB syntax, such as y = int(x^2). 4-2 Understanding MuPAD® Conceptually, each MuPAD notebook has its own symbolic engine, with associated workspace. [. . . ] The following expression present the Taylor series for an analytic function f(x) about the base point x=a: 6-195 taylor f ( x) = m =0 ( x - a) m f (m) (a) m! Examples The following table describes the various uses of the taylor command and its relation to Taylor and Maclaurin series. Before using the taylor command, define the function you want to expand. For example: syms x f = exp(x^2); Mathematical Operation MATLAB Operation taylor(f) m =0 n-1 m =0 x 5 5 m f (m) (0) m!f (m) (0) m! taylor(f, n) xm n is a positive integer. n is a positive integer m =0 ( x - a) m f (m) (a) m! taylor(f, a) a is a real number. a is a real number n-1 m =0 ( x - a)m f (m) (a) m! taylor(f, n, a) a is real and n is a positive integer. n is a positive integer and a is real. [. . . ]