MATLAB for Engineers

Transcription

1 MATLAB for Engineers Adrian Biran Moshe Breiner ADDISON-WESLEY PUBLISHING COMPANY Wokingham, England Reading, Massachusetts Menlo Park, California New York Don Mills, Ontario Amsterdam Bonn Sydney Singapore Tokyo Madrid San Juan Milan Mexico City Seoul Taipei

2 Contents Preface 1 MATLAB in a nutshell Desktop calculations Getting started Arithmetic operations Last-line editing A few built-in functions Naming constants and variables Format Diary One-dimensional arrays and graphics Arrays - elementary operations More operations on arrays Row vectors and column vectors The scalar product Simple plots Matrices Defining a matrix Elementary operations with matrices Printing a table Complex numbers Complex numbers - elementary operations Two notes on the use of i and j Plotting a complex number Trigonometric and exponential representations Functions of complex variables Arrays of complex numbers Systems of linear equations Determinants Cramer's rule Matrix inversion 31 v ix

3 X Solving Systems of linear equations in MATLAB Polynomials Polynomial roots Retrieving polynomial coefficients from polynomial roots Polynomial evaluation Multiplication and division of polynomials Programming in MATLAB Programming a function Repetitive control structures - FOR loops Conditional control structures Repetitive control structures - WHILE loops External files and programs Saving and loading data The CUMSUM and DIFF functions Reading data from external files Issuing commands to the operating system Writing output to external files Regression and interpolation Tables with one entry Tables with two entries Polynomial fit and polynomial interpolation Spline interpolation More about plotting Function evaluation Histograms Polar plots A more elaborate polar plot Three-dimensional plots in MATLAB Interpolation and 3D plots in MATLAB More interpolating functions in MATLAB The GRIDDATA function and 3D plots More 3D plots 62 1 MATLAB - AN INTRODUCTION FOR ENGINEERS 65 2 Desktop calculations with graphics Introduction Computer-aided mistakes Computer representation of numbers Roundoff Roundoff errors The set of machine numbers Vectors Column vectors A spreadsheet. 79

4 2.10 Geometrical significance of the scalar product Graphical solution of equations Summary Examples Exercises Appendix - a note on Fourier series Two-dimensional arrays and matrices Building a matrix out of vectors Vector-by-matrix multiplication Matrix-by-matrix multiplication Array division Summary Examples Exercises Where to find more examples and exercises Complex numbers Introduction The introduction of complex numbers Operations with complex numbers Geometric representation Trigonometric representation Functions of complex variables Mapping by functions of complex variables Conformal mapping Harmonic motion - phasors A simple MATLAB program - visualizing a rotating vector Summary Examples Exercises Where to find more examples Appendix Operations with complex numbers AC circuits - phasors in electrical engineering Geometric calculations Introduction Rotation of coordinate axes in the plane Matrix inversion Programming a function Euler's angles, Determinants Summary Affine transformations Inverse affine transformations 237 XI

5 Xll 5.10 Examples Exercises Solving equations Systems of linear equations - introduction Inhomogeneous linear equations Homogeneous linear equations MATLAB's solution of linear systems Overdetermined systems - least-squares solution Ill-conditioned systems Polynomial equations - introduction Finding roots of polynomials in MATLAB Retrieving polynomial coefficients from roots Summary Examples - linear equations Examples - polynomial equations Exercises Appendix - least squares fit Programming in MATLAB Introduction Conditional branching WHILE loops Iterative solution of equations The Newton-Raphson method Recursion A note on complexity Summary Examples Exercises Appendix - the contractive Lipschitz condition External files Introduction A log-book of calculations Reading data from M-files Linear interpolation Tables with one entry Tables with two entries Switching to the operating system Writing output to external files Additions in MATLAB Summary Examples Exercises 372

6 9 Regression and interpolation Introduction Polynomial fit Polynomial interpolation Assessing the quality of a regression Power regression Exponential regression Spline interpolation Summary Examples Exercises More about plotting Introduction Histograms Polar plots Three-dimensional plots Animation Examples Exercises Appendix - the equation of orbits of planets and satellites ХШ 11 MORE APPLICATIONS Numerical integration Introduction The trapezoidal rule Error of integration by the trapezoidal rule Simpson's rule Error of integration by Simpson's rule MATLAB QUAD and QUAD8 functions Examples Exercises Graph theory Definitions Graph of a railway network Sparse matrix Exercises Dimensional analysis Introduction Dimensional analysis Examples Summary Exercises 506

7 XIV 14 System modelling and simulation Introduction Five ways of modelling dynamic systems Transfer functions Zero-pole-gain models Partial fractions State space Cauchy form Numerical solution of ordinary differential equations Ordinary differential equations and simulation Stiff problems Conclusion Exercises Control Introduction Root locus design Design in the frequency domain Optimal design Exercises Signal processing Signals and signal processing The FILTER function Calling the filter with initial conditions Design of digital filters Definitions Defining the frequency characteristics of the filter The Tustin bilinear transformation The Discrete Fourier Transform A short introduction to the DFT The power spectrum Trigonometric expansion of a signal High frequency signals and aliasing Exercises Case studies in mechanical engineering Bending moment caused by a moving vehicle One-dimensional heat conduction Using a sparse matrix Exercises 613 Answers to selected exercises 615 Bibliography 653 Index 659