Engineering and Scientific Computing with Scilab

I The Scilab Package.- 1 Introduction.- 1.1 What Is Scilab?.- 1.2 Getting Started.- 2 The Scilab Language.- 2.1 Constants.- 2.1.1 Real Numbers.- 2.1.2 Complex Numbers.- 2.1.3 Character Strings.- 2.1.4 Special Constants.- 2.2 Data Types.- 2.2.1 Matrices of Numbers.- 2.2.2 Sparse Matrices of Numbers.- 2.2.3 Matrices of Polynomials.- 2.2.4 Boolean Matrices.- 2.2.5 Sparse Boolean Matrices.- 2.2.6 String Matrices.- 2.2.7 Lists.- 2.2.8 Typed Lists.- 2.2.9 Functions of Rational Matrices.- 2.2.10 Functions and Libraries.- 2.3 Scilab Syntax.- 2.3.1 Variables.- 2.3.2 Assignments.- 2.3.3 Expressions.- 2.3.4 The list and tlist Operations.- 2.3.5 Flow Control.- 2.3.6 Functions and Scripts.- 2.3.7 Commands.- 2.4 Data-Type-Related Functions.- 2.4.1 Type Conversion Functions.- 2.4.2 Type Enquiry Functions.- 2.5 Overloading.- 2.5.1 Operator Overloading.- 2.5.2 Primitive Functions.- 2.5.3 How to Customize the Display of Variables.- 3 Graphics.- 3.1 The Media.- 3.1.1 The Graphics Window.- 3.1.2 The Driver.- 3.1.3 Global Handling Commands.- 3.2 Global Plot Parameters.- 3.2.1 Graphical Context.- 3.2.2 Indirect Manipulation of the Graphics Context.- 3.3 2-D Plotting.- 3.3.1 Basic Syntax for 2-D Plots.- 3.3.2 Specialized 2-D Plotting Functions.- 3.3.3 Captions and Presentation.- 3.3.4 Plotting Geometric Figures.- 3.3.5 Some Graphics Functions for Automatic Control.- 3.3.6 Interactive Graphics Utilities.- 3.4 3-D Plotting.- 3.4.1 3-D Plotting.- 3.4.2 Specialized 3-D Plots and Tools.- 3.4.3 Mixing 2-D and 3-D Graphics.- 3.5 Examples.- 3.5.1 Subwindows.- 3.5.2 A Set of Figures.- 3.6 Printing Graphics and Exporting to LATEX.- 3.6.1 Window to Printer.- 3.6.2 Creating a Postscript File.- 3.6.3 Including a Postscript File in LATEX.- 3.6.4 Scilab, Xfig, and Postscript.- 3.6.5 Creating Encapsulated Postscript Files.- 4 A Tour of Some Basic Functions.- 4.1 Linear Algebra.- 4.1.1 QR Factorization.- 4.1.2 Singular Value Decomposition.- 4.1.3 Schur Form and Eigenvalues.- 4.1.4 Block Diagonalization and Eigenvectors.- 4.1.5 Fine Structure.- 4.1.6 Subspaces.- 4.2 Polynomial and Rational Function Manipulation.- 4.2.1 General Purpose Functions.- 4.2.2 Matrix Pencils.- 4.3 Sparse Matrices.- 4.4 Random Numbers.- 4.5 Cumulative Distribution Functions and Their Inverses.- 5 Advanced Programming.- 5.1 Functions and Primitives.- 5.2 The Call Function.- 5.3 Building Interface Programs.- 5.4 Accessing "Global" Variables Within a Wrapper.- 5.4.1 Stack Handling Functions.- 5.4.2 Functional Arguments.- 5.5 Intersci.- 5.5.1 A First Intersci Example.- 5.5.2 Intersci Descriptor File Syntax.- 5.6 Dynamic Linking.- 5.7 Static Linking.- 5.7.1 Static Linking of an Interface.- 5.7.2 Functional Argument: Static Linking.- II Tools.- 6 Systems and Control Toolbox.- 6.1 Linear Systems.- 6.1.1 State-Space Representation.- 6.1.2 Transfer-Matrix Representation.- 6.2 System Definition.- 6.2.1 Interconnected Systems.- 6.2.2 Linear Fractional Transformation (LFT).- 6.2.3 Time Discretization.- 6.3 Improper Systems.- 6.3.1 Scilab Representation.- 6.3.2 Scilab Implementation.- 6.4 System Operations.- 6.4.1 Pole-Zero Calculations.- 6.4.2 Controllability and Pole Placement.- 6.4.3 Observability and Observers.- 6.5 Control Tools.- 6.6 Classical Control.- 6.6.1 Frequency Response Plots.- 6.7 State-Space Control.- 6.7.1 Augmenting the Plant.- 6.7.2 Standard Problem.- 6.7.3 LQG Design.- 6.7.4 Scilab Tools for Controller Design.- 6.8 H? Control.- 6.9 Model Reduction.- 6.10 Identification.- 6.11 Linear Matrix Inequalities.- 7 Signal Processing.- 7.1 Time and Frequency Representation of Signals.- 7.1.1 Resampling Signals.- 7.1.2 The DFT and the FFT.- 7.1.3 Transfer Function Representation of Signals.- 7.1.4 State-Space Representation.- 7.1.5 Changing System Representation.- 7.1.6 Frequency-Response Evaluation.- 7.1.7 The Chirp z-Transform.- 7.2 Filtering and Filter Design.- 7.2.1 Filtering.- 7.2.2 Finite Impulse Response Filter Design.- 7.2.3 Infinite Impulse Response Filter Design.- 7.3 Spectral Estimation.- 7.3.1 The Modified Periodogram Method.- 7.3.2 The Correlation Method.- 8 Simulation and Optimization Tools.- 8.1 Models.- 8.2 Integrating ODEs.- 8.2.1 Calling ode.- 8.2.2 Choosing Between Methods.- 8.2.3 ODE Integration with Stopping Times.- 8.2.4 Sampled Systems.- 8.3 Integrating DAEs.- 8.3.1 Implicit Linear ODEs.- 8.3.2 General DAEs.- 8.3.3 DAEs with Stopping Time.- 8.4 Solving Optimization Problems.- 8.4.1 Quadratic Optimization.- 8.4.2 General Optimization.- 8.4.3 Solving Systems of Equations.- 9 SCICOS - A Dynamical System Builder and Simulator.- 9.1 Hybrid System Formalism.- 9.2 Getting Started.- 9.2.1 Constructing a Simple Model.- 9.2.2 Model Simulation.- 9.2.3 Symbolic Parameters and "Context".- 9.2.4 Use of Super Block.- 9.2.5 Simulation Outside the Scicos Environment.- 9.3 Basic Concepts.- 9.3.1 Basic Blocks.- 9.3.2 Inheritance and Time Dependence.- 9.3.3 Synchronization.- 9.4 Block Construction.- 9.4.1 Super Block.- 9.4.2 Scifunc Block.- 9.4.3 GENERIC Block.- 9.4.4 Fortran Block and C Blocks.- 9.4.5 Interfacing Function.- 9.4.6 Computational Function.- 9.5 Example.- 9.6 Palettes.- 9.6.1 Existing Palettes.- 9.6.2 Constructing New Palettes.- 10 Symbolic/Numeric Environment.- 10.1 Introduction.- 10.2 Generating Optimized Fortran Code with Maple.- 10.3 Maple to Scilab Interface.- 10.4 First Example: Simulation of a Rolling Wheel.- 10.5 Second Example: Control of an n-Link Pendulum.- 10.5.1 Simulation of the n-Link Pendulum.- 10.5.2 Control of the n-Link Pendulum.- 11 Graph and Network Toolbox: Metanet.- 11.1 What Is a Graph?.- 11.2 Representation of Graphs.- 11.2.1 Standard Tail/Head Representation.- 11.2.2 Other Representations.- 11.2.3 Graphs and Sparse Matrices.- 11.3 Creating and Loading Graphs.- 11.3.1 Creating Graphs.- 11.3.2 Loading and Saving Graphs.- 11.3.3 Using the Metanet Window.- 11.4 Generating Graphs and Networks.- 11.5 Graph and Network Computations.- 11.5.1 Getting Information About Graphs.- 11.5.2 Paths and Nodes.- 11.5.3 Modifying Graphs.- 11.5.4 Creating New Graphs From Old Ones.- 11.5.5 Graph Problem Solving.- 11.5.6 Network Flows.- 11.5.7 The Pipe Network Problem.- 11.5.8 Other Computations.- 11.6 Examples Using Metanet.- 11.6.1 Routing in the Paris Metro.- 11.6.2 Praxitele Transportation System.- III Applications.- 12 Modal Identification of a Mechanical Structure.- 12.1 Modeling the System.- 12.2 Modeling the Excitation.- 12.2.1 Decomposition of the Unknown Input.- 12.2.2 Contribution of the Colored Noise.- 12.2.3 Contribution of the Harmonics.- 12.2.4 The Final Discrete-State Model.- 12.3 State-Space Representation and an ARMA Model.- 12.4 Modal Identification.- 12.4.1 Instrumental Variable Method.- 12.4.2 Balanced Realization Method.- 12.5 Numerical Experiments.- 12.5.1 Basic Computations.- 12.5.2 Some Plots of Results.- 13 Control of Hydraulic Equipment in a River Valley.- 13.1 Introduction.- 13.2 Description of a Managed River Valley.- 13.2.1 Hydraulic Equipment in a River Valley.- 13.2.2 Power Production.- 13.2.3 Structural Analysis.- 13.2.4 Controller Structure.- 13.2.5 Central Hydraulic Supervision Station.- 13.2.6 Local Controllers.- 13.3 Race Modeling.- 13.3.1 Physical Description.- 13.3.2 Mathematical Model.- 13.3.3 Race Numerical Simulation.- 13.4 Choice of Observation.- 13.4.1 Volume Observer.- 13.4.2 Level Observer.- 13.5 Control of a Race.- 13.5.1 Race Dynamics Identification.- 13.5.2 Local Control Synthesis.- 13.5.3 Series Anticipations Design.- 13.5.4 Parallel Anticipation Design.- 13.5.5 Feedback Controller Design.- 13.6 Metalido Overview.- 13.6.1 Graphical User Interface.- 13.6.2 Scicos.- 13.6.3 Data Structures.