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National Instruments 370753C-01 manual

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NI MATRIXxTM

Xmath™ Control Design Module

Xmath Control Design Module

April 2007

370753C-01

Contents

Main Page Important Information Warranty Copyright Trademarks Patents Conventions Contents Chapter 1 Introduction Chapter 2 Linear System Representation Chapter 3 Building System Connections Chapter 4 System Analysis Chapter 5 Classical Feedback Analysis Chapter 6 State-Space Design Page Introduction Using This Manual Document Organization Bibliographic References Commonly Used Nomenclature Related Publications MATRIXx Help Control Design Tutorial Helicopter Hover Problem: An Ad Hoc Approach Use check( ) to convert the model to transfer-function form: Page Page Page Page Page Page Page Helicopter Hover Problem: State Feedback and Observer Design Page Page Page Page Helicopter Hover Problem: Discrete Formulation Page Inverted Wedge-Balancing Problem: LQG Control Page Page Page Page Linear System Representation Linear Systems Represented in Xmath Transfer Function System Models Page Page State-Space System Models Basic System Building Functions system( ) Page abcd( ) form. If the system is a transfer function, the conversion to state-space is Page numden( ) period( ) names( ) Size and Indexing of Dynamic Systems Using check( ) with System Objects Discretizing a System discretize( ) Numerical Integration Methods: forward, backward, tustins Pole-Zero Matching: polezero Z-Transform: ztransform Hold Equivalence Methods: exponential and firstorder Page makecontinuous( ) Page Page Building System Connections Linear System Interconnection Operators Page Page Linear System Interconnection Functions afeedback( ) Page append( ) Page connect( ) Page Page feedback( ) Page Page System Analysis Time-Domain Solution of System Equations System Stability: Poles and Zeros poles( ) zeros( ) Page Partial Fraction Expansion Page Page residue( ) combinepf( ) General Time-Domain Simulation Page Page Impulse Response of a System impulse( ) Page deftimerange( ) System Response to Initial Conditions initial( ) Page Step Response step( ) Page Page Classical Feedback Analysis Feedback Control of a Plant Model Root Locus rlocus( ) Page Frequency Response and Dynamic Response freq( ) Page Bode Frequency Analysis Page Page bode( ) Page margin( ) Page nichols( ) Nyquist Stability Analysis nyquist( ) Page Page Page Linear Systems and Power Spectral Density psd( ) Page State-Space Design Controllability Page controllable( ) Observability and Estimation Page observable( ) Minimal Realizations minimal( ) stair( ) Duality and Pole Placement poleplace( ) Page Linear Quadratic Regulator Page regulator( ) Page Linear Quadratic Estimator Page Page Page estimator( ) Linear Quadratic Gaussian Compensation Page lqgcomp( ) Page Riccati Equation riccati( ) The small residue indicates that the problem was well posed and the solution is reliable. A'PA PA'PB S+()RB'PB+() Steady-State System Response Using Lyapunov Equations Page lyapunov( ) Discrete Lyapunov Equation Continuous Lyapunov Equation Special Lyapunov Equation rms( ) Balancing a Linear System Page balance( ) Page Modal Form of a System modal( ) mreduce( ) Page Page Page Page A Technical References Page B Technical Support and Professional Services Page Index A B C D E F G H I K L M N O P Q R S T U W Z