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© National Instruments Corporation v Xmath Control Design Module
Contents
Chapter 1
Introduction
Using This Manual.........................................................................................................1-1
Document Organization...................................................................................1-1
Bibliographic References ................................................................................1-2
Commonly Used Nomenclature ......................................................................1-2
Related Publications........................................................................................1-3
MATRIXx Help...............................................................................................1-3
Control Design Tutorial.................................................................................................1-4
Helicopter Hover Problem: An Ad Hoc Approach .........................................1-4
Helicopter Hover Problem: State Feedback and Observer Design .................1-13
Helicopter Hover Problem: Discrete Formulation ..........................................1-18
Inverted Wedge-Balancing Problem: LQG Control........................................1-20
Chapter 2
Linear System Representation
Linear Systems Represented in Xmath..........................................................................2-1
Transfer Function System Models.................................................................................2-2
State-Space System Models...........................................................................................2-5
Basic System Building Functions....................................................................2-6
system( ) ..........................................................................................................2-6
abcd( )..............................................................................................................2-8
numden( ).........................................................................................................2-10
period( ) ...........................................................................................................2-10
names( )...........................................................................................................2-11
Size and Indexing of Dynamic Systems ........................................................................2-12
Using check( ) with System Objects..............................................................................2-12
Discretizing a System ....................................................................................................2-13
discretize( )......................................................................................................2-13
Numerical Integration Methods: forward, backward, tustins ...........2-14
Pole-Zero Matching: polezero ..........................................................2-15
Z-Transform: ztransform...................................................................2-15
Hold Equivalence Methods: exponential and firstorder ...................2-15
makecontinuous( )...........................................................................................2-17