National Instruments 370753C-01 Chapter 6 State-Space Design

Contents
© National Instruments Corporation vii Xmath Control Design Module
Bode Frequency Analysis..............................................................................................5-7
bode( )..............................................................................................................5-10
margin( ) ..........................................................................................................5-12
nichols( )..........................................................................................................5-14
Nyquist Stability Analysis .............................................................................................5-15
nyquist( )..........................................................................................................5-16
Linear Systems and Power Spectral Density.................................................................5-20
psd( )................................................................................................................5-20
Chapter 6
State-Space Design
Controllability................................................................................................................6-1
controllable( ) ..................................................................................................6-3
Observability and Estimation.........................................................................................6-4
observable( ) ....................................................................................................6-6
Minimal Realizations.....................................................................................................6-7
minimal( ) ........................................................................................................6-8
stair( )...............................................................................................................6-9
Duality and Pole Placement...........................................................................................6-10
poleplace( ) ......................................................................................................6-10
Linear Quadratic Regulator ...........................................................................................6-12
regulator( ) .......................................................................................................6-14
Linear Quadratic Estimator............................................................................................6-16
estimator( ).......................................................................................................6-20
Linear Quadratic Gaussian Compensation ....................................................................6-21
lqgcomp( ) .......................................................................................................6-23
Riccati Equation.............................................................................................................6-25
riccati( ) ...........................................................................................................6-26
Steady-State System Response Using Lyapunov Equations .........................................6-28
lyapunov( ).......................................................................................................6-30
Algorithm..........................................................................................6-30
rms( ) ...............................................................................................................6-32
Balancing a Linear System............................................................................................6-33
balance( ) .........................................................................................................6-35
Modal Form of a System ...............................................................................................6-37
modal( ) ...........................................................................................................6-37
mreduce( )........................................................................................................6-38