User`s guide

Introduction
2-3
Using LTI Models in the Control System Toolbox
You can manipulate TF, SS, and ZPK models using the arithmetic and model
interconnection operations described in Chapter 3, “Operations on LTI
Models,” and analyze them using the model analysis f unctions, such as
bode
and step, described in Chapter 5, “Model Analysis Tools.” FRD models can be
manipulated and analyzed in much the same way you analyze the other model
types, but analysis is restricted to frequency-domain methods.
Usinga varietyo f designtechniques,you can designcompensators for systems
specified with TF, ZPK, SS, and FRD models. These techniques include root
locus analysis, pole placement, LQG optimal control, and frequency domain
loop-shaping. For FRD models, you can either:
• Obtain an identified TF, SS, or ZPK model using system identification
techniques.
• Use frequency-domain analysis techniques.
Other Uses of FRD Models
FRD models are unique model types available in the Control System Toolbox
collection of LTI model types, in that they don’t have a parametric
representation. In addition to the standard operations you may perform on
FRD models, you can also use them to:
• Perform frequency-domain analysis on systems with nonlinearities using
describing functions.
• Validate identified models against experimental frequency response data.
LTI Objects
Depending on the type of model you use, the data for your model may consist
of a simple numerator/denominator pair for SISO transfer functions, four
matrices for state-space models,and multiple sets of zeros and poles for MIMO
zero-pole-gain models or frequency and response vectors for FRD models. For
convenience, the Control System Toolbox provides customized data structures
(LTI objects) foreach typeof model.Theseare calledthe TF, ZPK, SS,and FRD
objects. These four LTI objects encapsulate the model data and enable you to
manipulate LTI systems as single entities rather than collections of data
vectors or matrices.