LTI Models (Creating and Manipulating Models)

Creating and Manipulating Models

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) for each type of model. These are called the 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.

Creating an LTI Object: An Example

An LTI object of the type TF, ZPK, SS, or FRD is created whenever you invoke the corresponding constructor function, tf, zpk, ss, or frd. For example,

```
P = tf([1 2],[1 1 10])
```

creates a TF object, P, that stores the numerator and denominator coefficients of the transfer function

See Creating LTI Models for methods for creating all of the LTI object types.

LTI Properties and Methods

The LTI object implementation relies on MATLAB object-oriented programming capabilities. Objects are MATLAB structures with an additional flag indicating their class (TF, ZPK, SS, or FRD for LTI objects) and have pre-defined fields called object properties. For LTI objects, these properties include the model data, sample time, delay times, input or output names, and input or output groups (see LTI Properties for details). The functions that operate on a particular object are called the object methods. These may include customized versions of simple operations such as addition or multiplication. For example,

```
P = tf([1 2],[1 1 10])
Q = 2 + P
```

The object-specific versions of such standard operations are called overloaded operations. For more details on objects, methods, and object-oriented programming, see Classes and Objects"in the MATLAB documentation. For details on operations on LTI objects, see Operations on LTI Models.

Using LTI Models in the Control System Toolbox Precedence Rules