Creating and Manipulating Models

Precedence Rules

Operations like addition and commands like feedback operate on more than one LTI model at a time. If these LTI models are represented as LTI objects of different types (for example, the first operand is TF and the second operand is SS), it is not obvious what type (for example, TF or SS) the resulting model should be. Such type conflicts are resolved by precedence rules. Specifically, TF, ZPK, SS, and FRD objects are ranked according to the precedence hierarchy.

Thus ZPK takes precedence over TF, SS takes precedence over both TF and ZPK, and FRD takes precedence over all three. In other words, any operation involving two or more LTI models produces:

• An FRD object if at least one operand is an FRD object
• An SS object if no operand is an FRD object and at least one operand is an SS object
• A ZPK object if no operand is an FRD or SS object and at least one is an ZPK object
• A TF object only if all operands are TF objects

Operations on systems of different types work as follows: the resulting type is determined by the precedence rules, and all operands are first converted to this type before performing the operation.

LTI Objects

Viewing LTI Systems As Matrices