Introduction to Simulink with Engineering Applicatioins, Second Edition

This chapter is an introduction to the Simulink Extras Library. This is a new library and was added to the Simulink 6.5 Version. It consists of six sub-libraries and contains the blocks shown below. Their functions are illustrated with examples.

The Additional Discrete Group contains the blocks described in Subsections 19.1.1 through 19.1.5 below.

The Simulink documentation for the Discrete Transfer Fcn (with initial states) block provides the following description:
Specify the initial states for the transfer function. The state ordering is determined by the m-file tf2ss. There is no unique mapping of the states in a transfer function to states in a state-space representation. However, tf2ss will consistently use the same mapping for a given transfer function.
Let us consider the three models shown in Figure 19.1 below. The first model (on the top) includes the Discrete Transfer Fcn block described in Chapter 5. There are no provisions for initial states in this block. The second model includes the Discrete Transfer Fcn (with initial states) block and it is equivalent to the Discrete State-Space block included in the third model. To prove the equivalence, we need to convert the discrete transfer function to its state-space presentation, and, as we know, this can be achieved with the MATLAB function tf2ss. Thus, at the MATLAB command prompt we enter:
Num=[0 0.951 0]; Den=[1 0.618 1];