Modern Control System Theory and Design, 2nd Edition

2.23.  TRANSFORMATION BETWEEN THE STATE-SPACE FORM AND THE TRANSFER FUNCTION FORM USING MATLAB [36]

The presentation in this chapter so far has shown that the state-space and transfer-function forms are both very useful for analyzing control systems and complement each other. The state-space formulation has the major advantage of representing control systems containing multiple inputs and multiple outputs. The transfer function formulation is limited primarily to control systems containing a single input and having a single output, although it has limited use in control systems containing more than one input and output (see Problem 2.21). In the previous Sections 2.21 and 2.22, it was shown how transfer functions can be converted to the state-space formulation. In this section, the transformation of control systems from transfer function to the state-space form, and vice versa will be demonstrated using MATLAB.

Figure 2.32   Signal-flow graph corresponding to the state-variale diagram of Figure 2.30.

Figure 2.33   Signal-flow graph corresponding to the state-variable diagram of Figure 2.31.

A.  Transformation from Transfer Function to State-Space Form

Let us first consider the transformation from the transfer function representation of a control system to the state-space formulation. ...