Process Control Design for Industrial Applications

Appendix CDetermining the Attractor in a Nonlinear Process Controlled by Linear Decoupling

Let us consider the following second-order system:

[C.1]

which can be described by

[C.2]

with

[C.3]

To check whether the system without perturbation can have an input–output linearization, we need to determine the relative degree of the system by deriving y:

[C.4]

Since the input appears at the first derivative of we can stop the calculation. We obtain:

[C.5]

knowing that

[C.6]

we obtain

[C.7]

Since G* is inversible, we can set the input u to equal:

[C.8]

hence

[C.9]

we obtain:

[C.10]

[C.11]

The system’s ...