Process Control Design for Industrial Applications

Appendix BDetermination of the Maximum Error for Pole Placement for a Nonlinear Third-Order Process

Let us consider the process (S) for which the evolution is described by equation:

[B.1]

with

[B.2]

[B.3]

and

[B.4]

with

[B.5]

By linearizing the system without uncertainties around the operating point (x₀ = 0), we obtain:

[B.6]

with

[B.7]

The characteristic polynomial of the system is:

[B.8]

such that:

[B.9]

With the base change defined by matrix P_c:

[B.10]

by letting

[B.11]

[B.12]

we obtain a canonical ...