Process Control: Modeling, Design, and Simulation

Appendix 4.2

Discrete time models can be obtained directly from continuous time models, as summarized in this appendix. The MATLAB Control Toolbox can be used for these conversions, as shown in Module 4.

Consider a continuous state space model of the following form (where we have assumed D = 0)

Equation A4.1

A similar discrete state space model has the following form

Equation A4.2

Assuming that the sample time is Δt, and that the input u is held constant between time t_k and t_k+1, (A4.1) can be integrated to yield

which has the solution (although ...