M4.3 Converting Continuous Models to Discrete

The Control Toolbox can also easily convert continuous models to discrete, using the c2d command.

sysd =  c2d(sysc,Ts,method)  % continuous to discrete

where sysc is the LTI object for a continuous model, sysd is the discrete object to be created, Ts is the sample time, and method is the type of hold placed on the input variable. We always assume a zero-order hold ('zoh'); this is also the default if no entry is made for method.

Consider the continuous state space model for the van de Vusse reactor, vdv_ss. It can be converted to the discrete-time model using the following MATLAB commands:

» vdv_ssd = c2d(vdv_ss,0.1,'zoh')

a =
                        x1           x2
           x1      0.78625            0
           x2     0.066067      0.79947

b =
                        u1
           x1      0.62219
           x2    -0.075061

c =
                        x1           x2
           y1            0            1

d =
                        u1
           y1            0

Sampling time: 0.1
Discrete-time system.