cp2dp (Model Predicitve Control Toolbox)

Converts a single-input-single-output, continuous-time transfer function in standard MATLAB polynomial form (including an optional time delay) to a sampled-data transfer function.

Syntax

[numd,dend] = cp2dp(num,den,delt)
[numd,dend] = cp2dp(num,den,delt,delay)

Description

num and den are the numerator and denominator polynomials of the continuous-time system (in the standard Control Toolbox polynomial format), delt is the sampling period, and delay is the (optional) time delay (in time units). If you omit delay, cp2dp assumes zero delay. The calculated results are numd and dend, the numerator and denominator polynomials of the corresponding discrete-time transfer function. cp2dp adds a zero-order hold at the input of the continuous-time system during the conversion to discrete-time.

cp2dp accounts properly for the effect of a time delay that is a nonintegral multiple of the sampling period. If delay=0, cp2dp is equivalent to the MATLAB commands:

[a,b,c,d]=tf2ss(num,den); 
[phi,gam]=c2dmp(a,b,delt); 
[numd,dend]=ss2tf2(phi,gam,c,d,1);

Example

See poly2tfd, poly format for an example of the use of this function.

Algorithm

cp2dp first converts num and den to the equivalent discrete state-space form. It then accounts for the fractional time delay (if any) using the formulas in Åström and Wittenmark (1984), pages 40-42. Finally, it converts the discrete state-space model to a discrete transfer-function model, simultaneously accounting for the whole periods of delay (if any).

Reference

Åström, K. J.; Wittenmark, B. Computer Control Systems Theory and Design, Prentice-Hall, Englewood Cliffs, N.J., 1984.

Restriction

The order of num must be

that of den.