Process Control: Modeling, Design, and Simulation

M4.1. Forming Continuous-Time Models

Continuous-time models can be specified in one of three forms: state space (ss), transfer function (tf), and zero-pole gain (zpk).

The commands for forming these models are

sys  =  ss(a,b,c,d)  % state space
sys  =  tf(num,den)  % transfer function
sys  =  zpk(z,p,k)   % zero-pole-gain

where sys is the desired name of the model formed in each case. The a,b,c,d terms are the state space matrices. The num and den terms are vectors of polynomial coefficients, in decending order of powers in s. The z and p terms are row vectors of zero and pole locations (roots of numerator and denominator polynomials, respectively), while k is the gain term (note that this is not necessarily equal to the gain of the transfer function ...