User:Nillerdk/c2d

MATLAB c2d


 * zoh. Also called step invariant. Corresponds to $$G(z) = (1-z^{-1})Z(\frac{G(s)}{s})$$. Perfect for step input at sampling instants. Generally used for plant discretization.
 * ramp invariant
 * imp. Impulse invariant. Procedure: Partial fraction expansion of G(s), transform to time domain, replace t by nT, transform to z-domain. Perfect for impulse input at sampling instants.
 * tustin (bilinear transform). The definition $$z = exp(sT_a)$$ is approximated using the Padé approximant for the exponential function as $$z \approx \frac{1 + s T / 2}{1 - s T / 2}$$. Generally used for controller discretization. Frequency warping: this transform maps frequencies in s-domain uniquely in a non-linear fashion to frequencies in the z-domain (for frequencies well below Nyquist limit approx. 1 to 1). Can be compensated with the prewarping technique.
 * matched. Procedure: In factorised G(s), replace each factor (s-s0) by (1-exp(s0Ta)*z^(-1)). Very basic method, generally not to be used (poles and zeros are exactly mapped, but not what's in between them).