Step response in z-domain (FOH)

 

s = tf('s');
k=6.95
G = (k*100)/((s + 10)*(s + 20));
Gd = c2d(G, 0.01,'foh') % first order hold
sys_cl = feedback(G,1)
sys_cld = feedback(Gd,1)
step(sys_cl,'--',sys_cld,'-')

 Sampling time = 0.01 sec

Step response in z-domain (ZOH)

 

s = tf('s');
k=6.95   % from root locus plots in s domain
G = (k*100)/((s + 10)*(s + 20));
Gd = c2d(G, 0.1) % zoh is the default method
sys_cl = feedback(G,1)
sys_cld = feedback(Gd,1)
step(sys_cl,'--',sys_cld,'-')

Sampling time = 0.1 sec





Sampling time = 0.01 sec






Sampling time = 0.001 sec



MATLAB’s “c2d” command convert from continuous to discrete transfer functions. The methods of conversion include the Tustin approximation and a zero-order hold on the input to the transfer function.

Zero-order hold (ZOH)

Zero-order hold (ZOH) devices convert sampled signals to continuous-time signals for analyzing
sampled continuous-time systems.
G(s) =10/(s^2 + 3s + 10)

G = tf(10,[1 3 10]); % create transfer function
Gd = c2d(G, 0.1) % zoh is the default method
step(G,'--',Gd,'-')



 http://www.mathworks.com/help/control/continuous-and-discrete-time-conversion.html