166 SAMPLED-DATA CONTROL SYSTEMS 
ness factor can be obtained merely by readjusting the linear program of 
the controller and not by increasing its complexity or design. 
In the illustrative example a staleness factor of 0.5 was used arbitrarily. 
Output 

Time, sec. 
Fic. 7.12. Response of system with staleness factor used in example to unit ramp input. 
Output 

| Time, sec. 
Fia. 7.13. Response of system with staleness factor used in example to unit step input- 
By increasing the constant toward 1.0, increased damping effect in the 
system is produced. When the damping factor is to be reduced, the 
staleness factor is lowered toward zero, at which time the minimum proto- 
type is reached. It has been shown‘ that a logical procedure can be used 
to select a desirable value of staleness factor. This procedure minimizes 
