Response of control loop components to forcing functions

Forcing function is a term given to any disturbance which is externally applied to a system. A number of simple functions are of considerable use in both the theoretical and experimental analysis of control systems and their components. Note that the response to a forcing function of a system or component without feedback is called the open-loop response. This should not be confused with the term open-loop control which is frequently used to describe feed-forward control. The response of a system incorporating feedback is referred to as the closed-loop response. Only three of the more useful forcing functions will be described here. 

Here M is termed the amplitude of the signal and w its angular frequency in radians/unit time. The frequency may also be expressed as  

This may alternatively be represented by two successive step functions of the same magnitude but of opposite sign, i.e.  

By l H pital s rule(15) the limit of an indeterminate quantity is the same as that of the function obtained by independently differentiating numerator and denominator with respect to the variable which is approaching the limit. 

When A/ = 1 we have the special case of the unit impulse, often termed the Dirac function 5(f). 

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See also in sourсe #XX -- [ ]

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