It is frequently helpful to view a feedback loop as simply a method of altering one of the airplane’s inherent stability derivatives. When one of the main damping deriva­tives, Lp, M4, or Nr, is too small, or when one of the two main stiffnesses Ma or Nfj is not of the magnitude desired, they can be synthetically altered by feedback of the ap­propriate control. Specifically let x be any nondimensional state variable, and let a control surface be displaced in response to this variable according to the law

Д 8 = к Ax; к = const

(Here к is a simplified representation of all the sensor and control system dynamics!) Then a typical aerodynamic force or moment coefficient Ca will be incremented by

ДСа = CasA8 = CaJcAx

This is the same as adding a synthetic increment

A Cax = kCas

to the aerodynamic derivative CUr. Thus if x be yaw rate and 8 be rudder angle, then the synthetic increment in the yaw-damping derivative is


which might be the kind of change required to correct a lateral dynamics problem. This example is in fact the basis of the often-applied “yaw damper,” a stability-aug­
mentation feature. Again, if x be the roll angle and 8 the aileron, we get the entirely new derivative

С1ф = кСІВи (8.1,10)

the presence of which can profoundly change the lateral characteristics (see Exercise


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