The Systems Concept

The concept of the airplane’s airframe as only one object in a complete dynamical system is part of the thinking of today’s stability and control engineer, when faced with the need for stability augmentation. Yet, early researchers in airplane stability augmentation did not approach the problem that way (Imlay, 1940). Imlay enlarged on the classical Routh criterion for stability by the use of equivalent airplane stability derivatives. The equivalent derivatives are the basic control-fixed stability derivatives plus the products of control derivatives such as the yawing moment coefficient due to rudder deflection and a gearing ratio. The gearing ratio is an assumed control deflection per unit airplane motion variable. For example, Imlay studied gearings of 0.356 and 1.116 degrees of rudder angle per degree of bank and yaw, respectively.

The point is that the Imlay stability augmentation analysis method deals only with a modified airplane. No other dynamical elements are represented, although the lag effects of the servomechanism that would drive the control surfaces are suggested by a somewhat awkward representation of a simple time lag as the first three terms of the power series for the exponential.

The key mathematical concept that leads to modern augmentation analysis methods is the control element, which is represented graphically by a box having an input and an output. Control element boxes are linked one to another, with the output of one serving as the input to another. Control elements include sensors such as gyros; pneumatic, electric, or hydraulic control actuators; and, of course, the dynamics of the airframe, or control surface angle as an input and motion such as pitch or yaw rate as an output. Summing and differencing junctions act on inputs and outputs as needed, most notably to create an error signal. This is the difference between the commanded and actual system outputs.