Longitudinal Control 285Let: (Note q = x3) x A x5then:. SB = Kfiwhere: K = Afi + Bs,9.4.4 Additional Feedback TermsSometimes, to achieve required handling qualities, an additional feedback termbased upon the normal acceleration measured at the c.g.

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Is included in thefeedback control law used in pitch SAS thus:8~ = Kqq + Kazazcg (9.57)From the point of view of modern control theory, eq. (9.57) is no more thananother expression of a full state variable feedback control law. From the point of StabilityAugmentation Systems Controller and-4 Y(4 actuator + 6 ~ ( s ) Aircraft dynamics [ (4azcg sRate gyroJ~F- I Accelerometer Figure 9.13 Pitch rate and acceleration feedback SAS.view of a flight control engineer, eq. (9.57) is the practical alternative, requiringonly pitch rate and normal acceleration to be measured. Both variables arerelatively straightforward to measure using rate gyros and accelerometers locatedat the aircraft's c.g. The block diagram of a SAS, using the control law of eq.(9.57), is represented in Figure 9.13, with its corresponding dynamic responseshown in Figure 9.14.

This response should be compared with that of theuncontrolled aircraft which is shown in Figure 9.3(b). The closed loop responsesshown in Figures 9.8, 9.9 and 9.12 should also be inspected for comparisonpurposes. Acceleration feedback is generally considered to 'stiffen' the system,i.e.

The short period frequency is invariably increased. This can be appreciatedeasily by considering FOXTROT-c3ontrolled by the law of eq. (9. Manual For Xerox Memory Writer 62565. 57), where:1-0.01 0 I I I I I I ' II I 1 2 3 5 4 Time (s)Figure 9.14 Response of blended control to a(O)= lo.

Longitudinal Control --r 7 e - I.' F 'p, j i ~ l i ~chontdition 2 FlightO f1~lig hcot ndition 3 condition 4-0.035 -!!-0.040[ 1 I I I I I I I I I 0 12 3 4 5 Time (s)Figure 9.15 Response of pitch rate SAS for four flight conditions.The corresponding eigenvalues of the controlled system are: phugoid: XI, X2 = - 0.0066 f j0.005 short period: h3, X4 = - 26.4 f j43.55In American papers, a control law such as eq. (9.57) is often referred as 'blendedfeedback control'; such a control law is usually used to achieve, as nearly aspossible, invariant flying qualities throughout the flight envelope of the aircraft.The closeness with which this ideal is approached depends upon the ratio ofthe feedback gains, K, and K,.