Pilots' control behavior including feedback structures identified byan improved method

In controlling the flight path of an aircraft, the pilot has a choice of feedback structures. An improved identification method is applied in this paper to the determination of the feedback structure employed by the pilot. The improved method utilizes the autoregressive scheme and conducts a singular value analysis of the transfer function matrix from the innovations to the outputs in addition to the previously developed correlation analysis of the innovations. As a credibility study, the method is first applied to the da ta from a digital simulation work of an altitude tracking task in turbulence to show that it can distinguish between two hypothesized feedback structures quite clearly. The data from a fixed-base flight simulation work with the human pilots engaged in the same task are then analyzed to find that the pilots in the simulation prefer a direct altitude feedback single loop t o a multiple loop with a pitch attitude feedback inner loop. Reexamination of past flight test data is finally made to discuss the control feature of an experienced pilot, suggesting that a more careful design of the experimental situation is necessary to confirm the pilot's preference for the feedback structure. I n t r o d u c t i o n In controlling the motion of an aircraft manually, there exist various situations where the pilot has a choice of feedback structures. One such example is the control of flight path, in which it is assumed that the pilot makes either a flight path output feedback single loop or a multiple loop with an attitude feedback inner loop. Which feedback structure the pilot is actually employing is a matter in dispute to be investigated by analyzing flight test data. For the longitudinal flight path control where the vertical de\lation from the flight path, referred to as the altitude, is considered to be the primary outer loop feedback quantity, a procedure is proposed to distinguish between two hypothesized feedback structures'. In the procedure the covariance matrix of the innovations of the autoregressive model fitted to the da ta obtained from the feedback system is a key to the judgment on the feedback structure. The application of the procedure to flight simulation and flight test data, however, does not provide clearcut results. Additional information is needed to ma.ke the judgment more definite. Reference 2 proposes an improved identification procedure capable of distinguishing between two types of feedback structures more explicitly. The improved procedure 'Professor, Department of Aeronautics and Astronautics Associate Fellow AIAA conducts a singular value analysis of the transfer function matrix from the innovations to the outputs in addition to the correlation analysis introduced in Ref.1. This paper is aimed at extending the improved procedure to an aircraft control problem. Treating the altitude control of an aircraft, in which two candidates for the actual feedback structure can be hypothesized, the improved procedure is first applied to the data obtained from a digital simulation work. It then analyzes the data from a fixed-base simulation with human pilots to find which feedback structure is preferred by the human pilot. Finally the flight test da ta of Ref.1 are reexamined to discuss the control feature of an experienced pilot. P r o b l e m S t a t e m e n t Control of the altitude h by the elevator 6, has two candidates for the feedback structure, Figs. 1 and 3, either of which may be the real operational structure. Figure 1 is one candidate, a direct output feedback single loop system, referred to here as D model, while Fig.:! is the other, a multiple feedback system with a pitch attitude B feedback inner loop, referred to as I model. In Figs.1 and 2, Y,, Y,, and Y,, are pilot transfer functions, and r,, rh and ro are pilot remnants. G is the aircraft dynamics matrix comprised of h and B responses to 6, transfer functions, Gh,< and respectively, as where T denotes the transpose. The systems of Figs.1 and 2 are excited by a vertical gust ui, and a command input h,. These external signals and pilot remnants are assumed zero-mean, mutually independent random processes. The number of external signals should be consistent with the identifiability condition3. Given the definition of the system of interest, the ploblems to be posed are (1) to determine which is the actually operating feedback structure, D model or I model, and ( 2 ) to identify the transfer functions in the pertinent feedback loop. Greater emphasis is placed on the problem (1) here. Iden t i f i ca t ion P r o c e d u r e Ident if icat ion The autoregressive (AR) scheme is utilized here for the identification4,'. In the scheme the system of concern is reduced t o the feedback structure of Fig.36. In Fig.3 r-dimensional r(n) and s-dimensional n ( n ) are stationary Copyright@1993 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved 45 2 randon1 time series vectors that can be observed. The integer n is the sampling instant, n = 1 , 2 , . . .. U ( n ) and Ir(n), s-dimensional and r-dimensional, respectively, are innovation vectors. which are turned to actual external noises through the shaping filter matrices H,,(B) with the size s x s and H,(B), r x r . B denotes the backward shift operator: Rkz(71.) = x ( n I;). [Yp(B)]. s x r , and [G6(B)], r x s , are the transfer function matrices to be identified. From Fig.3 the closed-loop equation is obtained as M X (n) = A ( m ) X (1.2 m) + W (11)