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M.Goman et al (1993) - Aircraft Spin Prevention / Recovery Control System

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М.Г.Гоман, А.В.Храмцовский, В.Л.Суханов, В.А.Сыроватский, К.А.Татарников «Система предотвращения попадания / вывода самолёта из штопора», доклад на 3-й российско-китайской научной конференции по аэродинамике и динамике полёта самолёта, Центральный Аэрогидродинамический институт (ЦАГИ), г.Жуковский, 1993 г., 14 стр.

M.Goman, A.Khramtsovsky, V.Soukhanov, V.Syrovatsky and K.Tatarnikov "Aircraft Spin Prevention/Recovery Control System", presented at the Third Russian-Chinese Scientific Conference on Aerodynamics and Flight Dynamics of Aircraft, Central Aerohydrodynamic Institute (TsAGI), Zhukovsky, Moscow region, Russia, November 9-12, 1993, 14 pp.

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M.Goman et al (1993) - Aircraft Spin Prevention / Recovery Control System

  1. 1. Aircraft Spin Prevention/Recovery Control System M. Goman, A. Khramtsovsky, V. Soukhanov, V. Syrovatsky and K. Tatarnikov Central Aerohydrodynamic Institute Zhukovsky-3, Moscow region, Russia Third Russian–Chinese Scientific Conference on Aerodynamics and Flight Dynamics of Aircraft TsAGI, Zhukovsky, Moscow region, Russia November 9-12, 1993
  2. 2. Aircraft Spin Prevention/Recovery Control System M. Goman A. Khramtsovsky V. Soukhanov V. Syrovatsky K. Tatarnikov Abstract The problem of spin prevention and spin recovery for the high-performance, high-augmented airplane is formulated. The methods of the flight dynamics mathematical simulation, sta- bility and bifurcation analysis at high angles of attack are briefly outlined. Good correlation between the flight tests data and the results of mathematical modeling of the aircraft dy- namics at stall and spin regimes made it possible to use the flight simulation as the effective tool for the design of the algorithms of the automatic spin prevention/recovery system. The efficiency of various control methods for the spin recovery is analyzed. The efficiency of the resonance rocking technique for the recovery of the aircraft from deep stall and flat spin regimes was first demonstrated by the theoretical analysis and mathematical modeling and later confirmed during the flight tests. Introduction The problem of safe and controllable flight of the modern airplane at high angle of attack is closely joined with the problem of critical aircraft flight regimes such as stall and spin. For modern aircraft spin remains one of the dangerous regimes. That’s why the search for the means of spin prevention and recovery continues. One of the possible solutions is the utilization of the special automatic control system for spin prevention/recovery [1]. The analysis of the aircraft flight accidents shows that the majority of rank-and-file pilots are unable to cope with spin recovery. Very often they even can’t identify the situation and don’t use the standard methods recommended for recovery from critical flight regimes. It is impossible to eliminate totally the possibility of the spin entry by developing al- gorithms for automatic angle-of-attack limitation. The variety in flight conditions and the dependence of control system algorithms on a large number of flight parameters result in either extremely complex limitation system, or reduced maneuverability of the aircraft. Ex- tensive flight experience shows that various control system limiters, intended for keeping an aircraft within controlled flight envelope, in definite conditions can not prevent departures from controlled flight. The problems which lead to difficulties in maintaining stability and control during maneuvering flight are common to different types of aircraft configuration. An adverse behavior of aircraft at high angle of attack is related with the so called Nose slice, Loss of control power, Wing Rock and other dynamic phenomena. To improve aircraft dynamic characteristics at low angle of attack a stability augmentation system (SAS) is used, but for high angle of attack conditions more sophisticated control laws are needed Fig. 1. From our point of view, optimal solution to the problem lies in using relatively simple DPS (departure prevention system) together with automatic SRS (spin recovery system). 1
  3. 3. The SRS algorithms can be considered as ”back-up” algorithms intended for special flight situations. Figure 1: Maneuvering limitation factors. Control subsystems. The development of mathematical model of aerodynamics for high angle of attack con- ditions, the investigation of the aircraft behavior at stall and spin regimes are necessary research elements for control system design and finding the control laws for spin preven- tion/recovery system. In this paper some attention is given to the methods of mathematical modeling of aerodynamic coefficients using different wind tunnel data and to the methods of stability and bifurcation analysis at high angles of attack. The aircraft dynamics simulation excellently complements the qualitative methods of analysis for examination the different spin recovery techniques. The adequate mathematical model permit also to train the test pilots skills and to master new methods of aircraft handling at the simulator before real flights. Aerodynamic model for the modeling of the stall and spin regimes. The aerodynamic model intended for the modeling of the aircraft dynamics at high angle of attack and stall/spin regimes, is based on the experimental data obtained from the following wind tunnel tests: • static wind tunnel tests, • forced-oscillation tests, • rotary balance tests. The development of the rotation during high angle of attack excursions (at spin, for ex- ample) can influence significantly the flow pattern. As a result, the aerodynamic coefficients become nonlinear functions of the reduced rate of rotation. That’s why the aerodynamic coefficients measured in rotary balance tests are considered as basic ”nondisturbed” part of the aerodynamic model for high angle of attack conditions. In the rotary balance wind tunnel experiments the total rotation vector Ω usually is fairly closely aligned with the velocity vector. From these experiments, the following de- pendencies of the aerodynamic coefficients on α, β, ω = Ωb 2V and on deflections of control 2
  4. 4. surfaces δ are received: Ci = CiRB α, β, ω, δ where i ∈ {l, m, n, X, Y, Z}, δ = (δh, δe, δa)T , and RB subscript stands for ”rotary bal- anced”. There exist a number of methods of designing the ”combined” mathematical model using the results from various experiments [2], the authors used the approach described below. During the disturbed motion, the aircraft parameters deviate from their steady-state values at spin conditions, and the misalignment between the velocity vector and the total rotation vector appears. It can be assumed that the disturbed values of the aerodynamic coefficients are proportional to the kinematic values describing the disturbances. For the spatial motion with the total rotation vector being fairly closely aligned with the flight path, the projections of the total rotation vector onto the axes of the wind-body coordinate system can be considered as such kinematic parameters: pw = (p cos α + r sin α) cos β + q sin β qw = − (p cos α + r sin α) sin β + q cos β rw = r cos α − p sin α (1) The projection onto the direction of the velocity vector pw defines the rate of conical rotation. The values of qw and rw define the rates of change of the angles of attack and sideslip in the disturbed motion ˙α = qw/ cos β + ˙αT ˙β = −rw + ˙βT where ˙αT , ˙βT are due to the center-of-gravity translational motion. Assuming that the disturbances of the pure conical motion are small, the following representation of the aerodynamic coefficients can be used: Ci = CiRB α, β, pwb 2V , δ + Ciqw qwc 2V + Ci ˙α ˙αc 2V + Cirw rwb 2V + Ci ˙β ˙βb 2V = CiRB α, β, pwb 2V , δ + Ciqw + Ci ˙α / cos β qwc 2V + Cirw − Ci ˙β rwb 2V + Ci ˙α ˙αT c 2V + Ci ˙β ˙βT b 2V (2) The aerodynamic derivatives from (2) correspond to the conditions of the conical rota- tion. They can be measured, for example, by means of the oscillatory coning technique, such as already in use at ONERA–IMFL [2]. In the present investigations, the data obtained from ”traditional” forced oscillations tests (measured in the absence of the model rotation) were available, the usage of these data is certainly not quite consistent with the methodology described. The rotary and unsteady aerodynamic derivatives were calculated as follows (the influence of ˙αT and ˙βT was neglected): Ciqw + Ci ˙α Ciq + Ci ˙α F.O. Cirw − Ci ˙β Cir − Ci ˙β · cos α0 F.O. cos α0 − Cip + Ci ˙β · sin α0 F.O. sin α0 (3) where the subscript ”F.O.” denotes the data from forced oscillations tests. 3
  5. 5. In the situations when the nonlinear term in (2) can be approximated with a linear function of the angular rate, the representation (2) becomes equivalent to the common aerodynamic model usually used for low angles of attack. In this case, the results of static wind tunnel tests can also be incorporated into the mathematical model, especially at low angle of attack. The form of the aerodynamic model (2) for stall/spin conditions is quite natural. For example, the rotary derivatives Ciqw and Cirw don’t affect significantly neither the values of kinematic parameters at the steady-state spin conditions nor their mean values during the oscillations with moderate amplitude. These derivatives as well as unsteady derivatives Ci ˙α and Ci ˙β directly affect the placement of the eigenvalues of the linearized equations of motion in the complex plane. Thus they determine the oscillatory stability of the disturbed motion. Our experience shows that the usage of the dependencies CiRB α, β, ω, δ allows to get realistic values of the spin kinematic parameters during the modeling. To get the correct time histories and amplitudes of the oscillations, one can make some adjustments (if necessary) to rotary and unsteady derivatives Ciqw , Cirw , Ci ˙α , Ci ˙β . Cm Cn full nose-up full nose-down αu αs α Cn0 (α) Cncontr α Figure 2: Pitching and yawing aerodynamic moments Typical pitching and yawing aerodynamic characteristics. One of the important features in the modern aircraft high angle-of-attack aerodynamics are the insufficient nose-down pitching control power, and the development of large-magnitude 4
  6. 6. nonsymmetrical yawing moments Cn0 . The magnitude of Cn0 can exceed the available lateral control power. (see fig.2). The flight tests data analysis shows that the value of Cn0 do not correlate with the value of sideslip angle, it depends primarily on the value of the angle of attack. For example in the range of 40o ≤ α ≤ 50o the Cn0 coefficient has one sign, and in the range of α ≥ 50o it has the opposite sign. The direction of the aerodynamic nonsymmetrical moment repeats rather regularly during the same flight and for a number of successive flights, but may vary during long period of service. The deficiency in the nose-down pitching moment within a certain range of the angle of attack causes deep stall regimes. The unsymmetrical yawing moments may result in the development of the ”unrecoverable” flat spins. Methodology of nonlinear aircraft dynamics investiga- tion. Modern airplane is a highly nonlinear dynamical system. It is clearly seen during spatial (6 DOF) maneuvers and the flights at high angle of attack. Traditional methodology of aircraft motion investigation heavily relies on mathematical simulation of the aircraft dynamics by means of numerical integration of the full set of nonlinear equations of motion, and on linear stability analysis using frequency–domain and algebraic methods. It is not able to predict all the nonlinear phenomena exhibited by the airplane, for example, in stall, spin or in maneuvers with high roll rates. New methodology based on recent results in mathematics (Bifurcation theory, Qual- itative analysis of the nonlinear dynamical systems) is an efficient, but delicate tool for studying aircraft dynamics in these conditions [3]. And mathematical simulation is a good complement to it. New methodology implies calculations of the equilibrium flight conditions and oscilla- tory motions (for example, an aircraft is in equilibrium during spin if the angle of attack, sideslip and pitch, roll and yaw rates do not oscillate). The influence of the control in- puts or flight regime parameters on the aircraft equilibrium can be easily calculated. The data obtained enable the researcher to predict dangerous phenomena such as stall and spin entries, and to develop a recovery technique. Krit package was optimized for such calculations [4]. It is especially useful for studying the steady–state flight regimes (with or without oscillations, stable or unstable) and their dependence on certain factors. You may even use a set of mathematical models of the vehicle during a dialog with the package. A unique feature of the Krit package is an effective set of procedures for an exact cal- culation and analysis of the steady–state oscillatory flight regimes using Poincare mapping technique. Krit scientific package can be applied to the following problems in aircraft flight dy- namics: • Calculation of the equilibrium conditions for the spatial (6 DOF) maneuvers and high angle of attack regimes (stall, spin, regimes with rapid rotation). Local stability analysis of these regimes. • Calculation of the oscillatory flight regimes at high angles of attack ( wing rock, oscillatory spin). Local stability analysis of these regimes. • Numerical simulation of the arbitrary spatial aircraft motion. 5
  7. 7. • Computation of the critical values of the control inputs and the flight regime param- eters when an abrupt loss of stability and transfer to the dangerous regimes occur. • Calculation of the stability regions or stability to finite perturbations. • Determining control for spin recovery. Automatic system for the aircraft spin recovery. The control system of modern maneuverable aircraft may comprise the following subsys- tems: • stability and controllability augmentation system for operational flight conditions (SAS); • angle-of-attack and g-load limitation system; • departure and spin prevention system (DPS); • spin recovery system (SRS); In this section some aspects of the algorithms for spin recovery are discussed. The results of these flight tests are used for the improvement of the aircraft aerody- namic model and for determining of the recovery technique. After that the corresponding mathematical model for the simulation and the recovery algorithms are developed. During the investigations on ground-based simulators the parameters of SRS are ad- justed, and the interaction between SRS and main control system as well as the SRS–pilot interaction are studied. At the same time pilots assess the serviceability and convenience of SRS. ”Positional” recovery method. The experience of flight tests and mathematical simulation revealed the most effective ”po- sitional” (or ”static”) recovery method for different types of aircraft. It means for example that the control stick is set to the neutral position (in longitudinal control) hence the ele- vator deflection is near-zero according to control system algorithms. In lateral channel, the stick is deflected ”pro spin” (towards the rolling) while pedals are deflected against yawing. When aircraft rotation is stopped and angle of attack diminishes to operational values, the stick is pushed forward in order to recover from spin to diving at low angle of attack. SRS system can easily realize such a technique automatically. SRS system algorithm incorporates the following modules (see fig.3): • spin entry identification module; • the module implementing the ”positional” recovery algorithm; • the module that switches the signals going to control surfaces’ actuators; • spin recovery identification module. The ”positional” recovery algorithm can be realized using yaw rate signal r. The full aileron, rudder and differential elevator deflection is used taking into account the sign of the yaw rate r. The elevator is set to ϕmin Cm 0o ÷ 2o . After stopping the rotation and 6
  8. 8. Spin recovery identification Spin entry identification ”positional” recovery algorithm Control algorithms for normal flight Control surfaces’ actuators - - - -α β nz Q r r r r b b b b b b b b -r - - α r - - -α r Q - -key 6 δi δi Figure 3: Arrangement of spin recovery system diminishing angle-of-attack from ”spin level” values α 60o ÷ 80o to ”stall level” values α 30o ÷ 40o , the elevator for a short time t 0.5 ÷ 1 s is deflected to a full nose-down position ϕmax = 15o . After that spin recovery is checked, and the control system is switched from SRS to normal flight algorithms. if |r| < r if α ≤ 30o aeroelastic vibrations filter kr ka kde - - ?b b bb b - 61 r1r2 aileron rudder differential elevator α r ϕmin Cm ϕmax elevator Figure 4: Implementation of recovery algorithm Spin entry identification module is rather complex for implementation. The problem is due to reliability requirements. Turning on SRS by mistake will certainly result in an accident, especially because SRS algorithm uses full deflections of the control surfaces. It is possible to use an approach when the spin recovery is performed only if the pilot has toggled special switch and the spin entry identification module generates the ”aircraft in spin” signal. Pitch rocking method. In the absence of the sufficient nose-down pitching control power and low level of the control power in roll and yaw at high angle of attack additional problem arises. In these cases the deep stall and flat spin regimes can be hardly recoverable. In both cases, the ”positional” deflections of the control surfaces may be insufficient for the aircraft recovery from critical 7
  9. 9. regimes, since these regimes keep to exist even when the full controls against the regime are set. The resonance pitch rocking technique can be used to recover from these regimes (see also [5]). For example, the elevator is deflected according to the formula ϕ = ϕ0 + Aϕ · sign q (4) The rate saturation of elevator deflection also should be taken into account during incorporation of the law (4) into real control system. Since the change of sign of the pitch rate q must correspond to the elevator position in the middle between extreme deflections of the elevator during rocking, the signal for elevator reversal should be formed with some time advance. The level of oscillations is an important qualitative characteristic of the spin regime, the selection of the recovery technique depends on it. The higher the amplitude of the oscillations, the easier the recovery from the spin. This fact is supported by the flight tests data as well as by the mathematical simulation results. Both the intensity and the level of oscillations depend, in particular, on the form of the function Cn0 (α), Cn0 (α) is the aerodynamic nonsymmetrical moment. The magnitude of the aerodynamic nonsymmetrical moment vary from the airplane to airplane even for the same type of the aircraft. Moreover, it varies for the same plane during its operating period. No wonder that one can encounter different types of spins. Correspondingly, the recovery technique and the recovery time may vary. But at the same time, the above-mentioned qualitative features remain. Mathematical simulation proved that resonance rocking by means of longitudinal con- trols is the efficient method of spin recovery. Since rocking algorithms are ”universal” and independent of any aircraft aerodynamic coefficients, resonance rocking is the most effi- cient method of flat spin recovery. If high-level nonsymmetrical aerodynamic moments are developed at high angle of attack, aircraft can’t be recovered from spin using standard ”po- sitional” methods. In that case the ”static” deflection of longitudinal and lateral controls doesn’t affect significantly aircraft motion in spin. When applying the resonance rocking, the aircraft is recovered from flat spin no more than in 8 sec. Thus if the ”positional” method fails then rocking algorithm is used for spin recovery. The rocking algorithm can be switched on with some time delay after switching on ”positional” algorithm provided spin recovery identification module doesn’t signals the recovery. When the resonance rocking is used for recovery from deep stall or flat spin, the most complex problem is to determine the moment when the rocking should be switched off. The elevator deflection according to the algorithm (4) in some conditions doesn’t result in the transition to low angles of attack, and high-amplitude ±10o ÷ 15o angle-of-attack periodic oscillations take place instead. That’s why it is necessary to predict the possibility of recovery to low angles of attack on-board the airplane. When corresponding conditions are satisfied, the rocking algorithm is switched off and the elevator is placed into ”maximum nose-done moment” position. To assess the possibility of the recovery, the angle-of-attack, angle-of-attack rate ˙α and pitch rate q should be known. Some speculations and simulation results. The example of the mathematical modeling of the aircraft dynamics at the flat spin is shown on fig.5. The deflection of the lateral controls cannot stop the rotation, the rotation rate remains high (r 1 rad/sec) until t = 65 sec. After that asymmetric thrust of the engines is used to recover, the level of the yawing moment due to asymmetric thrust is 8
  10. 10. rather high because of the large thrust force arm along side axis. The resonance rocking technique may be also used for recovery from the flat spin. Figure 5: Simulation of spin recovery q S αu αs α δ (t) Figure 6: The domain of asymptotic stability S of the deep stall regime αs To illustrate the efficiency of the resonance rocking recovery technique, consider short- period motion of the statically unstable aircraft. At the full nose-down elevator deflection (see dashed line on fig.2), there exists stable high angle-of-attack trim at αs. The domain of stability of that deep stall regime is formed by the separating trajectories approaching unstable singular point in the phase plane (αu, q = 0). The aircraft can be recovered from deep stall regime only by applying such a control δ (t) that moves the aircraft out of the region of the asymptotic stability S of the deep stall regime at αs (see fig.6). The resonance rocking algorithm can be used to select the appropriate deflections of the control surfaces δ (t). The resonance rocking results to the increase in the amplitude of the oscillations due to the accumulation of the energy, and can lead to the leaving of the stability region S. 9
  11. 11. Figure 7: The diagram illustrating rocking method Figure 8: Spin recovery using resonance rocking For the aircraft spatial motion at flat spin, the idea of rocking can be illustrated using the ”potential” function with two minimums as an example (see fig.7). It is assumed that the minimum X2 corresponds to the stable critical regime (spin), and the minimum X1 corresponds to the normal low angle-of-attack flight regime. The efficiency of the resonance rocking technique as a complementary algorithm to the positional recovery technique is shown on fig.9. Spin recovery time can be drastically reduced due to resonance rocking, especially for the aft c.g. position and large values of the non-symmetrical yawing moment. The results of the mathematical modeling of the spin recovery using rocking algorithm are shown on fig.8. First the aircraft enters the flat spin. Then the pilot attempts to recover using positional deflections of the lateral controls, all these attempts fail. After that (t 75 sec) the rocking is initiated. The amplitudes of the angle-of-attack and roll rate oscillations rise, yaw rate decreases and later the angle of attack also decreases. The results of the mathematical modeling and the results of the experiments at flight 10
  12. 12. Figure 9: Efficiency of the resonance rocking technique. Time of the spin recovery. 11
  13. 13. simulators are in a good agreement with high angle-of-attack flight tests data provided the the nonsymmetrical yawing moments are included into the model of the aircraft aerody- namics. stall and spin entry steady-state spin automatic recovery from spin recovery from diving H, m Figure 10: Spin recovery simulation The example of flight path and the orientation of the aircraft during the modeled spin entry/spin recovery is shown in fig.10. 12
  14. 14. Conclusions Spin recovery technique for modern aircraft is too complicated for rank-and-file pilots. Only the best aces having many hours of the flight experience are able to recover from spin. This problem can be solved very efficiently by means of the special spin prevention/reco- very control system. The algorithms of such system take into account characteristic features of the airplane under consideration and use different recovery techniques for different flight situations. The control system for the spin recovery has to use ailerons, rudder, elevator deflections etc. in more optimal manner for high angle of attack conditions. In particular, the method of pitch rocking is very efficient for recovery from deep stall and steady flat spin regimes. Extensive simulation of aircraft spin recovery is necessary to select suitable values of the parameters of prevention/recovery system. The success of the whole project strongly depend on the development of an adequate mathematical model of aerodynamics and com- pleteness of the nonlinear dynamics analysis for aircraft spin conditions. References [1] Akhrameev V.I., Goman M.G., Khramtsovsky A.V. et al., “Automatic Spin Recovery System for Modern Fighter”, Technika Vozdushnogo Flota (the journal), no.3, 1991, (in Russian). [2] “Rotary-Balance Testing for Aircraft Dynamics”, AGARD-AR-265 Advisory Report, Advisory Group for Aerospace Research and Development, NATO, published Dec. 1990. [3] Zagaynov G., Goman M. “Bifurcation Analysis of Critical Flight Regimes”, – Proceed- ings ICAS–84-4.2.1, pp.217-223. [4] Goman M., Khramtsovsky A. “KRIT Scientific Package. User Guide.”, TsAGI, 1992. [5] Medina M., Shahaf M. “Post Stall Characteristics of Highly Augmented Fighter Air- craft”, Proceedings ICAS–90-5.10.2, pp. 1976-1983. 13

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