Research of Aircraft Flight Dynamics Peculiarities Due to the Using of Electric Actuators in Control System

03/02/2015
Auteurs : V. Kuvshinov
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Research of Aircraft Flight Dynamics Peculiarities Due to the Using of Electric Actuators in Control System

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Research of Aircraft Flight Dynamics Peculiarities Due to the Using of Electric Actuators in Control System V.M. Kuvshinov Central Aerohydrodynamic Institute, Zhukovsky city, Moscow reg., Russia, vmkouvsh@progtech.ru Abstract Modified type of electrohydrostatic actuator (EHA) - actuator with combined throttle-volume control is considered. Principle features of this actuator are using of irreversible electric motor and reversal servo valve for change of rod motion direction and throttle control at small input signal. Mathematical models of EHA with combined throttle-volume control and classical EHA are developed. Comparative analysis of dynamic characteristics of two considered EHA types and usual electrohydraulic servo-valve actuator is performed on the base of transient and frequency responses calculations. Mathematical simulation of longitudinal motion of airliner with controllability & stability augmentation system (CSAS) and EHA at action of critical wind gusts and at intensive maneuvering is performed. Results of simulation shows that aircraft stability characteristics with CSAS and EHA with combined control are close to corresponding characteristics for usual electro-hydraulic actuator, whereas using of classical EHA may result in essential decrease of closed loop stability margins and even in loose of aircraft-CSAS system stability at action of big disturbances. Introduction “Electrification” of aircraft control system is one of the advanced technologies, which can improve aircraft performance and maintainability characteristics. Practical use of electrically powered actuators in aircrafts began at the present time (А380, А400, F- 35B and others). Main attention at developing of electrically powered actuators is given now to the problems of actuator design – realization of required force and power at diminishing of weight and size, heating, reliability etc. But possible peculiarities of «aircraft-control system» closed loop dynamics at using of such actuators are researched scanty. Two types of electrically powered actuators are applied on aircraft: electromechanical (EMA) and electrohydrostatic (EHA). Both these actuators have some shortcomings in dynamics properties with respect to usual electrohydraulic servo-valve actuator (EHSA), first of all at small and very big input signals. For this reasons it is obligatory to perform analysis of electrically powered actuators dynamic behavior at its work as a part of aircraft control system. EHA with combined throttle-volume control To improve dynamic properties of classical EHA new type of EHA - EHA with combined throttle-volume control (EHAC) was developed [1]. EHAC principle structure is shown in fig. 1. Main differences of EHAC design from classical EHA consist in using of: – irreversible electric motor (4) and pump (5) rotating at zero input control signal with respectively small rate to provide initial pressure level and compensate pump leak, – servo valve (7) to provide change of rod motion direction and throttle control at small input signal, – electric motor (4) and pump (5) rotation rate control at large input control signals (volume control). Mathematical model of EHAC in MATLAB/Simulink was developed (fig. 2) which takes into account dynamic properties describing EHAC behavior in frequency range up to 2 Hz. Considered EHAC has parameters appropriate to middle range airliner elevator actuator: rod stroke ±35 mm, deflection rate 55 mm/s ( =30 deg/s), maximum force 2.8 T. max e δ& Power Inverter Actuator control unit Psup Pcil EM control unit BLEM Fig. 1: EHA with combined control Fig. 2: EHAC Simulink model EHA and EHAC dynamic characteristics Comparative analysis of dynamic characteristics of two considered EHA types and usual electrohydraulic servo-valve actuator was performed on the base of frequency and transient responses calculations. These responses shown in fig. 3, 4 were calculated at neglecting of nonlinearities in actuator characteristics at very small input signal for simplification. -10 -8 -6 -4 -2 0 2 L,dB 0.1 0.2 0.4 0.6 0.8 1 2 3 4 5 -120 -90 -60 -30 0 f Гц Фаза 3 2 1 0.5 0.2 0.1 0.05 Electrohydraulic actuator EHSA Phase EHA with combined control -10 -8 -6 -4 -2 0 2 0.1 0.2 0.4 0.6 1 2 3 4 5 -120 -90 -60 -30 0 f Гц 3 2 1 0.5 0.2 0.1 0.05 -10 -8 -6 -4 -2 0 2 0.1 0.2 0.4 0.6 0.8 1 2 3 4 5 -120 -90 -60 -30 0 f, Гц 3 2 1 0.5 0.2 0.1 0.05 Classical EHA f, Hz Fig. 3: EHSA, EHAC and EHA frequency responses At small input signals characteristics of EHSA and EHA with combined control are close with each other, but classical EHA has rather bigger delay than EHSA. At big input signals delay for EHA with combined control is rather bigger then delay for EHSA and classical EHA has considerable bigger delay than EHSA. For example phase delay of electrohydraulic actuator at the frequency 1 Hz is equal 18º, for EHAC falls within the range 18…27º (depending of magnitude of input signal) and for EHA is equal 29º. Corresponding results gives calculation of transient responses (fig. 4). Equivalent time delay t1 for EHSA is equal to t1=0.009 s for step input 0.2º and 1º. For EHAC this delay is equal 0.017 s and 0.041 s, for EHA considerable bigger: 0.032 s and 0.048 s. Phisical reason of EHA big delay first of all is need to spinup electric motor and pump which have big enough inertial moment. Second reason is presence of electric motor stator voltage (current) constraint. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 t, сек δ, гр t1 =0.032 - классический ЭГСП t1 =0.017 - ЭГСП с комб. упр. t1 =0.009 - ЭГРП классический ЭГСП ЭГСП с комб. упр. ЭГРП t, s deg , δ ⎯⎯ Electrohydraulic actuator ⎯⎯ EHA with combined control ⎯⎯ Classical EHA Electrohydraulic actuator EHA with combined control Classical EHA 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.2 0.4 0.6 0.8 1 t, сек δ, гр t rsp 0.95 =0.174 t rsp 0.95 =0.148 t rsp 0.95 =0.107 t 1 =0.048 t 1 =0.041 t 1 =0.009 классический ЭГСП ЭГСП с комб. упр. ЭГРП t, s deg , δ ⎯⎯ Electrohydraulic actuator ⎯⎯ EHA with combined control ⎯⎯ Classical EHA Fig. 4: EHSA, EHAC and EHA transient responses Aircraft-CSAS characteristics Well-known problems in aircraft with controllability & stability augmentation system (CSAS) dynamics due to the actuator characteristics are: – aircraft-CSAS closed loop stability margins, – stability at critical wind gusts action, – stability at maximum pilot command signal, – self-oscillations for unstable aircraft due to nonlinearities in actuator at small signal. To analyse possible peculiarities of aircraft-CSAS flight dynamic due to the using of EHA actuators closed loop aircraft-actuator-CSAS model was developed (fig.5). Longitudinal motion of middle range airliner with modern high feedback gains CSAS was considered. Different types of elevator actuator were considered. To analyze closed loop stability margins Ke-τs element is included in the loop. Ke-τs CSAS Actuator Aircraft Xp Wind Fig. 5: Aircraft-CSAS-Actuator closed loop model Search of boundary values of gain Kb and time delay τb producing closed loop loos of stability was performed for different type and intensity of disturbances and pilot comands. Self-oscillations due to the actuator rate constrains take place after loos of stability. Vertical wind gust of W=Wmax/2*cos(1- 2πt/TW) type was shown as critical for aircraft-CSAS closed loop stability. Fig. 6 shows dependence of boundary values of time delay τb and gain margin 20lgKb (dB) from the gust intensity Wmax for aircraft take off regime for minimum allowed static stability margin dCm/dCL=-2%. Analysing these dependence and appropriate transient responses to make following conclusions is possible. Aircraft-CSAS stability characteristics at small distarbancies Wmax ≤ 4 m/s are determineted by characteristics of actuators in zone of its linear dynamics. Stability margins at using of electro- hydraulic actuator and EHAC are the same, at using of EHA are slightly worse (phase margin on 4.5º, magnitude margin on 0.4 dB). Loss of stability at bigger distarbancies Wmax > 4 m/s takes place at reaching constraints in actuators, in particular deflection rate constraint. Decrease of phase and magnitude margins for electrohydraulic actuator is equal 2.5º and 0.4 dB, for EHAC – 17º and 2.9 dB and for EHA – 45º and 6.2 dB up to possible loss of aircraft-CSAS stability. Sharp pilot command signal action is not critical for aircraft-CSAS closed loop stability because of possibility to protect actuator from this action by using of special pilot signal prefilter included in CSAS FBW control algorithm. In considered case of own aircraft stability presence of nonlinearities in actuator characteristics at small input signal do not cause any problems (for example small magnitude self-oscillation). If we suppose that aircraft is statically unstable dCm/dCL=+7% we can see aircraft self-oscillation. Self-oscillation magnitude for the case of EHA with combined control using is close to the corresponding magnitude at electro- hydraulic actuator using and may satisfy to the established requirements at using of modern servo valve. Characteristics of classical EHA with reversible electric motor at small input signals are substantially worse due to the presence of quiescence friction in electric motor and pump and self-oscillation magnitude is inadmissibly large. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Скорость порыва, м/c ЭГРП ЭГСП с комб. управл. классический ЭГСП потеря устойчивости без доп. запаздывания ∆φ=46,5 град ∆φ=29 град ∆φ=44 град ∆φ=42 град ∆φ=-3 град Time delay τ margin, s Wmax, m/s ⎯ Electrohydraulic actuator ⎯ EHA with combined control ⎯ Classical EHA deg deg deg deg deg 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -2 -1 0 1 2 3 4 5 6 7 8 Скорость порыва, м/c ЭГРП ЭГСП с комб. управл. классический ЭГСП потеря устойчивости без доп. запаздывания ∆L=6.2 дБ ∆L=5.8 дБ ∆L=3.3 дБ ∆L= -0.4 дБ ∆L=5.8 дБ Gain K margin, dB Wmax, m/s ⎯ Electrohydraulic actuator ⎯ EHA with combined control ⎯ Classical EHA dB dB dB dB dB Fig. 6: Aircraft-CSAS stability at wind gust action Thus aircraft stability and controllability characteristics with CSAS at EHA with combined control using are close to corresponding characteristics at using of usual electro-hydraulic actuator, whereas using of classical EHA may result in essential decrease of closed loop stability margins and even in loose of aircraft-CSAS system stability at action of big disturbances. Conclusions Mathematical models of two EHA types (classical EHA and EHA with irreversible electric motor, reversal valve and combined throttle-volume control) are developed. Corresponding EHA program models for MATLAB/Simulink are created. Calculated model characteristics agree with the experimental data. Comparative analysis of dynamic characteristics of two considered EHA types and electrohydraulic servo-valve actuator (EHSA) shows that at small input signals characteristics of EHSA and EHA with combined control are close with each other, but classical EHA has rather bigger phase delay than EHSA. At big input signals phase delay for EHA with combined control is rather bigger then delay for EHSA and classical EHA has considerable larger delay than EHSA. Mathematical simulation of longitudinal motion of airliner with CSAS and EHA at action of design wind gusts and at intensive maneuvering is performed. Simulation showed, that: – at small disturbances level (Wmax≤4 m/s) aircraft stability and controllability characteristics with EHSA and EHA with combined control are close with each other, but at using of classical EHA aircraft-CSAS system stability margins decrease: phase on 4.5º, magnitude on 0.4 dB, – at large disturbances level (Wmax>4 m/s) essential decrease of stability margins takes place for EHA with combined control in comparison with EHSA: phase on 15º, magnitude on 2.5 dB. For classical EHA very big drop of stability margins takes place: phase on 47º, magnitude on 6.2 dB that may result in loss of aircraft-CSAS system stability at action of design wind Wmax=15 m/s. References 1 Yu.G. Zhivov, S.F. Ermakov, V.M. Kuvshinov, S.V. Konstantinov, G.S. Konstantinov, A.N. Mitrichenko, P.G. Redko, A.M. Selivanov. Flight control actuation systems development concept for future-technology aircraft. – «Polet», 2008, №1, pp.50-60. 2 Van de Bossche D., The A380 flight control electrohydrostatic actuators, achievements and lessons learnt ICAS 2006 conference. 3 Nintzel A. Design Study for an Electrohydrostatic Actuator for an A330/340 inboard aileron // Recent Advances in Aerospace Actuation Systems and Components. – Toulouse, France, 2001.