Dynamic loading systems for ground testing of high speed aerospace actuators
The Authors
Jean-Charles Mare, INSA/LGMT, Toulouse, France
Abstract
Purpose – To develop structured guidelines for the synthesis of dynamic force simulators that are required for the testing of high speed aerospace actuators. To provide realistic and proven solutions at both test bench hardware and control design levels.
Design/methodology/approach – The state of the art in control design applied to load simulators in mainly based on complex controllers and does not take into account practical considerations. The objective of the present work is to provide generic preliminary design rules to ensure that the test bench architectures (frame, power transmission and control) and the components specifications are consistent with the targeted performance. Once selected the appropriate power transmission architecture, a linear approach is used as a foundation to generate design rules. Then, preliminary design is achieved thanks to the introduction, as early as possible, of the unavoidable technological defects.
Findings – A step-by-step methodology allows the designer to select the controller architecture and to specify components with special care to their consistency with the required dynamic performance. The linear then practical approach generates key rules that can be used in the very early phase of the test bench design.
Originality/value – Practical considerations on the components static and dynamic limitations are introduced progressively to make the natural test bench performance as consistent as possible with the performance requirements. Consequently, the controller becomes simpler to design and robust.
Article Type:
Research paper
Keyword(s):
Actuators; Dynamics; Force; Simulation; Tests and testing.
Journal:
Aircraft Engineering and Aerospace Technology: An International Journal
Volume:
78
Number:
4
Year:
2006
pp:
275-282
Copyright ©
Emerald Group Publishing Limited
ISSN:
0002-2667
Nomenclature
A Equivalent leakage coefficient (m3/sPa)
C h Global actuator hydraulic capacitance (Pa/m3)
f c Phase margin frequency (Hz)
f s Sampling frequency (Hz)
F Actual force (N)
F* Force set-point (N)
F c Force feed-forward (N)
G sv(s) Servovalve transfer function, DC gain 1
I Servovalve current (A)
i c Velocity compensation current (A)
i o Reference servovalve current (A)
K p Proportional control gain (A/N)
K Qi Servovalve flow-current gain (m3/sA)
K v Loop gain (1/s)
P l Loading actuator pressure difference (Pa)
P s Net supply pressure (Pa)
Q sv Servovalve output flow (m3/s)
s Laplace variable (s)
S Jack effective area (m2)
T c Derivative set-point feed-forward gain (s)
x Servovalve opening (m)
V Load velocity (m/s)
Z(s) Tested actuator complex mechanical impedance (Ns/m)
α Gain factor (-)
δ Inverse gain function (−)
ξ c Low-pass filter damping ratio (−)
ω c Low pass filter natural frequency (rd/s)
ω sv Servovalve natural frequency (rd/s)
Introduction
The certification and qualification of position controlled aerospace actuators require ground testing in accordance with the operating conditions. In this attempt, the corresponding test benches involve not only static but also dynamic loading systems to assess the actuator closed-loop dynamic compliance (position sensitivity to external loads vs frequency) and its fatigue/endurance capability. The performance requirements of such force generators become particularly severe when the forces have to be applied on a moving load, with a velocity (being imposed by the actuator under test) being as high as 0.5 m/s. The following developments deal with the experience that has been acquired in the design of such dynamic load simulators, especially for helicopter swash-plate actuators, launcher thrust vector actuators and commercial aircraft thrust reversers.
Power architectures
The design of aerospace actuators test benches is mainly driven by the need to reproduce in-flight operating conditions. For this reason, the test bench must be representative of the structural compliance of the airframe and the driven load, the inertia of the actuated load and the instantaneous external force applied on it (Figure 1, Plate 1).
The structural compliance alters the performance of the actuator. As the position sensor used for position control only senses the relative position between rod and body, it introduces a steady state error under permanent load. Moreover, parasite dynamics are generated due to the coupling between the spring effect of the structure and the mass effect of the actuator body and rod. For hydraulic jacks, the lowest natural dynamics (a few Hz to a few tens Hz) is observed when the load mass combines with the anchorage/airframe, the rod/load and the hydraulic stiffness, all of them acting in series. The medium frequency dynamics (a few tens Hz to a few hundreds Hz) occurs when the actuator mass combines with the anchorage/airframe and the transmission/load stiffness acting in parallel. In the corresponding modal shape, the load is quasi steady. Most of the time, the highest natural dynamics (a few hundreds Hz) is neither influent nor observable because it is over-damped by the actuator seals and bearings. For these reasons, it is common to not reproduce the rod/load compliance and to reject it onto the anchorage structural compliance at the airframe/body level. However, when multiple actuators drive a same load, each rod/load compliance must be reproduced to be representative of the force-fighting effects between the tested actuators.
The inertia of the actuated load requires an activation force proportional to acceleration. Owing to the presence of the above-mentioned dynamics and the limited bandwidth of the load generator, it is generally not possible to reproduce the inertia effect with the loading actuator without generating unacceptable phase lag. For this reason, the load inertia is physically reproduced on the test bench as a pure mass. When the design of the test bench leads to drive this mass among a vertical axis, the gravity effect must be balanced by a dedicated device opposing to the weight force.
As explained, the loading device has only to generate the external forces applied to the load that is driven by the actuator under test. In most of the applications, these forces are due to fluid/structure interactions and cannot be reproduced in their original form. For high speed actuation in the range 0.2-0.5 m/s, this concerns typically engine thrust reverser actuators, helicopters main rotor actuators or launchers thrust vector control actuators.
Loading systems
For certification or qualification as well as development or integration tests, it is of particular importance that the loading system does not introduce any undesired effects. As displayed on Figure 2, the performance of position actuators is sensitive to the load characteristic that introduces a loop between output position and disturbing force. Recent industrial experiences have proven that badly designed loading devices can either lead to optimistic or pessimistic test results. A summary of loading system design is presented in Table I and is explained hereunder.
Passive systems
Despite their poor versatility, passive systems are attractive when the load effect to be reproduced is simple and not varying with time. When low interaction between loading and tested actuators is a key criteria, passive systems are preferred because they generate quasi pure effects. This is typically the case of flight control actuators on iron birds.
When constant forces are required, resort to gravity must be put aside due to the inertia effect that is associated with the weight effect. Most of the time, spring effect (even a non linear algebraic relation between position and load) is required to represent air load on flight control surfaces (Figure 3). It can be easily produced by mechanical springs or torsion bars (Plate 2). This solution also applies for constant force generation but requires low stiffness/high preload springs. Stiffness and preload can be adjusted prior to the test by an appropriate setting of the spring attachment points. Even if they allow a wide set of possibilities by face-to-face or face-to-back arrangement, spring washers must be avoided due to the significant dry friction occurring at the contact between elements that leads to unacceptable hysteresis. The sizing of mechanical springs generally leads to high size and heavy test benches.
In order to get more compact test benches, hydro-pneumatic systems offer an interesting alternative to generate either constant or spring force. This time, the designer has to manage the effects of seals friction, pressure losses between components, gas thermal losses and pressure/volume non linearity due to polytropic gas evolution.
Semi-active systems
Semi active systems allow to electrically control the loading system in accordance with the mission profile without external power source (excepted from the moving mass). This solution can be used when dissipative effects are to be generated under aiding load. Unfortunately, it also suffers from many drawbacks. The operating range is narrow because it is impossible to input power. Moreover, the metering components generally do not allow a correct operation below a few percent of the nominal opening. In addition, oil compressibility and metering components dynamics introduce uncontrolled transients at the velocity reverse.
Active systems
Thanks to their high power density and low inertia, electro-hydraulic actuators still appear as the today's response to the need of high force, dynamic loading systems. In this design, the hydraulic jack is associated with a flow servovalve as displayed by Figure 4. Despite electro-hydraulic actuators have been used for years, test bench designers cannot rely of efficient methodologies and key rules to synthesise such loading devices. It is observed in applications that the test bench mechanical design is mainly based on strength considerations while the controller is kept as a serial PID which is set on-site.
Linear analysis of the electro-hydraulic loading system
Typical electro-hydraulic loading systems are designed from a constant pressure supplied, servovalve controlled jack. Pressure servovalves can directly control a pressure difference that is representative of the jack force if friction and rod mass are neglected. These latest effects washout the interest of such servovalves for high performance applications. Moreover, pressure servovalves must be set at factory to fit the test bench stability requirements. For these reasons, flow servovalves are preferred due to the amount of standard products.
As the force to be controlled is a very dynamic state variable compared with position, an efficient design of high speed, force controlled, electro-hydraulic actuators involves multi-domain considerations: test bench compliances (introduced by structure and force sensors), close link between power sizing and natural closed loop performance, unavoidable and parasite non-linearities, limitations induced by digital control and so on. Consequently, the engineer has to face with the definition of a huge number of design parameters that requires an appropriate methodology.
Coupling with the tested actuator dynamics
In practice, the driven load has a compound impedance that links the load velocity to the applied force, as given by equation (1): Equation 1 The complex impedance Z(s) is fixed by the position actuator under test and the devices installed to reproduce the load inertia and the structural compliances. Most of the time, it is difficult to get accurate dynamic models of the tested actuator from its manufacturer. Moreover, the loading actuator controller shall not use any signals from the tested actuator sensors or controllers in order to ensure non intrusive testing. According to the experience acquired on many aerospace test benches, it appears first that the design of advanced force controllers (e.g. quantitative feedback, adaptive or predictive control) is well documented and supported by dedicated software toolboxes while in practice test benches are run with simple PID controllers. On the other hand, there is a lack of methodology the help the designer in the specification of the test bench, consistently with the required force control performance. In the following paragraphs a step-by-step methodology is proposed for the preliminary design of the test-bench as a whole system.
Reference performance
It is of high interest to get a reference of performance in order to evaluate how demanding the requirements are. In this attempt, the driven load influence is neglected and the loading actuator control is supposed to be proportional and in the continuous time domain. Moreover, the load actuator is considered as perfect (negligible friction and rod mass). Under these assumptions, the open loop dynamics is made of the servovalve equivalent second order G sv(s) and the cylinder hydraulic time constant C h/A, leading to the closed loop transfer function equation (2): Equation 2 Considering the servovalve response time is negligible in comparison with the hydraulic time constant, the actuator loop gain ensuring practical stability can be set to K v=αω sv with 0.3 < α<0.5 depending on the selected stability criteria. Therefore, the corresponding closed loop dynamics at low frequencies is typically of first order with a time constant of 1/αω sv, which is also representative of the low frequency force tracking delay. With steady set-point or load velocity, the force error is given by equation (3): Equation 3 The above reference performance evaluation suggests important practical design recommendations:
- The servovalve dynamics has a direct influence on the loading system performance (200 Hz can be found on-the-shelf for nominal flows up to 100 l/mn).
- In order to reduce the force error, the hydraulic compliance of the hydraulic jack can be increased by adding dead volumes on each chamber. This action is, however, bounded by the flow capability of the servovalve. Indeed, volumes under pressure must be fed to compensate for the compliance of oil and walls during transients. Excessive dead volumes will so require larger servovalve size leading generally to a bandwidth reduction.
- Increasing the leakage between jack chambers improves the velocity disturbance rejection but augments the static error. Once again an excessive bypass leakage will require higher servovalve size. It may also reduce the closed loop stability due to the greater hydraulic time constant.
Series or parallel control
Even in the case of complex loads, it generally appears that the open loop low frequency poles are not too badly damped (damping is greater 0.4). In this situation, the closed loop performance can be significantly increased thanks to a series PD controller or a derivative force feedback. The controller setting and the corresponding performance when the servovalve dynamics dominates are summarized on Table II. It is pointed up that such a controller allows to increase the loop gain by +150 percent while the response time decreases by 48 percent.
Steady state error
As given by equations (2) and (3), the force control error is due to force tracking (set-point follower function) and velocity disturbance (regulator function). For high performance applications, PI controllers must be avoided as far as possible. On the first hand, in the presence of static non linearities (e.g. jack friction or servovalve hysteresis) the integral control generates limit-cycles which magnitude cannot be controlled. On the other hand, it generates windup under high dynamics set-points, leading to unacceptable output overshoot. Consequently, it is suggested to achieve the accuracy requirements with appropriate force set-point of load velocity compensations.
Force set-point compensation
As the desired force is most of the time not known in advance from the mission profile, a low frequency set-point feed-forward is applicable as given by equation (4): Equation 4 Considering the flow pressure coefficient A has generally a negligible effect, the set-point compensation may be applied at the first order from the force set-point, after derivation and low frequency filtering: Equation 5 In practice, the compensation gain T c can be identified from the plot of the actual force vs force set-point derivative. The controller is then set using a reduced value, only 80 or 90 percent, to avoid any over-compensation. In addition, jack friction compensation or gravity compensation may also be added if required.
Finally, force derivative feedback and force derivative feed-forward combines well as they allow to separate the setting of the loop dynamics and the tracking error.
Load velocity compensation
As the load velocity is imposed by the actuator under test, even at null force the servovalve must supply flow to compensate for the rate of change the cylinder volumes. To improve the rejection of load speed on the force control, a static velocity compensation has been implemented with success many times. In this solution, a compensation signal is summed at the servovalve input, being proportional to the load velocity. The theoretical compensation gain, equation (6) is directly derived from equation (3). In practice, the velocity compensation suffers from various limitations: Equation 6 Firstly, its requires a velocity signal that cannot be got from the tested actuator (non intrusive tests imposed). Moreover, as the compensation applies directly on the servovalve input, it is very sensitive to the noise level and the phase lag of the velocity signal. The derivation of LVDT position sensor signals induces either remaining of the excitation frequency or phase lag due to its filtering. Using a high frequency excitation of the LVDT sensor (typically 10 KHz) is necessary to not reduce the load generator performance. On their side, most of the magnetostrictive position sensors provide a velocity output but either at low frequency or with a low resolution. This puts them aside for high performance load generators. Cable position sensors must be used with care as the uncontrolled cable vibrations may disturb the velocity compensation.
Secondly, the compensation is equivalent to a positive derivative force feedback when the tested actuator behaves as a spring, that often occurs at low frequencies. In such conditions, the compensation gain is limited by closed-loop stability conditions. When at least a first order model of the actuator under test is available, it is possible to estimate the load velocity from the position set-point of the tested actuator. Thus, the velocity compensation does not introduce any loop. However, its efficiency highly depends on the accuracy of the tested actuator model.
Thirdly, the K qi and A parameters of the linearised model change rapidly and significantly versus the operating conditions. In particular, they are very sensitive to the level of force to be generated. Once again a limited gain must be used in order to avoid any over-compensation.
Methodology of preliminary design
Components specification
As a key rule, the open loop behaviour of the loading actuator must be consistent with the required level of performance. The above recommendations have already fixed the natural performance of the loading actuator and suggested the architecture of its controller. In addition, it must be checked that the test-bench dynamic effects must not introduce any significant performance reduction.
The test bench frame has to be stiff enough to avoid any mechanical mode below twice the servovalve natural frequency. It is common that the test bench is carefully designed with respect to stress and fatigue but stiffness is rarely taken into consideration. In a recent experience, the coupling between the test-bench compliance and the loading actuator mass generated a mechanical mode exactly at the servovalve natural frequency.
The hydraulic supply of the loading actuator must be designed in order to avoid any pressure pulses that can excite high frequency mechanical modes. This requires and adequate circuit design considering pump ripple, lines length, and accumulators (9 pistons pumps run at 1,500 rpm generate 225 Hz pressure spikes that may correspond to the original phase margin frequency of the force control).
The force sensor stiffness also contributes to fix the natural modes of the load generator and requires an appropriated specification, based on modes calculation. Its bandwidth (including signal conditioner) has to be specified in order to not alter the phase margin. If a contribution of −5° is accepted when the force measure is equivalent to a critically damped second order, its natural frequency has to be 16 times higher than the initial phase margin frequency of the force control.
High frequency badly damped dynamics
High frequency modes cannot be actively controlled by the loading actuator that has a limited bandwidth. In this case, bypassing the jack chambers is the simplest way to efficiently damp the test bench. This function can be performed thanks to an adjustable nozzle, using a standard sandwich servovalve plate. The amount of bypass flow is generally small and has a little influence on the A parameter. If not, it may lead to increase the nominal flow of the servovalve to be used.
Compensation of servovalve non linearity
Putting aside the first stage magnetic hysteresis, the opening of the servovalve hydraulic power stage orifices is proportional to its input current. Unfortunately, the servovalve flow is depending on the orifices pressure drop, this effect being modelled in statics as follows: Equation 7 It clearly points up the influence of the actuator pressure difference of the overall flow-opening gain that alters the effective performance from linear analysis. This effect can be partly removed as it is possible to compensate for the valve non linearity thanks to a serial inverse gain function δ in the force controller: Equation 8 The δ function involves the cylinder pressure difference and the valve opening signals and must be implemented with care. When not available on the servovalve, the opening can be replaced by the valve current that is almost equivalent in static. It can be filtered using a second order representative of the mean servovalve dynamics. In the same manner, the cylinder pressure difference can be replaced by the transmitted force, if jack friction and rod mass generate negligible force losses: Equation 9 Finally, the non linearity compensation has to be kept continuous around the null current and robust against signal biases. In particular, the sign function must be linearised, e.g. assuming sgn(i)≈tanh(i/i 0).
Sampling frequency and digital control
Position control electro-hydraulic actuators operate on low frequency state variables as the gain margin frequency is fixed by the hydro-mechanical mode (a few Hz). Opposite to it, the force control operates on high dynamics state variables, the gain margin frequency being typically fixed by the servovalve dynamics (a few hundred Hz). For this reason, digital electro-hydraulic force control requires high sampling rates and rapid computers to not introduce any phase lag nor delay. Considering only the sampling effect at frequency f s with an associated second order anti-aliasing filter having a cut-off frequency of f s/2, the digital control reduces the phase margin by no more than 10° when the sampling frequency is greater than 41 times the continuous time domain phase margin frequency f c: Equation 10 This points up the potential limitations introduced by inappropriate hardware selection. Most of the industrial axis control boards only offers a maximum sampling frequency of 1-2 kHz while several kHz are required.
Stop-ends
Extension/retraction actuators, like thrust reverse actuators, move from one stop-end to the other. Starting or stopping induces high load accelerations, leading to sudden changes in velocity. Under these conditions, the force controller has to rapidly vary the servovalve current in response the stop-end effect. Unfortunately no external signal is available to generate such a change. It is only detected after it has already appeared by its influence on the force and velocity signals. This situation has been solved efficiently inserting a load acceleration feedback in the force control loop. Once again, unavoidable phase lag and noise introduce severe limitations and may require dedicated additional sensors.
The design of high performance dynamic loading systems for ground testing of aerospace actuators has been presented paying a special attention to practical considerations. It is shown on Figure 5. Correspondingly, the control architecture is shown on Figure 6. As an example of the efficient of the proposed sizing methodology, Figure 7 shows the results got for a thrust vector control test bench. It can be seen that parasite dynamics and non linear effects have a controlled and non excessive influence on the force control while allowing realistic specification of the test-bench components.
Conclusion
The first part of this communication has been dedicated to power architectures. Passive (mechanical, pneumatic), semi passive (hydraulic) and active (electro-hydraulic) design have been presented and compared with respect to their capability to suit the performance requirements.
In the second part, electro-hydraulic load simulators have been assessed using firstly a linear approach. Starting from a reference case, practical considerations have pointed up the natural behaviour and have suggested proven control architectures and design recommendations dealing with servovalve bandwidth, additional dead volumes and bypass leakage. Dynamics and improved stability have been achieved on basis PD series or first derivative feedback controllers while static and dynamic errors have been reduced thanks to force set-point derivative and load velocity compensations.
In the third part, having in mind the results from the reference and the linear approaches, a design methodology has been proposed. The test bench components have been specified progressively in order to control their contribution to the performance limitation. This deals especially with the compliances of the test bench frame and the force sensor, the design of the hydraulic supply, the damping of high frequency dynamics, the compensation of the servovalve non-linearity, the controller sampling frequency and the compensation of the stop-end effect.
Despite their high level of performance for load simulators, electro-hydraulic actuators are still felt as difficult to control while being the only available response to high force, dynamic load simulators. The proposed approach has been used with success in many aerospace applications for the main rotor actuators of the Eurocopter NH90 helicopter, the thrust reverse actuators of the Airbus A340-600 and A380 or the thrust vector actuator of the French strategic missile.
In the next future, the developments of high performance electric actuators will probably offer an attractive alternate solution for dynamic load simulators. Standard actuators, involving a roller screw that is directly driven by a brushless motor are about to fulfil the power needs for a single aisle aileron actuator testing (50 kN stall, 25 mm/s no load). A research program is now in progress to assess the key design procedures and parameters for such electric loading systems.
Equation 1
Equation 2
Equation 3
Equation 4
Equation 5
Equation 6
Equation 7
Equation 8
Equation 9
Equation 10
Figure 1Vertical in-line architecture of actuator test bench
Plate 1The NH90 main rotor actuator test bench at CEAT Toulouse
Figure 2Interaction between tested actuator and loading device
Figure 3Typical air load plot for a primary flight control actuator
Plate 2Triplex rudder actuator testbench supplied by Certia
Figure 4Electro-hydraulic force generator
Figure 5The proposed methodology
Figure 6Controller architecture
Figure 7Compared responses – ideal and realistic loading systems
Table IVarious design of loading systems
Table IIController setting and corresponding performance (servovalve dynamics is dominant)
Further Reading
Bohr, G., Hamilton, S. (2000), "Force control is the issue in aerospace structural test lab", Hydraulics and Pneumatics, pp.43-7.
Maré, J-C. (2000a), "Force control of electrohydraulic actuators driving various load mechanical impedances", Proceedings of the Second Internationales Fluidtechnisches Kolloquium in Dresden, pp.149-62.
Maré, J-C. (2000b), "Considérations pratiques sur les correcteurs PID dans le domaine de l'énergie fluide", Revue Fluides, Numéro Spécial Matériels, pp.8-17.
Maré, J-C. (2002), "Actionneurs hydrauliques", Encyclopédie des Techniques de l'Ingénieur, Articles S7530 and 57531, série Mesure et Régulation, pp.35.
Maré, J-C., Cregut, S. (2001), "Electrohydraulic force generator for the certification of a thrust vector actuator", Proceedings of the International Conference on Recent Advances in Aerospace Actuation Systems and Components, Toulouse, pp.59-63.
About the author