Nomenclature
- ACE
actuator control electronics
- ACM
actuator control module
- Cmd.
command
- DP
differential pressure
- EHA
electronic-hydrostatic actuator
- EMF
electromotive force
- FCC
primary flight control computer
- FCM
flight control module
- MCE
motor control electronics
- P-Q
pressure and flow
- PID
proportion integral differential
1.0 Introduction
The transmission of signals in mechanical form offers relatively good reliability, which often makes the use of the redundant channel unnecessary. With the increasing advantage of electrical signals, it is becoming more and more tempting to remove auxiliary actuators. It even becomes possible to eliminate the mechanical information chain altogether if all its functions can be performed by electrically signaling the primary actuators. This leads to the invention of the fly-by-wire solution, where the primary hydro-mechanical actuator is replaced by a hydraulic actuator [Reference Maré1, Reference Xue and Yao2]. Nowadays, multiple servo actuators are commonly used in the primary flight control system of aircraft. This is because in active-active mode, the output displacement of each actuator is not strictly consistent. Therefore, one actuator drives another actuator, so that multiple actuators hold each other back, resulting in a force fighting scenario. Force fighting is defined as the difference between the forces produced by two or more actuators in the same flight control surface.
For reasons of safety and availability, the primary flight control surfaces (rudders, ailerons, elevators, etc.) are moved by a combination of two or more actuators, either in an active-passive configuration or in an active-active configuration. A turboprop regional aircraft’s rudder is moved by three EHAs with triple active control mode. In the active-passive-passive configuration, a single actuator has the ability to drive the rudder surface. The weight and volume of the actuator are comparable large, but it does not involve the problem of force fighting. While for the active-active-active configuration, the size and weight of each actuator is relatively small, the actuators share their workload equally and can therefore be sized accordingly, but they can be influenced by the dissimilar output force of the actuators, resulting in a force fighting scenario, leading to unacceptable fatigue damage to the aircraft structure. If the flight actuation system is operating in all active mode, the controller must control the position of the surface and minimise force fighting.
In previous literature, Carlton Y. Ma utilised a pressure flow control servo-valve and an electronic auto-rigging to minimise the force fighting between two or more channels. The servo actuator may generate null difference because of thermal drift during flight, for large temperature variations at high altitude. After auto-rigging, the force fighting that is caused by the additional null difference is minimised by the smooth pressure gain of the P-Q valve [Reference Ma3].
Olaf Cochoy et al. proposed a hybrid actuator scheme, in which an electro-hydraulic servo actuator (EHSA) and an electromechanical actuator (EMA) operate on the same control surface. And the authors state the most effective technology is to feed back all three error representing signals, position differences of the actuators, the difference between the velocities and the occurring fighting force at the same time. Maximum force fighting between all actuators is decreased from 500% to 7% of the stall load in active-active mode [Reference Cochoy, Hanke and Carl4]. Vojislav Soronda presents a system and solution of reducing a force fighting between hydraulic actuators which are coupled to a single flight control surface. First, differential pressure across each hydraulic actuator is detected. Second, using a plurality of user interface position sensors, the position of a user interface is detected. Third, using one or more position sensors, flight control surface position is detected. The sensed flight control surface position, user interface positions, and differential pressures are used to create a plurality of substantially equal actuator commands [5].
Lijian Wang et al. propose in the position control loops, to add equalisation offsets based on the integral of the force difference between the actuators to achieve static force equalisation, and by forcing the two actuators to follow the same trajectory to achieve the dynamic force equalisation. A path generator is introduced to generate the required acceleration, position, and velocity from the position set point with real reproduction of the actuators’ power limitation. Using feed forward actions to compensate the invariant and major effects such as electro-mechanical actuator inertial torque and servo-hydraulic actuators functional flow. By this approach, tracking errors are greatly reduced without reducing robustness [Reference Wang and Mare6].
Ur Rehman Waheed et al. present four position synchronisation methods. The first one uses proportion integral differential (PID) controller to improve load rejection performance, and self-tuning Fuzzy PI controller to control position loop dynamics. The second method uses a PID controller to balance position loop dynamics. The third and fourth strategies use PID for pre-compensators and position loop dynamics to equalise force dynamics [Reference Rehman, Wang, Wang and Kamran7].
Tobias Röben et al. propose electro-hydrostatic, electro-mechanic and servo-hydraulic to build a hybrid all-active actuation system. Using a feed-forward control method and a conventional PI controller, which addresses remaining static force fight, to reduce force fighting during acceleration or deceleration process. A control electronic is developed for generic use with each single actuator, which includes kinematic conversion, position control, force fighting control and safety monitoring functions [Reference Röben, Stumpf, Weber and Grom8].
Additionally, other different control algorithms are invented to achieve force fighting equalisation of flight control actuators, such as model reference adaptive controller, feed-forward controller and feedback controller, fractional order PID (FOPID) controllers, fault-tolerant synchronisation controller, feedback loop designed as an optimal linear quadratic output regulator (LQR) and a feed-forward controller based on a general regression neural network (GRNN) [Reference Rehman, Wang, Wang and Azhar9–Reference Li, Yang, Cao, Xie and Wang12].
In order to solve the force fighting problem of the rudder actuating system for a certain type of aircraft’s active-active-active operational mode, taking into account the reliability, maturity, safety and cost of the technical solution, this paper uses position feedback and differential delta pressure feedback to establish a dual closed-loop servo control, using a PI controller as an outer loop controller plus an inner loop PI controller to achieve force fighting equalisation. Through the equivalent transformation of the physical model, mechanical kinetic analysis and mathematical modeling, an accurate virtual test rig is built by the AMEsim modeling software. The simulation results and the results of the iron bird test show that the dynamic fighting force decreases significantly and can be considered as a force fighting equalisation scheme for other aircraft types.
2.0 Mathematical model of rudder redundant actuation system
2.1 Problem formulation and context
The primary flight control system of a turboprop regional aircraft mainly contains aileron, rudder, elevator and aileron, and has the functions of manual trim operation, control surface variation limitation and stall protection, etc. It adopts electrical signal transmission control and hydraulic power drive. The primary flight control system mainly consists of control stick/disc assembly, pedal assembly, flight control panel, trim control panel, deceleration control handle, primary flight control computer (FCC), actuator control electronics (ACE), control surface position sensors, spoiler actuators, elevator actuators, aileron actuators and rudder actuators, etc. Each FCC comprises a flight control module (FCM) and an actuator control module (ACM). Each FCM is equipped with control and monitoring channels; ACM and ACE have the same function, both are equipped with monitoring and control channels, but adopt different hardware configuration. The simplified architecture of a turboprop regional aircraft’s rudder flight control actuation system is shown in Fig. 1.
Rudder control system scheme.
The rudder is driven by three electronic-hydrostatic actuators (EHA). The EHAs are identical to provide the necessary system redundancy and can be installed in any of the three mounting locations. The primary control system uses an active-active-active mode to proportionally control the EHA position from the aircraft control system commands. The EHA’s input current commands control the flow of fluid to control the position and rate of the EHA. The triple active mode requires the shut-off-valve (SOV) to be activated and the supply pressure to be above a threshold pressure. The maximum rudder panel movement is reduced as the airspeed increases. Maximum rudder panel deflection is approximately around +/−8 degrees at a typical cruising altitude, +/−20 degrees on the ground.
Figure 2 shows the general structure of an EHA. It mainly consists of control and power electronics, the electric motor, the fixed displacement pump, symmetrical linear hydraulic cylinder, the re-feeding valves, pressure relief valves, solenoid valve, hydraulic restrictor, fluid filter, oleo-pneumatic accumulator and solenoid valve, etc. [Reference Maré13].
Hydraulic architecture of an EHA [Reference Maré1].
As shown in Fig. 3, EHA contains a permanent magnet synchronous machine (PMSM), a fixed displacement pump and a hydraulic cylinder. The movement of piston is computed by the shaft speed of a permanent magnet synchronous machine. The fixed displacement piston pump generates the flow of hydraulic fluid. By pressurising a hydraulic cylinder, the linear motion of an electro-hydrostatic actuator is achieved.
EHA architecture with servo motor, fixed pump and hydraulic cylinder.
2.2 Mathematical model of PMSM
In order to build the mathematical model of electronic-hydrostatic actuator, with regards to the nonlinearities, some assumptions are made in order to obtain one linear differential equation. The maximum EHA performance (torque and speed) is defined by external load, valve gain and the supply pressure potential. However, the electric motor’s output is only limited by means of control. According to reference [Reference Ijaz, Hamayun, Anwaar, Yan and Li14–Reference Li, Shang, Jiao, Lin, Wu and Li19], the dynamic behaviour of a PMSM is mainly influenced by the characteristic winding resistance(R) and winding inductance(L), it is calculated using Equation (1) [Reference Röben16].
\begin{align} {T_M}\;=\;{{{K_M}} \over R}{1 \over {{\textstyle{L \over R}}s + 1}} \cdot {\rm{ }}(U - {K_{EMF}} \cdot {\rm{ }}{{\rm{\omega }}_M})\end{align}
Where
${T_M}$
is static torque of the motor shaft,
$U$
is the scalar voltage requirement as output of the MCE’s control stage. The motor constant
${K_M}$
is influenced by motor material and geometry.
${{\rm{\omega }}_M}$
is the motor’s rational speed.
${K_{EMF}}$
represents the electromotive force constant.
The rotational movement of the motor shaft induces a back electromotive force (EMF) voltage into the stator coils. With its rotating mass, EMF has a lagging effect on the acceleration of the motor shaft. By neglecting the dynamic induced by these lag elements, the static motor shaft torque becomes approximately proportional to the current intake:
\begin{align} {T_M} \approx {K_M}{I_M}\end{align}
2.3 Mathematical model of piston pump
The theoretic volume flow (
${Q_P}$
) results from the motor shaft speed:
\begin{align} {Q_P}{\rm{\;=\;\upsilon }} \cdot {\rm{ }}{n_m}\;=\;{{\rm{\upsilon }} \over {2{\rm{\pi }}}} \cdot {\rm{ }}{{\rm{\omega }}_M}\end{align}
Where
${\rm{\upsilon }}$
represents the axial piston pump displacement which determined the fluid flow, and
${n_m}$
represents rotational speed of the motor.
The axial piston pump displacement
${\rm{\upsilon }}$
and the rotational motor speed
${n_m}$
mainly influence the piston pump’s hydraulic fluid flow. The axial piston pump displacement
${\rm{\upsilon }}$
, it is calculated using Equation (4) [Reference Bauer20].
\begin{align} {\rm{\upsilon\;=\;}}z \cdot {\rm{ }}{{{\rm{\pi }}{d^2}} \over 4}{D_z}\tan {\rm{\alpha }}\end{align}
Where
${\rm{\alpha }}$
means the swash plate inclination,
$({D_z},d)$
means other geometrical parameters of the piston pump,
$z$
means the piston numbers within the cylindrical drum.
Considering losses of fluid compression and filling, the following theoretic volume flow equation can be modeled using Equation (5) [Reference Röben16].
\begin{align} {Q_P}\;=\;{{\rm{\upsilon }} \over {2{\rm{\pi }}}}\left[1 - {{\Delta p} \over B}\left(1 + {{2{{\rm{\upsilon }}_{dead}}} \over {\rm{\upsilon }}}\right)\right]{{\rm{\omega }}_M}\end{align}
Where
${{\rm{\upsilon }}_{dead}}$
represents the dead volume,
$\Delta p$
represents differential pressure within the cylinder,
$B$
stands for bulk modulus.
By formulation of a power equilibrium and introducing the load torque
${T_L}$
, the mechanical coupling of pump and motor is built as follows:
\begin{align} {P_M}\;=\;{T_L} \cdot {\rm{ }}{{\rm{\omega }}_M}\end{align}
\begin{align} {P_P}{\rm{ \;=\; \Delta p}}\!\mathop V\limits^ \bullet {\rm{ \;=\; \Delta p}} \cdot {\rm{ }}{Q_P}\end{align}
\begin{align} {T_L}\;=\;{P_M}/{{\rm{\omega }}_M}\;=\;{P_P}/({{\rm{\omega }}_M}{{\rm{\eta }}_{mech}}){\rm{ \;=\; \upsilon \Delta p}}/(2{\rm{\pi }} \cdot {\rm{ }}{{\rm{\eta }}_{mech}})\end{align}
Where
${P_M}$
represents power of the motor,
${P_P}$
represents power of the pump,
${{\rm{\eta }}_{mech}}$
represents mechanical efficiency.
Differential pressure between pump outflow and in generate the load torque, and drag torques which are caused by bearing and viscous friction between pump parts.
The drag torque
${T_D}$
can be approximated by kinetic friction (
${d_{kin}}$
) and static (
${d_{stat}}$
), and calculated using Equation (9) [Reference Fesenmayr21] as follows:
\begin{align} {T_D}\;=\;{d_{stat}} \cdot {\rm{ }}sign({{\rm{\omega }}_M}) + {d_{kin}} \cdot {\rm{ }}{{\rm{\omega }}_M}\end{align}
The actuator dynamic is influenced by friction effects and external cylinder load. Consideration of load torque
${T_L}$
and drag torque
${T_D}$
, the delivered fluid flow and the piston rod motion is determined by the operational speed
${{\rm{\omega }}_M}$
:
\begin{align} {J_{res}}\mathop {{{\rm{\omega }}_M}}\limits^ \bullet \;=\;{T_M} - {T_D} - {T_L}\end{align}
The inertia
${J_{res}}$
is composed of the rotating mass of rotor and axial piston pump.
2.4 Mathematical model of cylinder
The hydraulic cylinder of the EHA, whose force dynamics and flow dynamics are given by the force balance equation and the continuity equation respectively:
\begin{align} {Q_p} \;=\; {A_e}{\ddot x_{eha}} + {{{V_e}} \over {4{E_e}}}\mathop {{F_{ext}}}\limits^ \bullet + {C_{el}}{F_{ext}}\end{align}
\begin{align} {A_e}{F_{ext}} \;=\; {m_e}{\ddot x_{eha}} + {B_e}{\ddot x_{eha}} + {F_e}\end{align}
Where
${F_{ext}}$
represents the load pressure of the hydraulic system,
${F_e}$
stands for the load force acting on the actuator,
${Q_p}$
stands for output flow of the hydraulic pump,
${A_e}$
stands for effective area of hydraulic cylinder piston,
${x_{eha}}$
stands for EHA output displacement,
${V_e}$
stands for total volume of hydraulic cylinder,
${E_e}$
stands for effective bulk modulus,
${C_{el}}$
stands for total leakage factor,
${m_e}$
stands for mass of hydraulic cylinder rod,
${B_e}$
stands for viscous resistance in hydraulic cylinder.
2.5 Mathematical model of control surface
The mathematical model of the rudder of the aircraft can be constituted as coupling of mass-spring system, which is driven by the different EHA in parallel. A rigid connection is considered between EHA and control surface. The rotation angle of the control surface is very small, and are accounted for as linear movement of the control surface.
Actuator motion
${x_i}$
relative to the surface position
${x_d}$
results in a linear force, which drives the rudder against its own inertia, external load and friction [Reference Ren, Esfandiari, Song and Sepehri22–Reference Chen, Tian and Wang25]. Deviations between the single EHA output positions result in force fighting, which is influenced by the single channel’s effective stiffness. If the direction of an output force is contrary to the other, it does not contribute to the surface positioning, but constitutes an additional load for adjacent channels. Force dynamics of aircraft rudder are given can be calculated by Equation (16) and (17):
\begin{align} {F_{ei}} \;=\; K({x_i} - {x_d})\end{align}
\begin{align} {F_d} \;=\; \Sigma {F_{ei}}\;=\;{m_d}\mathop {{x_d}}\limits^{ \bullet \bullet } + {B_d}\mathop {{x_d}}\limits^ \bullet + {F_l} + {K_d}{x_d}\end{align}
Where
${F_{ei}}$
represents output force of EHA number
$i$
,
$K$
represents transmission stiffness,
${F_d}$
represents forces used to drive control surface,
${m_d}$
represents mass of the control surface,
${x_d}$
represents rudder displacement,
${B_d}$
represents rudder viscous damping coefficient,
${F_l}$
represents equivalent air load force,
${K_d}$
represents aero elasticity.
3.0 Control strategy
In practical engineering applications, from a safety point of view, priority should be given to a mature and reliable control law. Therefore, the inertial integral balance control or PI control algorithms can be considered. Figure 4 describes the loop closures used for a turboprop regional aircraft.
Force fighting equalisation control concept scheme.
Each EHA has an outer position loop, dynamic pressure feedback, force limiting, force equalisation, snubbing, and rate limiting. The actuator position loop uses quad-redundant linear variable differential transformers (LVDTs) to sense EHA position and provide feedback to close the electronic loop. The pressure transducer is also used for force equalisation between EHAs on a control surface. The EHA position feedback signal is also used for position snubbing towards the end of actuator stroke and for rate limitation of the surface commands. Quad-redundant differential pressure transducers provide feedback used to dampen the load resonance mode required for the relatively high loop gain of the aircraft. The pressure transducer is also used for force limitation. Due to the relatively asymmetrical loading requirement of the aircraft, the force limiter has a dramatic effect on reducing structural weight.
In the PI control model, proportional amplification and the integral link are used. The integral link is used to reduce the steady-state error of the input response, and at the same time, make the force fighting equalisation command output more stable signal; the proportional amplification link is used to compensate for rapid pressure changes. The control mechanism of the inertial integral equalisation is the difference between the differential pressure (DP) of the EHA. The DP is used as the input of the inertia link to obtain the force balance control by tracking the system pressure difference. Dead zone link is used to avoid performing differential pressure equalisation when DP is small. The limitation link before the equalisation command is mainly used to take into account of the deviation of the rudder surface.
4.0 Virtual test bench build and physical experiment
As shown in Fig. 5, according to the actuator position closed-loop servo model and PI force fighting balance control block, a virtual test bench is built by AMEsim simulation software to evaluate the robustness of the force fighting equalisation strategy by analysing the force fighting scenario.
The virtual test bench model.
A virtual simulation of the force fighting equalisation control law is performed to simulate an aircraft on the ground with aerodynamic loads, with a step signal input, to study the system response. The simulation time is set to 5 s, and the simulation step size is 0.01 s.
The simulation results without control strategy enabled are shown in Fig. 6, and the simulation results with control strategy enabled are shown in Fig. 7. In all active mode, Fig. 6 implies that the three EHA output different force, smaller output force of the other two EHAs was compensated by the other actuator. By the use of proposed methodology, Fig. 7 implies that the three EHAs output nearly the same force about 3048.68N, fighting force scenario was eliminated, and as shown in Fig. 8, the total force of three EHAs stabilise at about 9146.05N (3048.68×3), which is nearly equal to the final stabilise total force of ‘without proposed methodology’. Figures 9 and 10, indicates that differential pressure of each EHA was reduced to a same curve, smaller than 50 psi by simulation. Figures 11 and 12, indicates that displacement of each EHA has a synchronisation motion, and the flight control surface has position difference. By control strategy, compared to curves of Fig. 11, curves of Fig. 12 more close to the input step signal. From the above simulation results (fighting force, differential pressure and position), it can be concluded that the fighting force between the three EHA actuators is reduced by the proposed control strategy.
Step response of the system without force fighting equalisation strategy.
Step response of the system with proposed force fighting equalisation strategy.
Total force of the three EHAs by comparison.
Differential pressure of each EHA without proposed methodology.
Differential pressure of each EHA by proposed methodology.
Displacement of each EHA without proposed methodology.
Displacement of each EHA by proposed methodology.
Physical tests are carried out on a flight control system ground simulation test rig (iron bird), where the rudder pedal is manually operated and the step signal from the rudder pedal is converted into an electrical signal by sensors that pass through the actual flight control computer, the actuator, the electronic controller driving the actuator and the actual flight control surfaces. The test equipment collects the rudder pedal command, the equalisation command and the DP signal, so that for a single actuator it is possible to understand how the system operates in relation to the DP change equalisation control.
The curves collected through physical tests are shown in Figs. 13, 14 and 15. The raw data in Fig. 14, indicates three EHAs has a static differential pressure below about 50psi, and when EHA moves, three EHAs has a dynamic differential pressure below about 300 psi. Compare Fig. 14 (physical test) and Fig. 10 (simulation test), it indicates that physical test results have a more real and complicated differential pressure fluctuation than simulation test results. To a certain type of civil aircraft, which is a twin turboprop regional aircraft with about 60 seats, its design requirement about differential pressure fluctuation is dynamic DP smaller than 500psi, static DP smaller than 100psi. From Fig. 14, it can be concluded the physical test results meet with design requirements of the research subject of this paper. Figure 15 shows that the ram position of each EHA has the same trend.
Test results of each EHA’s pressure curve. (A, B stands for chamber A, chamber B of each EHA)
Test results of each EHA’s Differential pressure curve.
Test results of each EHA’s displacement.
5.0 Conclusion
This paper describes the architecture of a triple active redundant actuation system for the rudder of a turboprop regional aircraft. The mathematic modeling of the actuation system is analysed and an innovative force fighting control strategy is proposed. A detailed simulation model is built in order to investigate the interaction behaviour of the different channels coupled by a control surface. Through simulation and physical experiment, it can be concluded that the main cause of force fighting in a triple active actuating system is the difference between the input commands of the residual actuator. The proposed control methodology can effectively reduce the fighting force and a uniform actuation profile can be obtained, thus meeting the design requirements of the flight control system.
Acknowledgements
This research received no specific grant from any funding agency in public, commercial or non-profit sectors.
