In more-electric-aircraft flight control, the electro-hydrostatic actuator (EHA) integrates a speed-controlled motor and a hydraulic pump into a sealed local loop at the control surface; its adoption bottleneck is motor heating, because copper loss dominates under heavy, low-speed aerodynamic loads and the closed loop has no fluid exchange to carry heat away. The active load-sensitive EHA (ALS-EHA) inserts a controllable pressure-follow valve (PFV) between the load-sensing port and the pump's swash-plate mechanism so that pump displacement, and hence the hydraulic reduction ratio between motor speed and actuator velocity, can be actively scheduled with load: a 2020 prototype cut total motor loss by 31.6% versus the fixed-displacement EHA, but its maximum tracking error near the maximum-velocity point (~1.0 mm versus ~0.75 mm for the fixed-displacement baseline) was worse and its displacement schedule did not conform to actuator velocity. The open problem, stated by the source paper and pursued but not closed by its successors, is to complete the active concept: an appropriate active load controller, that is, a regulation law of pump displacement that conforms to the velocity variation of the ALS-EHA, so that the tracking penalty near maximum velocity is removed without sacrificing the demonstrated thermal and power-matching benefit. Same-group follow-ups produced a fuzzy-scheduled controller validated on a bench prototype, an efficiency-model-based energy-optimal law, and Lyapunov-verified dual-loop control of a related active load-sensitive drive, but none claims a velocity-conforming displacement law that removes the maximum-velocity tracking penalty while retaining the heating benefit, so the core remains open.

Background

A more electric aircraft replaces centralized engine-driven hydraulics with electrically fed, power-by-wire actuation, and the electro-hydrostatic actuator (EHA) is its leading form for flight-control surfaces: a bi-directional electric motor drives a bi-directional hydraulic pump directly connected to the actuator cylinder, forming a highly integrated closed volume-control loop. Because the loop has no fluid exchange with a central reservoir, heat generated inside it — dominated by motor copper loss under heavy, low-speed load — must be dissipated locally, which limits continuous working time, lifetime, and achievable power density. The conventional architecture varies only motor speed at fixed pump displacement (EHA-FPVM), so a single transmission ratio between motor rotation and actuator motion must cover the whole load envelope, forcing an oversized motor that often runs in an inefficient region. Load sensing offers a way out: in a direct load-sensitive EHA (DLS-EHA), the load pressure itself, routed through a shuttle valve (a small valve that automatically selects the higher of two pressures) to the pump's spring-loaded swash plate (the inclined plate of an axial-piston pump, whose tilt angle sets the piston stroke and therefore the pump displacement), passively reduces pump displacement as load rises, cutting motor torque and current. But the back-pressure spring must be stiff enough for the maximum load pressure, which pins the displacement-to-pressure gradient to a fixed constant and limits the adjustment range. The active load-sensitive EHA (ALS-EHA) of Huang, Yu, Jiao and Li (Applied Sciences 2020) adds a pressure-follow valve (PFV) — an electro-hydraulic valve whose outlet pressure is set by a control input — between the load-sensing port and the swash-plate actuator, so the effective load sensitivity, and with it pump displacement, becomes an actively adjustable quantity. Pump displacement DpD_p relative to actuator piston area AaA_a defines the hydraulic reduction ratio kh=va/ωm=Dp/Aak_h = v_a/\omega_m = D_p/A_a (actuator velocity over motor angular speed), the central design variable: at stall, motor current is proportional to DpPlD_p P_l, so a lower khk_h under heavy load directly lowers current, copper loss, and heating, and because the motor-pump inertia appears to the load as Jm/kh2J_m/k_h^2, a lower khk_h also raises low-frequency dynamic stiffness (the actuator's resistance to displacement under disturbing load force). Experiments on the 2020 prototype against an EHA-FPVM baseline under a heavy spring load confirmed both benefits: after 140 s the accumulated total motor loss was 17.02 kJ versus 24.89 kJ (a 31.6% reduction), and tracking error near zero velocity was smaller thanks to the higher impedance. The price is a new coupling: near the maximum-velocity point of a maneuver the measured maximum tracking error is larger than the fixed-displacement baseline's (~1.0 mm versus ~0.75 mm). The source explains this by stating that the displacement ratio is not the largest at that time, while its reported ratio trace states that for the ALS-EHA the maximum displacement is maintained at the top velocity point (ratio 1) and drops only as velocity decreases (to a ratio of 0.4 at 14 MPa load pressure); the two passages do not agree, so the mechanism behind the penalty is not settled by the source. The paper's own stated next research work (Sec. 5.2) frames what remains: the regulation law of pump displacement should conform to the velocity variation of the actuator, which requires an active load controller that does not yet exist; selecting actuator area, pump displacement, and motor speed is noted (Remark 3) as a coupled design consideration (a high-speed motor with small pump displacement favors stiffness but demands more energy for acceleration, and motor size is not the primary stiffness determinant); and the analysis rested on simplifying assumptions — an approximately zero average swash-plate moment at high speed, an elastic-link simplification of the load-sensitive loop, and omission of motor iron loss and pump efficiency losses from the heating model, which the authors state needs further modeling. Independent of this thread, multi-objective EHA preliminary design (weight versus efficiency via Pareto optimization) had been studied for conventional fixed-displacement EHAs by Wu, Yu, Jiao, Shang and Luk (2016), but that formulation does not encode the active scheduling of khk_h that couples stiffness, heating, and acceleration energy in the ALS-EHA.

Problem Statement

For an ALS-EHA — a variable-displacement axial-piston pump driven by a speed-controlled electric motor, with pump displacement set through an actuated pressure-follow valve (PFV) load-sensitive loop — design the active displacement regulation that the 2020 prototype of Huang, Yu, Jiao and Li (Applied Sciences 2020) lacked: an appropriate active load controller, that is, a regulation law of pump displacement that conforms to the velocity variation of the actuator. The required law is a regulation law that prescribes the pump displacement DpD_p (equivalently the hydraulic reduction ratio kh=Dp/Aak_h = D_p/A_a) as a function of the actuator's commanded and measured velocity. The regulation law must serve one joint objective (making active load sensitivity deliver both thermal and tracking performance across the operating envelope): it must be coordinated with the motor-speed loop of the two-control-variable system (motor speed plus pump displacement) so that position tracking — specifically including the maximum-velocity point of heavy-load maneuvers, where the 2020 prototype's error (~1.0 mm) exceeded that of the fixed-displacement baseline EHA-FPVM (fixed pump displacement, variable motor speed) (~0.75 mm) — must not exceed the fixed-displacement baseline's value, that is, the maximum tracking error at the maximum-velocity point must be at or below the baseline's ~0.75 mm under the documented maneuver; and the accumulated total motor loss over the documented test must remain below the fixed-displacement baseline's by at least the demonstrated 31.6% margin (in the source tests: 17.02 kJ versus 24.89 kJ over 140 s under heavy spring load, so no more than the source's ~17.02 kJ under that maneuver) — with the motor-current and heating predictions grounded in a loss model that must include motor iron loss and pump efficiency losses; the source's remaining dynamic simplifications (the approximately zero average swash-plate moment at high speed and the elastic-link representation of the load-sensitive loop) are not required to be removed and may be retained.

Both are relative to a fixed-displacement EHA-FPVM baseline under the same documented heavy-load conditions, with the source benchmark as the reference configuration: a 0.1 Hz sinusoidal position command of 40 mm amplitude against a 3.5×1063.5\times10^{6} N/m spring load run for 140 s, in which the accumulated total motor loss (copper plus iron) was 17.02 kJ for the ALS-EHA versus 24.89 kJ for EHA-FPVM and the maximum tracking error was ~1.0 mm versus ~0.75 mm. The thermal metric is that same accumulated total motor loss over the test duration; where a different maneuver, duration or hardware is used, the tracking and thermal figures are commensurable with the source numbers only when the comparison is against a fixed-displacement baseline measured under matching conditions.

Source context that bears on the design but is not a requested result: the source notes (Remark 3) that its stiffness analysis must be considered when selecting actuator piston area, pump displacement and motor speed — a high-speed motor with a small-displacement pump is advantageous for stiffness but more energy is needed for acceleration, and motor size is not the primary stiffness determinant — and its successor states that the entire design process is coupled and requires repeated iterative design. The source also notes that once motor iron loss and the pump efficiency losses are comprehensively considered the relation between total motor heat generation and pump displacement becomes complicated and needs further modeling research, and suggests (without requiring it) that a reasonable control law can reduce motor current and heating.

References

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