Dong, Yan, Feng and Tan (2018) proposed an energy-efficient electro-hydrostatic actuator for gravity-dominated lifting (EHA-VPVM): a single servo motor mechanically drives two swash-plate pumps whose displacements are coupled in a fixed proportion kk, and two high-pressure accumulators preset at designated pressures statically balance the gravity load on an asymmetric single-rod cylinder. The authors derived a six-state nonlinear state-space model whose two control inputs enter multiplicatively (pump displacement times motor speed) and reported AMESim simulations for a single 1000 kg lifting scenario showing energy savings of 97.5% against a valve-controlled cylinder and 79.5% against a fixed-pump EHA. The paper itself leaves open the systematic design of the swash-plate proportion kk (set ad hoc from the steady-state area ratio), control with formal stability guarantees for the multiplicative-input model, and validation under realistic leakage, friction, and accumulator pressure drift. No later work establishes a design principle for kk, a stability-guaranteed controller for this plant, or a validation of the architecture. The problem is therefore open.

Background

An electro-hydrostatic actuator (EHA) is a self-contained servo drive in which an electric motor drives a hydraulic pump that meters flow directly to a hydraulic cylinder, replacing throttling-valve control with volumetric (pump) control. Classical EHA topologies are named by which element is variable: fixed pump/variable motor (EHA-FPVM), variable pump/fixed motor (EHA-VPFM), and variable pump/variable motor (EHA-VPVM). Most industrial linear cylinders are single-rod (asymmetric) cylinders, whose cap-side piston area A2A_2 exceeds the rod-side annular area A1A_1; extension then demands more inflow than retraction returns, so a closed pump-controlled circuit has an inherent flow imbalance that must be compensated — by valves, by additional pumps, or by matching pump displacement to chamber areas. In lifting applications the gravity load dominates the energy budget: a valve-controlled cylinder burns continuous power merely holding the load, while accumulators (gas-charged pressure vessels) preset to designated pressures can statically offset the weight so the motor supplies only the dynamic share. Large-scale synchronous load-lifting systems of the kind used in reconstructing bridges and buildings are the motivating application (Dong, 2017; Dong, 2018).

Dong, Yan, Feng and Tan (2018) combined these ideas into one architecture: a servo motor mechanically drives two swash-plate axial-piston pumps (pumps whose flow per revolution is set by the inclination angle of a swash plate), with the two swash plates coupled in a fixed proportional relation by a linear motor through a proportional adjustment device; the two pump inlets are fed by high-pressure accumulators preset at different designated pressures, with a low-pressure compensating accumulator closing the circuit. The accumulators balance the gravity-induced static load, and the swash-plate proportion k=(A2−A1)/A1k=(A_2-A_1)/A_1 is chosen from the steady-state area ratio to equalize inflow and outflow so that the asymmetric cylinder behaves like a symmetric one. Because the delivered flow is the product of motor speed and pump displacement, the plant has two control inputs that enter multiplicatively; the paper derives an explicit six-state nonlinear state-space model of this coupled electro-mechanical-hydraulic plant and reports AMESim simulations (a standard hydraulic system simulator) in which the design consumes 193 J over a 40 s cycle lifting 1000 kg, against 942 J for a traditional EHA-FPVM and 7812 J for a valve-controlled cylinder — savings of 97.5% and 79.5% — while tracking 1–4 Hz sinusoidal references nearly as well as the valve-controlled system. Control used only a basic overall feedback loop with proportional allocation between the two inputs, and the study examined a single lifting scenario with idealized constant accumulator pressures and constant friction and leakage coefficients.

The surrounding field treats the pieces of this problem but not the combination. For the flow imbalance of single-rod pump-controlled cylinders, matching pump displacement to chamber areas is a standard design rule: a double-displacement pump with two displacement states matched to the two chambers (Sun et al., 2018), two individually motor-driven pumps (Zhang et al., 2020), and two individually controlled pump/motors — for which Kärnell and Ericson (2023) note that fixed, same-shaft pump/motors 'should be well matched' with the cylinder areas and deliberately avoid the fixed-ratio constraint by individual control; valve-based compensation with pilot-operated check or shuttle valves is another route (Imam et al., 2019; 2023), and the accumulator-assisted displacement-pump control of differential cylinders goes back to Quan (2006). For gravity-dominated lifting, alternative architectures use a dedicated gravity self-balancing cylinder chamber connected to an accumulator in a closed-loop pump circuit (Wang et al., 2021), an active load-sensitive dual-control EHA (Huang et al., 2021), or energy-regeneration schemes (Qu et al., 2021; Shang et al., 2016). For control of dual-variable EHAs, an adaptive-displacement design converts the two-input plant into a single-input plant through pressure-dependent displacement (Wang et al., 2020), and the recent dual-pump coordinated-operation work of Jin et al. (2026) targets power-source redundancy and low-speed flow accuracy with counter-rotating pumps, not displacement-ratio design. Accumulator parameter optimization for EHA exists only for pulsation damping of a different, fixed-displacement-pump system (Chen et al., 2021).

Against this landscape, the open question left by Dong et al. (2018) is whether their accumulator-balanced, dual-pump architecture can be systematically designed and validated rather than demonstrated in one idealized scenario: what principle (not a steady-state area-ratio shortcut) should fix the proportional setting of the two swash plates and the designated accumulator pressures, what controller with provable properties can handle the multiplicative two-input nonlinearity, and whether the energy and tracking claims survive realistic leakage, friction, and accumulator gas-law drift in high-fidelity simulation.

Problem Statement

For the dual-pump, accumulator gravity-balanced electro-hydrostatic actuator (EHA-VPVM) of Dong, Yan, Feng and Tan (2018), establish a systematic and validated design-and-control methodology that replaces the paper's ad-hoc, single-scenario demonstration. The requested results, which jointly support this one objective, are: (1) a design principle or optimization procedure for selecting the fixed proportional setting kk of the two mechanically coupled swash-plate pumps — together with the designated accumulator precharge pressures it couples to — that accounts for the inflow/outflow balance of the asymmetric single-rod cylinder, servo-motor torque, tracking dynamics, and energy consumption, and that is shown to improve on the baseline steady-state choice k=(A2−A1)/A1k=(A_2-A_1)/A_1 over an operating envelope that includes the original 1000 kg, 40 s lifting scenario and spans more than one load mass and more than one reference profile, in at least one of these criteria without degrading the others; (2) a control law for the published two-input nonlinear state-space model with multiplicative input coupling (pump displacement times motor speed), that comes with formal stability or tracking guarantees of the kind the paper's basic overall feedback with proportional allocation lacks; and (3) high-fidelity simulation validation of the architecture, the derived nonlinear model, and the resulting design under realistic leakage, friction, and accumulator pressure drift (gas-law behaviour), showing to what extent the claimed energy savings (97.5% versus valve control, 79.5% versus fixed-pump EHA in the original single 1000 kg, 40 s scenario) and the near-valve-like tracking survive. All three requested results are required; no proper subset of them resolves the task. The question is resolved only by deciding whether and how this architecture should be systematically configured and controlled — not merely that one idealized simulation of it exists.

References

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