# Novel Concept for Electro-Hydrostatic Actuators for Motion Control of Hydraulic Manipulators

^{*}

## Abstract

**:**

## 1. Introduction

- Grid-connected machines in docks, shipyards, and factories.
- Machines on ships connected to electric generators.
- Battery powered mobile machines.

## 2. Novel Concept

## 3. Considered System

## 4. Electro-Hydrostatic Actuator Design

#### 4.1. Electric Servo System

- ${u}_{d}$ = d-axis voltage;
- ${u}_{q}$ = q-axis voltage;
- ${u}_{a}$ = a-phase voltage;
- ${u}_{b}$ = b-phase voltage;
- ${u}_{c}$ = c-phase voltage;
- ${\theta}_{e}$ = electrical rotor angle;

- ${R}_{s}$ = stator resistance;
- ${L}_{d}$ = d-axis inductance;
- ${L}_{q}$ = q-axis inductance;
- ${N}_{p}$ = number of pole pairs;
- $\omega $ = motor speed;
- ${\lambda}_{m}$ = permanent magnet flux linkage;
- T = rotor torque;

#### 4.2. Hydraulic System

#### 4.3. Control System for EHA

## 5. Numerical Analysis of Four Quadrant Operation

#### 5.1. Tuning of Controller Parameters

#### 5.2. Simulation Results From Simscape Model

## 6. Thermal Considerations

## 7. Valve-Controlled System

- ${p}_{p}$ = compensated pressure at port p;
- ${p}_{a}$ = pressure at port a;
- ${p}_{b}$ = pressure at port b;
- ${p}_{set}$ = spring pressure setting;
- ${p}_{load}$ = load pressure;
- ${u}_{spool}$ = position of the main spool, $-1\le {u}_{spool}\le 1$;

- ${u}_{a}$ = opening of valve a, $0\le {u}_{a}\le 1$;
- ${u}_{b}$ = opening of valve b, $0\le {u}_{b}\le 1$;
- ${p}_{a1}$ = pressure at valve a input side;
- ${p}_{a2}$ = pressure at valve a actuator side;
- ${p}_{b1}$ = pressure at valve b input side;
- ${p}_{b2}$ = pressure at valve b actuator side;
- ${p}_{crack,a}$ = crack pressure of valve a;
- ${p}_{crack,b}$ = crack pressure of valve b;
- $\psi $ = pilot area ratio;
- $\Delta p$ = pressure difference for full opening;

- Leakage inductances ${L}_{ls}$ and ${L}_{lr}$ are 5% of the magnetizing inductance ${L}_{m}$. The nominal stator flux ${\lambda}_{s}$, magnetizing current ${I}_{m}$, and inductances ${L}_{s}$ and ${L}_{r}$ can then be calculated as$$\begin{array}{cc}\hfill {\lambda}_{s}& =\frac{400\mathrm{V}}{2\pi 50\mathrm{Hz}}=1.2732\mathrm{Wb}\hfill \end{array}$$$$\begin{array}{cc}\hfill {I}_{m}& =j{I}_{n}sin\left(\varphi \right)=j29.73\mathrm{A}\hfill \end{array}$$$$\begin{array}{cc}\hfill {L}_{m}& =\frac{{\lambda}_{s}}{|{I}_{m}|}=42.8\mathrm{mH}\hfill \end{array}$$$$\begin{array}{cc}\hfill {L}_{ls}& =0.05{L}_{m}=2.2\mathrm{mH}\hfill \end{array}$$$$\begin{array}{cc}\hfill {L}_{lr}& =0.05{L}_{m}=2.2\mathrm{mH}\hfill \end{array}$$$$\begin{array}{cc}\hfill {L}_{s}& ={L}_{ls}+{L}_{m}=45\mathrm{mH}\hfill \end{array}$$$$\begin{array}{cc}\hfill {L}_{r}& ={L}_{lr}+{L}_{m}=45\mathrm{mH}\hfill \end{array}$$
- Stator conduction losses contribute to 40 % of the losses. The stator resistance ${R}_{s}$ is then calculated as$$\begin{array}{cc}\hfill {R}_{s}& =\frac{0.4{P}_{n}(1-\eta )}{3{I}_{n}^{2}}=0.0852\phantom{\rule{3.33333pt}{0ex}}\Omega \hfill \end{array}$$
- Rotor conduction losses contribute to 40 % of the losses. The rotor current ${I}_{r}$ and rotor resistance ${R}_{r}$ are calculated as$$\begin{array}{cc}\hfill {I}_{s}& ={I}_{n}cos\left(\varphi \right)+j{I}_{n}sin\left(\varphi \right)\hfill \end{array}$$$$\begin{array}{cc}\hfill {I}_{r}& ={I}_{s}-{I}_{m}={I}_{n}cos\left(\varphi \right)\hfill \end{array}$$$$\begin{array}{cc}\hfill \phantom{\rule{4pt}{0ex}}{R}_{r}& =\frac{0.4{P}_{n}(1-\eta )}{3{I}_{r}^{2}}=0.1208\phantom{\rule{3.33333pt}{0ex}}\Omega \hfill \end{array}$$
- The last 20 % of the losses are modeled as Coulomb friction losses. The friction torque ${T}_{fric}$ is calculated as$$\begin{array}{cc}\hfill {T}_{fric}& =0.2{T}_{rated}(1-\eta )=2.47\mathrm{Nm}\hfill \end{array}$$

## 8. Load Case: Path Control and Anti-Swing for Hydraulic Crane

#### 8.1. Simulation with Valve-Controlled Actuators

#### 8.2. Simulation with Electro-Hydrostatic Actuators

## 9. Discussion

## 10. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Bozhko, S.; Hill, C.; Yang, T. More-Electric Aircraft: Systems and Modeling. Wiley: Hoboken, NJ, USA, 2018; pp. 1–31. [Google Scholar] [CrossRef]
- Wheeler, P.; Bozhko, S. The More Electric Aircraft: Technology and challenges. IEEE Electrif. Mag.
**2014**, 2, 6–12. [Google Scholar] [CrossRef] - Wang, X.; Liao, R.; Shi, C.; Wang, S. Linear Extended State Observer-Based Motion Synchronization Control for Hybrid Actuation System of More Electric Aircraft. Sensors
**2017**, 17, 2444. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Henke, M.; Narjes, G.; Hoffmann, J.; Wohlers, C.; Urbanek, S.; Heister, C.; Steinbrink, J.; Canders, W.R.; Ponick, B. Challenges and Opportunities of Very Light High-Performance Electric Drives for Aviation. Energies
**2018**, 11, 344. [Google Scholar] [CrossRef] [Green Version] - Wheeler, P. Technology for the more and all electric aircraft of the future. In Proceedings of the 2016 IEEE International Conference on Automatica (ICA-ACCA), Curico, Chile, 19–21 October 2016; pp. 1–5. [Google Scholar] [CrossRef]
- Semi-Electric AHC Cranes. Available online: https://www.macgregor.com/Products/products/offshore-and-subsea-load-handling/semi-electric-ahc-cranes/ (accessed on 26 January 2021).
- Wu, X.; Lai, X.; Zhu, J.; Huang, H.; Chen, L.; Du, S.; Wu, M. Intelligent Control System Design for Electric-drive Rig in Complex Geological Drilling Process. In Proceedings of the 2019 Chinese Control Conference (CCC), Guangzhou, China, 27–30 July 2019; pp. 7079–7082. [Google Scholar] [CrossRef]
- LR 1250.1 Unplugged - The First Battery-Powered Crawler Crane in the World. Available online: https://www.liebherr.com/en/aus/products/construction-machines/deep-foundation/product-launch/lr-1250-unplugged.html (accessed on 26 January 2021).
- Hagen, D.; Pawlus, W.; Ebbesen, M.K.; Andersen, T.O. Feasibility Study of Electromechanical Cylinder Drivetrain for Offshore Mechatronic Systems. Model. Identif. Control.
**2017**, 38, 59–77. [Google Scholar] [CrossRef] [Green Version] - The Best of Both Worlds: Combine Hydraulic and Servo Technology and Save up to 80% of Energy Costs. Available online: https://www.baumueller.com/en/insights/drive-technology/change-to-servo-hydraulic (accessed on 26 January 2021).
- Self-contained Hydraulic Actuators–Intelligent Hybrid Power for Extreme Force Control. Available online: https://www.boschrexroth.com/en/xc/products/product-groups/industrial-hydraulics/topics/self-contained-hydraulic-actuators/ (accessed on 26 January 2021).
- Sytronix – Variable-speed Pump Drives for Hydraulic Applications. Available online: https://www.boschrexroth.com/en/us/products/systems-and-modules/sytronix-variable-speed-pump-drives/index (accessed on 26 January 2021).
- How Variable Speed Drives Become Simpler and More Efficient. Available online: http://blog.parker.com/how-variable-speed-drives-become-simpler-and-more-efficient (accessed on 26 January 2021).
- Padovani, D.; Ketelsen, S.; Hagen, D.; Schmidt, L. A Self-Contained Electro-Hydraulic Cylinder with Passive Load-Holding Capability. Energies
**2019**, 12, 292. [Google Scholar] [CrossRef] [Green Version] - Hagen, D.; Padovani, D.; Choux, M. A Comparison Study of a Novel Self-Contained Electro-Hydraulic Cylinder versus a Conventional Valve-Controlled Actuator—Part 1: Motion Control. Actuators
**2019**, 8, 79. [Google Scholar] [CrossRef] [Green Version] - Hagen, D.; Padovani, D.; Choux, M. A Comparison Study of a Novel Self-Contained Electro-Hydraulic Cylinder versus a Conventional Valve-Controlled Actuator—Part 2: Energy Efficiency. Actuators
**2019**, 8, 78. [Google Scholar] [CrossRef] [Green Version] - Casoli, P.; Scolari, F.; Minav, T.; Rundo, M. Comparative Energy Analysis of a Load Sensing System and a Zonal Hydraulics for a 9-Tonne Excavator. Actuators
**2020**, 9, 39. [Google Scholar] [CrossRef] - Agostini, T.; De Negri, V.; Minav, T.; Pietola, M. Effect of Energy Recovery on Efficiency in Electro-Hydrostatic Closed System for Differential Actuator. Actuators
**2020**, 9, 12. [Google Scholar] [CrossRef] [Green Version] - Hagen, D.; Padovani, D.; Choux, M. Enabling Energy Savings in Offshore Mechatronic Systems by using Self-Contained Cylinders. Model. Identif. Control.
**2019**, 40, 89–108. [Google Scholar] [CrossRef] - Ketelsen, S.; Andersen, T.O.; Ebbesen, M.K.; Schmidt, L. A Self-Contained Cylinder Drive with Indirectly Controlled Hydraulic Lock. Model. Identif. Control.
**2020**, 41, 185–205. [Google Scholar] [CrossRef] - Zhang, S.; Li, S.; Minav, T. Control and Performance Analysis of Variable Speed Pump-Controlled Asymmetric Cylinder Systems under Four-Quadrant Operation. Actuators
**2020**, 9, 123. [Google Scholar] [CrossRef] - Gøytil, P.H.; Padovani, D.; Hansen, M.R. A Novel Solution for the Elimination of Mode Switching in Pump-Controlled Single-Rod Cylinders. Actuators
**2020**, 9, 20. [Google Scholar] [CrossRef] [Green Version] - Ketelsen, S.; Padovani, D.; Andersen, T.O.; Ebbesen, M.K.; Schmidt, L. Classification and Review of Pump-Controlled Differential Cylinder Drives. Energies
**2019**, 12, 1293. [Google Scholar] [CrossRef] [Green Version] - Qu, S.; Fassbender, D.; Vacca, A.; Busquets, E. A high-efficient solution for electro-hydraulic actuators with energy regeneration capability. Energy
**2021**, 216, 119291. [Google Scholar] [CrossRef] - Xue, L.; Wu, S.; Xu, Y.; Ma, D. A Simulation-Based Multi-Objective Optimization Design Method for Pump-Driven Electro-Hydrostatic Actuators. Processes
**2019**, 7, 274. [Google Scholar] [CrossRef] [Green Version] - Huang, L.; Yu, T.; Jiao, Z.; Li, Y. Active Load-Sensitive Electro-Hydrostatic Actuator for More Electric Aircraft. Appl. Sci.
**2020**, 10, 6978. [Google Scholar] [CrossRef] - Jensen, K.J.; Kjeld Ebbesen, M.; Rygaard Hansen, M. Development of Point-to-Point Path Control in Actuator Space for Hydraulic Knuckle Boom Crane. Actuators
**2020**, 9, 27. [Google Scholar] [CrossRef] [Green Version] - Jensen, K.J.; Ebbesen, M.K.; Hansen, M.R. Anti-swing control of a hydraulic loader crane with a hanging load. Mechatronics
**2021**, 77, 102599. [Google Scholar] [CrossRef] - Low Voltage Process Performance Motors. Available online: https://library.e.abb.com/public/8b08bf36a95844a8a275e5883223736b/PPM_catalog_13042016.pdf (accessed on 27 January 2021).

**Figure 2.**Examples of topologies for load holding and overload handling. (

**a**) Traditional counterbalance valves and shock valves for a single rod cylinder; (

**b**) Counterbalance valves opened by 3/2-valve and external pilot pressure; (

**c**) Load holding design for EHA. Counterbalance valves are used in (

**a**,

**b**), while (

**c**) uses poppet valves.

**Figure 6.**Torque and power curves for the selected motor with maximum, continuous, and rated operation. (

**a**) Speed-torque curve; (

**b**) Speed-power curve.

**Figure 7.**Servomotor closed loop dynamic response using FOC. Rated speed step at $t=0.01$ s and rated load step at $t=0.04$ s.

**Figure 14.**Simplified linear models used for tuning. (

**a**) Linear model for tuning ${k}_{p}$; (

**b**) Linear model for tuning ${k}_{pf}$.

**Figure 16.**Cylinder position and position error for all four quadrants. (

**a**) Cylinder position ${x}_{c}$; (

**b**) Cylinder position error ${e}_{c}$.

**Figure 17.**Cylinder velocity and motor speed for operation in quadrant 1. (

**a**) Cylinder velocity ${\dot{x}}_{c}$; (

**b**) Motor speed $\omega $.

**Figure 18.**System pressures for all four quadrants during motion. (

**a**) Quadrant 2; (

**b**) Quadrant 1; (

**c**) Quadrant 3; (

**d**) Quadrant 4.

**Figure 19.**Electric power and efficiency for all four quadrants. Operation in quadrants 1 and 3 consume power, while operation in quadrants 2 and 4 regenerate power. (

**a**) Electric power ${P}_{el}$ from/to the DC-bus; (

**b**) Efficiency $\eta $ of the system.

**Figure 21.**Position reference and temperature for the load cycle running repeatedly for 5 h. (

**a**) Position reference; (

**b**) Temperatures with different loads.

**Figure 23.**Pump total efficiency $\eta $ as a function of pressure and flow with estimated parameters.

**Figure 25.**Motor speed and efficiency during startup and full load. (

**a**) Motor speed using the estimated parameters; (

**b**) Motor efficiency using the estimated parameters (solid line) and motor data (dash-dotted).

**Figure 29.**Pump pressure and flow during motion with valve-controlled actuators. (

**a**) Pump pressure; (

**b**) Pump flow.

**Figure 30.**Power and energy during motion with valve-controlled actuators. (

**a**) Power from the grid and to the cylinders; (

**b**) Consumed energy with valve-controlled actuators.

**Figure 31.**Cylinder position error and swing angle during motion with valve-controlled actuators. (

**a**) Cylinder position error; (

**b**) Swing angle.

**Figure 32.**Pressure and flow in the knuckle circuit with EHAs. (

**a**) Pressure in knuckle circuit; (

**b**) Flow in knuckle circuit.

**Figure 35.**Cylinder position error and swing angle during motion with EHAs. (

**a**) Cylinder position error; (

**b**) Swing angle.

Functional Requirement | Typical Solution |
---|---|

Passive load holding | Counterbalance valves, POCVs, locking valves |

Overload handling | Shock valves, relief valves |

Differential flow compensation | Mode switching valves, accumulator, multiple pumps |

Four-quadrant operation | Closed circuit with bidirectional pump |

Name | Parameter | Value |
---|---|---|

Main cylinder piston diameter | ${D}_{p,m}$ | 0.160 m |

Main cylinder rod diameter | ${D}_{r,m}$ | 0.100 m |

Main cylinder stroke | ${h}_{m}$ | 0.75 m |

Knuckle cylinder piston diameter | ${D}_{p,k}$ | 0.150 m |

Knuckle cylinder rod diameter | ${D}_{r,k}$ | 0.100 m |

Knuckle cylinder stroke | ${h}_{k}$ | 0.85 m |

Name | Parameter | Value |
---|---|---|

Proportional gain, speed loop | ${k}_{p,\omega}$ | 10 As/rad |

Integral gain, speed loop | ${k}_{i,\omega}$ | 10 A/rad |

Proportional gain, current loop | ${k}_{p,i}$ | 10 V/A |

Integral gain, current loop | ${k}_{i,i}$ | 100 V/(A·s) |

Controller sampling frequency | ${f}_{c}$ | 20 kHz |

Inverter switching frequency | ${f}_{sw}$ | 2 kHz |

DC-bus voltage | ${u}_{DC}$ | 565 V |

Name | Parameter | Value |
---|---|---|

Standstill torque | ${T}_{0}$ | 49.6 Nm |

Standstill current | ${I}_{0}$ | 30.8 A |

Max torque | ${T}_{max}$ | 148 Nm |

Max current | ${I}_{max}$ | 108 A |

Rated torque | ${T}_{rated}$ | 36.5 Nm |

Rated current | ${I}_{rated}$ | 24.4 A |

Rated speed | ${n}_{rated}$ | 3000 rpm |

Rated power | ${P}_{rated}$ | 11.5 kW |

Torque constant | ${k}_{T}$ | 1.61 Nm/A |

Line resistance | ${R}_{L}$ | 0.35 $\Omega $ |

Line inductance | ${L}_{L}$ | 3.40 mH |

Friction torque | ${T}_{fric}$ | 0.2 Nm |

Rotor inertia | J | 38.6 kgcm${}^{2}$ |

Pole pairs | ${N}_{p}$ | 5 |

Thermal time constant | ${t}_{th}$ | 44 min |

**Table 5.**Components of the hydraulic system shown in Figure 8.

Component | Manufacturer | Model Number | Data |
---|---|---|---|

Servomotor (M) | Beckhoff ${}^{1}$ | AM8064R | 11.5 kW |

Hydraulic pump (P) | Bosch Rexroth ${}^{2}$ | A10FZG018 | 18 cm${}^{3}$/rev |

Accumulator (ACC) | Bosch Rexroth | HAB20 | 18.1 L |

Check valve (CV) | Sun Hydraulics ${}^{3}$ | CXADXCN | 28 L/min |

Pilot-operated check valve (POCV) | Sun Hydraulics | CKCBXCN | 57 L/min |

Relief valve (RV) | Sun Hydraulics | RDDALCN | 95 L/min |

2/2 poppet valve (PV) | Parker Hannifin ${}^{4}$ | DSH121CR | 90 L/min |

Name | Parameter | Value |
---|---|---|

Proportional gain | ${k}_{p}$ | 5 s${}^{-1}$ |

Pressure feedback gain | ${k}_{pf}$ | 0.001 m/(bar·s) |

Pressure feedback bandwidth | ${\omega}_{pf}$ | 5.32 rad/s |

Load mass | m | 30,000 kg |

Viscous friction | ${b}_{c}$ | 150 kNs/m |

Coulomb friction | ${F}_{c}$ | 4 kN |

Smoothing parameter | ${\dot{x}}_{0}$ | 0.001 m/s |

Name | Parameter | Value |
---|---|---|

Nominal power | ${P}_{n}$ | 30 kW |

Nominal torque | ${T}_{n}$ | 193 Nm |

Nominal speed | ${n}_{n}$ | 1483 rpm |

Nominal current | ${I}_{n}$ | 54.8 A |

Rotor inertia | J | 0.385 kgm${}^{2}$ |

Power factor | $cos\left(\varphi \right)$ | 0.84 |

Efficiency | $\eta $ | 0.936 |

Pole pairs | ${N}_{p}$ | 2 |

Parameter | Valve-Controlled | Electro-Hydrostatic |
---|---|---|

Main cylinder error | 5.8 mm | 5.8 mm |

Knuckle cylinder error | 5.4 mm | 3.3 mm |

Swing angle | 4.3 mrad | 4.4 mrad |

Energy consumed | 505 kJ | 88 kJ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jensen, K.J.; Ebbesen, M.K.; Hansen, M.R.
Novel Concept for Electro-Hydrostatic Actuators for Motion Control of Hydraulic Manipulators. *Energies* **2021**, *14*, 6566.
https://doi.org/10.3390/en14206566

**AMA Style**

Jensen KJ, Ebbesen MK, Hansen MR.
Novel Concept for Electro-Hydrostatic Actuators for Motion Control of Hydraulic Manipulators. *Energies*. 2021; 14(20):6566.
https://doi.org/10.3390/en14206566

**Chicago/Turabian Style**

Jensen, Konrad Johan, Morten Kjeld Ebbesen, and Michael Rygaard Hansen.
2021. "Novel Concept for Electro-Hydrostatic Actuators for Motion Control of Hydraulic Manipulators" *Energies* 14, no. 20: 6566.
https://doi.org/10.3390/en14206566