# Design and Control of an Energy-Efficient Speed Regulating Method for Pump-Controlled Motor System under Negative Loads

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## Abstract

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## 1. Introduction

## 2. System Formulation

#### 2.1. Typical Configuration with CBV

#### 2.2. Principle of the Proposed Scheme Based on EPCBV

## 3. System Modelling

#### 3.1. Model of PCMH System

#### 3.2. Flow Model of EPCBV

#### 3.3. Motor Leakage Estimator (LEOR)

## 4. Controller Design

#### 4.1. Supervisory Controller

#### 4.2. Velocity Controller (VCOR)

#### 4.2.1. Feedforward Control

#### 4.2.2. Feedback Control

#### 4.3. Pressure Control (PCOR)

## 5. Experimental Investigation

#### 5.1. Test Bench Setup

#### 5.2. Experimental Programs

#### 5.2.1. T-CBV System

#### 5.2.2. EPCBV System

#### 5.3. Experimental Results Analysis

#### 5.3.1. Stability Analysis

#### 5.3.2. Accuracy Analysis

#### 5.3.3. Energy Consumption Analysis

## 6. Discussions

## 7. Conclusions

- Both the EPCBV system and T-CBV system can effectively prohibit the motor from self-accelerating. However, the EPCBV system shows better adaption than T-CBV system to varying negative loads and maintains higher stability than T-CBV in all the working conditions.
- The speed control accuracy of the EPCBV system can be maintained above 95% in most of the operating conditions, while the speed accuracy of the T-CBV system is varying from 48% to 90%, depending very much on working conditions.
- Under most operating conditions, the maximum power consumption is about 4 Kw and is far less than that of the T-CBV system, which is about 13.79 Kw under the same operating condition. The power-saving ratio between the EPCBV and T-CBV varies from 20% to 82%, depending on the working conditions of the PCMH system; however, it goes beyond 50% in most of the operating range of the system.
- The EPCBV system shows accuracy decrease and power consumption increase in the regions where the flow saturation of the EPCBV occurs.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Typical configuration of CBV for PCMH system, (

**b**) characteristic plot of typical CBV in PCMH system.

**Figure 3.**(

**a**) Proposed configuration with EPCBV for PCMH system, (

**b**) four-quadrant operation modes for the proposed scheme.

**Figure 4.**(

**a**) Linear fitting curve for dead-band vs. inlet pressure of EPCBV, (

**b**) polynomial fitting curve for effective signal vs. flow gain of EPCBV.

**Figure 5.**(

**a**) Polynomial fitting curve for motor leakage estimation model with ${\omega}_{m}<1000\mathrm{r}/\mathrm{min}$, (

**b**) polynomial fitting curve for motor leakage estimation model with ${\omega}_{m}>=1000\mathrm{r}/\mathrm{min}$.

**Figure 7.**(

**a**) Schematic of the test bench for EPCBV system, (

**b**) photograph of the test bench 1—IPM1; 2—pump; 3—EPCBV; 4—IPM2; 5—hydraulic motor.

**Figure 9.**EPCBV system responses under different negative torque ${T}_{s}$ (

**a**) ${T}_{s}=-5\mathrm{N}\cdot \mathrm{m}$, (

**b**) ${T}_{s}=-15\mathrm{N}\cdot \mathrm{m}$, (

**c**) ${T}_{s}=-25\mathrm{N}\cdot \mathrm{m}$, (

**d**) ${T}_{s}=-35\mathrm{N}\cdot \mathrm{m}$.

Components | Type | Parameters | Components | Type | Parameters |
---|---|---|---|---|---|

IPM1 | Hilectro HP12529-G402F-R1 | Rated Power: 109 Kw | Torque and Speed Sensor 2 | Interface T4-300 NM | Torque range: 0–150 Nm |

Rated Torque: 260 Nm | Torque accuracy: ±0.2% | ||||

Speed range: 500–4000 r/min | Speed accuracy: ±0.03% | ||||

IPM2 | Hilectro HP11812-G502F-R1 | Rated Power: 57 Kw | Pressure Sensor 1–3 | HYDAC HDA4745-A-600-Y00 | Pressure range: 0–400 bar |

Rated Torque: 110 Nm | Accuracy: ±0.25% | ||||

Speed range: 0–5000 r/min | Output: 4–20 mA | ||||

Pump | Rexroth A4VG40EP4 | Displacement: 0–40 cc/r | Flow Sensor 1–2 | Hydrotechnik QT 110 | Flow range: 0–75 L/min |

Control signal: 200–600 mA | Accuracy: 1% | ||||

Rated Pressure: 400 bar | Output: 4–20 mA | ||||

Hydraulic motor | Rexroth A6VE28EP2 | Displacement: 28 cc/r | Torque and Speed Sensor 1 | Interface T4-300 NM | Torque range: 0–300 Nm |

Rated pressure: 400 bar | Torque accuracy: ±0.2% | ||||

EPCBV | SUN CWCG-T21A | Pilot ratio: α = 5 | Speed accuracy: ±0.03% | ||

Rated Flow: 60 L/min | Torque and Speed Sensor 2 | Interface T4-150 NM | Torque range: 0–150 Nm | ||

Output pressure: 0–100 bar | Torque accuracy: ±0.2% | ||||

VTOZ MA-RZGO-a-010-100 | Output pressure: 0–100 bar | Speed accuracy: ±0.03% | |||

Control signal: 200–600 mA | T-CBV | SUN CACALHN | Pilot ratio: α =3 | ||

Controller | Rexroth-RC28/14 | Periods: 5 ms | Rated flow: 60 L/min |

Parameters | Value | Parameters | Value |
---|---|---|---|

K_{P} | 1 | k_{γ} | 0.05 bar/s |

K_{I} | 0.3 | nD_{pmax} | 1 L/min |

K_{D} | 0.04 | k_{t} | −0.05 bar^{−1} |

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**MDPI and ACS Style**

Wang, H.; Zhang, Y.; Li, G.; Liu, R.; Zhou, X.
Design and Control of an Energy-Efficient Speed Regulating Method for Pump-Controlled Motor System under Negative Loads. *Machines* **2023**, *11*, 437.
https://doi.org/10.3390/machines11040437

**AMA Style**

Wang H, Zhang Y, Li G, Liu R, Zhou X.
Design and Control of an Energy-Efficient Speed Regulating Method for Pump-Controlled Motor System under Negative Loads. *Machines*. 2023; 11(4):437.
https://doi.org/10.3390/machines11040437

**Chicago/Turabian Style**

Wang, Huashuai, Yanbin Zhang, Geqiang Li, Rongsheng Liu, and Xin Zhou.
2023. "Design and Control of an Energy-Efficient Speed Regulating Method for Pump-Controlled Motor System under Negative Loads" *Machines* 11, no. 4: 437.
https://doi.org/10.3390/machines11040437