MODELLING AND CONTROL OF A HYDROSTATIC ... - cIRcle

M O D E L L I N G A N D C O N T R O L OF A H Y D R O S T A T I C TRANSMISSION FOR A L O A D - H A U L - D U M P UNDERGROUND-MINING MACHINE by A M R I T P A L SINGH G O S A L B . A . S c , The University of British Columbia, 2001 A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF APPLIED SCIENCE * in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Mechanical Engineering

We accept this thesis as conforming to the required standard

T H E UNIVERSITY OF BRITISH C O L U M B I A August 2004

© Amritpal Singh Gosal, 2004

Abstract

This thesis focuses on the modelling and control of the hydrostatic transmission (HST)

on an extremely-low-profile, front-end-loader configuration, load-haul-dump

(LHD) machine: the 88XLP, designed and built by EJC Mining Equipment Inc. of Burlington, Ontario. The machine uses four pump-motor hydrostatic closed loops to power its four wheels. Speed regulation is required on such a machine in order to achieve the differential effect needed when the machine turns, as well as to maintain consistent wheel speeds and efficiency when travelling straight. Hydraulic pressure/flow sharing/coupling techniques are commonly employed to create the differential effect: experimental evaluation of eleven such hydraulic arrangements is presented to determine the efficacy of each, based on a calculation of a drivability-index for each arrangement. A review of techniques for feedback control of HSTs is presented, and proportional-integral (PI) control is selected to implement-speed feedback control for the variable-pump-variable-motor (PVMV) HST on the 88XLP. The results of tuning and drivability tests using the PI controller are presented. A model of the HST and controller, based on offline system-identification of the HST is implemented in Simulink, including nonlinearities, such as hysteresis and controller feedback quantization, as well as the discrete-time nature of the controller. It is found that this model does not provide close correspondence to behaviour of the actual system under feedback control.

This

discrepancy is attributable to the nature of the HST: its components with extremely nonlinear and time-varying characteristics, which further have a strong dependence on the operating conditions. As a result of the comparison between the various hydraulic sharing/coupling techniques and speed-feedback control, it is concluded that simple feedback control does not yield the best performance for this application, and that hydraulic system redesign is a more effective means of achieving design objectives for this application. The best performing hydraulic sharing/coupling technique is identified and suggestions are made to further improve its performance through simplifying the overall configuration of the HST.

11

Table of Contents

Abstract

ii

Table of Contents

iii

List of Tables

vi

List of Figures

vii

Nomenclature Preface

xv

Acknowledgements 1.0

Introduction

1.1

x

The Machine

xvi 1 2

1.1.1

Drive-train considerations in Underground Mining Vehicles

3

1.1.2

The 8 8XLP Hydrostatic Drive

4

1.1.3

Cheater Lines and Power-Sharing Lines

7

1.1.4

Sensors

9

1.1.4.1

Speed Sensor

9

1.1.4.2

Articulation Sensor

9

1.1.5

The I Q A N System

10

1.2

Issues concerning the 88XLP

13

1.3

Scope of Work

14

2.0

Literature Review

15

2.1

Applications of the Hydrostatic Transmission

15

2.2

Modelling the HST

18

2.2.1

Simple Modelling Relations

19

2.2.2

Leakage Losses

20

2.2.3

Compressibility

22

2.2.4

Friction

23

2.2.5

Models based on Systems Theory

25

2.2.6

Other Modelling Methods

28

2.3

Control

31

in

2.3.1

PI controllers

31

2.3.2

Adaptive Controllers

33

2.3.3

Fuzzy-Logic Controllers

34

Literature Review Summary

38

2.4 3.0

Experimental Methodology

3.1

Hydraulic-Sharing Testing

3.1.1

Testing S cheme

40 40 40

3.1.1.1

Configuration of test 1

41

3.1.1.2


41

3.1.1.3


41

3.1.1.4


41

3.1.1.5


41

3.1.1.6


42

3.1.1.7


42

3.1.1.8


42

3.1.1.9


42

3.1.1.10


42

3.1.1.11


42

3.1.2

The Test Course

43

3.1.3

Test Procedures

43

3.1.3.1

3.2

Analysis of the data

44

3.1.3.1.1

Articulation Angle Calculations

45

3.1.3.1.2

Articulation Radius Calculations

46

3.1.3.1.3

Drivability Index Calculations

47

System Identification

48

3.2.1

Description of Testing

50

3.2.2

MatLab for System Identification

51

3.3

Controller Design and Simulation

52

3.4

Field Implementation of the Controller

56

4.0 4.1

Results and Discussion Results of Hydraulic-Sharing Testing

59 59

iv

4.1.1 4.2

Problems encountered during testing System Identification Results

64 :

65

4.2.1

Pump Response Results

65

4.2.2

Motor Response Results

71

4.2.3

Formulating Transfer Functions

77

4.3

Controller Simulation Results

79

4.4

Results of PI Control Implementation

81

5.0

Conclusions

84

5.1

Contributions of the research

84

5.2

Feasibility of Implementing Feedback Control

85

5.3

Design Recommendations

86

5.4

Hydraulic System Redesign - 88XLP Mark-II

87

References

122

v

List of Tables Table 1: Ziegler-Nichols Rule-Table [after 28]

33

Table 2: Fuzzy Rule Set [27]

35

Table 3: Pump fuzzy rule set used by Huhtala [4]

.35

Table 4: Motor fuzzy rule set used by Huhtala [4]

36

Table 5: Hydraulic sharing configurations tested

41

Table 6: Drivability indexes and their averages

61

Table 7: Sorted drivability indexes

62

Table 8: Normalized drivability indexes

63

Table 9: The best DI's often trials from all tests

64

Table 10: The worst DI's often trials from all tests

64

Table 11: Change in motor speed vs. change in pump input current

68

Table 12: Model fit summary

78

Table 13: Pi-gains used for driving tests

82

Table 14: Drivability Calc Results, Pi-Control Included

83

vi

List of Figures

Figure 1: The low-profile L H D developed by EJC Mining known as the 88-XLP

3

Figure 2: A simplified schematic of the hydrostatic drive for one wheel circuit

4

Figure 3: Simplified schematic of the D P R valve

5

Figure 4: Model of the pump installation

6

Figure 5: H D C control and connection ports for the M46 pump

7

Figure 6: Pump Power Sharing

8

Figure 7: H D C control of the VI2-160 motor

8

Figure 8: I Q A N control, simplified inputs and outputs

11

Figure 9: Schematic of the I Q A N control system

12

Figure 10: Bondraph model of the HST system [20]

28

Figure 11: PI control flow-chart (after [27])

32

Figure 12: Course followed during testing

43

Figure 13: Articulation angle calculations

45

Figure 14: Articulation radius calculations

46

Figure 15: A detail of the turning radius calculations

47

Figure 16: Test bench at Feldcamp Equipment Ltd

49

Figure 17: The I Q A N computer interface at Feldcamp Equip. Ltd

49

Figure 18: Feedback model using the simplified pump transfer function

53

Figure 19: Feedback model with the fitted pump transfer function

54

Figure 20: Pump model with feed-forward and non-linearities

55

Figure 21: Feedback control scheme

57

Figure 22: Left-turn in reverse (Test 1)

59

Figure 23: Left-turn in reverse (Test 4)

60

Figure 24: Pump response at low input speed

66

Figure 25: Pump response at medium input speed

67

Figure 26: Pump response for high input speed

68

Figure 27: Pump response for low input speed and input stepped down

69

Figure 28: Pump response for medium input speed and input stepped down

69

vii

Figure 29: Pump response for high input speed and input stepped down

70

Figure 30: Pump and DPR response

71

Figure 31: Motor and DPR response for low input speed

72

Figure 32: Motor and DPR response for medium input speed

73

Figure 33: Motor speed vs. modulating pressure, a non-linear relationship [41]

74

Figure 34: Motor and DPR response for high input speed

74

Figure 35: Motor and DPR response for low input speed and signal stepped down

75

Figure 36: Motor and DPR response for medium input speed and signal stepped down. 76 Figure 37: Motor and DPR response for high input speed and signal stepped down

76

Figure 38: Compared pump response of the real and modelled data

77

Figure 39: Pump-response using feedback and PI controller (without feedforward or dead-band)

79

Figure 40: Effect of Hysteresis on the model (without feedforward or dead-band)

80

Figure 41: Complete model response

81

Figure 42: Pi-Controller tuning on the machine (on stands)

82

Figure 43: Pump step input 0-12.5%

103

Figure 44: Pump step input 12.5-25%

103


104


104


105


105


106


106


107


107


108


108


„.. 109


109


110


110

Figure 59: Motor step input 0-12.5%

111

Figure 60: Motor step input 12.5-25%

111


112


112


113


113


114


114


115


115


116


116


117


117


118


118

ix

Nomenclature

a

ai

Empirical constant Actual swashplate angle pump swashplate angle Displacement setting of the primary unit

a

Displacement setting of the secondary unit

AC A

Alternating Current Effective control piston area

Ai

area of the large actuator

a

Desired swashplate angle

V

area of a single piston

As

area of the small actuator

A

control valve spool area

b B b b

Empirical constant The bulk modulus Moment-arm length at the swashplate hydraulic fluid bulk modulus projection of control moment arm to neutral position x area of the control piston (ARcosa) Empirical constant Empirical constant/losscoefficient

a a

2

e

0

v

n

P C

Ci..

CAD CAN

Cp

Cf

Computer-Aided Design Control-Area-Network Coulomb friction torque loss coefficient

Cf

Empirical constant

c

Hydrodynamic friction coefficient

C

Leakage coefficient

Ct

Turbulent slip coefficient

C

Viscous friction torque loss coefficient

0

h

s

s

v

d D,

Empirical constant Volumetric displacement of the primary unit

D

Volumetric displacement of the secondary unit

DI DPR e

Drivability Index Direct-Pressure-Reducing valve Empirical constant Empirical constant

2

s

EDC E

Electronic Displacement Control Speed-error

EVPS

Earth-moving Vehicle Powertrain Simulator Empirical constant Feedback Feedforward Fuzzy state controller Empirical constant pressure carry-over angle on the port-plate pump flow constant The DC-gain of the system pump displacement gain (same as K above) control gain Hydraulic Displacement Control Hydraulic position servo Hydrostatic Transmission Hertz mass moment of inertia of the motor and load Infinitely Variable Transmission swashplate moment of inertia Empirical loss constant Empirical loss constant controller flow gain effective control line fluid bulk stiffness control piston fluid effective bulk stiffness control valve spool stiffness Integral Gain system leakage gain

k

/

FB FF FSC

g g 7 G G G HDC HPS HST Hz P s

/

1VT Jsp k, k K Kd K K Ki 2

c

cp

cs

KI

K

P

K

P

kph K pp

•«vpr

K K kW L L lbs LHD LPF LRT M sp u

p

Proportional Gain pump flow gain kilometers per hour effective pump plenum fluid bulk stiffness Coefficients of an empirical equation relating torque to swashplate angle and velocity swashplate return spring rotational stiffness The ultimate-gain that causes oscillatory response Kilo Watt moment arm of actuator acting on the swashplate Large pounds Load-Haul-Dump machine Low pass filter Linear Resistive Transducer Medium

XI

M

Torque at the input shaft of the primary unit Torque at the output shaft of the secondary unit

MDC

Manual Displacement Control

MDM ML

Master Display, Mini Medium-large Torque function obtained from polynomial fitting of the data corresponding to the minimum angular speed used in the test, n. Torque function obtained from polynomial fitting of the data corresponding to the maximum angular speed used in the test, n+ Torque function obtained from polynomial fitting of the data corresponding to the minimum pressure used in the test, pTorque function obtained from polynomial fitting of the data corresponding to the maximum pressure used in the test, p+ miles per hour milliseconds Medium-small control valve spool mass Empirical constant total number of pistons Minimum speed used in test Maximum speed used in test Speed of the primary unit Speed of the secondary unit Normalized drivability index Pressure gradient Minimum pressure used in test Maximum pressure used in test Atmospheric pressure Discharge pressure Proportional-Derivative Effective control piston pressure Fixed Pump, Variable Motor dynamic hose pressure Proportional-Integral Proportional-Integral-Derivative constant hose pressure Variable Pump, Fixed Motor Variable Pump, Variable Motor Flow from the primary unit Flow to the secondary unit Amount of compressed flow Ideal flow Flow lost to leakage Flow function obtained from polynomial fitting of the data corresponding to the minimum angular speed used in the test, n.

Mi 2

M. H

M

n+

M. p

M

p+

mph ms MS My

n N n. n+ nt n NDI 2

P PP+ Palm

PD Pe

PFMV Ph

PI PID Po

PVMF PVMV qi Qc Qi QL Qn-

xii

Flow function obtained from polynomial fitting of the data corresponding to the maximum angular speed used in the test, n+ Flow function obtained from polynomial fitting of the data corresponding to the minimum pressure used in the test, p. Flow function obtained from polynomial fitting of the data corresponding to the maximum pressure used in the test, p+ Fluid density piston rotational radius pump control line resistance

Qn

+

QP

p r Rd Rep

control piston leakage resistance

Rev

control valve orifice resistance

Ru

motor inter-chamber leakage resistance

Rin

Radius of the inside wheels in a turn

Ri

resistive load at motor

Rm

motor plenum leakage resistance

R,out

Radius of the outside wheels in a turn

R

pump plenum leakage resistance

RPM

Revolutions per minute

RPS

Revolutions per second swashplate rotational damping coefficient control valve spool damping coefficient

P

Rsp R

v

Sin

Small Simplified pump model constants Speed of the inside wheels in a turn

SOC

Self-organizing fuzzy-logic controller

S S,...

S

3

Speed of the outside wheels in a turn The time constant of the first-order function

Sout T

Small torque losses Coulomb friction torque loss

T

e

Tf

TF v TL

Transfer function Ideal torque Total torque loss

T

Time-period of the oscillations

tUfflactual

Actual turning ratio

turn

Predicted turning ratio

Tv

Viscous friction torque loss

M

Fluid viscosity

Mi

tangent of the pump swashplate angle (tan a)

VDC

Voltage — Direct Current

u

pred

(Ri /R ut) n

0

(R /R ) in

out

xiii

v

v

volume of discharge hose Very-large motor volumetric displacement input flow of the motor

Vo

reference volume of the large actuator

V

Ratio of total clearance volume to swept volume at maximum displacement

VS

Very-small nominal servo volume Angular speed The cut-off frequency for the low pass filter angular speed of the motor shaft Maximum angular speed of the unit The natural frequency

h

VL V

m

m

r

Vso CO OJc G)m G>max 0)

n

C0

0

0J

0

COp

XLP zoh

Empirical constant desired motor speed pump angular velocity Extremely Low-Profile Zero-order-hold

xiv

Preface

The author, Amritpal Singh Gosal, completed a Bachelor of Mining Engineering degree at the University of British Columbia, in 2001. He started his work on the Master of Applied Science degree in the department of Mechanical Engineering, in 2002, under the supervision of Dr. Robert Hall and Dr. Laeeque Daneshmend. The research was a part of a collaborative agreement between EJC Mining Equipment, the University of British Columbia and Queen's University, funded in part by an N S E R C C R D grant. Under the agreement, the students (including the author) gained access to EJC's equipment for study, while EJC benefited from the research resources available at the universities and the pool of knowledge and research expertise provided by the thesis supervisors.

xv

Acknowledgements This work would not have been possible without the blessings of God - first and foremost thanks to Him.

I would like to thank my thesis supervisors Dr. Robert Hall and Dr. Laeeque Daneshmend for all their help and guidance. I would also like to thank Dr. Farrokh Sassani and Dr. Ian Yellowley for sitting on the thesis examination committee.

A special note of appreciation goes to M r . Patrick Murphy and Mr. David Sargent, as well as others from EJC Mining Equipment, Burlington, Ontario, for providing direction with research goals and the opportunity as well as the means to pursue an experimental undertaking of such magnitude, and to Mr. Larry Feldcamp and Mr. Rick Taylor from Feldcamp Equipment Inc. for their technical expertise.

Many thanks go to my family for providing support through love and encouragement.

xvi

1.0

Introduction Mining has been an integral part of society for millennia.

As with other

technological pursuits, the practice of mining has evolved with time. Currently, having taken the form of a competitive industry, it too faces significant socio-economic challenges.

Cost reduction is important for mining to stay profitable, like other

industries. As mines get deeper and ore-bodies get more complex and challenging to mine, the demand for specialized equipment is increasing at an accelerated rate. Labour is being replaced by mechanization as standards for safety and production are raised all over the world.

In some places, such as South Africa, the shift to mechanization is

dictated by the forecast lack of labour in the near future, resulting in a push towards acceptance of new technology. The South African Platinum mines are a good example of changing mining practices worldwide, where low mine headings are required to stay profitable as only the valuable raw materials are extracted, and mechanization is readily accepted as it results in higher production rates and safer working conditions. To meet the needs of a growing market, a hydrostatic machine was designed and built by EJC Mining Equipment Inc. in Burlington, Ontario, in 2002. The purpose of the machine was to fulfill the demand of a specialized market, specifically the South African Platinum mines, where an extremely low profile, front-end loader machine was needed, to improve production efficiency and personnel safety. The design was conceptualized as a machine that would use a hydrostatic transmission to transfer power from a diesel engine to its four wheels. A purely hydrostatic transmission, without a gearbox, required that a controller capable of meeting sophisticated control requirements be selected.

A

C A N (control-area-network) based controller (called IQAN®, built by Parker) was chosen for this task. Due to the absence of mechanical differentials for power distribution, a method needed to be devised to facilitate transmission of power where required.

Based on

previous experience with similar transmissions, the designers chose hydraulic pressure sharing to accommodate the differential distribution of power between the left and right side wheels. The degree of effectiveness of the hydraulic sharing was not known. It was required for the hydraulic sharing to be tested and documented, and alternative methods

1

to be researched. One of the objectives of this research was to test various arrangements of hydraulic sharing/coupling and rate them, based on their performance results, and also, to develop an alternative if required. This thesis commences with a review of the literature as applicable to the task at hand. Other applications where the hydrostatic transmission (HST) method was selected are discussed. Various modelling techniques used by the researchers in the literature, to predict the behaviour of the HST, are also reviewed. An overview of the various control schemes applied to the HST in the literature is also given. The aforementioned machine is then presented in the form of a case study, where the currently practised methods of HST control are evaluated. The methodology for conducting the various tests, analyzing the results and designing a model and a controller is presented. Results from the testing are then presented and discussed. Finally, conclusions and recommendations regarding design and control of the HST are presented.

1.1 The Machine In order to increase productivity and worker-safety in narrow reef platinum mining of South African mines, a low-profile load-haul-dump (LHD) machine was designed by EJC Mining Equipment [1]. Mechanization was desirable to relieve the intensive manual labour associated with mining in the low mine headings, only 1.1-1.2m in height. The machine was to replace the existing battery-powered machines adapted from coal applications. These machine experienced problems such as insufficient battery life to last a whole shift, which is undesirable as it interrupts production. A significant design constraint was posed by the low working environment of the machine. The lowprofile design precluded the use of conventional hydro-mechanical transmissions utilizing torque-converters. It was decided to use a hydrostatic transmission powered by a diesel power-plant, with four independent pump-motor closed-circuits. Control of the transmission and other machine functions was to be facilitated by the Parker IQAN system. The production of the first 88XLP, serial number 3445, was completed in November of 2002. This machine became the in-house prototype machine - it would never be shipped to the field but would stay at the plant in Burlington for prototyping of

2

any design changes.

The 88-3445 was also used for this research for testing and

experimentation. Figure 1 shows a schematic-drawing of the 88XLP.

1549 mm

I *

3098 mm 7743 mm

J *

Figure 1: The low-profile LHD developed by E J C Mining known as the 88-XLP The 88XLP, unlike traditional mechanically driven loaders, is a hydrostatic machine, which uses no differentials in either the front or the rear axles. The machine's small size does not allow utilization of mechanical differentials because of spatial constraints. Like most underground mining equipment, it is centre articulated; this means that the front wheels are laterally fixed and turning is facilitated by articulating the machine about its centre hinge, by making use of hydraulic steer cylinders. A 94-kW diesel powered engine is situated in the rear half of the machine that provides the power for all machine functions. Control of the machine is achieved by means of drive-by-wire. A C A N (control-area-network) interface enables exchange of system information and operator commands between the controller and the operator. Electronic commands from the controller are physically realized through hydraulic actuators.

1.1.1 Drive-train considerations in Underground Mining Vehicles Underground mining vehicles have distinct design requirements to meet the harsh demands of the underground mining environment. Various considerations have to be made when selecting components in an underground mining vehicle design. For instance, size is a constraint that has to be met by all underground vehicles. The maximum size of an underground machine is dictated by the size of the underground opening. Similarly, the specified task of a machine demands further requirements. For instance, a loader requires better traction abilities than a haul-truck and the latter more climbing power versus the former. Also, because of traction requirements, underground mining loaders are invariably four-wheel drive, so that power can be made available

3

where needed, for best traction performance. As underground mining vehicles, operate on rough surfaces formed by broken rock, efforts must be made to reduce or eliminate wheel spin so useful power can be sent to the wheels with the most traction.

1.1.2 The 88XLP Hydrostatic Drive On the 88-XLP, each of the four wheels has a hydraulic motor that is independently driven by a hydraulic pump. The pumps are driven via a triple-pump drive by a Deutz diesel engine. Between each pump and the motor, a closed-loop hydraulic circuit is implemented. The closed loop circuit consists of a charge pump, a hydraulic pump and motor, and a common hydraulic reservoir. The inlet of the charge pump is directly fed from the reservoir. The inlet and the outlet of the drive pump are connected to the outlet and the inlet of the motor, respectively; hence the term closed loop hydraulic circuit. Four pumps were chosen to independently drive four motors because of the flexibility available with being able to independently control the amount of power sent to each wheel. Traction control of independent wheels equates to power available to only the wheels doing work, and therefore, a higher efficiency. The pumps and motors have hydraulic-displacement-control (HDC) implemented. Other commercially available control options include electronic-displacement-control (EDC) and manual-displacement-control (MDC). The H D C was selected because of cost benefits over the EDC. Figure 2 shows a simplified schematic of one wheel circuit of the hydrostatic drive.

Figure 2 : A simplified schematic of the hydrostatic drive for one wheel circuit

Among the selected components for the 88XLP hydrostatic transmission are the Sauer-Dan Foss M46 series axial piston pumps and Parker V12-160 series axial piston

4

motors. The hydraulic control pilot pressure to the pumps and motors, which actuates motion of the swashplate, is metered via DPR (Direct Pressure Reducing) valves (Figure 3), which in turn are controlled by proportional electric solenoids. The current signal sent to the DPR valve-solenoids is calculated and provided by the onboard I Q A N controller, built by Parker. The key components of this electro-hydraulic drive system are: the I Q A N M D M , I Q A N satellite modules, DPR valve stack, and the H D C pump and motor controls. From Charge Pump (21 bar)

IQAN Analog Out

To Pump/Motor HDC F i g u r e 3: S i m p l i f i e d schematic o f the D P R v a l v e

The hydraulic pumps and motors have various ports that are used for working connections, as well as test ports. Two #16 ports (ports A and B) on the M46 pump are dedicated to main-pressure.

Depending on the direction the swashplate is displaced,

which one of the two ports will be high pressure is determined. For example, i f the operator has engaged forward on the transmission control, the pump will swash in a given direction, which will be opposite to the swashing direction when reverse on the transmission is selected. The direction the swash plate is displaced dictates whether port A or B will have a higher pressure or energized fluid. The lines connected to ports A and B on the pump are directly connected to the motor main-pressure A and B ports in a closed-loop hydraulic circuit. In equipment equipped with hydraulic displacement control (HDC), a higher hydraulic pressure on either side of the control spool pushes it in the opposite direction, which, through mechanical and hydraulic linkages, causes the swashplate to displace in the prescribed direction, by the prescribed amount. As mentioned earlier, the M46 pumps and the V12 motors used on the 88XLP are equipped with hydraulic displacement

5

control. The motor swashplate is unidirectional, i.e. it is not allowed to travel overcentre. The direction of motion of the machine is governed by the direction in which the bidirectional pumps are swashed. The Sauer-Dan Foss pumps as installed are called M46-PT.

The "T" in the

nomenclature stands for "tandem". Two pumps are connected together with a gerotorgear charge pump in between. As configured on the 88XLP, two banks of tandem pumps are installed on a triple-gear pump drive, and each bank is dedicated to provide power to motors on only one side. Furthermore, each of the pumps in the tandem orientation drives one motor each. A 3D CAD model of this arrangement is shown in Figure 4. The third location on the triple-pump-drive is reserved for two more pumps: the implement and cooling pumps (not shown in Figure 4 for clarity). For further pump and motor physical specifications, please refer to APPENDIX A. TANDEM PUMP INSTALLATION

Figure 4: Model of the

pump installation

6

Since the machine does not have conventional differentials to account for the speed variance between the left and the right side wheels, hydraulic coupling between the various pump and motor ports was employed (a.k.a. cheater lines and power-sharing lines).

1.1.3 Cheater Lines and Power-Sharing Lines The cheater lines allow pressure balancing between A and B lines of two pumps via ports M l and M 2 (see Figure 5). B y allowing flow to be shared through the cheater lines, the pump that experiences more resistance from its connected motor sheds flow toward the pump with lesser resistance.

This is the simplest way of creating the

differential effect during turning.

Figure 5: HDC control and connection ports for the M46 pump

Power-sharing lines are used to render the internal feedback in the H D C control less effective. Two test-gauge ports (#6 or Vs") on each side of the servo piston of the pump (M4 and M5) are connected to similar ports on the opposite side pump. A high pressure is created on one of the sides of the control-servo-piston when the pump experiences resistance caused by the infighting due to the lack of a differential effect. This causes the internal feedback to demand a greater swashplate stroke setting. This concept is illustrated in Figure 6. The darker shading in the figure depicts areas with higher pressure than the areas depicted by the lighter shade. When the machine is turning without a differential in place, the inside wheels fight the turning by attempting to go at

7

the same speed as the outside wheels (A and B). With the internal feedback working nominally, the resistance caused by turning at the inside wheels demands a higher flow, making the problem of fighting even worse (M4 and M5).

Servo Piston

B

M4

M5 Figure 6: Pump Power Sharing

On production 88XLP machines, power-sharing is also employed on the wheel motors. Ports X I and X6 from the front and rear left motors are connected to similar ports on the front and rear right motors through 0.9-mm (0.035-in) diameter control orifices (see Figure 7).

Figure 7: HDC control of the V12-160 motor

Power-sharing lines help to make the internal feedback in the pump and motor internal control less effective. By preventing the inside wheels from speeding up and by shedding the higher pressure at the servo-piston to the opposite pump, power-sharing

8

should cause the outside wheels to turn faster, resulting in the desired, but somewhat unregulated, differential effect. The 88XLP, as it is currently produced, uses pump and motor power-sharing lines. Cheater-lines have never been used on a production 88XLP machine. Powersharing lines between the motors have 0.9-mm (0.035") diameter orifices controlling the amount of flow sharing.

The appropriate orifice size was determined through

experimentation by others.

1.1.4 Sensors Several sensors are used on the 88XLP that enable feedback to the I Q A N controller. Currently, feedback is only used for diagnostic purposes, not for enabling or maintaining control. Some sensors of interest include: four speed sensors, one position sensor and eight pressure transducers. A l l I Q A N compatible sensors are excited by the controller voltage of 5-VDC and output a signal ranging from 0.5 to 4.5-VDC, except the speed sensor, which is excited by the machine power (24-VDC) and outputs a digital signal. 1.1.4.1

Speed Sensor

Four Parker speed sensors are used on the 88XLP-prototype. The sensors are installed in the speed-sensor port made available on the VI2-160 series motors. The sensors are magnetic Hall-effect proximity sensors that detect teeth on the motor shaft. There are thirty-six teeth per revolution on the motor shaft. The signal, in the form of a square-wave, is sent to the I Q A N frequency-counter-connection for speed detection. The frequency counter on the I Q A N system is interrupt driven and runs at a frequency of 10kHz. Number of pulses counted per scan time is converted to a frequency within the I Q A N controller and further scaled to give the motor R P M . 1.1.4.2 Articulation Sensor

One position sensor is located within the steering cylinder and is used to detect steering extension which allows calculation of the articulation angle. The sensor is a linear-resistive-transducer (LRT). This sensor is essentially a voltage divider that sends a portion of the input voltage to the output connector, based on the position of its moving

9

brush. As the steering-cylinder extends, the resistance is increased and so is the voltage at the output connector.

1.1.5 The IQAN System The I Q A N system is a C A N (control-area-network) based system that is primarily designed for control of industrial and mobile hydraulic equipment. Satellite modules are connected to the M D M (Master Display, Mini) through C A N . Please see APPENDIX B for detailed specifications of the I Q A N components. Analog and digital information is exchanged between the controller and the sensors and actuators via channels on the modules. The 88XLP has four satellite modules: two I Q A N X S , and one of each IQANXP2 and IQAN-XT2 modules.

Each module is designed with a specific purpose

governed by the type of channels it offers for input and output. For instance, the XT2 is SAE-J1939 ready: it is capable of interfacing with the diesel engine controller. J1939 is the most widely accepted heavy-duty diesel engine controller CAN-protocol. The IQANM D M is the main controller, but it is incapable of input or output itself: it acquires data and sends actuator commands by communicating with satellite modules over the C A N bus. Therefore, at least one satellite module must be used in conjunction with the M D M . The M D M has a display where critical system information, such as alerts and warnings, are made available for the operator or the maintenance personnel. The M D M also allows connection with a computer running the IQAN-develop software through a serial port. The IQAN-develop software is used to write programs for the M D M which are loaded over the serial connection. Limited data-acquisition capabilities are also available with an online computer while tests are being conducted. In the graph window of IQANdevelop, up to ten channels of data acquisition can be displayed in real time.

The

acquired data can be transferred in ASCII format to supporting programs for further manipulation.

If more than ten channels need to be monitored, another stand-alone

module must be used, such as the IQAN-TOC8 module. Since the TOC8 has no serial connection, a test box was constructed to facilitate its installation. The test box provided a serial connection for computer and banana jacks for channel-signal connections. On the 88XLP, all machine functions are controlled through programming of the I Q A N - M D M . Driving with the hydrostatic transmission is made possible by the I Q A N

10

system, as it controls the pump and motor swash plate angles, while monitoring the engine speed, to prevent the engine from stalling (anti-stall). The feedback for the antistall loop is engine rpm, over the J1939-bus. The controller gets the throttle and brake (inch-pedal) inputs and controls the DPR solenoid currents to change pump and motor swash-plate settings (see Figure 8). The two pumps for each side share the same pilot hydraulic signal from the DPR's. A total of four pilot signals are sent to the pumps: two for each side - for forward and reverse driving directions. A l l four motors share a single pilot signal.

So under ideal conditions, the two pumps for each side have the same

swashplate setting and so do all four motors. Figure 9 depicts the workings of the I Q A N system: in the open loop system described in Figure 8, the box labelled IQAN is further detailed in Figure 9, without the articulation corrections for differential compensation. Engine RPM Engine

IQAN

Controller

Current output to drive DPR-solenoids

Throttle

D P R stack

Inch-Pedal

Left D r i v e ^ Pumps

Right Drive j

r

Pumps

Pilot S i g n a l to Motors

Drive Forward Pilot Drive Reverse Pilot L_

L

Drive Forward Pilot Drive Reverse Pilot

J

Figure 8: IQAN control, simplified inputs and outputs

11

Current out values to DPR's are limited between 0 and 100% of the min and max range

IQAN

To Pump DPR's

16.5

•Q

850

: To Motor D P R

THROTTLE 0-100% Predetermined Factor 1.

1

iVCAN7.i.939Vi Engine Controller — * —

Fuel Regulator

Engine Tach| Sensor

Figure 9: Schematic of the I Q A N control system

The 8 8 X L P decelerates through hydrostatic-braking.

Mechanical brakes are

installed for safety reasons, for emergency stops and for parking. The brakes are applied and will remain applied i f there is not enough hydraulic pressure to release them (failsafe). The pressure required to release the brakes is supplied by the charge pumps, and is only available when the engine is running. Pushing the emergency stop button releases the pressure and the brakes are applied for situations when abrupt stopping is required. Hydrostatic braking works by reversing the roles of the hydrostatic pumps and motors. Inertia of the machine is transferred by the motors to the pumps, which in turn, drive the diesel engine as a compressor. The hydrostatic braking comes into effect by depressing the inch-pedal or automatically, as the machine is allowed to coast with the accelerator

12

pedal released. A l l of these functions are effected by the I Q A N system, by swashing the motors and pumps as required. The I Q A N controller monitors and controls multiple functions on the 88XLP. A function on the M D M , known as "utilization", monitors resource usage and translates the value to a percentile of the maximum available resources.

The optimum cycle time

(refresh time) was found to be 50-ms (20-Hz), based on resource utilization, through trial and error. If this is reduced any further, the controller utilization exceeds acceptable levels and information is lost as the controller tries to prioritize tasks.

1.2 Issues concerning the 88XLP •

Since the 88XLP does not have conventional differentials distributing power from

side to side, power-sharing lines are used between the hydrostatic pumps and motors, as mentioned before. understood.

However, the functionality of any flow-sharing was not fully

There

are numerous

combinations of flow-sharing that can be

conceptualized. Through experience, certain combinations were known to work better than others. Other than the operator's subjective evaluation, no method was available to quantify the efficacy of flow-sharing. •

Several hours of setup time is required to finalize the I Q A N minimum and maximum

currents for D P R control for every machine. This procedure requires that all powersharing lines to be removed when settingTup the I Q A N currents. Installation and removal of power-sharing lines during setup opens up ports through which contaminants can enter the hydraulic system.

The author witnessed several cases where a wheel motor

(sometimes two) had to be replaced, because its performance became erratic during setup. The cause for such cases, when the motors were inspected, was mostly dirt blocking an internal orifice. A l l of these problems with the initial setup result in unplanned personhours and cost money. EJC is, therefore, seeking ways to reduce the setup time and improve setup methods so that dirt is not introduced into the hydraulic system. •

The machine drives shakily, especially while turning. This is attributed to the lack of

an adequate differential effect, which causes disagreement between the speed of the inside wheels compared to the outside wheels. This tendency of the inside wheels to

13

travel faster than required causes the machine to react against the steering cylinders by trying to drive straight and causing the machine to shake. The shakiness is significant enough to cause operator discomfort. •

Cost cutting has caused the removal of some sensors: only one speed sensor is

installed on all production units and the articulation sensor is also not available any longer.

Any new improvements on the 88XLP must be geared toward reducing the

overall cost.

1.3 Scope of Work •

Based on the problems encountered with the current hydraulic setup and to combat

the inadequacies experienced with the existing control, this research focuses initially on testing the hydraulic flow and pressure sharing arrangements, to develop a better understanding of their efficacy. •

System-identification of the drive as a whole, to capture the interaction of the D P R

valves with the pump and motor dynamic components is conducted. •

To develop a drive controller employing speed feedback, a simple model of the

system as a whole is created, based on system identification using experimental data. A Simulink/MatLab® simulation model of the drive is created to evaluate stable ranges for Pl-controller-gains. •

The Pi-controller is designed and implemented on the 8 8XLP-prototype, and

drivability results

are

compared with the results

from the

various hydraulic

sharing/coupling configurations. •

A n assessment is performed based on the above analysis with respect to the most

feasible control/design strategy to be employed on the hydrostatic transmission of the 88X L P machine.

14

2.0

Literature Review No publications pertaining to design guidelines or design constraints for flow or

pressure sharing in hydrostatic transmissions could be found, specifically using powersharing lines and cheater lines (please see section 1.1.3), even after a thorough search of the published literature. The search was then directed towards hydrostatic transmissions with feedback control. It was found that designers have utilized feedback control with hydrostatic transmissions, in applications similar to the one that is the focus of this research. Speed as feedback for control of HSTs was found to be universally adopted. Various applications with slip control using speed comparison for multi-wheel drive machines were located [35, 36]. Various control strategies were also encountered: PI, fuzzy, hybrid fuzzy-PI and so on [4, 23, 25, 27, 29, 30].

2.1

Applications of the Hydrostatic Transmission A hydrostatic transmission (HST) works by converting mechanical energy from a

prime-mover (a diesel engine or an electric motor) into hydraulic energy in a primary hydrostatic unit, and by reconverting the hydraulic energy into mechanical energy in a secondary hydrostatic unit. The primary and secondary hydrostatic units are commonly referred to as pump and motor, respectively. In contrast to a hydrodynamic transmission, energy in a HST is transferred by the high static pressures and relatively lower fluid velocities or lower dynamic pressures [2]. The hydraulic energy is carried by a nearly incompressible hydraulic fluid from the input shaft of the pump to the output shaft of the motor, via an arrangement of pistons in rotation-groups in both pumps and motors. If air is entrained in the fluid, compressibility can become an issue. Generally in HST design, provisions are made for the air to escape the fluid and to prevent further mixing of air into the fluid. Air entrainment is primarily a result of highly turbulent fluid velocities in the reservoir. To prevent this from happening, provisions should be made in the design to allow the fluid to settle, allowing the entrained air to escape before it is reintroduced into the hydraulic circuit. To prevent air-entrainment, turbulent fluid should be kept from coming in contact with the atmosphere.

15

HST's are used in a wide range of applications: agriculture, mining, earthmoving, turf-maintenance, cranes, as well as stationary equipment applications. Design considerations of a HST and component selection concerns for a turf-maintenance application are presented by Betz [3]. Being able to changing vehicle speed without shifting gears or varying engine-speed are attractive features of the HST for the turfmaintenance industry. Maximum desired tractive-effort is used to determine the expected value for the pressure generated in the system, which is used in component selection and in fail-safe mechanisms selection, such as relief valves. The HST is preferred in applications where a high power to size ratio (power density) is desired. Some of the advantages of the HST as listed in the literature include [4, 5]: •

Continuously variable output speed

•

High stiffness

•

Flexibility

•

Ease of assembly

•

Good controllability

•

Simplicity in operation

•

High starting torque

•

Self lubricating and cooling

•

Upgradeable modular design

The efficiency of the HST is low compared to mechanical transmissions, as energy transformation takes place in two stages: from mechanical to hydraulic-pressure in the primary unit and back to mechanical in the secondary unit. Mechanical gear boxes are often used in conjunction with the HST to improve the overall efficiency. A n example of such an application is the Infinitely Variable Transmission (IVT) of John Deere 7000 T E N Series tractors [6].

The IVT has an electro-hydraulic closed loop

controller with speed feedback. The HST discussed in [6] consists of a variable and a fixed hydrostatic unit. The HST is installed as a single module, unlike other applications where the primary and secondary units are connected with hydraulic hoses and are found at the engine and the wheel pr the mechanical differential, respectively. The HST module

16

is connected to a clever arrangement of gears and clutches to effect desired speed/torque requirements. In another example, an HST design by International Transmissions Ltd. (ITL), offers a maintenance free, noise free and compact transmission for small mobile equipment, such as forklifts and telehandlers. The transmission uses Hall-effect sensors for speed monitoring and feedback control [7].

The sensors are installed in a non-

contacting position close to gear-teeth in the transmission. A n HST built by Poclain, termed SmartDrive™, allows customization of system parameters through programming. A software package, known as Phases, allows the user to connect a PC to the HST controller, and display and change functional parameters. The listed features that can be programmed are: maximum speed, acceleration and deceleration

control, braking control, an

inching feature,

motor

displacement

management and an engine anti-stall feature [8]. A hydrostatic-mechanical hybrid, termed "the S-matic power split drive," was developed by Steyr Antriebstechnik in Austria.

This transmission benefits from the

advantages of both hydrostatic and mechanical transmissions as continuous variability of speed is made possible by the hydrostatic transmission, and high efficiency and durability are provided by the mechanical component of the S-matic power split drive [9]. Pedersen and Nielsen [10] presented an application of the HST in a city bus in Aarhus, Denmark.

The low floor of the city bus (0.325 m) precluded the use of a

mechanical transmission. However, the lower efficiency of the HST was a concern. To combat the inefficiencies associated with HST's and to lower fuel consumption by the prime mover (diesel engine), a computer controller aimed at optimizing fuel-efficiency was employed.

The diesel engine and the P V M V HST transmission were directly

controlled by the computer through electronic actuators.

The controller was aimed at

controlling the hydraulic unit displacements to generate the torque demanded by the application, as a function of the vehicle speed. In iterative-loops, the unit displacement indices and the engine rotational speed were changed to result in values that demand the lowest fuel consumption, while meeting the driving demands.

Application of the

computer controller resulted in fuel savings of up to 2.4%.

17

2.2

Modelling the HST With the advent of microprocessor controllers and their acceptance in industrial

control applications, system designers are now able to implement controllers which improve the machine performance in such areas as efficiency and safety.

This trend

towards computer control has also motivated further efforts to understanding the internal workings of hydraulic systems, in order to base controller designs on valid system models. Models also need to be established to compare performance and performance constraints of various configurations of the HST, allowing component and configuration selection to be made prior to the implementation stage, hence shortening the product design and development cycle, and consequently, saving time and money and improving competitiveness. As hydraulic pumps and motors are the key components of an HST, a majority of the relevant modelling research is focussed on quantifying functional parameters and prediction of the dynamic and steady-state behaviour of these components. Computer simulations that are helpful in making informed decisions require accurate models to give meaningful and useful results. Some of the published models range from simple physical relations to detailed mathematical derivations of the parameters affecting performance.

Where test data is available and experimental

modelling is preferred, empirical relationships are drawn to model functional parameters, such as losses and fluidic effects, like compressibility. As mentioned before, hydraulic fluid is nearly incompressible; however, at high pressure levels, compressibility can result in lower than ideal flow from a pump. The machining tolerances in internal components of pumps and motors can allow hydraulic fluid to leak, causing less than expected flow from a pump and less than expected speed from a motor for a given flow. These loss effects are modelled at great lengths in the literature and examples are given in sections 2.2.2, 2.2.3 and 2.2.4. Leakage is also necessary as it is responsible for cooling and lubricating moving components. It also prevents development of hot-spots within the pumps and motors and prolongs component life by providing cooling, lubrication and flushing of particles resulting from wear. Leakage flow generally drains from a separate port on the housing of the hydraulic unit and is filtered and cooled in a heat-exchanger. When reintroduced

18

into the system, the purified and cooled oil helps in improving cleanliness and reducing temperature of the entire hydraulic system.

2.2.1 Simple Modelling Relations The primary and the secondary hydraulic units can each have either fixed or variable displacements.

In a simple arrangement with a variable primary and fixed

secondary, the flow produced by the primary is dependent only on its displacement setting, provided the input shaft speed is kept constant. Therefore, the output shaft speed is dependent only on the displacement setting of the primary unit. This relationship can be represented algebraically by equation (1) [2, 11], where n\ and n , qi and q are speeds 2

2

and flows (per revolution) of primary and secondary units, respectively, and aj is the displacement setting (ranging from -1 to 1 for a reversible pump, or 0 to 1 otherwise) of the primary unit. n =n —a 2

x

(1)

x

This equation ignores leakage losses and compressibility of the fluid.

However, the

maximum possible speed of the output shaft or the ideal speed for a given displacement setting of the primary is correctly represented.

In a more practical arrangement, the

primary and the secondary are both variable, in which case the relationship is given by equation (2). Clearly, from equation (2), the secondary unit cannot have a displacement setting (a ) equal to or close to zero, as this would result in very high speeds of the 2

secondary unit. In mathematical terms, n approaches infinity as a approaches zero. 2

2

The minimum displacement setting of the secondary unit in practice is mechanically limited based on the rated maximum speed by the manufacturer or speed demands of a specific application. q «, x

n =n 2

(2)

x

q

2

a

2

The Principle of Conservation of Energy also leads to equation (3), where in a lossless transmission, torques of the input (Mi) and output shafts (M ) can be related [2]. 2

19

M =M^^2

q

(3)

a

2

2

Reiterating, losses due to leakage result in a less than ideal amount of flow at the outlet port of a pump and less than ideal speed in a motor. The ideal flow and speed can be calculated according to equations (4) and (5) [12]. The volumetric displacement of the pump is denoted by Dj and the motor volumetric displacement by D . 2

q = n D, x

(4)

x

(5)

i =— =— D D

n

2

2

2

As mentioned before, leakage in pumps and motors causes behaviour that is different from the idealized models presented. To accurately predict the behaviour of hydraulic units, leakage has been modelled in various ways and examples from published literature are summarized next.

2.2.2 Leakage Losses Examples of many loss models are found in the literature. Dorey [13] suggests that losses in hydrostatic units are attributed to slip or leakage due to pressure gradients, and fluid compressibility.

Since clearance in hydrostatic units is small, resulting

Reynolds numbers are also small, and therefore, leakage flows are laminar. The leakage and friction coefficients are also taken as variables by Dorey over the entire range of operation of the units. The leakage coefficient (C ) is described as a dimensionless value s

relating the flow lost to leakage (Q ), ideal flow (Qi), pressure gradient (P), fluid L

viscosity (ju), and angular speed (co), as shown in equation (6).

Qi

MG>

Dorey [13] suggests that significant changes in the internal geometry of hydrostatic units are caused by pressure, speed and fluid viscosity. So, C cannot be taken as constant over s

the entire range of operation to correctly characterize hydrostatic units.

Instead, C * s

correctly describes leakage dependence on speed and pressure, as shown in equation (7), where a and b are coefficients of a linear relationship of C with speed. The coefficients s

a and b are determined experimentally. In equation (7), C is defined as the product of s

20

the rate o f c h a n g e o f f l o w w i t h respect to the p r e s s u r e d r o p a c r o s s the h y d r a u l i c u n i t a n d ju/V,

w h e r e the a n g u l a r - s p e e d

P

pressure (or i n the unit.)

is kept constant;

a n d V is the v o l u m e o f the f l u i d

denotes the a t m o s p h e r i c pressure, a n d

atm

a n g u l a r s p e e d o f the u n i t ; e q u a t i o n (7) results i n a d i m e n s i o n l e s s

f p

N

c; = c.

f

a + b\

co

comax

under

is the m a x i m u m

C*.

N

(7)

V^max J

c. =i[dp)) w dQ

CO

I n the

1940's, W . E . W i l s o n published a f l o w m o d e l for hydrostatic

assuming laminar leakage.

machines

Others have extended W i l s o n ' s m o d e l b y including empirical

leakage and frictional terms.

W i l s o n ' s l e a k a g e m o d e l is s h o w n i n e q u a t i o n (8) [4, 13],

where D is v o l u m e t r i c displacement per radian.

PD

QL=C, Schlosser

(8)

included a

e q u a t i o n (9), w h e r e C

st

term

considering leakage

to

be

turbulent,

is a turbulent s l i p c o e f f i c i e n t , a n d p is the f l u i d d e n s i t y [4, 13].

PD Q =C— +C L

M T h o m a , u s i n g the

in Wilson's model

IP 2/ — D* VP

(9)

s i m p l e W i l s o n m o d e l and accounting for turbulent

leakage

flows,

f o u n d that l o s s c o e f f i c i e n t s e x h i b i t e d a s i g n i f i c a n t v a r i a t i o n , o f u p to 2 0 % , d e p e n d i n g o n the

operating

conditions.

Examining models

for gear-type

pumps,

Tessmann

made

l e a k a g e l i n e a r l y d e p e n d e n t o n s p e e d , u s i n g e m p i r i c a l l o s s c o n s t a n t s , k i a n d k.2, as s h o w n i n e q u a t i o n ( 1 0 ) [4, 13].

Q = -k a>D + k. L

PD

(10)

x

Z a r o t t i a n d N e r v e g n a created a n e m p i r i c a l m o d e l w h e r e leakage w a s dependent o n the s q u a r e o f p r e s s u r e , o n s p e e d t o t h e p o w e r o f 1.5, a n d s l i g h t l y o n d i s p l a c e m e n t . included

e m p i r i c a l t e r m s to

equation (11), Q

account

for compressibility.

T h e y also

In their m o d e l , s h o w n

t o Cs a r e e m p i r i c a l l o s s c o e f f i c i e n t s a n d a i s t h e u n i t ' s

in

displacement

21

setting as described before. Also, Qi in equation (11) shows the total flow lost to both leakage and compressibility [4, 13]. Q* = C , P + C P

2

2

+ C P co 2

]S

3

+ C Pco{C + Da) 4

(11)

5

Huhtala [4] experimentally examined all of the models discussed thus far. His results showed poor correlation between the predicted and experimental results over the entire operating range of the tested hydraulic unit. Satisfactory correlation was found near the verification points; i.e., in the range close to where empirical constants or model coefficients were determined. Huhtala proposed two line models for pumps and motors. The modelling technique involved determining the system variables at two points in the operating range. First, by keeping the pressure constant at a low value and varying the speed from minimum to maximum, and repeating with the pressure held constant at a higher value, gave dependence of leakage losses on speed.

Second, for pressure

dependence, speed was held constant at two values and pressure was varied from minimum to maximum. Using polynomial fitting, two curves were produced from the data that defined the extremities of the range where flow and torque losses are dependent on speed. Flow from a hydraulic unit is modelled by equation (12), where Q +, Q ., Q + p

p

n

and Q . are flow functions obtained from polynomial fitting as described above and p+,p. n

and n+, n. are notations used for the maximum and minimum test pressures and speeds. n-n

(

Q , =[Q M)-Q Sn)\ n P

P

P

(Q (p)-Q Sp)Y n+

n

n

K

+

^ -n_j

+ QAP) + Q _(n) p

(12)

2.2.3 Compressibility Similar to leakage, compressibility also affects flows at the pump and motor outlets. Losses due to compressibility of hydraulic fluid are noticed as a reduction in the amount of flow at the pump outlet as fluid is compressed, and as an increase in the amount of fluid flow at the outlet of the motor, where the oil is allowed to expand. Compressibility of hydraulic fluid in a hydrostatic unit can be derived from the definition for bulk modulus. A change in pressure AP of a volume Vof fluid causing it to compress and decrease in volume by AV, gives the definition of bulk modulus as shown in equation (13).

22

B = -—V AV

(13)

The negative sign accounts for the negative change in volume as the fluid is compressed (V~2

Qc'^-D Li

Dorey [13] suggests that the actual compressed flow volume is higher than as described by equation (14) above because of "clearance-volumes within the unit": the actual volume of compressed oil is increased due to the clearance volumes. For variable units, varying the displacement has an effect on the volume of compressed oil. Equation (14) is modified to include these compressibility effects, resulting in equation (15). V is r

the ratio of total clearance volume to swept volume at maximum displacement [13] and a is the unit displacement setting.

v l±SL

(15)

+

2.2.4 Friction Losses due to friction are manifested as torque losses.

Two types of friction

losses are discussed: friction caused by viscous forces between moving parts due to the presence of a film of fluid known as viscous friction, and dry friction taken to be dependent on pressure, called coulomb friction. Both types of friction cause the resulting torque to be less than ideal. The ideal torque

in a motor may be given by equation (16).

= PD

T

t

(16)

Torque loss attributed to viscous friction r , equation (17), is speed dependent and to v

coulomb friction loss Tf, equation (18), is pressure dependent. C and Cf are viscous v

friction and coulomb friction coefficients, respectively, // is absolute fluid viscosity, co is angular velocity of the shaft, P is the difference in pressure of the inlet and outlet ports, and D is volumetric displacement per radian of the hydraulic unit.

T = C pcoD v

v

(17)

23

r = C PD f

(18)

f

Wilson's torque loss TL can be summarized by equation (19) [13]. T in this equation is a e

small torque loss that is dependent on neither speed nor pressure. T = C jucoD + C PD + T l

v

f

(19)

e

Schlosser introduced a relationship replacing T

e

in Wilson's model based on

hydrodynamic torque loss as shown in equation (20), where Ch is a hydrodynamic friction coefficient [13]. z = C fiaD + C PD + C pco D^ 2

L

v

f

(20)

h

Thoma suggested that hydrodynamic friction cannot be independent of unit displacement, a. His addition to Schlosser's model is shown in equation (21) [13]. T = C jucoD + CfPD + C pa l

v

co D

(21)

/3

h

Hibi and Ichikawa used the Wilson model by modifying the coulomb friction coefficient to describe torque losses in hydraulic units. They formulated an empirical relationship of coulomb torque loss being dependent on the unit's port pressures, Pi and P . Equation 2

(22) describes their model, with C/ , co , sand n being empirical constants [13]. 0

T = C p.coD + l

0

PD + T

v

1+ *>/

(22)

co„

Zarotti and Nervegna, similar to their flow loss to leakage model in equation (11), created a non-linear empirical model of torque loss with Cj to Cg being the empirical constants of their model as shown in (23) [13]. r =co(c +C coa )+C P-(l 3

L

V

}

2

3

1

+ ^L+ I 4P

^

C

a

"

+ C6

CO + C

7

}

C, + •co + C

(23) a

Dorey proposes that all of the empirical models lose generality and flexibility of application from one unit to another. Also, extensive testing is a prerequisite to most of the empirical models as empirical constants must be derived from test data. Similar to his leakage flow model, Dorey suggests modification of the coefficients in the Wilson torque

24

model, as detailed in equation (24) below, where C* and C / are the modified friction coefficients [13].

T = C'ficoD + C/PD

(24)

l

C ' =C (a + ba) v

v

In the above equation for C*, a and b are terms that define C to be a linear function of v

the displacement, a. Similarly, coefficients c, d, e, f, and g define Cf to be a quadratic function of angular velocity co, in the following Dorey model. C,

< CO * = C , a + b-co + c

(d + ea)

Torque in hydraulic units is also modelled by Huhtala as shown in equation (25), using a formula similar to the flow formula from equation (12). Here M +, M ., M + and p

p

n

M„_ are torque functions obtained from polynomial fitting as described before and p+, p. and n+, n. are notations used for the maximum and minimum test pressures and speeds [4](

M , =[M (n)-M _(n)\ n p

p+

p

(M (p)-M _(p))n+

n

n-n

^

+ M„_(P) + M(n)

(25)

2.2.5 Models based on Systems Theory Schoenau et al [16] created a mathematical model of a variable displacement pump by analyzing the torques acting on the swashplate due to the control mechanism, rotating pistons, and associated frictional forces. non-linear.

The resulting model is complex and

Some of the model non-linearities were linearized for simplification, and

terms causing insignificant effects were neglected. In this model, torque exerted by the pistons on the swashplate due to the line pressure was also considered. Swashplate angle was shown to have a strong dependency on the return spring constant. The results of the modelled swashplate angle showed good correlation with the physical measurements. Also, the simplified-linearized model showed "virtually no difference" from the complete mathematical model. Implementation of such a model for control purposes is not viable because of the complexity associated with the modelling. This model is only applicable

25

to the Vickers No. PVB5 pump, for which it was specifically formulated.

Online

calculation of the coefficients in the model and real-time acquisition of the various measurable parameters in the model would require significant computer power and instrumentation - hence further rendering the model unacceptable for control purposes due to its complexity. In equation (26), the simplified model by Schoenau et al [16] is shown.

The K

pr

terms are coefficients of an empirical equation relating the torque

generated by pressure to the swashplate angle (a) and swashplate angular velocity. Si, S

2

and S3 are simplified pump model constants. A is the effective control piston area; P is e

e

the effective control piston chamber pressure; b is the moment arm length of the control piston on the swashplate; APp is the differential pressure of the pump; and I is the e

moment of inertia. - P A b + K AP e

e

pr2

+ 5, = (S - K AP

p

2

pri

p

(26)

)cc-S,d + T a e

A similar model, based on simple principles of physics, to develop equations describing torques acting on the swashplate of a pump, was created by Manring and Johnson [17] for a pressure compensated pump. Swashplate dynamics were justifiably considered negligible with respect to the control actuator. Their model is built on the assumption that "destabilizing forces of the discharge-pressure" are combated by the "restoring forces of the control actuator." The dynamic system model is expressed in equation (27), where a, a and Pa are the actual swashplate angle, desired swashplate Q

angle and discharge pressure, respectively; coefficients a, b, c, d, e and f are composed of physical internal dimensions of the constituents of the pump and flow-characteristic constants. •

a

•

a

—

c

b

a

d A.

e

{A L-NA ry/(27r)y s

p

a=

(27)

+

o

-K p

c = —K , p

K

(A,L-

c

A,L

> ° =

d = ——K,, e = -a and f

NA ry/{l^ p

l

/

K

ULfV

h

=-c

26

A Ai A K Ki K L N r s

p

P

c

r

v v

0 h

= area of the small actuator = area of the large actuator = area of a single piston = pump flow gain = system leakage gain = controller flow gain = moment arm of actuator acting on the swashplate = total number ofpistons = piston rotational radius pressure carry-over angle on the port-plate reference volume of the large actuator volume of discharge hose ,

In a different publication by Manring and Luecke [18], based on the work of modelling a variable pump in [17] and by including models for the motor and the hose, a complete model of the HST was developed. The load-torque acting on the motor is considered constant in this model, as shown in equation (28). b

0"

—u

0 / P 0 —i a

h

t(IiJ '- T '

iJ

K

Ph a V I m

P

G Vso G Po p

s

COo

u=

p

+

0

+

(28)

w

-T -- ^

T

miw

g

= angular speed of the motor shaft = dynamic hose pressure = pump swashplate angle = motor volumetric displacement = mass moment of inertia of the motor and load = hydraulic fluid bulk modulus = pump displacement gain (same as K above) = nominal servo volume = control gain - constant hose pressure = desired motor speed p

27

Tafazoli, de Silva and Lawrence [19] created a non-linear friction model of an apparatus for decapitation of salmon. The decapitating blade was moved to the correct position with the aid of a digital camera. The position of the blade was controlled by varying the current to the electro-hydraulic valve. The force acting at the hydraulic actuator was modelled by considering coulomb friction between the lubricated metal guide ways. The coulomb friction was estimated online using the modified FriedlandMenzelopoulou's coulomb friction observer algorithm.

Only a simple model of the

hydraulic-valve controlling the position of the blade was considered because pressures after the control-valve were measured and used to calculate the acting force.

It was

recognized that hydraulic-actuator dynamics resulted in a fixed delay in the response of the blade in following a command. To remedy the delay, feed-forward compensation was suggested but not implemented. 2.2.6

Other Modelling Methods Dasgupta has presented a model of an open circuit HST with a variable pump and

a low-speed-high-torque, orbital-rotor motor [20].

Using Bondgraphs, he created a

model of the HST consisting of a pump, an integrated pressure control valve and a motor to study the dynamic performance of the system. The bondgraph model of the HST, as presented by Dasgupta, is shown in Figure 10. r

i I

p.oiT R;Rm

D«D_T R-.Rp

PUMP

c:K -r PP

I

»T>

T

.

-^Ppc-T- -4S '

tjritnn MOTOR

~~

"1

!

- S E : f (v ,RU,Ri) j m

T

J

&

c-x,

1

'"SiTrT SE:SE

!se:SE«>c: CONTROL | VALVE

1

V

1

^TF

%Sv1

CK

p

R:R | V

C S

I

Figure 10: Bondraph model of the HST system [20]

28

The equations pertaining to system dynamics can be deduced from the bondgraph model. Each bond represents a directional flow of relating effort or flow variables between two considered components. The product of the bond effort and flow variables equals power. The term "bondgraphs" is a concise form of power-bondgraphs. SF in the bondgraph model of Figure 10 represents a flow source, i.e., the pump. Similarly, the motor is shown as an effort source (SE) where the effort, torque, is originating due to a load. S and P junctions are used to show series and parallel connections (analytic, not necessarily physical) in bondgraphs.

An S junction signifies that the flow variable

through the junction is constant and the effort is distributed; whereas a P junction is used where the effort variable is constant and the flow variable is distributed. For a further examination of the Bondgraph simulation techniques, please see references [21] and [22]. In Dasgupta's model, the variables are defined as:

r (Dp

Mi

K R

pp

P

R/n

V Ru m

Ri

Rci Ki c

Rev Rep Kp C

P R

SP

Jsp

A R v

v

K My cs

= pump flow constant = pump angular velocity = tangent of the pump swashplate angle (tana) = effective pump plenum fluid bulk stiffness = pump plenum leakage resistance = motor plenum leakage resistance = input flow of the motor = motor inter-chamber leakage resistance = resistive load at motor = pump control line resistance = effective control line fluid bulk stiffness = control valve orifice resistance = control piston leakage resistance = control piston fluid effective bulk stiffness projection of control moment arm to neutral = position x area of the control piston (ARcosa) = swashplate rotational damping coefficient = swashplate return spring rotational stiffness = swashplate moment of inertia = control valve spool area = control valve spool damping coefficient = control valve spool stiffness control valve spool mass

29

Dasgupta examined his model experimentally. He found a delay in the experimental response of the swashplate and the control piston spool when compared to the theoretical response, and attributed it to positional stiction; this quantity was not modelled in the analysis. Some of the values required for the model were experimentally determined: spring constants, control piston leakage and pump leakage. It was shown that the pump leakage varies almost linearly with pressure. The test speeds were slow compared to real applications.

The tests were conducted at 125, 158 and 195 revolutions per minute.

From the data presented by Dasgupta, a slight dependence of leakage on speed can be observed. Njabeleke et al [23] used a hydraulic system modelling software package, known as BATH/p, developed at the University of Bath, to obtain linearized system equations to represent the components of the hydraulic system. They have suggested that non-linear mathematical models of hydraulic components are complex and their application to system design even more difficult, where system components and parameters can be easily changed. This is truly the case with HST's, where components may be replaced for maintenance purposes and component behaviour changes with use and wear. The response of a system to an applied input can be measured and a transfer function can be deduced i f the system is treated as a black-box. A degree of complexity of the system has to be assumed and the input and output data can be fitted to acquire a transfer

function of the assumed shape.

The classical approach of black-box

identification has two distinct steps: data acquisition and transfer-function deduction. Some of the disadvantages of using the classical approach listed by Landau [24], include: •

Test signals during data-acquisition are not characteristic of the real process. In other words, the input signal in the classical approach is generally a step signal and the real process seldom experiences such signals.

•

The end result has a reduced accuracy.

•

Disturbances are not modelled.

For a system that is assumed to have a first-order response, the resulting transfer function takes the form of equation (29), where t is the delay in response, r is the time constant and G is the DC gain or the steady state value of the response [24].

30

T(s) = fl+

(29) ST

A n example of offline system identification of a hydraulic test-rig is available in [25], where an "earthmoving vehicle powertrain simulator (EVPS)" is modelled by collecting the process data and making use of M A T L A B to develop the transfer-function. Landau [24] suggested the use of high-performance, recursive algorithms that are capable of real-time identification.

The recursive algorithms result in discrete-time

models of the plant and are suitable for application to a digital controller. A simple system-identification technique was used by Tafazoli et al [26] to model a position controlled hydraulic cylinder, using the least-squares method to maximize model accuracy by minimizing the error between the model and the collected data. A first-order system was assumed to represent a hydraulic cylinder. Having presented various methods used for modelling the process, the next section will show examples of control strategies employed by researchers in controlling hydrostatic transmissions.

2.3 Control Various control strategies such as PI (proportional-integral), adaptive PI, fuzzy, and hybrids of fuzzy and other control-techniques have been applied to the control of hydrostatic transmissions. Since the HST is a highly nonlinear plant, the application of purely linear controllers like PI is limited; however, PI or PD control has been applied to other hydraulic components such as actuators and valves.

2.3.1

PI controllers Publications dealing purely with the application of PI controllers to hydrostatic

transmissions could not be located in the literature; however, ones comparing the performance of linear (PI) and other control techniques were found. Ambuel et al [27] conducted tests to control the output speed of a variable-pump, fixed motor (PVMF) HST, implementing a PI and a hybrid PI controller. The motor load was simulated by a flywheel and a load pump that pumped into a relief valve. The control scheme was transformed to the discrete-time domain to implement with a digital controller having, a 31

cycle time of 50ms. A flowchart of the PI controller is shown in Figure 11. Ambuel et al's approach to a hybrid PI controller will be discussed in the next section. Compute Speed Error at Time T = Tk Ek = Speed Error = Setpoint - Speed

Compute Proportional Term using Proportional Gain K P = K xE

p

p

k

Compute Integral Term Using Integral Gain Kj k-\ I

= i K

k

x E

k + h-x» where7 _,

=K x^ E

t

i

J

}

Determine Total Output 0 =P+I =

K xE K xf E p

k+

i

j

j

7=1

Figure 11: PI control flow-chart (after

[27])

For the PI controller, values of 0.2 for the proportional gain and 0.1 for the integral gain resulted in an under-damped response, whereas values of 0.1 and 0.05 for the former and latter, respectively, resulted in an over-damped response.

Tests were repeated on the

system when it had aged and experienced wear. It was shown that the PI controller's performance degraded as the system's behaviour changed with age.

The same gain

values that resulted in an over-damped response previously, outputted a high overshoot and a slow rise-time. Huhtala [4] discussed application of a PI controller to a hydrostatic transmission, specifically, to a hydrostatic unit (pump or motor). His end result took the form of an adaptive PI controller, which is discussed in the next section.

The gain of the PI

controller was shown to strongly depend on the unit's displacement setting.

He

suggested that a controller with a fixed gain could not be implemented to provide sufficient control over the entire operating range of the unit. Huhtala showed that a 32

controller tuned at a low speed setting of the hydraulic-unit results in an under-damped behaviour at high speeds. For the inverse case when the tuner is tuned at a high unit speed, a longer rise-time or a slower response is resulted. Tuning of P, PI and PI D controllers is discussed by Jantzen [28] by citing the Ziegler-Nichols method. The proportional gain is increased until stable oscillations are achieved to determine the ultimate gain (K ), at which point, the time-period of the u

oscillations is measured (T ). Finally, using the Ziegler-Nichols rule-table (Table 1), the u

PID gains are estimated. Table 1: Ziegler-Nichols Rule-Table [after 281

CONTROLLER P PI PID

K Q.5K 0A5K »aj.c OI 150 SSU © 1 CO-F ;32 cSli

PV3'

Parker Hannifin

Hi

Corporation

• ':-J--::;-:J •|y:J- :..

-

'5

: s [1 v •*:>* anas, USA

92

Catalog HY16-3500'US

D S Coil

Technical Information

Series 5/8*

I.D.

Features >re pwr,K K r : : a p s L l a t t ! : :

::esigr

•

C:::rnpH:1

•

Minimal amperage

•

Numerous t e r m i n a l s a n a

•

High watt sesigr

•

H e a v y gauge r-obr :::x:ea lean w i r e with built-ir relief

craw voltages

optional

•

1 5 0 C C l a s s H w i r e s t a r s arc

•

200 C Class N wire on high watt

strair

models

Specifications

Wattage

11 Watts — Stanoara - Black Coil 3-0 Watts High Watt Rerj Coil

Duty Rating

Continuous @ 100% voltage

Wins C l a s s

Class H for all voltages 17 Watt Class N for all voltages 30 Watt

A.C. Rectifier

Integral lull wave bricge

Lead Wire

H i :jai.:je \-A" long SOD volt rating

Lead Wire Strain Relief

34 kg (75 lbs.) Q 21 C (70 F) & 18 kg (40 lbs.) @ 93 C (2 00'F)

Encapsulating Material

lass filler: r y b r , resistant to m o i s t L r e . caustic solutiors. fungus, arc lemp.eralures Irom - 4 0 C (-40 T ) to 200 C (392 Fi

AC Coil Assembly No inductive cr capacitive leads can be installed between surge suppressor and rectified valves J

NOTE:

Parker A C Coils incorporate integrally molded full wave rectifiers which are rated for reverse voltage p-eaks cf *0OC vclts maximum. For voltage transients greater than 'CCS volts P.I.V., Harris Thyrector V' 5CLA' CA or V 5CLA2CA for " 5 VAC and V250LA 5A or V250LA4CA for 200 VAC is recommended.

AC Cot Assembly

1

Suppressor {Thyredor >

dsS8pnS5 » 103

arkcr

CL9

Parker Hannifin Corporation M«gr*t«d HydiaJics Dwiaon Uncomaftire. iitmas JSA

APPENDIX B

I Q A N specifications: I Q A N M D M , I Q A N X S , I Q A N X P 2 and I Q A N X T 2 (J1939 capable module). [45, 46, 47, 48]

94

Electronic Remote Controls IQAN-MDM

Technical Data General Weight

0,2 kg

Rated power supply Mirv'max power

12-24Vdc 9/32Vdc

Op eratin g t em pe ratu r e

-30°Cto+70°C (-30°Cto 0°C reduced display update) outdooruse m a x 0.1 A ( 2 8 V d c ) . m a x 0,18 A ( 1 4 Vdc) Parker I CP (IQAN C A N Protocol)

Protection Current consumption Data interface

72

® © ® (S>

Display Type Resolution

L E D back-lit L C D 2 0 2 x 3 2 pixels

Digital output Number Type Output

1 pes high side switch max 1.2 A d c

Serial communication Interface

R S 2 3 2 "handshake"

Bit rate

57,6 Kbit's

Protocol

PARKER IDP

Environmental Protection

unit = m m

PC communication port

Power LED

EMI I S 0 1 1 4 5 2 - 2 (immunity vs E M field) I S 0 14982 (radiated emission) I S 0 1 1 4 5 2 - 4 (immunity v s injected RF) I S O 7637-2.-3 ( i m m u n i t y v s supply transients)

ESD EN 61000-4-2 (externaD

Mechanical environment IEC 68-2-64 Fh (random)) IEC 68-2-29 E b ( b u m p )

Power and C A N - b u s connection

Climate environment IEC IEC IEC IEC IEC IEC

68-2-18 Rb2 (water) 68-2-30 Db ( v a r l , damp, cyclic) 68-2-3 C a (damp, heat steady state) 68-2-2 B b (heat) 68-2-1 A b (cold) 68-2-14 N b (changs of temperature)

Chemical environment I E C 6 8 - 2 - 5 2 K b (salt mist, cyclic)

95

Electronic Remote Controls IQAN-XS

Technical Data General Weight R a t e d power supply Min/max power Operating temperature Protection Current c o n s u m p t i o n (idle) D a t a interface

0.7 Kg 12-24Vdc 11/32 V d c - 2 5 to +70 X in-cab use 0,1 A (28 Vdc), 0,1 A (14 V d c ) Parker I C P ( I Q A N C A N Protocol'!

Digital inputs Number S i g n a l range Active range

16 pes 0-32 V d c "0"=0.O-1,2 V d c , "1 =4,0-32,0 V d c a

Digital outputs Number Type Signal

A pes high side switch 0.1 A d c

Analog/Digital inputs Number S i g n a l range Active range Resolution

10 pes 0,0-5,0 V d c 0.5-4.5 V d c 5 mV

r

/

/

/

/

/

nMitimriRnnrinnn

Environmental protection Electrical disturbance by conducting a n d coupling Radiated susceptability Radiated susceptability Radiated e m i s s i o n Conducted emission C o n d u c t e d susceptability E S D , electrostatic discharge Vibration, random Shock Bump High temperature

I S O / D P 7637-2-3 E N V 50140 ( E N 61000-4-3) E N V 50204 E N 55022. class B E N 55022 EN61O00-4-6 E N 61000-4-2 I E C 68-2-64 Fh IEC 68-2-27 E a IEC 6 8 - 2 - 2 9 E b IEC 68-2-2 B b

Temperature, c y c l i c Low temperature D a m p heat, cyclic D a m p heat, steady state Salt mist, cyclic Sealing

IEC IEC IEC IEC IEC IEC

68-2-14 N b 68-2-1 A b 6 8 - 2 - 3 0 D b var, 1 68-2-3 C a 68-2-52 K b 529

96

Electronic Remote Controls

IQAN-XP2

Technical Data General Weight Operating temperature Protection Voltage supply Current consumption (idle) Data interface

0.7 Kg -40 - +70 "C out door use 9 - 34 Vdc 105 mA (28 Vdc) 90 mA (14 Vdc) Parker ICP (IQAN CAN Protocol)

B 7 rnnvMSjxZI

Outputs Proportional current

outputs

4 double Number 20-1800 mA Signal range 25 -150 Hz Dither frequency 0 500 mA Dither amplitude 0.7 mA Resolution Digital/ PWM (no current feedback) outputs '< Nurn ber 4/ 2 double Type high side switch Max load 3A P v\M frequency 25 - 2000 Hz

Inputs Voltage/Frequency

Number Signal range Resolution Frequency range

4/2 0 - 5 Vdc 5mV 1-30000 Hz

ItTheOisiisI sod PWM outputs s h a r e me asms physical pin. Pin cor.fcursiion, =s either OfeSstorPi/VM outputs is carried oui with iQANdcv'dop.

Environmental Protection EMI

EN 61000-4-3 EN 50204-4-3 ESD

EN 61000-4-2 (external) Mechanical environment IEC 68-2-64 Fh (random, 10- 250 Hz) IEC 68-2-27 Es (shock, 11ms) IEC 68-2-29 Eb (bump, 6ms} Climat

environment

IEC 68-2-18 Rb3 (water) IEC 68-2-30 Db (varl, damp, cyclic) IEC 68-2-3 Ca (damp, heat steady state) IEC 68-2-2 6b (heat) IEC 68-2-1 Ab(cold) IEC 68-2-14 Nb (change of temperature) Chemical environment IEC 68-2-52 Kb (salt mist, cyclic)

2) The volume eixi frequencyinputs stoieaertio physical input plie. Pincorifeuraikjn, 3 5 either'Voasoeor rre