Philippe Proost electrically adjustable hydraulic valve Sensorless position estimation on a ...

120 Pages·2015·3.2 MB·English

Sensorless position estimation on a proportional
electrically adjustable hydraulic valve
Philippe Proost
Supervisors: Prof. dr. ir. Jan Melkebeek, Dr. ir. Frederik De Belie
Master's dissertation submitted in order to obtain the academic degree of
Master of Science in Electromechanical Engineering
Department of Electrical Energy, Systems and Automation
Chairman: Prof. dr. ir. Jan Melkebeek
Faculty of Engineering and Architecture
Academic year 2014-2015
The author gives permission to make this master dissertation available for consultation and
to copy parts of this master dissertation for personal use. In the case of any other use, the
copyright terms have to be respected, in particular with regard to the obligation to state
expressly the source when quoting results from this master dissertation.
January 19, 2015
ii
Sensorless position estimation on a proportional
electrically adjustable hydraulic valve
Philippe Proost
Supervisors: Prof. dr. ir. Jan Melkebeek, Dr. ir. Frederik De Belie
Master's dissertation submitted in order to obtain the academic degree of
Master of Science in Electromechanical Engineering
Department of Electrical Energy, Systems and Automation
Chairman: Prof. dr. ir. Jan Melkebeek
Faculty of Engineering and Architecture
Academic year 2014-2015
Preface
I would firstly like to thank supervisor Dr. ir. Frederik De Belie for the continuing support
and guidance throughout the entire thesis period.
I also want to extend my gratitude to Dr. ir. Thomas Vyncke, for the specific input about
the studied solenoid, and for the constructive comments on this report.
Finally I would like to thank my friends and family for being helpful and supportive during
this thesis period. Special thanks to my father and brother for their contribution in reading
and revising my final report.
Ghent,
January 19, 2015
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Sensorless position estimation on a proportional
ellectrically adjustable hydraulic valve
Supervisors:
Author:
Prof.Dr.ir. Jan Melkebeek
Philippe Proost
Dr.ir. Frederik De Belie
January 19, 2015
Proportional solenoid actuators are used to operate hydraulic valves and are omnipresent
in hydraulic systems. To improve their control characteristics, a feedback loop containing
a position measurement can be added. Position sensors are relative expensive though, and
require space and extra cabling. To avoid the use of sensors, the principle of selfsensing is
explored and the feasibility of a sensorless position estimation on a proportional solenoid
actuator is studied.
A finite element model is built and a multitude of simulations is performed to study the
variation in flux linkage with changing position. This variation of flux linkage results in
variation of inductance and resistance. In which the latter is a result of eddy currents. An
electrical model for the current response of the solenoid is built in Matlab. This model is
used to simulate a proposed position estimation technique in which the amplitude of the
ripple current is used to sense the pilot position. An adjusted control scheme is proposed to
improve the control of the studied proportional solenoid actuator.
Extended abstract
Proportional solenoid actuators are widely used to control hydraulic valves. They are com-
pact, robust and relatively cheap to produce. But some local non-linearities, for example
electromagnetic hysteresis and static friction, in their control characteristic remain present.
To improve control, position estimation trough use of the selfsensing principle is proposed.
In this thesis, the feasibility of such a position estimation on a pilot-operated proportional
solenoid actuator is investigated.
A solenoid actuator is a variable reluctance machine. The behaviour of flux linkage is stud-
ied using finite element (FE) simulations. It was found that eddy currents play a massive role
on the behaviour of flux linkage trough skin effect. Variation of magnetic flux with regard
to the pilot position is dependent on the skin depth, and thus frequency. In other words, the
ratio Lmax can be optimized by choosing the right frequency.
L
min
An electric model for the solenoid is built. The electrical parameters, resistance and in-
ductance, are identified using a LCR meter. Based upon these measurements, a suitable
frequency range for position sensing is identified. For frequencies between 250Hz and 500Hz
changes up to 38% with regard to air gap are measured for resistance. Changes in induc-
tance are highest for frequencies below 250Hz. Up to 35% is measured around 100Hz. These
measurements are imported in Matlab and a 2D look-up table of resistance and inductance
against frequency and air gap is constructed.
The solenoid actuator is driven by a puls-width-modulated (PWM) voltage with frequency
f and duty ratio δ. Its driver circuit consists of a single DC voltage source and a ’smart’
switch, connecting solenoid to the source during δT. Often a so-called dither signal is in-
jected. This is an alternating voltage signal with frequency between 100Hz and 300Hz and
dutyratio50%. Itspurposeistosuperimposeasmallup-anddownmovementontheplunger,
in order to avoid standstill. At standstill static friction would occur, disturbing the linear
relationship between current and force. Two possibilities occur, when the main frequency is
around 600Hz or lower, no dither signal is needed because plunger will experience enough
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vibrations resulting from the PWM voltage. When this frequency is above 2.5kHz, a dither
signal with an amplitude of 2 - 10% of the main voltage is injected. For frequencies between
600Hz and 2.5kHz, an injection of dither signal depends on the situation. A secondary volt-
age signal, such as a dither signal, is injected in the duty ratio, δ = δ +δ , in which
tot dither
δ is a square test signal, alternating symmetrically around zero.
dither
An analytic solution for the current response is presented. Two components are present
in the current response. The main current, i from which the electromagnetic force is
DC
created, and a highly exponential ripple current, i symmetrical oscillating around i .
AC DC
The former, i , is in steady state dependent on the DC resistance and the duty ratio δ of
DC
the PWM voltage. While the ripple current is dependent on the AC resistance, inductance
and again duty ratio δ. Information about the pilot position is thus contained in the ripple
currents amplitude.
Unlike in rotary machines, the electrical time constant is very small, resulting in a highly
exponential ripple current. And it stays exponential for all interesting measurement frequen-
cies. As a result a jump in duty ratio translates into a difficult analytical equation for the
ripple current. Making it hard to compensate for variations in duty ratio. It is mathemat-
ically proven, however, that because of this small time constant, the ripple current reaches
steady state within two PWM periods.
A selfsensing technique is then proposed and simulated in a Matlab environment. In the
proposed selfsensing technique, a secondary sensing signal is injected. This sensing signal
is a PWM voltage signal with duty ratio 50% and zero mean. The corresponding current
ripple is measured and pilot position is estimated out of it. Because the sensing signal uses
a duty ratio of 50%, the corresponding current ripple will only depend pilot position. A one
dimensional look-up table current ripples amplitude against pilot position will be sufficient.
Optimal sensing frequencies are in the range of 100Hz to 750Hz. In accordance with the
dither signal. Again like with the dither signal, when high driving frequencies are used, this
secondary sensing signal is advised to use. However, when the driving frequency is sufficient
low, the ripple current resulting from it may be just fine to sense the pilot position. Al-
though a two dimensional look-up table is then needed, to include the variation of current
ripple with duty ratio. It is obvious that the optional dither signal can be integrated in this
sensing signal.
To measure the current, a bandpass filter and a lowpass filter is proposed. If a sensing
signal is injected, the current will contain three components, the main current, i , a high
DC
frequency ripple current and a low frequency ripple current. In which the latter corresponds
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to the sensing signal. The bandpass filter is needed to pass the low frequency current ripple
for estimating the position. The lowpass filter will be used to pass the main current as feed-
back to the current controller.
Allthesesimulationsarebasedupontheconstructedmodelandtheconstructed2Dlook-up
table for resistance and inductance. To verify this model and the conducted LCR measure-
ments, current measurements were conducted.
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Contents
1 Introduction and thesis research goals 1
1.1 Structural Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Functionality of the solenoid actuator 4
2.1 Magnetic circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Electrical circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Electrical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Dither signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Mechanical subsytem . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Hydraulic circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Position sensing 13
3.1 Position sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Analogue sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.2 Digital sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.3 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Selfsensing on rotary machines . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Selfsensing on solenoid actuators . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Finite Element Model Simulations 20
4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.1 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.2 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Magnetic flux behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.1 Functionality of the Stopper . . . . . . . . . . . . . . . . . . . . . . . 26
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Contents Contents
4.2.2 Functionality of the ’little stick’ . . . . . . . . . . . . . . . . . . . . . 26
4.2.3 Principle of skin depth δ . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Inductance simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.3.1 Calculating the inductance . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.2 Influence of the skin depth . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3.3 Influence of saturation . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.5 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 Identification of electric parameters 38
5.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.4 Importing measurements to Matlab . . . . . . . . . . . . . . . . . . . . . . . 43
6 Selfsensing on the solenoid 44
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.2 Identification of the solenoid current . . . . . . . . . . . . . . . . . . . . . . 46
6.2.1 Influence of air gap and frequency . . . . . . . . . . . . . . . . . . . . 46
6.2.2 Influence of harmonics in a square wave . . . . . . . . . . . . . . . . . 48
6.2.3 Modelling current during duty jump . . . . . . . . . . . . . . . . . . 50
6.3 Position sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.3.1 Injecting sensing voltage . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.3.2 Measuring current ripple . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.4.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.4.3 Simulating measurement error . . . . . . . . . . . . . . . . . . . . . . 61
6.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.5 Practical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7 Solenoid current measurements 65
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.1.1 Verifying theoretic model for current waveforms . . . . . . . . . . . . 65
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