This paper presents the further developments and working principle of the speed-variable switched differential pump (SvSDP) concept proposed, designed and produced in [1]. The SvSDP system is designed to remove the throttling losses associated with typical valve driven control (VDC) systems. The hydraulic and mechanical system is modelled and linearised. The linearisation point is studied to provide an usable basis for controller design. It is proposed, in this paper, to model the converter and motor using a black box approach, where designed and informative input sequences are used to estimate the mathematical behaviour of the electrical drive based on the equivalent output data. The complete non linear model is verified against available trajectory data from the physical system, obtained from [1]. The linear model is analysed through a relative gain array (RGA) analysis to map the input output couplings present in the system. The results show that the system includes heavy cross-couplings. Results presented in [1] indicate, that it is possible to utilise a input output compensated decoupling to redefine the MIMO system into multiple SISO systems. The SvSDP concept is over-determined in relation to the amount of control inputs compared to possible outputs. It is proposed in [1] to introduce two new input states and two new output states. The decoupling approach has been investigated in this paper. The decoupling results provided a basis of using decentralised control. The linear control strategies are designed independently based on the notion of decoupling. The first controller is related to the level flow, designed to maintain a desired minimum pressure level. The second load flow controller is related to the cylinder motion. The controller results indicate, that it is possible to achieve a good dynamic tracking performance with an error of maximum 0.5 mm for a given position trajectory. This paper is also considering the energy consumption issues stated in [1], where two conceptual solutions are proposed, to solve the power loss associated with holding a load at a constant cylinder position. This paper is written as the product of an appendix report describing the whole project.

1. Speed-variable Switched Differential Pump (SvSDP) System
Peter Sloth-Odgaard, Rasmus Aagaard Hertz, Søren Valentin-Pedersen
Department of Mechanical and Manufacturing Engineering
Aalborg University
DK-9220 Aalborg East
Denmark
Abstract
This paper presents the further developments and working principle of the speed-variable switched differential pump (SvSDP)
concept proposed, designed and produced in [1]. The SvSDP system is designed to remove the throttling losses associated with
typical valve driven control (VDC) systems. The hydraulic and mechanical system is modelled and linearised. The linearisation
point is studied to provide an usable basis for controller design. It is proposed, in this paper, to model the converter and motor
using a black box approach, where designed and informative input sequences are used to estimate the mathematical behaviour of
the electrical drive based on the equivalent output data. The complete non linear model is verified against available trajectory data
from the physical system, obtained from [1]. The linear model is analysed through a relative gain array (RGA) analysis to map the
input output couplings present in the system. The results show that the system includes heavy cross-couplings. Results presented
in [1] indicate, that it is possible to utilise a input output compensated decoupling to redefine the MIMO system into multiple
SISO systems. The SvSDP concept is over-determined in relation to the amount of control inputs compared to possible outputs.
It is proposed in [1] to introduce two new input states and two new output states. The decoupling approach has been investigated
in this paper. The decoupling results provided a basis of using decentralised control. The linear control strategies are designed
independently based on the notion of decoupling. The first controller is related to the level flow, designed to maintain a desired
minimum pressure level. The second load flow controller is related to the cylinder motion. The controller results indicate, that it
is possible to achieve a good dynamic tracking performance with an error of maximum 0.5 mm for a given position trajectory.
This paper is also considering the energy consumption issues stated in [1], where two conceptual solutions are proposed, to solve
the power loss associated with holding a load at a constant cylinder position. This paper is written as the product of an appendix
report describing the whole project.
Keywords: Electro-Hydraulic Drive, Compact Drive, Dynamic Estimation of Electric Drive, Black Box Identification,
Over-determined Control, Decoupling, Input Output Compensation, Pressure Control, Motion Control, Load Hold Efficiency,
Direct Drive
1. Introduction
The focus on the environmental aspect of production lines
have increased in recent years. Hydraulic drive systems
are typically associated with high force operation and
low efficiency. The subject of developing energy efficient
hydraulic solutions is expanding in correlation with the
increased focus on minimising CO2 output and maximising
energy savings. It is common to actuate linear cylinders with
a valve controlled hydraulic drive, where the primary power
loss is related to valve throttling (P = Q·∆p). It was recently
proposed to actuate a linear differential cylinder using only
pumps, thereby fully removing the throttling losses. The
initial concept (SvDP) proved to be unusable in relation to
its achievable tracking performance.
The concept was further developed in multiple student
projects to the stage it has reached today, where the concept
has been built and tested experimentally by [1]. The test
bench finalised in [1] is driven by a speed-variable switched
differential pump (SvSDP) system, where three pumps are
connected to a single motor unit using a common shaft. The
hydraulic diagram of the SvSDP system is shown in figure 1.
The SvSDP system is designed to always build up pressure
in the return side chamber, by switching the support pump P2
in relation to the motor velocity equivalent to a flow difference
defined in equation (1). The pressure build up in the return
side, in relation to motor velocity and pressure, is defined by
Fig. 1 Hydraulic overview of the SvSDP system. The dotted area
indicate the manifold system. [1]
the match ratio χ.
(QP 1 + QP 2) · α > QP 3 for ωm ≥ 0 (1)
QP 1 · α < QP 3 for ωm < 0 (2)
The check valves seen in figure 1 governs the switching
of the second pump (CVAP21) and further adds an anti-
cavitation feature to the system by allowing idling modes in
the pumps. The SvSDP system uses inherited proportional
1

2. valves, which were included in the SvDP design by [2].
The proportional valves adds the possibility of lowering the
chamber pressures during operation, thus adding an extra
necessary control feature. It was proven in [1] that a converter
driven permanent magnet synchronous motor (PMSM) drive
was capable of producing the desired tracking capabilities. It
was later proposed in [3] and [4] that the overall application
cost could be greatly reduced (see table I), if the drive were
to be replaced with a performance equivalent induction motor
(IM, [5]) and Sytronix converter [6], both supplied from
Bosch Rexroth A/S.
Solution Retail price [DKK]
Servo drive + PMSM 45714.00
Frequency converter + IM + Encoder 23000.00
Tab. I Retail price related to different drive solutions. [4]
It was never verified in either [3] or [4], that it is possible to
achieve an equivalent performance of the IM drive compared
to the PMSM solution. The verification of the IM drive is
an essential part of the appendix project, where the related
results are presented, but will not be covered in this paper. It is
chosen to present some of the methods proposed and derived
in [1] in relation to analysis results. The presentation of
methods is done to provide an overview of the mathematical
foundation of the SvSDP system.
2. System model
The hydraulic model is derived and parametrised with respect
to research done in [1] and [3]. It is chosen to follow the
same notation as [1] for easier comparability of results. The
parameter subscripts through this paper are equivalent to the
ones used in figure 1. The governing parts used to model the
SvSDP system are a combination of four different component
categories defined as
• Check valves
• Pumps
• Cylinder
• Proportional valves (2/2 way)
The check valves and manifold dynamics are for simplicity
purposes neglected in this paper. The related dynamic effects
are still included in the non linear system, to ensure the
correct functionality of the designed anti-cavitation system
and switching of the support pump P2. It is chosen to
only represent the equations later used in relation to the
system analysis and controller design. The flows out of
both pump QP 1 and QP 2 are combined to an equivalent
velocity dependent flow QP 12 in relation to the manifold
dynamics. The second order leakage term related to the
mathematical estimate of the pump flow is, for simplicity
purposes, neglected in the paper, such the flow equations are
equivalent to the linearised flow models. The flow equations
are functions of motor velocity ωm and the pressure drop
across the pumps ∆p12
and ∆p3
defined as
QP 12 = K12ω(ωm)ωm − K12p(ωm)∆p12
(3)
QP 3 = K3ωωm − K3p∆p3
(4)
where Kω is the effective displacement constant, propor-
tional to the rotational speed at zero pressure drop across the
pump. The constant Kp describes the pressure depend leakage
over the pump. The motor dependent pump logic is defined
as
K12ω(ωm) =
K1ω + K2ω if ωm ≥ 0
K1ω if ωm < 0
(5)
K12p(ωm) =
K1p + K2p if ωm ≥ 0
K1p if ωm < 0
(6)
The relevant chamber pressure gradients are defined in
equation (7) and (8) where the manifold dynamics, pressure
relief valves and cylinder leakage (KQL·∆pAB
) are neglected.
˙pA
=
βe,A(pA
)
VA,0 + x · Ap
(QP 12 − QAV − ˙x · Ap) (7)
˙pB
=
βe,B(pB
)
VB,0 − x · Ar
(−QP 3 − QBV + ˙x · Ar) (8)
where βe,A and βe,B are defined as the pressure dependent
bulk modulus in relation to the control volumes (VA,0+x·Ap)
and (VB,0 − x · Ar) respectively.
The two proportional valves are identical. The valve model
is formulated based on data sheet data using a combination of
look-up tables and a second order transfer function between
input voltage reference and output. Assuming the look-up
table to be representative for the valve flow, it is possible, by
inverting the look-up table, to only account for the dynamic
behaviour in the valve as
QV (s)
QV,ref (s)
=
133.32
s2 + 2 · 133.3 · s + 133.32
(9)
The mechanical dynamics described by Newton’s second
law of motion, is simplified by neglecting both the Coulomb-
and Stribeck friction terms used in the non linear model thus
only leaving the viscous slider velocity dependent friction
(Bv · ˙x). It is further assumed that the external load can
be considered as a disturbance hence being negligible. The
simplified and linear mechanical model is defined as
¨x =
1
m
(pA
Ap − pB
Ar − Bv · ˙x) (10)
3. Drive model
In this paper it is proposed to use an alternative approach
to describe the dynamics of both the motor and converter
using methods related the subject of system identification. It
is desired to find a usable dynamic estimate which covers both
the motor and controller dynamics without the requirement of
time consuming- and advanced system models.
The achievable performance of the SvSDP system is highly
dependent on the chosen converter and motor. This notion
indicate, that it will be useful to provide a simple black box
tool for estimating drive dynamics in relation to controller
2

3. tuning. The black box tool may increase the application
flexibility of the SvSDP concept, if proper (informative) input
output data can be obtained, such any drive unit can be
modelled and implemented in the tuning process.
The estimated transfer function is describing the relation-
ship between input reference- and output velocity, equivalent
to the transfer function of a closed loop velocity system.
It is chosen to employ a black box estimation using two
methods; ARX and ARMAX presented in [7] and [8]. The
ARMAX method is an extension of the ARX method, with
the difference in its noise handling capabilities. It was seen,
that the velocity signal included noise, thus it was chosen to
utilise ARMAX as the primary estimation method.
The transfer function estimation is employed on results
both related to V/f (voltage/frequency) control and FOC (field
oriented vector control). The estimation results related to the
FOC strategy are seen in figure 2, where the input output data
is related to the estimated and simplified estimated dynamic
models.
Fig. 2 FOC transfer function verification related the simplified
second order model estimate compared to the z-domain model and
actual system.
The results show that the estimated model is capable
of tracking the actual system almost perfectly using a
fifth order z-domain transfer function. The estimated system
dynamics resembled a second order transfer function, up
until the system bandwidth. This notion made it possible
to successfully estimate the drive and motor dynamics with
a second order transfer function, as shown in figure 2.
The tuning process of the proposed Sytronix converter [6]
provided unusable results. The maximum achieved bandwidth
of the FOC controlled closed loop system was 1 Hz, which
is far from the Nyquist frequency [9] stating that a control
system should at least have twice the bandwidth of the plant,
which in this case is equivalent to a minimum required
bandwidth of 30 Hz.
To solve this issue it was concluded by Bosch Rexroth
A/S and the group, that the solution would be to replace
the converter with an equivalent model [10] without the
Sytronix user interface. Based on the data sheet [10] of the
new converter, where no restrictions are mentioned, it was
assumed that it would be possible to achieve the desired
closed loop bandwidth. The tuning results, indicated that
the same unknown performance limitations existed in both
products. The solution was to utilise the PMSM motor [11]
described in [1] for modelling purposes, hence it was not
possible to verify the IM [5] solution at this stage.
4. Linearisation
The non linear system is linearised based on assumptions
related to the operation condition of the hydraulic system. The
primary non linearities are present in the pressure dynamic
equations (7) and (8), in terms of a pressure dependent bulk
modulus and a cylinder position dependent volume. The linear
pump flow equations are presented in equation (3) and (4).
The mechanical system is also, for simplicity purposes, stated
in its linear form in equation (10).
It is chosen to assume a constant bulk modulus for the
controller design. The maximum oil stiffness is achieved
for pressure levels equal or larger than 30 bar, making the
assumption of constant bulk modulus valid based on the
notion that 30 bar is easily reached during operation. The
constant bulk modulus at 30 bar is chosen based on the
assumption of initial velocity. This assumption is deemed
valid based on the notion that the motor is going to follow a
controller reference, which is always varying during reference
tracking. Having a varying motor speed and direction is
assumed to ensure oil pressure levels of minimum 30 bar
throughout the operation with respect to the match ratio.
The validity of this effect is challenged, if the motor is kept
inactive for too long periods of time at zero velocity and load
hold situations.
The position dependent volume changes are analysed using
a pole sweep, to determine the x value where the system has
the minimum possible natural frequency, equivalent to the
slowest dynamic behaviour. The hydraulic system is converted
into its state space form to easily plot the eigenvalues (poles)
in relation to variations in the cylinder position. The dynamic
model between input motor velocity and output cylinder
position consist of four poles and a zero (seen from the
hydraulic transfer function matrix). The free integrator present
when integrating the velocity to position is disregarded. The
root locus plot showed, that the three last poles are equivalent
to a first order system combined with a second order under
damped system. The pole of the first order system is located
closer to ω = 0 rad/s than the second order dynamics. If the
velocity transfer function is stepped (disregarding the free
integrator), it is seen, that the second order dynamics are
dominating the response, thus indicating that the first order
system dynamics are cancelled out by the nearby zero.
5. Model verification
The non linear system model is verified against data from [3].
The inputs used to obtain the experimental data and verify
the non linear model are shown in figure 3a. The dataset is
obtained with an active load side force controller using a load
reference of 0 kN.
3

4. 0 2 4 6 8 10
Time [s]
0
20
40
60
ωm,ref
[rad/s]
0
50
100
xAV,ref
&xBV,ref
[%]
ωm
xAV
xBV
(a) Input sequence for motor and valves.
0 2 4 6 8 10
Time [s]
0
10
20
30
Pressure[bar]
pA:Exp
pA:NL
pB:Exp
pB:NL
(b) Pressure level.
0 2 4 6 8 10
Time [s]
-350
-250
-150
-50
50
x[mm]
Exp
NL
(c) Cylinder position.
0 2 4 6 8 10
Time [s]
0
50
100
˙x[mm/s]
Exp
NL
(d) Cylinder velocity.
Fig. 3 Experimental and simulated responses related to the non linear model verification.
It is seen in [3], that the force controller is incapable of
holding the load of 0 N, thus it is necessary to feed back
the measured load data to compensate for this error in the
model response. The simulated responses are compared with
the experimental data as shown in figure 3.
The responses of the non linear model shows a good
correlation with the experimental data. Both the slider
position and velocity responses are almost identical for the
two systems as seen in figure 3c and 3d respectively. It
should be noted, that the model is showing a less damped
response in comparison to the data. The under damped
behaviour is related to the oscillations present in both the
pressure dynamics and slider velocity seen in figure 3b and
3d respectively.
6. System decoupling
The SvSDP system is a MIMO system, meaning that the
control strategy can be formulated using different approaches.
The system is analysed to verify whether input output
coupling exist or not. If cross-coupling is found, it may prove
beneficial to apply a decoupling approach, thus converting the
MIMO system into multiple SISO systems. An alternative
approach, would be to accept the found cross-couplings and
solve the problem using a non linear control approach.
The input output couplings are analysed for a chosen
frequency range using the relative gain array (RGA) approach.
The transfer function matrix used to obtain the RGA, is
divided into six sub systems. The results show that all sub
systems contain heavy couplings throughout the frequency
sweep, it is further seen that the gain signs changed at the
natural frequency of 102
rad/s. It is proposed and concluded
in [1] that a system decoupling is beneficial based on the
amount of cross coupling in the system.
It is proposed in [1] that by applying both an input-
and output-compensator W1
and W2
respectively, it may
become possible to achieve a fully decoupled system within
the desired frequency range. The original system G(s) is thus
transformed into a compensated system ˜G(s) (see figure 4)
defined as
˜G(s) = W2
G(s) W1
(11)
The input- and output-compensation will modify the inputs
and outputs of ˜G(s) as
˜y = W2
y ˜u = W−1
1
u (12)
The used input- and output compensation structure is
shown in figure 4, where the new decoupling environment
is denoted with tilde.
GAC
(s) GH
(s)W1
W2
G(s)
˜G(s)
˜uref uref u y ˜y
Fig. 4 The compensated system with respect to the original system
consisting of the actuator system GAC
(s) (drive and proportional
valves) and the hydraulic mechanical system GH
(s).
6.1 Output compensation
It is desired to formulate an output-compensation which
makes it possible to consider more appropriate states than
the original control system. It is proposed in [1] to define
a virtual, but measurable, load pressure pL
state and further
introduce a fictive level pressure pH
state. The load pressure
is implicitly describing the available load force seen on the
cylinder shaft, whereas the level pressure can be seen as a
weighted sum between the two chamber pressures. The two
virtual output states are defined as
4

5. pL
= pA
− α · pB
(13)
pH
= pA
+ H · pB
(14)
It is possible to rewrite equations (13) and (14) to describe
both the pA
and pB
pressures in relation to the two defined
output states as
pA
=
H
H + α
· pL
+
α
H + α
· pH
(15)
pB
=
−1
H + α
· pL
+
1
H + α
· pH
(16)
By taking the derivative of both equation (13) and (14)
it is possible to substitute the linear pressure gradients of
chamber A and B from equation (7) and (8). By expanding
the expression of ˙pH
it is possible to show, that by choosing
the parameter H = VB
α·VA
, it is possible to cancel out the piston
velocity ˙x influence in the level pressure dynamics ˙pH
. The
output compensator W2
is defined in equation (17) as the
relation between the actual output states and the two virtual
outputs.


x
pL
pH


˜y
=


1 0 0
0 1 −α
0 1 H


W2


x
pA
pB


y
(17)
6.2 Input compensation
The definition of H is used together with equations (15) and
(16) to rewrite both ˙pH
and ˙pL
in terms of pL
and pH
. This
new definition is used to determine the input compensator
W1
. The load flow QL and level flow QH are defined as the
input related terms of the rewritten ˙pH
and ˙pL
equations. The
input relation is defined as


QL
QH
Q0


˜u
=


H·ΛKω
α+H − H
α+H
1
α+H
(α + H)∆Kω −(α + H) −α+H
α
v31 v32 v33


W −1
1


ωm
QAV
QBV


u
(18)
Q0 is defined as the flow constraint and can be used to
achieve different utilisation methods as described in [1]. This
paper is only considering the flow constraint where Q0 ≡ 0.
Based on the flow constraint chosen, it is possible to create
different input compensations due to the relation between the
compensated input to the original input as


ωm
QAV
QBV


u
=


w11 w12 X
w21 w22 X
w31 w32 X


W1


QL
QH
Q0


˜u
(19)
The column W1
(:, 3) is not of interest due to the definition
of Q0 and is therefore denoted with an "X". It is decided
to utilise the input compensation method 1, described in
[1], where the shaft speed is controlled only by the load
flow QL. The method is obtained by cancelling the term
QAV − QBV
H in the derived load flow gradient ˙pL
. The
dynamic behaviour of the load flow will therefore only be
affected of the shaft speed and not the proportional valve
inputs. It should be noted that both of the proportional valves
are activated for both directions which introduces some losses.
The input compensator is defined as
W1
=
α
H · ΛKω



α+H
α 0 X
∆Kω − H·ΛKω
(α+H)2 X
H · ∆Kω −H2
·ΛKω
(α+H)2 X


 (20)
The input QAV and QBV are physically restricted due to
the fact that they can only lead flow away from the cylinder.
This constraint has to be modelled to obtain the proper
performance of the system. The cylinder motion control
is the main focus of the project, which is why it is not
desirable to limit the load flow QL implicitly describing
the allowable force on the cylinder. The restriction of the
proportional valves are therefore related to the level flow QH.
The following relation has to be obtained.
QAV , QBV ≥ 0 ⇒ QH ≤ (α + H)∆Kω · ωm (21)
The relation in equation (22) has to be fulfilled to ensure
a positive flow through the proportional valves and to avoid
discontinuous references with respect to shaft speed.
1
∆K−
ω
≤ (α + H)w12 ≤
1
∆K+
ω
(22)
6.3 Decoupling results
The results related to the implementation of the output
compensation indicate that it is possible to achieve a less
coupled system with only an output compensation. The pure
output compensation is not capable of fully eliminating the
coupling effects, which is why the input compensation is
included. The input and output compensated system ˜G(s) is
manipulated to have the RGA numbers seen in figure 5. The
system is considered fully decoupled, thus proving the validity
of the approach.
100
101
102
103
Frequency [rad/s]
0
2
4
RGAnumber
x(QL
) , PH
(QH
)
x(QH
) , PH
(QL
)
Fig. 5 RGA number of the input and output compensated system
˜G(s).
5

6. 7. Control
The decoupling results indicate, that it will be possible
to utilise a decentralised control approach. The SvSDP is
thought of as a general application to cylinder drives, resulting
in no strict control objective. Instead the difficulty lies in
designing a system that is stable for all pressures and slider
positions. Considering the effective oil stiffness described by
bulk modulus, it is desired to be able to have a minimum
pressure in the cylinder chambers to ensure robustness against
external forces and to improve performance with respect to
position tracking. The control is divided into two parts being
pressure level- and position control. It is tried to design
both control strategies separately based on the notion of
decoupling.
7.1 Pressure level control
The pressure level control is designed to keep a minimum
return side pressure of 30 bar. The controller output is related
to the level flow reference QH. The controller structure is
shown in figure 6.
Level
pressure
reference
generator
pset
+
−
pH,ref
Gc,H
eH
W1
QH
QL
ZZQ0
SCM
ωm,ref
QAV,ref
QBV,ref
W2
pA
x
pB
pL
x
pH
Decoupler
H HH
Fig. 6 Block diagram of the pressure level control structure.
The level pressure error is only dependent on one of
the chamber pressures, which effectively reduces the effect
of pH,ref
to a scaling, dependent on what chamber should
be controlled and the position of the slider. The controller
is designed towards the final goal of finding the optimum
between a maximum possible bandwidth of the compensated
system without being able to excite possibly non decoupled
frequencies caused by possibly occurring errors in the H
estimation. The simplified transfer function between QH and
pH
is defined as
pH(s)
QH(s)
=
1
KHpH
·
1
VA·(α+H)
β·KHpH
· s + 1
(23)
The transfer function in equation (23) is dependent on both
H and VA making it implicitly dependent on the cylinder
position x. The value of x is chosen equivalent to the system
with the largest time constant (slowest possible configuration).
The controller designed is a combination of a PI controller,
a gain and a second order low pass filter. The filter is
used to damp the magnitude after a certain frequency, thus
providing safety against the previously mentioned coupling
effects by ensuring a proper magnitude damping before the
natural frequency is reached. The controller is implemented
and simulated, producing the results shown in figure 7. The
simplified system has a phase margin of 67 degree and a gain
margin of 11.7 dB.
The controller is capable of keeping the minimum set
pressure of 30 bar in the chambers as soon as the set pressure
is reached the first time (see figure 7b), with the exception
of the oscillations present when QL is stepped. The cylinder
velocity response is unaffected by the pressure level control
and still oscillate equivalent to the natural frequency of the
hydraulic system (≈ 16 Hz). It is further seen in figure 7a,
that the valve command signals are strictly positive, governed
by the feasibility bound.
7.2 Motion control
The motion control is divided into three parts, being a
combination of PI position control, pL
feedback damping and
velocity feed forward. A simplified transfer function between
QL and x is constructed based on the load pressure dynamics
˙pL
and (10) rewritten to depend on the load pressure.
x
QL
=
1
s
·
K1
s2 + K2 · s + K3
(24)
where
K1 =
Ap · (α + H) · β
H · VA · M
(25)
K2 =
Bv
m
+
β · KLpL
VA · (α + H)
(26)
K3 =
α + H
H · VA
·
β
m
· A2
p +
Bv · KLpL
α + H
(27)
Assuming perfect decoupling, it is possible to neglect the
term containing pH
. The Kad gained load pressure feedback
is used to achieve a damping coefficient of 0.7 equivalent to
a desired trade off between overshoot and settling time. The
used motion structure is illustrated in figure 8.
+
−
xref
Gpos,P I
ex
Ap
ex +
+
˙xref
+
−
Q∗
L ˜GCM
pset
QL pL
x
pH
Kad
Fig. 8 Block diagram of the motion control structure.
The motion controller is designed such it can ensure
stability for a minimum pressure of 4 bar while still
performing well in the high pressure range. The coherent
stability margins are shown in table II.
Pressure Phase Margin [o] Gain Margin [dB]
Pressure: p0 = 30 bar 52 16
Pressure: p0 = 4 bar 46 6
Tab. II Gain and phase margins of the designed controller and plant,
obtained from the open loop bode plots.
The motion and pressure level controlled system is
simulated and the coherent results are presented in figure 9.
6

7. 0 0.5 1 1.5 2 2.5
Time [s]
0
20
40
Valvesignal[%]
xAV
xBV
(a) Valve opening signals.
0 0.5 1 1.5 2 2.5
Time [s]
0
20
40
60
80
Pressure[bar]
pA
pB
(b) A- and B side pressures.
0 0.5 1 1.5 2 2.5
Time [s]
-20
0
20
QL
[L/min]
(c) Load flow reference.
0 0.5 1 1.5 2 2.5
Time [s]
-200
0
200
˙x[mm/s]
(d) Cylinder velocity.
Fig. 7 Performance of the pressure level control strategy.
The used position reference is shown in figures 9a where the
position is differentiated to produce the velocity reference.
It is seen that the trajectory is followed with a maximum
error of 0.5 mm, which is concluded acceptable. It should
also be noted that the minimum pressure control is unable to
keep minimum 30 bar in chamber B when the reference is
stationary. This effect is caused by the match ratio χ present
in the system.
In correlation to decoupling method 1, it is seen in 9d that
the proportional valves are activated at the same time. The
motion controller is proved to be stable for both small and
large pressure levels and is successfully implemented in the
non linear model. The results indicate, that it is possible to
use the system in a general purpose application.
8. Efficiency analysis
It has previously been proven in [1] that the SvSDP system is
capable of minimising the power consumption compared to a
conventional valve controlled drive (VCD), due to the almost
non-existent throttling losses present in the proportional
valves included in the SvSDP set-up. The power losses
associated with both system types have been experimentally
evaluated in [1] for a predefined load and trajectory case as
shown in figure 10a. The sequence uses an applied load of 20
kN and a maximum slider velocity of 125 mm/s. The input
and output power of both systems, related to this trajectory,
is seen in figure 10b.
It is seen that the tracking performance of both systems are
similar, where the main difference is present in the amount
of input power used compared to output power ( ˙x · FL).
The SvSDP system is drawing much less input power, for
velocities different from zero, compared to the equivalent
VCD solution. The output power of both systems are close to
being the same due to the performance equivalence between
the two solutions. This notion is also indicating the capability
of the SvSDP system since it is possible to obtain the same
tracking performance as the VCD for the given trajectory.
The statement of increased efficiency related to the SvSDP
solution holds true, if the targeted application uses trajectories
with more position variance than periods of constant piston
position.
It is shown in figure 10b that approximately 600 W will be
used at zero slider speed for the SvSDP system. The power
used is both related to the leakage present over the pumps
and the required hold shaft torque. The power consumption
problem has previously been stated, without further analysis
in [1]. The problem is further investigated in this paper to
locate the primary source of loss. The mechanical power over
the pumps is compared to the input power from the converter
bus, thus giving an idea of the power drawn related to both
components separately.
The pump torque multiplied with the shaft velocity will
produce the mechanical power consumption related to the
pumps at standstill of the slider. The pressure drop dependent
pump torque equation [12] is defined as
TP x =
1.56 · KP xω · ∆pP x
η
(28)
where η is the efficiency of the pump, that for simplicity is
chosen to 100 %. For all three pumps the total torque is given
as
TP = TP 1 + TP 2 − TP 3 (29)
The torque equation is only used to provide an estimation of
the power consumption and it has not been possible to test
the coefficients and efficiency in the laboratory. The power
consumption in the three phase induction motor, near zero
velocity, can be described by
PMotor = 3 · Rw · I2
(30)
7

8. 0 5 10 15
Time [s]
-350
-200
-50
100
250
x[mm]
xref
x
(a) Position response.
0 5 10 15
Time [s]
-0.6
-0.3
0
0.3
0.6
ex
[mm]
(b) Maximum tracking error.
0 5 10 15
Time [s]
0
20
40
60
80
Pressure[bar]
pA
pB
(c) A- and B side pressures.
0 5 10 15
Time [s]
0
1
2
3
4
QxV,ref
[L/min]
QAV,ref
QBV,ref
(d) Reference proportional valve flows.
Fig. 9 Simulated response showcasing the motion controller performance.
0 5 10 15
Time [s]
-350
-250
-150
-50
50
150
250
x[mm]
xref
xSvSDP
xVCD
(a) Trajectory used for power consumption analysis. [1]
0 5 10 15
Time [s]
-3
-1.5
0
1.5
3
4.5
6
7.5
9
Power[kW]
Wi
Wi:VCD
WO
WO:VCD
(b) Power consumption results. [1]
Fig. 10 Tracking performance comparison with equivalent input and output power, used to showcase the difference between the SvSDP and
VCD systems.
Rw being the wire resistance and I being the current. The
drawn current at standstill, holding 20 kN equivalent to 28
Nm, can be found in the data sheet [11]. The motor runs slow
in load hold situations and assuming that the current can be
estimated from the pump torque, it is possible to estimate the
power consumption related to the motor by
PMotor = 3 · Rw ·
I · TP
Thold
2
(31)
The values of Rw, Thold and I are found to be 0.79Ω, 28 Nm
and 15.8 A respectively [11]. The Mechanical power used to
actuate the pumps are given as
PP ump = TP · ωm (32)
The low speed input output power consumption related to
both the pumps and motor are shown in figure 11. Note that
the x-axis starts at 6 s, as it corresponds to the load holding
situation shown in figure 10a.
The results in figure 11 indicate that input power measured
at the DC bus, is mainly consumed by the losses in the motor
unit, caused by the large moment acting on the shaft. The
pump leakage makes it impossible to hold constant chamber
pressures over time without activating the motor to counteract
6 6.5 7 7.5 8 8.5 9
Time [s]
-500
0
500
1000
1500
P[W]
PDC:BUS
PPump
PMotor
PPump
+ PMotor
Fig. 11 Power consumption related to different parts of the drive
compared to experimental measured DC-Bus data.
the leakage flow. The variation in backside pressures will
cause slider movement, thus requiring motor actuation to
counteract the leakage dependent changes. The valve based
system has the possibility of fully closing the valve at zero
position error, meaning that the piston velocity and flow
will stay at approximately zero dependent on leakage in the
cylinder, indicating that no power is drawn or lost. The power
loss associated with the motor is the reason why it is essential
to modify the SvSDP design such a load hold feature is
included.
9. Load hold
The load hold problem is investigated in this paper, where
two conceptional solutions are proposed. The first load hold
8

9. concept is a pure mechanical solution using two pilot-operated
check valves (POCV). The check valve implementation (see
figure (12)) is analysed using the non linear model.
Fig. 12 Hydraulic diagram of the modified load hold system using
the POCVs.
The results indicate, that the POCVs are capable of holding
the load, if the motor is forced to zero velocity. The initial
results of the POCV solution shows that it can work with the
designed pressure level control. A better performance can be
achieved, if the influence of the pilot pressures are balanced
in relation to the applied load. The motion controlled system
with included POCVs showed a decrease in performance. This
result indicate that the check valve implementation is less
applicable, at least if the control is not modified to compensate
for the check valve functionality.
It is further chosen to evaluate the proportional valve
load hold (PVLH) concept. The proportional valves should
in theory, only be active during low speed velocity. They
are designed, such maximum flow is achieved at minimum
possible pressure drop. The valve opening diameter should be
equivalent to the tubes diameters, to cause no flow restriction
at fully open position. By adding two new proportional
valves, the system will become even more over-determined
in relation to the number of inputs compared to outputs, thus
increasing the control complexity. If the control problem can
be solved, this solution may provide the wanted effects while
not affecting the performance of the system. The proportional
valve implementation is shown in figure 13.
The PVLH related simulation results are shown in figure
14, where the responses are compared to the non modified
system. It is seen in figure 14c that the expanded SvSDP
system is capable of tracking a position with similar capability
as the non modified system. The existing proportional valve
flows are not affected, indicating no increase in flow related
losses. It is seen in figure 14a and 14b that the chamber
pressures are kept constant for the load hold sequence,
indicated with the constant slider position seen in figure
14c. The overall performance of the PVLH concept is better
compared to the POCV concept.
Fig. 13 Hydraulic diagram of the modified load hold system using
the PVLH approach.
Both proposals showed load hold capabilities on a
conceptual level. It is known, that the maximum achievable
performance is related to the difficulties of choosing the
proper control strategy. The control should be designed to
take advantage of the valve functionalities thus removing the
unwanted power loss associated with load hold sequences
without reducing the current performance of the SvSDP
system.
10. Conclusion
Based on the non linear model verification, it is concluded that
the model of the SvSDP system is capable of representing the
dynamic behaviour of the physical set-up. The results further
indicate that the system will build up a return side pressure
equivalent to the match ratio χ of the pumps for regular non
loaded motion, regardless of input motor direction.
It was proposed to estimate the non linear dynamic be-
haviour of the converter and induction motor, through black
box system identification, using the ARX or ARMAX meth-
ods. Based on the estimation results, it is concluded the esti-
mated models are capable of representing the actual electric
drive. It was further seen that for a given frequency range,
the estimated z-domain models could be described using a
standard second order transfer function. The simplified second
order models is capable of reproducing the output data used
to estimate the system. The identification methods proposed
are concluded to perform well and will provide an increase
in the versatility of the system, related to drive replacements.
The RGA analysis showed that the original system contained
heavy cross couplings, making it difficult to control. It has
been possible to fully decouple the system by employing both
input- and output compensation. The compensation strategies
are both parameter dependent. The decoupling ensures that
the position is controlled by the motor and that the pressure
level is controlled by the two proportional valves. Using
the decoupled system, it was possible to design two linear
controllers; a pressure level controller and a motion controller.
The designed controllers are successfully implemented in the
9

10. 0 2 4 6 8 10
Time [s]
0
50
100
Pressure[bar]
pA
pA
load valve pLVA
(a) A side related pressure levels.
0 2 4 6 8 10
Time [s]
0
20
40
60
Pressure[bar]
pB
pB
load valve pLVA
(b) B side related pressure levels.
0 2 4 6 8 10
Time [s]
-100
0
100
200
Position[mm]
x
x load valve
(c) Position responses.
0 2 4 6 8 10
Time [s]
0
1
2
Flow[L/min]
QAV
QBV
QAV
load valve
QBV
load valve
(d) Proportional valve flows.
Fig. 14 Simulated response related to the implementation of the proportional valve concept.
non linear system, providing a maximum error of 0.5 mm
for a given trajectory. It is concluded, that the SvSDP drive
is ineffective for load hold situations. Experiments show that
approximately 0.6 kW power is drawn when the SvSDP is
used to hold a 20 kN load in a fixed cylinder position.
The distribution of input DC bus power has been analysed,
showing that the majority of the loss associated with load
hold is related to the motor.
To minimise the energy consumption in load hold situa-
tions, two concepts are proposed and analysed with respect
to applicability. The simulation results of the implemented
POCV concept showed moderate performance when used in
relation to the designed controllers. To add the desired feature
of control, it is proposed to implement two proportional valves
(PVLH). The simulated results are promising. Furthermore it
can be assumed that, it is possible to uphold a stiffness in the
return chamber at movement not forced by the pumps actively
moving oil into the chamber. To be able to apply this structure,
a new control strategy has to be devised, that accounts for
the added valve dynamics and further input output cross
couplings. If it is possible to control the PVLHs in a proper
way, that does not influence the tracking performance of the
system in a negative way, it can be concluded to be a viable
solution to the energy consumption problem.
Acknowledgement
The authors would like to thank Bosch Rexroth A/S
Denmark for their interest and support throughout the span
of the project.
References
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