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MEMS SENSOR NETWORK BASED ANTI-SWAY CONTROL SYSTEM FOR
ARTICULATED HYDRAULIC CRANE
Janne Honkakorpi∗
Department of Intelligent Hydraulics
and Automation
Tampere University of Technology
Tampere, Finland FI-33101
firstname.lastname@tut.fi
Juho Vihonen
Department of Signal Processing
Tampere University of Technology
Tampere, Finland FI-33101
firstname.lastname@tut.fi
Jouni Mattila
Department of Intelligent Hydraulics
and Automation
Tampere University of Technology
Tampere, Finland FI-33101
firstname.lastname@tut.fi
ABSTRACT
Hydraulic articulated multi-joint crane systems are widely
used for the transportation of heavy loads. High productivity re-
quires a short cargo transportation time which can lead to unde-
sirable oscillations during crane load acceleration and deceler-
ation. Typically it is the task of a crane operator to suppress the
load swing, but with ever-increasing demand for faster operation
the need for supporting control systems is evident. For overhead
gantry cranes such assisting control systems can be considered
as state of the art. However, for more complex articulated multi-
link cranes only a few applicable control concepts have been pro-
posed. Load swing angle and angular velocity measurement, or
corresponding state observer based estimation, has been seen
as a main problem in the realization of such assisting control
systems. To tackle the problem, we present a novel suspended
load anti-sway control system for heavy-duty articulated hyd-
raulic cranes using solely low-cost linear MEMS accelerometers
and angular rate gyroscopes embedded into easy-to-install sen-
sor units. The proposed closed-loop anti-sway controller uses a
network of embedded MEMS sensors for the crane motion state,
suspended load inclination angle and angular velocity estima-
tion. The control concept uses a semi-active approach where the
desired load velocity is set by the crane operator via e.g. joystick
input and the underlying load oscillation damping control sys-
tem creates the desired crane tip velocity. Comparative results of
anti-sway control are obtained using high resolution incremental
encoder feedback for the articulated crane and suspended load
∗Address all correspondence to this author.
motion states. Our experimental results verify effectiveness of
the proposed anti-sway control system for articulated hydraulic
cranes as well as applicability of the proposed MEMS sensor
network for real-time closed-loop control of multi-body manipu-
lators.
INTRODUCTION
Hydraulic articulated crane systems are well-established in
many fields of application including e.g. the transfer of cargo
in offshore operations between ship and shore as well as in con-
struction sites and factory operations. A payload suspended from
the crane tip exhibits pendulum-like characteristics with promi-
nent uncontrolled oscillation during acceleration and decelera-
tion of the crane tip. This type of crane system is underactu-
ated by nature since the position and velocity of the crane tip can
be controlled, but the load swing angle and angular velocity are
only indirectly controlled. While a skilled operator may be able
to control the load oscillation, the need for an automated control
system lessening the burden of the human operator is nonetheless
evident.
Load sway suppression systems have been of considerable
research interest in the field of rotary boom and overhead gantry
cranes where such applications can be considered state of the art.
Typical approaches use an open-loop technique called input com-
mand shaping where the crane operator control commands are
filtered to remove components that induce load oscillations. In
practice however these systems are frequently augmented with a
1
Copyright © 2013 by ASME
Proceedings of the ASME/BATH 2013 Symposium on Fluid Power & Motion Control
FPMC2013
October 6-9, 2013, Sarasota, Florida, USA
FPMC2013-4439
feedback loop when disturbance rejection and accurate position-
ing of the load is required, see e.g. [1–4]. More recently research
has been made into more energy efficient control concepts [5]
and the effects of system parameter variation and model uncer-
tainties, see e.g. [6–9]. However, only few control concepts are
realized on full-scale systems [10, 11]. For more complex ar-
ticulated multi-link cranes the proposed control concepts relate
to cargo transfer operations on ships and floating platform rigs,
where the stabilization of the load movement against ocean wave
disturbance is critical, see e.g. [12–14].
In several studies the angular measurement of crane joints
and load swing and particularly the estimation of angular veloci-
ties are seen challenging. Typical solutions for the angle mea-
surement rely on retrofitting potentiometer or incremental en-
coder installations using custom-made mechanisms. Similarly
the estimation of the load angular velocity is obtained either via
straightforward differentiation of the load swing angle or by us-
ing a state observer approach. Here the trade-off is between poor
quality of the resulting angular velocity signal and system mod-
eling effort, which may be extensive.
In this paper we present a novel MEMS sensor network
based solution for the motion state estimation of both the hyd-
raulic articulated crane and the suspended load. The key advan-
tage of the proposed MEMS based solution is the use of low-cost
sensors realizing a contact-free measurement, i.e. no direct me-
chanical contact to rotating joint mechanisms is required, as the
MEMS sensors may be simply “strapped down” to the mechan-
ical bodies. Further, the proposed sensor network is applicable
in theory to any multi-body system consisting of nbodies con-
nected by rotary joints. This makes it ideally suitable for e.g. off-
shore applications where the motion state estimates of both the
articulated multi-body manipulator joints and its floating base are
required.
The paper is organized as follows. First, the MEMS net-
work based motion state estimation for generic multi-body ma-
nipulator systems is presented. The following section details the
kinematics and the velocity control of the hydraulic manipulator
under study. Then, linearized equations of motion are derived
for the suspended load followed by the concept of the load anti-
sway controller. Finally, the experimental setup and results are
presented with the paper ending in discussion and conclusions.
MEMS SENSOR NETWORK BASED MULTI-BODY MA-
NIPULATOR MOTION STATE ESTIMATION
In this section, we provide an observational model for the
motion state estimation of a multi-body manipulator system
based on a network of MEMS angular rate gyroscopes and linear
accelerometers. The presented estimation approach is applicable
to fully three-dimensional motion for a manipulator consisting of
an arbitrary amount of rigid bodies connected by revolute joints.
No knowledge of the manipulator system dynamics is needed, as
the only system-specific information required is the positions of
the attached MEMS sensors on the manipulator with respect to
the rotating joints.
Consider an open-chain manipulator fixed to a base plat-
form. Three-dimensional frames of rectangular (xyz) axes are
attached to the center of each joint and the links of length liare
directed along the y-axes as shown in Fig. 1. Let Ridenote the
FIGURE 1. RIGID BODY OBSERVATION MODEL
3×3 body fixed rotation matrix, det(Ri)=1 and RT
i=R−1
i, relat-
ing the ith link frame to the inertial reference frame (XYZ). The
“ground” frame R0is fixed to a (stationary) base platform.
The angular rate output of a MEMS gyroscope attached to
the ith link can be expressed as
˜
Ωi= (I+Si)Ωi+bi+µg∈R3×1,(1)
where Ωiis the true rate value, Iis the identity matrix, Siis the
scale factor error expressed as a percentage of Ωi,bidenotes a
constant or slowly varying gyro bias, and µgdenotes additive
measurement noise. In view of the rigid body assumption, one
may write
Ωi=ωi+
i−1
∑
m=0
RT
iRmωm(2)
denoting that the total true angular rate is the sum of the angular
velocities produced by the ith joint, given by ωi, and each of the
preceding joints expressed in frame i. Then, an estimate of the
angular velocity of the ith joint, as sensed by a MEMS angular
rate gyroscope attached to the ith link, i=1,2,. . . , can be given
by
ˆ
ωi=˜
Ωi+ˆ
bi−
i−1
∑
m=0
RT
iRmˆ
ωm(3)
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Copyright © 2013 by ASME
where ˜
Ωiis the ith gyro rate reading. The term ˆ
biis introduced
to cancel a characteristic constant or slowly time-varying MEMS
gyro bias present in ˜
Ωi. The differentiation
ˆ
αi=ˆ
˙
ωi(4)
yields a bias-free estimate of the ith joint’s angular acceleration,
but is generally plagued by high frequency perturbations as the
differentiation amplifies noise.
FIGURE 2. MEMS ACCELEROMETER AND GYRO CONFIGU-
RATION ON A RIGID MANIPULATOR LINK
The linear accelerations sensed by a MEMS accelerometer
attached to the ith link, i=1,2,. . . , can be expressed by
ai= (I+Si)(vi−RT
ig) + ba+µa∈R3×1,(5)
where Siis the scale factor error, gis the gravitational field
g=|g0|e3,|g0| ≈ 9.8 m/s2,bais a bias term, and µadenotes ad-
ditive measurement noise. If ×denotes the cross product, the
instantaneous linear acceleration vican be given as
vi=αi×di+ωi×(ωi×di) + (6)
i−1
∑
n=0(RT
iRnαn)×dn+
(RT
iRnωn)×(RT
iRnωn)×dn.
where αiis the true angular acceleration produced by the ith joint,
the vectorial distance from the ith joint’s rotation center is
di= [0py
ipz
i]T=pi(7)
and for the other rotation centers
dn=RT
i
i−1
∑
m=n
Rm[0lm0]T+di(8)
for a low number of coordinate system transforms. The posi-
tion (7) is typically known to a high degree of accuracy. Given
that the “ground” frame is stationary, we assume l0=0, R0=I,
and ω0=α0=d0= [0 0 0]Tfor clarity. We will also take the
Z-axis rotation of Rifor granted, since it is not observable from
the accelerometer readings. Figure 2 represents a minimum con-
figuration in view of the discussed observational model.
R0
p1
az
1
R1
ay
1
˜
Ωx
1
R2
p2
ay
2
az
2
˜
Ωx
2
˜
Ωx
3
R3
p3
ay
3
az
3
FIGURE 3. MEMS SENSOR CONFIGURATION ON THE HYD-
RAULIC MANIPULATOR
Computing an algebraic estimate of the instantaneous linear
acceleration ˆviis possible by replacing the “true” angular accel-
eration and angular velocity in (6) with (3) and (4). Hence, we
may estimate two degrees of freedom of the “true” link inclina-
tion rotation matrix Riin accelerative motion since, for a triaxial
accelerometer located at pi, the above yields
ai−ˆvi≈ −RT
ig.(9)
Note that the required estimates of angular velocity (3) and accel-
eration given by (4) can be obtained without complicated trans-
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Copyright © 2013 by ASME
forms. This applies for small angle rotations between successive
real-time updates of the link-wise inclinations. A high-enough
sampling rate is thereby required.
Under the assumption that the links behave as rigid bodies,
real-time estimates of the manipulator joint angles can be given
by
ˆ
θi=ˆ
ϕi−ˆ
ϕi−1,i=1,2,. . . (10)
which denotes pair-wise subtraction of successive link inclina-
tion estimates ˆ
ϕiof the “true” rotation matrix Ri. The “ground”
frame’s rotation around x-axis is here simply included by us-
ing the horizontal position with respect to the gravity vertical
as our reference, i.e. ˆ
ϕ0=0 deg. Consequently, low-delay high-
bandwidth estimates of ˆ
ϕiare available by applying the well-
known principles of complementary and Kalman filtering to the
accelerometer and gyroscope readings. For a description of the
complementary filtering, please see [15].
Figure 3 illustrates the discussed MEMS configuration at-
tached on the links of the articulated planar hydraulic manipula-
tor under study as well as on the suspended load. The MEMS are
located at points p1=[0 0.21 0.23]Tm respective to R1, at p2=
[0 0.24 0.22]Tm respective to R2and at p3= [0 0.19 0.045]Tm
respective to R3.
ARTICULATED CRANE KINEMATICS
In this section the forward and inverse kinematics for the ar-
ticulated hydraulic crane are derived. Consider the kinematics
representation of the hydraulic crane shown in Fig. 4. The po-
sitions of the two actuated revolute joints are denoted by q1and
q2. A third prismatic joint is available, but it is unused in this
study, which sets the manipulator into non-redundant operation
mode. A rigid bar with a mass attached is suspended from the
fourth revolute joint which is unactuated.
Careful identification of the physical dimensions of the ma-
nipulator structure yields a fixed relationship between the ma-
nipulator angles θi,i=1,2 and the actuated joint angles qiis as
θi=qi+βi,βi= [−56.43◦−155.25◦]as detailed in [16].
The forward kinematics relating the manipulator joint vari-
ables q= [q1q2]Tto the end effector position x= [x y ]Tare
obtained as
x=L1cos(q1+β1) + L2cos(q1+q2+β1+β2)−e(11)
y=L1sin(q1+β1) + L2sin(q1+q2+β1+β2) + c(12)
where L1=1.6m and L2=1.82 m.
Expressed in a more compact form the forward kinematics
simplify to
x=h(q)(13)
eO
c
L11
L12
θ1
xc1
q1
L1
q2
L21 L22
xc2
θ2<0
L2
x
θ3<0
FIGURE 4. HYDRAULIC CRANE KINEMATICS
The widely known differential kinematics equation relating the
manipulator joint velocities ˙
qto the resulting end effector linear
velocities ˙
xis
˙
x=J(q)˙
q(14)
where the Jacobian matrix is
J(q) = ∂h(q)
∂q(15)
Given a desired end effector velocity ˙
xre f the required joint ve-
locities ˙
qre f are conversely given by
˙
qre f =J−1(q)˙
xre f (16)
since the manipulator in question is non-redundant and the Ja-
cobian matrix Jis square and directly invertible. To translate
the required joint space motion into movement of the hydraulic
cylinders in actuator space, the following transformation from
joint angle to hydraulic cylinder position is applied
xc=C(q)(17)
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Copyright © 2013 by ASME
by defining
C(q) = c10
0c2(18)
where ciis a function of the joint angles
ci(q) = qL2
i1+L2
i2−2Li1Li2cos(qi)(19)
and L11 = 1.0 m, L12 = 0.376 m, L21 = 1.13 m and L22 = 0.31 m.
CARTESIAN LOAD TRACKING CONTROL WITH AC-
TIVE SWAY COMPENSATION
In this section the control schemes for the suspended load
position tracking and anti-sway control are presented. The ob-
jective of the combined control system is to drive the suspended
load mass to the position desired by the human operator without
excessive oscillations. The underlying Cartesian velocity con-
troller drives the crane tip at a required reference velocity which
in turn is generated by the load anti-sway controller based on the
human operator inputs.
Cartesian velocity control
The structure of the Cartesian velocity controller is pre-
sented in Fig. 5. The controller reference input is the desired
Cartesian velocity ˙
xre f , which is multiplied with the Jacobian in-
verse J−1of the measured joint positions q. The result is the
desired joint velocity vector ˙
qre f . The desired joint velocities are
integrated to give desired joint positions and transformed through
C(q)to desired cylinder positions xre f
cgiving the input to the
cylinder position controller detailed below.
˙
xre f
q J−1(q)
×˙
qre f Zqre f
C(q)xre f
c
FIGURE 5. CRANE TIP CARTESIAN VELOCITY CONTROLLER
Hydraulic cylinder position control
The structure of the cylinder position controller is shown in
Fig. 6. The feedforward branch contains an experimentally iden-
tified look-up table based mapping Ffrom desired cylinder ve-
locity ˙
xcto required valve control output uv. The table values are
obtained as averages from various crane postures which induce
variable loading levels on the cylinders. The use of the feed-
forward branch improves the dynamic response of the position
controller and lessens the effects of plant non-linearities. The
closed-loop feedback section uses a filtered proportional posi-
tion control to correct for any remaining cylinder position error.
The time constant τwas chosen as τ=2/ωn(see [17]), where
ωn≈28.3 rad/s is the lowest natural frequency of the manipu-
lator around the operating point of the experiments. A suitably
chosen time constant prevents undesirable high-frequency exci-
tations of the manipulator without sacrificing the control band-
width excessively.
xre f
c∑∑
qC(q)xc
d
dt F(˙
xc)
Kp
τs+1uv
FIGURE 6. CYLINDER POSITION CONTROLLER
Suspended load dynamics and anti-sway control
Consider the body diagram of the suspended load assem-
bly illustrated in Fig. 7. The position of the center of mass
xcm = [xcm ycm ]Tis given by
xcm =x+Lcm sinφ(20)
ycm =y−Lcm cosφ(21)
where
φ=θ1+θ2+θ3+π
2=ϕ3+π
2(22)
and Lcm is the distance of the center of mass from the joint. The
forces disturbing the suspended load from its equilibrium point
are the inertial forces Fiand the friction force Fk
Fi+Fk=Icm ¨
φ+b˙
φ(23)
where Icm is the mass moment of inertia of the load respective
to the center of mass and bis a coefficient representing the joint
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Copyright © 2013 by ASME
φ
x
xcm
Lcm
¨xcm
¨ycm
FR
Fi+Fk
φ
FIGURE 7. SUSPENDED LOAD DYNAMICS
friction. Conversely the restoring forces consist of gravity and
the component accelerations of point xcm
FR=−mP(g+¨ycm)Lcm sinφ−mP¨xcmLcm cos φ(24)
where mPis the total mass of the suspended load assembly. The
equation of motion for the load now becomes
Icm ¨
φ+b˙
φ=−mPgLcm sinφ−mP¨xcmLcm cos φ
−mP¨ycmLcm sin φ(25)
The acceleration of the center of mass is obtained by differenti-
ating the position xcm twice resulting in
¨xcm =¨x+Lcm cosφ·¨
φ−Lcm sinφ·˙
φ2(26)
¨ycm =¨y+Lcm sinφ·¨
φ+Lcm cosφ·˙
φ2(27)
Substituting Eqns. (26) and (27) into Eqn. (25) results in
(mPL2
cm +Icm)
| {z }
Ix
¨
φ+b˙
φ=−mPgLcm sinφ−mP¨xLcm cos φ
−mP¨yLcm sinφ(28)
where Ixis the mass moment of inertia of the load respective to
point x. By linearizing the equation of motion around the equilib-
rium point φ=0 using the small angle approximation sin φ≈φ,
cosφ≈1 and sin φ·˙
φ2≈0 and restricting the motion of the crane
tip to the horizontal direction, the motion state of the suspended
load
xPS = [x1x2x3x4]T= [ xcm ˙xcm φ˙
φ]T(29)
can be represented in state space form as (see [14])
˙x1=x2
˙x2=u+Lcm ¨
ϕ3=u−mPgL2
cm
Ixx3−Lcmb
Ixx4−mPL2
cm
Ixu
˙x3=x4
˙x4=−mPgLcm
Ixx3−b
Ixx4−mPLcm
Ixu
(30)
where the system input uis the horizontal acceleration of the
crane tip ¨x. In a more compact matrix form the system dynamics
are
˙
xPS(t) = Ax PS(t) + BuPS (t)(31)
where
A=
0 1 0 0
0 0 −mPgL2
cm
Ix−Lcmb
Ix
0 0 0 1
0 0 −mPgLcm
Ix−b
Ix
(32)
B=h0 1−mPL2
cm
Ix0−mPLcm
IxiT
(33)
and uPS =u=¨x.
With the suspended load dynamics represented in state-
space form, a state feedback controller can now be designed,
which can be used to drive the system to a desired state. The
state feedback controller gains can be derived using direct pole
placement, from position control settling time requirements or
by using common criteria based on various error measurements
between the desired and plant system model response e.g. ITAE.
As the objective of the anti-sway controller is to stabilize the load
while simultaneously driving the center of mass to a desired po-
sition, the state feedback controller gain solution given by the
linear quadratic regulator (LQR) is a natural choice in this situa-
tion. By introducing a position reference input for the center of
6
Copyright © 2013 by ASME
mass xcm the LQR controller aims to quadratically minimize the
deviation of the load position from the reference while driving
the other states ˙xcm φ˙
φto zero. The use of the weighting matri-
ces Rfor the control input and Qfor the state deviations keeps
the expended control effort limited while allowing for the tuning
of the closed-loop control stiffness. Solving the associated Ric-
cati equation results in a full state-feedback tracking controller
with a control law in the typical form of
u=−KxPS +r=−KxPS +¯
Nx re f
cm (34)
where xre f
cm is the reference position for the load center of mass
and the scalar ¯
Nis chosen such that KxPS equals rin steady
state. To combine the anti-sway controller to the Cartesian ve-
locity controller of Fig. 5 the acceleration output from Eqn. (34)
is integrated over time to give the desired Cartesian velocity as il-
lustrated in Fig. 8. The resulting reference velocity is then given
as the reference input for the velocity controller in Fig. 5.
˙
xre f
cm
xPS
˙
xre f
K
Z¯
Nr
xre f
cm Z
∑u
FIGURE 8. SUSPENDED LOAD CARTESIAN POSITION CON-
TROLLER WITH ANTI-SWAY CONTROL
EXPERIMENTS
The motion control experiments with the MEMS-based
closed-loop state feedback were performed on a HIAB 031 hyd-
raulic manipulator, which was installed on a rigid base as shown
in Fig. 3. The swinging load consisted of a rigid 13 kg arm 1.7
m in length with a 50 kg load mass mounted on the tip. The fluid
flow to the lift and tilt cylinders, both ø80/45-545 mm in size,
were controlled by directly operated NG10 size servo solenoid
valves. The nominal flow rates of the valves controlling the lift
and tilt cylinder were 100 l/min (∆p = 3.5 MPa per control notch).
The bandwidth of the valves was 100 Hz for a ±5% control in-
put. The hydraulic power supply was set to 19.0 MPa supply
pressure. A PowerPC-based dSpace DS1103 system was used
as a real-time control interface to the servo valves and for samp-
ling of the joint sensors at a rate of 500 Hz (Ts= 0.002 s). The
MEMS sensor chips are 8.5×18.7×4.5 mm in size containing a
digital 3-axis accelerometer integrated with a one x-axis gyro by
Murata [18]. The sensing ranges are ±2gfor the accelerometer
and ±100 deg/s for the gyro. The best case-inclination resolu-
tion of the MEMS accelerometer is 0.55 ·10−3rad when parallel
to the ground. The MEMS gyro resolution is 0.35·10−3rad/s.
The frequency ranges of the MEMS components are 30 Hz for
the accelerometer and up to 50 Hz for the gyroscope.
In order to verify the developed MEMS-based closed-loop
feedback performance, Heidenhain ROD 486 encoders out-
putting 5000 sine waves per revolution were also installed on
the manipulator and suspended load joints to serve as high ac-
curacy reference joint sensors. Connected to IVB 102 units for
100-fold interpolation and with each incremental pulse further
sub-divided by 4 in the DS1103, the final encoder position reso-
lution was π·10−6rad. This means that the reference encoder
sensors provide at least 100 times more accurate position feed-
back compared to the MEMS sensors. Interface to the MEMS
sensor modules was through the CAN-bus operating at 1 Mbit/s.
The CAN-bus was also used to supply the power to the MEMS
sensors.
The authors note that in the case of the load being sus-
pended from a cable and swinging in 3D, the sensing system
can be modified to include a more complex mechanical assem-
bly to accommodate for sensing of the two dimensions of the
cable swing; see e.g. [5] for details. As given in Eqn. (9) the
MEMS based inclination sensing is suitable for the estimation of
two-dimensional cable swinging motion.
To allow comparison of the MEMS-based anti-sway state
feedback control to encoder based state feedback, the manipu-
lator and suspended load joint angular velocities were estimated
from encoder position feedback with a general finite difference
method suited for real-time control applications (see [19]) de-
fined as the discrete difference of position P(t)with respect to
time tgiven by
˙
P(t)≈1
Ts
n−1
∑
k=0
CkP(t−k Ts)(35)
where the weights C= [5 3 1 −1−3−5]/35 yielded the best
performance.
Cartesian motion control results
The Cartesian motion control experiments consisted of hori-
zontal motion between two coordinate points. To enable repeat-
able experiments, the user supplied reference Cartesian velocities
were generated using a second order polynomial. Figure 9 illus-
trates the resulting uncontrolled swinging of the load when the
Cartesian velocity reference for the crane tip is directly the user
input, i.e. ˙
xre f =˙
xre f
cm . With no sway compensation active the
crane tip follows the user input reference and the uncontrolled
position of xcm (dashed line) overshoots the reference position
7
Copyright © 2013 by ASME
xre f
cm (gray line) by 60% followed by a slowly decaying oscilla-
tion back to equilibrium.
The positioning performance using the anti-sway controller
with encoder feedback is represented by the black solid line
in Fig. 9 and correspondingly by the dash-dot line when us-
ing MEMS feedback. The performance using the two feedback
sources is almost identical with the positioning response having
an overshoot of only 6% and a settling time of approximately
3 seconds, which demonstrates clearly the effectiveness of the
proposed control concept.
0 2.4 4.8 7.2 9.6 12
2
2.5
3
xcm (m)
Time (s)
Encoder
MEMS
FIGURE 9. LOAD CENTER OF MASS POSITION WITHOUT
CONTROL AND WITH LOAD SWAY COMPENSATION USING
ENCODER AND MEMS FEEDBACK
As is evident from Fig. 9 the price paid in oscillation damp-
ing is the increased settling time. To enable a fair comparison of
the anti-sway controller performance, the Cartesian movement
was also executed without load sway compensation with a tran-
sition time of 3 seconds. The resulting motion of the load center
of mass is illustrated in Fig. 10 with the previously shown re-
sponses of the state feedback controller included for comparison.
Even with a slower transition time, the uncontrolled position of
the suspended load overshoots by 12% and exhibits oscillatory
behavior.
In general, state feedback control is a very effective ap-
proach for stabilizing a control system and realizing a rapid dy-
namic response with increased damping provided that the lin-
earized system model is accurate and the state feedbacks are
close to ideal. By giving higher weights in the matrix Qfor
the states, the closed-loop response can be shaped as desired.
In practice however, the gains of the LQR controller cannot be
set as high as would be desirable due to various error sources
present in the actual system as well as in the state feedback sig-
nals. For the experiments presented above, the diagonal elements
of Qwere set to Qi,i= [5 6 0.1 0.1]which yielded the feedback
gain vector K= [7.07 11.05 −33.2−9.4]. Higher values in
Kquickly resulted in an unstable system despite being numeri-
cally well within stability limits. The major contributing sources
0 2.4 4.8 7.2 9.6 12
2
2.5
3
xcm (m)
Time (s)
FIGURE 10. UNCONTROLLED RESPONSE WITH 3 SECOND
RAMP VERSUS CONTROLLED RESPONSE
limiting the anti-sway controller performance are the non-linear
friction effects in the joint of the suspended load, the non-ideal
state feedback signals and the errors in the crane tip Cartesian
velocity controller.
DISCUSSION AND CONCLUSION
In this paper a network of MEMS linear accelerometers and
angular rate gyroscopes was used for the motion state estimation
of an articulated hydraulic crane and applied to the closed-loop
Cartesian motion control of the crane. Further, the MEMS-based
state estimation was also used for full state feedback control to
actively dampen the oscillations of a suspended load attached
to the end of the crane. Reference results of anti-sway control
were obtained using high accuracy incremental encoders as mo-
tion sensors providing the joint positions at a resolution of 2 mil-
lion increments per revolution.
The application of the MEMS network for the estimation
of the suspended load sway angle and angular velocity was mo-
tivated by key advantage of the MEMS sensors, which is that
they can be simply “strapped down” on the mechanical bodies
requiring no mechanical contact to rotating joint pins. Further-
more, the angular velocity of the load is measured directly by the
MEMS gyroscope without the need of any noise amplifying dif-
ferentiation, which would be case with incremental encoder or
potentiometer feedback.
With the MEMS network providing full motion state feed-
back from the manipulator joints as well as the suspended load
sway angle and angular velocity, the suspended load could be po-
sitioned with a 6% overshoot in position compared with a 60%
overshoot and significant oscillation when no anti-sway control
was used. The control concept was also shown to yield a bet-
ter positioning response of the suspended load even if the load is
simply moved at a slower speed. As a further key result, despite
the 100-fold advantage in position resolution over the MEMS
sensors, the positioning results obtained using encoder feedback
based state estimation were almost identical.
8
Copyright © 2013 by ASME
Thus, owing to the straightforward and relatively effortless
installation, robustness against harsh environmental conditions,
size and cost advantage, we consider the proposed MEMS net-
work well-suited for closed-loop feedback control of multi-body
articulated cranes and for use in suspended load anti-sway con-
trol systems.
ACKNOWLEDGMENT
This work was supported in part by the Academy of Finland
under the project “Sensor Network Based Intelligent Condition
Monitoring of Mobile Machinery”, grant no. 133273. This fund-
ing is greatly appreciated. The authors would also like to thank
researcher Erkki Lehto from TUT/IHA for the valuable support
with the MEMS sensor design and manufacture.
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