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Aschemann, Harald; Hild, Ingo; Hofer, Eberhard P.
Non-linear Model Based Control for a Hydraulically
ActuatedMobile Harbour Crane
Active damping of oscillations performed by the rope suspended
payload becomes a more and more important feature
for mobile harbour cranes characterised by their non-linear
kinematic structure. This contribution presents a non-
linear control scheme for a hydraulically actuated mobile
harbour crane, which is based on a multibody model of
the mechanical configuration. The decentralised control
structure consists of a combined feedforward and feedback
control law for each crane axis and includes a compensation for
the most dominant coupling between the axes due
to centrifugal acceleration. By this, crane operation can be
simplified and handling performance can be increased in
particular for less experienced crane operators and, moreover,
automatised container handling becomes an attractive
feature for operating mobile harbour cranes. The efficiency of
the proposed control scheme is emphasized by selected
simulation results.
1. Introduction and Modelling of the Mobile Harbour Crane
Topic of this paper is a model based trajectory control scheme
[1] for a mobile harbour crane that is depicted infig. 1. This
allows for tracking desired trajectories in cylindrical coordinates
for the position of the rope suspendedcrane load, i.e. the
container. In the sequel, the focus is on the raising axis,
exemplarily. The boom of the harbourcrane, with which the radial
position of the rope suspended crane load can be determined, is
driven by a hydrauliccylinder. Hence, the drive system of the
raising axis is governed by non-linear kinematics. The dynamics of
theeffective pressure generation within the cylinder represents a
nearly stiff subsystem and can be simplified under theassumption of
incompressible oil. The resulting kinematical constraint equation
leads to additional expressions in
the equations of motion due to the hydraulic system part. The
mechanical structure of the mobile harbour craneis modelled by a
multibody system consisting of three rigid bodies: the tower, the
boom, and the payload, i.e. thecontainer (fig.1, left part). A
complete description is obtained with five generalised coordinates
combined in thevector q = [DStASr zL]
T. The corresponding equations of motion are derived by applying
Jourdains principle.In order to employ the technique of extended
linearisation [2], the non-linear equations of motion are formally
writtenin linear form, which in consequence leads to parameter
dependent matrices. At this, less important terms in theseequations
have been neglected. The vector of varying system parameters p = [A
mL lS]
T that contains the raisingangle A, the load mass mL and the
rope length lS is completely available by measurements. The
decentraliseddesign model of reduced order for the raising axis
MA(p)qA + DA(p)qA + KA(p)qA = fuA(p) + feA(p) (1)
is directly obtained by means of coordinate transformation using
an appropriate Jacobian. The according mechanical
model is shown in the left part of fig. 2 consisting of the boom
(mass mA, mass moment of inertia JA, length lA,centre of gravity
distance sA, raising torque A applied by the hydraulic cylinder),
the rope with length lS, and theload mass mL. At this, the vector
of generalised coordinates qA = [A Sr ]
T is used, where the relative angle Ais introduced as deviation
from an operation point A0 according to A = A0 + A. Consequently,
as controlledvariable the relative radial position rL as deviation
from operation point rL0 is utilised instead of the radial
positionrL = rL0 + rL (fig. 2, left part). The centrifugal force as
dominant dynamic coupling is included in the disturbancevector feA.
These reduced order equations are transformed into state space
representation so as to apply state spacemethods.
2. Control Structure and Simulation Results
The implemented raising axis control law consists of four main
components as can be seen in the block diagram
depicted in the right part of fig. 1: 1) linear PI state
feedback consisting of uRA,I and uRA,P, 2) linear feedforwarduSA
evaluated with the reference trajectory and its first four time
derivatives combined in the vector of reference
functions wA = [rL,ref rL,ref r(IV)L,ref]
T, 3) non-linear feedforward coupling compensation uC based on
the
reference functions of both raising axis wA and turning axis wD
= [D,refD,refD,ref]T, and 4) non-linear gravity
PAMM Proc. Appl. Math. Mech. 3, 148149 (2003) / DOI
10.1002/pamm.200310349
7/30/2019 Non-Linear Model Based Control for a Hydraulically
Actuated Mobile
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jDL
j
j
Sr
AjSt
length compensation
hoistingwinch
hydraulic cylinderraising
hydraulic motorsturning
boom
tower
boom
payload(container)
l
z
Srope
feedforward
control
mobile harbour craneraising axis
signalprocessing
anddisturbance
observer
Integralfeedback
adapted to varying system parameters p
couplingcompensation
gravity torquecompensation
proportionalstate feedback
uRA, P
jA
jAuSA
uRA, I
uV
rLuC
wA
xA
wD
uRA, G
Lr%
,L refr%
jSr
Figure 1: multibody model (left), block diagram of the raising
axis controller (right)
lS
rL
m , J ,l A A As A jS r
tA mL
0 0cosL A Ar l= j
0A A Aj = j + j%
Lr%
0
0
5
10
15
20
25
-5
-10
-1520 40 60
time in s
rel.
radial
pos
itio
n
inm
80 100 120
simulatedreference
time in s
simulatedreference
rel.
radial
pos
ition
inm
0
0
-5
-10
5
10
15
20 40 60 80 100 120
Figure 2: decentralised design model for the raising axis
(left), simulation results for the relative radial position
rL:comparision of reference position and simulated position without
compensation measures (middle), comparision ofreference position
and simulated position with centrifugal force compensation
(right)
compensation uRA,G. The raising angle A is measured by an
encoder, the angular velocity Sr by a gyroscope.The raising angular
velocity A is obtained by numerical differentation, whereas the
angular displacement Sr isacquired by use of a disturbance observer
in order to cope with disturbances like gyroscope drift and rope
oscillations.Herewith, both active damping of load pendulum
oscillation and tracking of desired trajectories within the
workspaceare achieved.
The simulation results are obtained for a synchronised reference
motion of both turning axis and raising axis. Themiddle part of
fig. 2 depicts the effect of uncompensated centrifugal forces on
the relative radial position rL ofthe payload. This indicates the
dominant dynamic coupling between the turning axis and the raising
axis. Afeedforward compensation based on the vectors of reference
functions wA and wD leads to a compensation of thedeviation caused
by the centrifugal force with small tracking errors as shown in the
right part of fig. 2. Steady-stateaccuracy is achieved due to the
integral control part.
3. Conclusions
This contribution presents a model based control approach for a
mobile harbour crane that allows for trajectorycontrol of the load
position. The design is based on a multibody model and takes
advantage of the gain schedulingtechnique to adapt the complete
control structure to measurable system parameters. Selected
simulation resultsemphasise both efficiency of the proposed control
structure and the necessity of compensation measures with respectto
the centrifugal force as main dynamic coupling.
4. References
1 Aschemann H.: Optimale Trajektorienplanung sowie
modellgestutzte Steuerung und Regelung fur einen Bruckenkran.
Fortschritt-Berichte VDI, Reihe 8, Nr. 929, VDI-Verlag, 2002
2 Friedland B.: Advanced Control System Design. Prentice-Hall,
1996
Dr.-Ing. Harald Aschemann, Dipl.-Ing. Ingo Hild, Prof. Dr.
Eberhard P. Hofer, University ofUlm, Dept. of Measurement, Control
and Microtechnology, D-89081 Ulm, Germany, e-mail:
[email protected]
Section 3: Multibody systems and kinematics 149
