Boom Crane Control System. Gordon G. Parker. Mechanical Engineering-Engineering Mechanics Department. Michigan Technological University. Houghton, MI ...
Proceedings of the American Control Conference San Diego, California June 1999
Experimental Verification of a Command Shaping Boom Crane Control System Gordon G. Parker Mechanical Engineering-Engineering Mechanics Department Michigan Technological University Houghton, MI 4993 1 ggparker @ rntu.edu Kenneth Groom Johnny E. Hurtado John Feddema Rush D. Robinett Sandia National Laboratories Intelligent Systems and Sensors Albuquerque, NM 87185 Frank Leban Naval Surface Warfare Center, Carderock West Bethesda, MD 208 17
For this reason, these at-sea replenishment operations are restricted to relatively calm conditions, below sea-state three. The motivation for this work is to develop a swing control strategy to allow safe operation of ship cranes under more severe sea-states. This will ultimately require a control strategy which addresses the three primary sources of payload swing excitation: operator commands, sea-induced base motion, external disturbances. The results presented here are for the component of the control strategy which mitigates operator induced payload swing as described in [ 13.
Abstract This paper presents experimental results of a command shaping control method for suppressing payload swing caused by operator commanded maneuvers, in rotary, shipbased, boom cranes. The crane configuration investigated, consists of a payload mass that swings on the end of a spherical pendulum of varying lift-line length (hoisting). The lift-line is attached to a boom capable of elevation (luffing) and rotation about a vertical axis (slewing). Positioning of the payload is accomplished through luff, slew and hoist commands issued in real-time by an operator. The command shaping strategy, consisting of a time-varying filter, reduces payload oscillation by 18 dB in experiments using the 1/16th scale Navy Crane Testbed at Sandia National Laboratories.
1. Introduction The U.S. Navy has a fleet of crane ships used to move containers between ships as part of the Container Off-loading and Transfer System (COTS). Each ship contains several boom cranes which can be operated separately or in tandem, as shown in Fig. 1. A typical maneuver positions the crane ship between a cargo ship and a smaller beach landing craft (lighter). An operator uses a coordinated combination of the crane’s hoist, luff and slew degrees-of-freedom to move the container from the cargo ship to the lighter. During the maneuver, the container often passes over the deck of the crane ship. Damage to personnel, cargo, and the participating ships can occur if the payload undergoes excessive swing. 0-7803-4990-6199$10.00 0 1999 AACC
Figure 1.
86
U.S. Navy Crane Ship
payload relative to the slewing pedestal, in conjunction with inertial visual queues such as the horizon. Commands are issued using a combination of joystick and foot pedal inputs. The right-hand stick effects luffing and slewing whereas the left-hand stick controls hoist. A foot pedal is used to operate the crane’s Rider Block Tagline System (RBTS). This system is used to change the effective lift-line length for pendulation and sway. Its influence is not considered in this work.
Several swing-free strategies have been developed in the past, mostly motivated by the need for increasing the speed at which cargo is moved between a ship and a stationary dock. In these studies, the ship was always assumed to be stationary. Most methods can be classified according to the level of realtime operator involvement in the maneuver. For instance, a number of techniques for open-loop residual oscillation free maneuver generation were developed [2], [3]. However, their applicability to the ship crane system described above is limited due to the need to keep the operator in-the-loop to increase reliability.
Boom
Rotary boom crane control systems have been proposed which rely on modifications to the nominal crane system [4]. Although these would be excellent choices for newly designed cranes, the motivation of this work necessitates a minimum of crane modification. The resulting subset of applicable published work uses command shaping for operator input induced oscillations as discussed in [ 11. Recently, there has been interest in the synchronization problem of setting the payload down onto the moving lighter. Simulation studies demonstrate the ability to synchronize the payload’s speed for a gentle set-down, however, the time to synchronize may be long. Although this research area is outside the scope of this paper, some practical set down method will be required to implement a full scale, rough sea, COTS.
Figure 2.
Boom Crane
The sway and pendulation equations of motion were obtained using Lagrange’s equations
2. Crane Description and Dynamics The payload is considered as a particle with mass rn and is attached to the crane’s lift-line. The lift line can be extended or retracted by the operator’s hoist speed command L . The lift-line is attached to the boom (of length Lb ) at its tip. The boom can be rotated by the operator’s luff rate command p . The end of the boom opposite to the lift-line attachment point is attached to a slewing pedestal, again controlled by the operator’s slew speed command, a . The spherical pendulum motion of the payload is described using two independent generalized coordinates 8, and e,, referred to as pendulation and sway respectively. An inertial rcference frame is used for generating the kinematic quantities necessary for developing the sway and pendulation equations of motion. Its origin is along the slew axis, at the base of the crane’s support column. The inertial X axis is oriented such that the angle between it and the boom is zero when the slew angle is zero. In addition, the inertial Y axis is along the crane’s slew axis.
and used as the basis of a simulation tool for performing preliminary testing of control strategies. While the simulation used the full nonlinear equations of motion, the command shaping control design exploits the linearizing assumptions that sway and pendulation states have amplitudes significantly less than one. In addition, luff rates and accelerations. and slew rates and accelerations are
The operator typically sits in a cab attached to the slewing pedestal and therefore sees the motion of the boom and
87
assumed small. The resulting pendulation and sway equations
a = awn
(4)
where o, is, of course, a function of lift-line length L . If a is held constant in Eq. 3, then the filter's roll-off characteristics will change according to lift-line length, from a quasi-static interpretation. This phenomenon was determined to be undesirable from the standpoint of the operator's expected response of the crane to stick commands.
Sway
Previous results [ 11 demonstrated the capability of this filter to reduce residual sway and pendulation using an operator inthe-loop simulation. A typical 3-axis (luff, slew, hoist) coordinated maneuver predicted that the residual sway and pendulation amplitudes would be reduced by approximately 20dB. In the next section, the experimental verification of these results is presented using a 1/16th scale ship crane testbed.
are dynamically decoupled. The oscillation excitation is through nonlinear combinations of the slew, luff, and hoist states.
3. Command Shaping Filter Overview The form of the command shaping filter, where p is the differentiation operator,
4. Experimental Verification (3)
The Navy Crane Testbed at Sandia National Laboratories was used for the final verification of the control strategy simulated in Section 3. The system is shown in Fig. 4 and represents a 1/16th scale version of the Hagglunds Model TG3637 crane and has an 8 foot boom length. Although there are differences between the test crane and the idealized simulated crane of Fig. 2, the relevant kinematics and the primary payload oscillation characteristics are equivalent.
is described in detail in [ 11. The variable q represents both the luff rate, 0 , and slew rate, a . That is, the same filter is applied to both crane degrees-of-freedom. The subscript "i" denotes the operator's input where as the subscript "0" indicates the signal going to the crane's speed servo controllers. The notch frequency, w, is allowed to change continuously according to changes in lift-line length, L .The parameter a determines the roll-off characteristics and was chosen using the nondimensionalized frequency response plots of the filter shown in Fig. 3.
Five independently controlled D.C. servo motors are used to actuate the crane's degrees-of-freedom. A 3 h.p. motor is used for the slew axis in conjunction with a 120:l gear reduction providing a range greater than 180" . Luff and hoist axes each use 1 h.p., direct drive motors where the luff range is from horizontal to vertical. The Rider Block Tagline System (RBTS) uses a 1 h.p. motor for hoisting the rider block in addition to a 1 h.p. motor for actuating the taglines. Although this system is not used here, it can be seen in Fig. 4 located at the midpoint of the lift-line. For the tests described later, the rider block is removed.
s o 4? -20 a,
3 -40 .& -60 4-
2 -80
-100
10-2
Figure 3.
lo-' 100 10' Normalized Frequency, o/o, (n.d.)
102
Effect of a on the roll-off characteristics of the command shaping filter (2 = a / w , ).
After determining the desired roll-off characteristics, the constant parameter 2 is chosen. The parameter a used in the filter is varies in time according to
88
the input profile of Fig. 5 -- one with command filtering, the other without. The lag induced into the crane's axes as a result of the filter is quite apparent. Fig. 9 and Fig. 10 show the sway and pendulation for the two runs. The residual swing reduction afforded by the filter is approximately 18 dB, agreeing well with the 20 dB reduction predicted in [l]. The primary error source is postulated to be the slew axis gear train, and is currently being investigated further.
20
luff rate (degkec)
v)
'D
Figure 4.
z
Navy Crane Testbed
10
0 U
ln
n. 0)
Comparison of Fig. 4 to the idealized crane of Fig. 2 also illustrates the difference in rigging. The Navy Crane Testbed level-luffing rigging was designed to match the actual crane. If no hoist is commanded by the operator, the luffing action of the crane moves the payload radially, with minimal vertical displacement. Therefore, during a one-axis luffing maneuver, the lift-line changes length to maintain the payload's vertical position approximately constant.
E $
O
0" -1 0
10
0
20
30
Time (sec)
Figure 5.
The crane body rests on a 6 degree-of-freedom, Stewart Platform motion base for duplicating sea-induced crane base motion. A resistive lift-line swaylpendulation sensor, accurate to 0.1 degrees, was developed and attached at the lift-line attachment point. The swaylpendulation sensor is used to both assess the residual swing, and as an integral component of a closed-loop active swing cancellation controller under development. Operator inputs are delivered to the computer controller via joysticks, allowing for realtime, arbitrary commands. Command sets can also be recorded and played back for comparing the capability of different controller strategies.
100
Operator luff, slew, and hoist commands 1
I
I
I
0
I
I
10
i
I
I 20
I
I 30
Time (sec)
A typical 3-axis, coordinated maneuver was generated using the operator joysticks and recorded at 0.00095 second intervals as shown in Fig. 5. The filter design parameter, ii was set to 1.0. Lift-line length changes resulted as the by product of the level-luffing rigging and hoist commands. Over the duration of the maneuver, the quasi-static natural frequency of the payload changes from 0.3 Hz to 0.6 Hz (Note: a typical swaylpendulation frequency for the full scale ship crane is 0.09 Hz). This doubling of the sway and pendulation frequencies was purposely used to exercise the time-varying aspect of the filter of Eq. 3. In addition, it is more aggressive than the frequency changes examined in [ 11 of 0.4 Hz to 0.5 Hz over the maneuver duration.
Figure6.
The crane's actual luff, slew, and hoist motion, as recorded by joint encoders (324K. 2K, 2K count respectively), are shown in Fig. 6 through Fig. 8. Two runs were made using
89
Measured hoist for the filtered and unfiltered maneuvers.
and sway after a coordinated, 3-axis maneuver. The timevarying filter is designed to yield consistent crane degree-offreedom performance in the presence of changes in sway and pendulation natural frequencies.
50 40 h
m
3- 30 s 20
As described in the introduction, this work only addresses the source of payload oscillation attributed to the operator’s commands. The other two sources: sea induced crane base motion and external payload disturbances are currently under investigation both in simulation and experimental testing.
UJ
m0 10
0
10
0
20
30
Time (sec)
Figure7.
30
-
Measured luff for filtered and unfiltered maneuvers. I
I
1
I
I
1
I
0)
“ z.
5
a, cn
s
I
C
O
U I) 5
-5
0 .c
Filter Off
\I
a
-10 L
0
I
I 10
I
\ I I II I I ’ I
20
I
J
30
Time (sec)
Figure 10. Measured pendulation for filtered and unfiltered maneuvers. 20
10
0
30
6. References
Time (sec)
Figure 8. 20
Lewis, D., Parker, G.G., Driessen, B., and Robinett, R.D., “Command Shaping Control of an Operator-inthe-Loop Boom Crane,” Proceedings of the 1998 American Control Conference.
Measured slew for filtered and unfiltered maneuvers. I
I
I
Filter Off m
P. Vaha, S . Pieska and E. Timonen, “Robotization of an Offshore Container Crane,” Robots: Coming of Age, Proceedings of the 19th ISIR International Symposium, pp. 637-648, 1988.
10
U W
v
-
2c
$
” 0
Sakawa, Y., Shindo, Y., and Hashimoto, Y., “Optimal Control of a Rotary Crane,” Journal of Optimization Theory and Applications, Vol. 35, No. 4, pp. 535-557, 1981.
-10
-20
‘
0
I
I 10
I
I
20
I
I
30
Ott, E., “Control of Container Cranes,” Proceedings of the National Conference on Noise Control Engineering, Vol. 1, No. 1, pp. 407-410, 1996.
Time (sec)
Figure 9.
Measured sway for filtered and unfiltered maneuvers.
7. Acknowledgment 5. Summary and Future Work This work performed at Sandia National Laboratories and Michigan Technological University is supported by the U.S. Department of Energy under contract DE-AC0494AL85000.
The filters described in [I] were tested using a newly developed Navy Crane Testbed. Use of the filters demonstrated an 18 dB reduction in the residual pendulation
90
