- Email: [email protected]
Active Position Control of Dynamic Platforms
eopyrigtb Cl IFAC Motion Control for Intelligent Automation Perugia• Italy. October 27-29. 1992
ACTIVE POSITION CONTROL OF DYNAMIC PLATFORMS K. BOUAZZA-MAROUF and J.R.
HEWIT
Loughborough University of Technology, Department of Mechanical Engineering Loughborough, Leicestershire, LE 11 3TU, United Kingdom
Abstract: The loading and unloading of offshore supply vessels pose severe problems in adverse weather conditions when the supply vessel may be heaving, pitching and rolling violently. This is currently overcome by relying on the crane operator's skill and weather windows which may be dangerous and costly. A dynamic platform system (DPS) is proposed here to solve the problem of offshore load transfers. A method of control based on the principle of invariance is used here on an experimental rig to investigate the control problem of disturbance isolation of the DPS. Good results have been obtained. Keywords: Invariance control; offshore load transfers; dynamic platform; disturbance isolation; active force control.
1. INTRODUCTION
[3] and many types of absorbers have been developed [3,4]. Out of the six degrees-offreedom of a stationary ship only roll, surge, sway and yaw have been successfully controlled. The two uncontrolled motions are heave and pitch. It is extremely difficult, if not impossible, to reduce a ship's heave motion [3]. Pitch is considerably dampened by the vessel's hull and large stabilizing moments would be required for any further increase in the damping [5]. The twodegrees-of-freedom dynamic platform proposed here could be used to compensate for these two motions which can be regarded as base motion disturbances to the dynamic platform system (DPS).
The safety and performance of certain operations offshore are severely limited by wave induced vessel motions, for example there is the problem of loading and unloading supply boats, by a crane on an oil production platform, in the face of wave disturbance. The lauer operations, especially when vital e~uipment is involved, must sometimes be performed in adverse weather conditions as it is not always possible to wait for calm weather. This can be difficult and even dangerous. Crane failure is a frequent occurrence and derating of cranes has been introduced [I]. Some of these failures are caused by extreme overloading of cranes [2] due to the relative velocity between hook and load. The impulsive force the crane experiences while snatching a load from a moving deck acts like a hammer blow on the crane. Here it might be useful to equip a supply boat with a deck which, despite the gross movements of the boat itself due to wave disturbances, maintained itself absolutely at rest so that loading and unloading operations might proceed easily and safely. Other applications of such a deck could be as an active landing platform for helicopters in adverse weather conditions.
The DPS consists of a platform and a base. TIle platform is supported on actuators which are actively controlled to isolate the platform from the motion of the base_ A schematic diagram of the DPS is shown in Figure I. Applications of the DPS of a different scale might be onshore. Some of these applications are active control of mobile robots subjected to base disturbances. active suspension control of road, off-road and rail vehicles, and active isolation of a helicopter cabin from rotor disturbances.
Overcoming the disruptive effeet of sea induced motions on ships has been of interest for may years
241
HEWIT J.R.. ROCA77A-MAROUF K.
A dynamic platfonn experimental rig has been designed to demonstrate the concept of the DPS and to assess the effectiveness of the control algorithms in a situation more close to the "real world". A novel type of active isolation, based on the well known principle of invariance [6], is investigated. Here we consider disturbances which are both force-type at the platfonn and displacement type at the base.
where Em is the overall unknown disturbance vector given by
The tenn J.K/.A.AT in equation (3) is the actuators inertia matrix referred to the platform Our objective here is to cancel the disturbance vector Em without direct measurements.
2. EXPERIMENTAL RIG An estimate of Em could be obtained from (3) as Figure 2 shows a photograph of the two degrees-offreedom experimental dynamic platfonn rig. The base of the DPS is supported and disturbed in the two degrees of freedom, vertical and angular motions, by a cam-actuation system. The platfonn is supported by two electromechanical actuators which are mounted on the base. Each actuator is composed of a rolled thread ballscrew driven by a D.C. electric motor whose torque is transduced by measurement of armature current The power amplifiers which drive the D.C. motors are actively controlled using and IBM compatible computer via the appropriate interface electronics. The platfonn is instrumented with two accelerometers one at either end.
Em* =
KB*A*I (5)
Let us assume that the torque I is generated by
(6)
I=W.£,
where W is a (2x2) diagonal matrix representing the transfer functions of the actuators, and C is a (2x 1) controller output vector given by
(7) where £c is derived from the system error and £0 is the disturbance cancellation or reduction vector.
3. ACTIVE FORCE CONTROL Let £0 be derived from The equations of motion of the system are given by:
M.X = -Eo + A·E
(8)
(1)
where * denotes measured or estimated quantities
where M and X are the mass matrix and position (state) vector of the platfonn respectively, Eo is the disturbance vector on the platfonn, E is the actuators force vector and A is a (2x2) system matrix.
Substituting for I in equation (3) we get 2
T"
Assuming identical actuators, the force vector E is given by: E
Figure (3) shows a block diagram of the complete controller.
2 • • .. = KB· er -L) - J.KB2.AT" .X - KB .Q(K.K..Y..Y,y)
Provided W .G ~ identity matrix, and the measured and estimated value are accurate, then equation (9) becomes
(2) where Y is the base position (state) vector, J is the inertia of each actuator, KB is the effective gear ratio of each actuator ballscrew system, and Q is a disturbance vector.
2
T
"
(10)
Hence, in the ideal case, if £c = 0 then X = O. This may be very useful if a small drift of the mass M is allowed which could be the case when the dynamic platfonn system is used for some offshore operations where measurements of x or y, for a closed loop position feedback, may be difficult to obtain.
L
is the actuators unknown frictional torque vector, and I is the motors torque vector.
Equation (I) becomes (3)
242
ACIlVE POSITION CO:o.;'llWL OF DYNAMIC PLATFURMS
If we now let ~ be given by
other similar applications. The dynamic platform could in all of these cases be remotely controlled by a human operator. i.e. a visual feedback loop could be established by the human operator as shown by the block diagram of Figure 6.
(11)
where
(12)
It has been shown. using equation (10). that in the ideal case Active Force Control would overcome the disturbances without position feedback. However. in real systems a drift of the platform would be unavoidable if no position feedback is used. Here it is intended to use the human operator, visual feedback, to overcome the drift of the platform. This visual feedback corrects only for the drift resulting from non-ideal active open loop control.
g is the system error vector and Qc is a diagonal matrix.
Then assuming what W.G = identity matrix. the measured and estimated quantities are accurate and the actual
Expe.rimental tests were carried out. Without Active Force Control the platform had the same motion as the base and it was practically impossible to reduce the effect of the base motion disturbance with visual feedback control alone. The effect of the base motion on the platform was considerably reduced, as shown in Figure 6, when Active Force Control was introduced. Complete disturbance isolation was, however, not possible. This was attributed to the effect of the back ernf of the DC motors as discussed in 4.1 (Experimental Results) above. Additional instrumentation is being added to the experimental rig in order to improve the results.
4. RESULTS AND DISCUSSION 4.1 Simulation Results The simulation results in Figure 4 show the ideal response of the DPS. Here Active Force Control is used with position feedback. A proportional controller with a very low gain is used in the closed loop. . The disturbance input is a pure sinusoidal heave and pitch motions of the base at a frequency of 6 radlsec. Up untilt=lO seconds. the Active Force Control is not used and the heave x and pitch of the platform is clearly seen. After t=IO seconds the Active Force Control system is introduced and the resulting attenuation of the platform heave and pitch is clearly seen.
4.4 Feedforward of Base Disturbance
e
Another method of control is to use a feedforward loop to compensate for the base disturbance. This could be used when the force applied directly on the platform is small or constant, and when the unknown friction disturbances are small.
4.2 Experimental Results The experimental results in Figure 5 show the same trend as the simulation results but poorer results are obtained. This is attributed to the effect of the back ernf of the DC motors which was purposely omitted from the simulation tests. A current feedback loop was added to overcome/reduce such effect, however the gain on this loop was limited by the stability of the system. Work is continuing to attach tachogenerators to the motors to provide a signal to overcome the back ernf.
The amount of base disturbance transmitted to the platform depends on the acUIators' inertia and friction . The latter contains Coulombic and viscous friction. The effects of the inertia and viscous friction could be compensated for using a feedforward loop. Measurements of acceleration and velocity of the base, and estimates of the inertia and coefficient of viscous friction of both actuators would thus be required for this method. It must, however, be noted that this method, unlike the "Active Force Control" method described in 3 above, does not compensate for the unknown Coulombic friction, in the acUIators, which is complex and difficult to model accurately, especially in ballscrews. Coulombic friction is non-linear containing 'static' and •dynamic' components which require conditional
4.3 Practical Systerns
In real systems absolute vertical poslUon measurement may not always be feasible. For remote offshore locations when. for example. the DPS is used as a hclideck on a vessel. absolute position reference may not be possible. There are
243
HEWIT JR. BOUAZZA-MAROUF K.
calculations and whose coefficients are difficult to detennine and may in any case vary.
Now that it has been shown that the control strategy applied here could be successfuUy used for the DPS, it is planned to replace the electromechanical actuators by hydraulic ones in order to investigate a system more close to a real system for offshore applications.
ACU
5. REFERENCES 1. KV Johnson, "Theoretical Overload Factor
Effect of Sea State on Marine Cranes", Paper No. 2584, Eighth Annual Offshore Technology Conference, Houston, Texas, 1976.
_L------------==::J Fig. 1
2. J Strengehagen and S Gran, "Supply Boat Motion, Dynamic Response and Fatigue of Offshore Cranes", Paper No. 3795, 12th Annual Offshore Technology Conference, Houston, Texas, 5-8 May 1980. 3. JB Hunt and AJ McGill, "A Fluid Dynamic Vibration Absorber" Dynamic Vibration Isolation and Absorption, Conference, University of Southampton, September 1982, pp. 109-124. 4. D Vassalos and C Kuo, "Making Effective Use of Ship-Stabilisation Devices", 2nd International Conference on Stability of Ships and Ocean Vehicles, Stability '82, Tokyo, Japan, October 1982, pp. 347-363. 5. R Bhattacharyya, "Dynamics of Marine Vehicles", John Wiley and Sons, 1978. 6. JS Burdess and JR Hewit, "An Active Method for the Control of Mechanical Systems in the Presence of Unmeasurable Forcing", Mechanism and Machine Theory, Vo!. 21, No. 5, 1986, pp. 393-400.
Fig . .2
244
BASE
K. HEWJT JR. ROU A77A -MAR OUF
Act ive For ce Con trol
J ON
! o
10
20
)0
40
TIM E(s)
Fig . 5
BLOCK DIAGRAM OF FIG. 3
VISUAL FEEDBACK Fig . 6
Base dist urb anc e (y)
Plat form mot ion (x)
o
10
20
)0
Fig . 7
245
40 TIM E(s)
x
0.02 rad
ACT1VE POSnlON CONlROL OF DYNAMIC PLAIT{)RMS
x ACCELERA TlON
Fig~
--~- .~-----
(m)
Ac tive 0 . 008
f o rce
0. 006
Control ON
0 . 00 4 0 . 007 0 . 000 -0 . 007 -0 . 004 -0.006 -0.008 _0 . 010
8
4
0
Base disturbance
I
12
14
Base and Platform disturbances
..
~nlY
10
·1
\ I
I
a
i
0 . 030
I
(rad) 0 . 02'5 0.020
O. OIS 0 . 010
O. OOS
'(
0 . 000
_O . ooS _0 . 01()
_O . OIS _0.020 -0 . 02'5 -0.030
-0.035
0
2
10
6
TIME
12
14
(s)
Fig. 4
246
3
ACTIVE POSITION CONTROL OF DYNAMIC PLATFORMS K. BOUAZZA-MAROUF and J.R.
HEWIT
Loughborough University of Technology, Department of Mechanical Engineering Loughborough, Leicestershire, LE 11 3TU, United Kingdom
Abstract: The loading and unloading of offshore supply vessels pose severe problems in adverse weather conditions when the supply vessel may be heaving, pitching and rolling violently. This is currently overcome by relying on the crane operator's skill and weather windows which may be dangerous and costly. A dynamic platform system (DPS) is proposed here to solve the problem of offshore load transfers. A method of control based on the principle of invariance is used here on an experimental rig to investigate the control problem of disturbance isolation of the DPS. Good results have been obtained. Keywords: Invariance control; offshore load transfers; dynamic platform; disturbance isolation; active force control.
1. INTRODUCTION
[3] and many types of absorbers have been developed [3,4]. Out of the six degrees-offreedom of a stationary ship only roll, surge, sway and yaw have been successfully controlled. The two uncontrolled motions are heave and pitch. It is extremely difficult, if not impossible, to reduce a ship's heave motion [3]. Pitch is considerably dampened by the vessel's hull and large stabilizing moments would be required for any further increase in the damping [5]. The twodegrees-of-freedom dynamic platform proposed here could be used to compensate for these two motions which can be regarded as base motion disturbances to the dynamic platform system (DPS).
The safety and performance of certain operations offshore are severely limited by wave induced vessel motions, for example there is the problem of loading and unloading supply boats, by a crane on an oil production platform, in the face of wave disturbance. The lauer operations, especially when vital e~uipment is involved, must sometimes be performed in adverse weather conditions as it is not always possible to wait for calm weather. This can be difficult and even dangerous. Crane failure is a frequent occurrence and derating of cranes has been introduced [I]. Some of these failures are caused by extreme overloading of cranes [2] due to the relative velocity between hook and load. The impulsive force the crane experiences while snatching a load from a moving deck acts like a hammer blow on the crane. Here it might be useful to equip a supply boat with a deck which, despite the gross movements of the boat itself due to wave disturbances, maintained itself absolutely at rest so that loading and unloading operations might proceed easily and safely. Other applications of such a deck could be as an active landing platform for helicopters in adverse weather conditions.
The DPS consists of a platform and a base. TIle platform is supported on actuators which are actively controlled to isolate the platform from the motion of the base_ A schematic diagram of the DPS is shown in Figure I. Applications of the DPS of a different scale might be onshore. Some of these applications are active control of mobile robots subjected to base disturbances. active suspension control of road, off-road and rail vehicles, and active isolation of a helicopter cabin from rotor disturbances.
Overcoming the disruptive effeet of sea induced motions on ships has been of interest for may years
241
HEWIT J.R.. ROCA77A-MAROUF K.
A dynamic platfonn experimental rig has been designed to demonstrate the concept of the DPS and to assess the effectiveness of the control algorithms in a situation more close to the "real world". A novel type of active isolation, based on the well known principle of invariance [6], is investigated. Here we consider disturbances which are both force-type at the platfonn and displacement type at the base.
where Em is the overall unknown disturbance vector given by
The tenn J.K/.A.AT in equation (3) is the actuators inertia matrix referred to the platform Our objective here is to cancel the disturbance vector Em without direct measurements.
2. EXPERIMENTAL RIG An estimate of Em could be obtained from (3) as Figure 2 shows a photograph of the two degrees-offreedom experimental dynamic platfonn rig. The base of the DPS is supported and disturbed in the two degrees of freedom, vertical and angular motions, by a cam-actuation system. The platfonn is supported by two electromechanical actuators which are mounted on the base. Each actuator is composed of a rolled thread ballscrew driven by a D.C. electric motor whose torque is transduced by measurement of armature current The power amplifiers which drive the D.C. motors are actively controlled using and IBM compatible computer via the appropriate interface electronics. The platfonn is instrumented with two accelerometers one at either end.
Em* =
KB*A*I (5)
Let us assume that the torque I is generated by
(6)
I=W.£,
where W is a (2x2) diagonal matrix representing the transfer functions of the actuators, and C is a (2x 1) controller output vector given by
(7) where £c is derived from the system error and £0 is the disturbance cancellation or reduction vector.
3. ACTIVE FORCE CONTROL Let £0 be derived from The equations of motion of the system are given by:
M.X = -Eo + A·E
(8)
(1)
where * denotes measured or estimated quantities
where M and X are the mass matrix and position (state) vector of the platfonn respectively, Eo is the disturbance vector on the platfonn, E is the actuators force vector and A is a (2x2) system matrix.
Substituting for I in equation (3) we get 2
T"
Assuming identical actuators, the force vector E is given by: E
Figure (3) shows a block diagram of the complete controller.
2 • • .. = KB· er -L) - J.KB2.AT" .X - KB .Q(K.K..Y..Y,y)
Provided W .G ~ identity matrix, and the measured and estimated value are accurate, then equation (9) becomes
(2) where Y is the base position (state) vector, J is the inertia of each actuator, KB is the effective gear ratio of each actuator ballscrew system, and Q is a disturbance vector.
2
T
"
(10)
Hence, in the ideal case, if £c = 0 then X = O. This may be very useful if a small drift of the mass M is allowed which could be the case when the dynamic platfonn system is used for some offshore operations where measurements of x or y, for a closed loop position feedback, may be difficult to obtain.
L
is the actuators unknown frictional torque vector, and I is the motors torque vector.
Equation (I) becomes (3)
242
ACIlVE POSITION CO:o.;'llWL OF DYNAMIC PLATFURMS
If we now let ~ be given by
other similar applications. The dynamic platform could in all of these cases be remotely controlled by a human operator. i.e. a visual feedback loop could be established by the human operator as shown by the block diagram of Figure 6.
(11)
where
(12)
It has been shown. using equation (10). that in the ideal case Active Force Control would overcome the disturbances without position feedback. However. in real systems a drift of the platform would be unavoidable if no position feedback is used. Here it is intended to use the human operator, visual feedback, to overcome the drift of the platform. This visual feedback corrects only for the drift resulting from non-ideal active open loop control.
g is the system error vector and Qc is a diagonal matrix.
Then assuming what W.G = identity matrix. the measured and estimated quantities are accurate and the actual
Expe.rimental tests were carried out. Without Active Force Control the platform had the same motion as the base and it was practically impossible to reduce the effect of the base motion disturbance with visual feedback control alone. The effect of the base motion on the platform was considerably reduced, as shown in Figure 6, when Active Force Control was introduced. Complete disturbance isolation was, however, not possible. This was attributed to the effect of the back ernf of the DC motors as discussed in 4.1 (Experimental Results) above. Additional instrumentation is being added to the experimental rig in order to improve the results.
4. RESULTS AND DISCUSSION 4.1 Simulation Results The simulation results in Figure 4 show the ideal response of the DPS. Here Active Force Control is used with position feedback. A proportional controller with a very low gain is used in the closed loop. . The disturbance input is a pure sinusoidal heave and pitch motions of the base at a frequency of 6 radlsec. Up untilt=lO seconds. the Active Force Control is not used and the heave x and pitch of the platform is clearly seen. After t=IO seconds the Active Force Control system is introduced and the resulting attenuation of the platform heave and pitch is clearly seen.
4.4 Feedforward of Base Disturbance
e
Another method of control is to use a feedforward loop to compensate for the base disturbance. This could be used when the force applied directly on the platform is small or constant, and when the unknown friction disturbances are small.
4.2 Experimental Results The experimental results in Figure 5 show the same trend as the simulation results but poorer results are obtained. This is attributed to the effect of the back ernf of the DC motors which was purposely omitted from the simulation tests. A current feedback loop was added to overcome/reduce such effect, however the gain on this loop was limited by the stability of the system. Work is continuing to attach tachogenerators to the motors to provide a signal to overcome the back ernf.
The amount of base disturbance transmitted to the platform depends on the acUIators' inertia and friction . The latter contains Coulombic and viscous friction. The effects of the inertia and viscous friction could be compensated for using a feedforward loop. Measurements of acceleration and velocity of the base, and estimates of the inertia and coefficient of viscous friction of both actuators would thus be required for this method. It must, however, be noted that this method, unlike the "Active Force Control" method described in 3 above, does not compensate for the unknown Coulombic friction, in the acUIators, which is complex and difficult to model accurately, especially in ballscrews. Coulombic friction is non-linear containing 'static' and •dynamic' components which require conditional
4.3 Practical Systerns
In real systems absolute vertical poslUon measurement may not always be feasible. For remote offshore locations when. for example. the DPS is used as a hclideck on a vessel. absolute position reference may not be possible. There are
243
HEWIT JR. BOUAZZA-MAROUF K.
calculations and whose coefficients are difficult to detennine and may in any case vary.
Now that it has been shown that the control strategy applied here could be successfuUy used for the DPS, it is planned to replace the electromechanical actuators by hydraulic ones in order to investigate a system more close to a real system for offshore applications.
ACU
5. REFERENCES 1. KV Johnson, "Theoretical Overload Factor
Effect of Sea State on Marine Cranes", Paper No. 2584, Eighth Annual Offshore Technology Conference, Houston, Texas, 1976.
_L------------==::J Fig. 1
2. J Strengehagen and S Gran, "Supply Boat Motion, Dynamic Response and Fatigue of Offshore Cranes", Paper No. 3795, 12th Annual Offshore Technology Conference, Houston, Texas, 5-8 May 1980. 3. JB Hunt and AJ McGill, "A Fluid Dynamic Vibration Absorber" Dynamic Vibration Isolation and Absorption, Conference, University of Southampton, September 1982, pp. 109-124. 4. D Vassalos and C Kuo, "Making Effective Use of Ship-Stabilisation Devices", 2nd International Conference on Stability of Ships and Ocean Vehicles, Stability '82, Tokyo, Japan, October 1982, pp. 347-363. 5. R Bhattacharyya, "Dynamics of Marine Vehicles", John Wiley and Sons, 1978. 6. JS Burdess and JR Hewit, "An Active Method for the Control of Mechanical Systems in the Presence of Unmeasurable Forcing", Mechanism and Machine Theory, Vo!. 21, No. 5, 1986, pp. 393-400.
Fig . .2
244
BASE
K. HEWJT JR. ROU A77A -MAR OUF
Act ive For ce Con trol
J ON
! o
10
20
)0
40
TIM E(s)
Fig . 5
BLOCK DIAGRAM OF FIG. 3
VISUAL FEEDBACK Fig . 6
Base dist urb anc e (y)
Plat form mot ion (x)
o
10
20
)0
Fig . 7
245
40 TIM E(s)
x
0.02 rad
ACT1VE POSnlON CONlROL OF DYNAMIC PLAIT{)RMS
x ACCELERA TlON
Fig~
--~- .~-----
(m)
Ac tive 0 . 008
f o rce
0. 006
Control ON
0 . 00 4 0 . 007 0 . 000 -0 . 007 -0 . 004 -0.006 -0.008 _0 . 010
8
4
0
Base disturbance
I
12
14
Base and Platform disturbances
..
~nlY
10
·1
\ I
I
a
i
0 . 030
I
(rad) 0 . 02'5 0.020
O. OIS 0 . 010
O. OOS
'(
0 . 000
_O . ooS _0 . 01()
_O . OIS _0.020 -0 . 02'5 -0.030
-0.035
0
2
10
6
TIME
12
14
(s)
Fig. 4
246
3