CN107741744A - A kind of optimal bow of observation platform is to control method - Google Patents
A kind of optimal bow of observation platform is to control method Download PDFInfo
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- CN107741744A CN107741744A CN201711130259.8A CN201711130259A CN107741744A CN 107741744 A CN107741744 A CN 107741744A CN 201711130259 A CN201711130259 A CN 201711130259A CN 107741744 A CN107741744 A CN 107741744A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The present invention is to provide a kind of optimal bow of observation platform to control method.One：Input the desired locations [x of observation platformd yd]；Two：By the derivative of the positional information of observation platformAs the input of extended state observer, ocean current force direction β is judgedeAffiliated quadrant；Three：The ocean current force direction quadrant obtained according to step 2 carries out the selection in the center of circle；Four：Observation platform is controlled around selected center of circle pρWith the optimal bow of radius ρ motions to position, and to ensure center of circle p selected by the bow to face all the time of the observation platform in motion processρ.The optimal bow of the present invention can allow the dynamic positioning of marine observation platform using as far as possible few propeller to control method, observation platform is turned bow angle with minimum and be optimal bow to making control is simpler efficiently and to save the energy.
Description
Technical field
The present invention relates to a kind of control method of observation platform, specifically a kind of vertically and horizontally symmetrical sea
The control method of foreign observation platform.
Background technology
With the depth of ocean development and the expansion of range, the development of deep-sea observation technology is swift and violent, and observation platform should
Transport and give birth to, in some job tasks, observation platform needs spot hover it is necessary to use dynamic positioning technology.Dynamic positioning skill
Depending on the control strategy of art needs to refer to the specific features of specific observation platform, for some direction and propeller arrangement sides in length and breadth
For the full symmetric observation platform in face, optimal bow can be selected to then selecting propeller as few as possible to resist
The interference effect of ocean current, so it is easy to control and can reduce the consumption of the energy.Make observation platform arrival optimal simultaneously
Bow is during, it is also desirable to design certain control method, make its with minimum turn bow angle be optimal bow to.
Fossen for the optimal bow of dynamic positioning system to definition, and the summary of its developing stage, it is proposed that a kind of
Bow in the case of unknown disturbance is to adjust automatically.The main feature of this method is exactly that the measurement for not needing any environmental forces fills
Vessel operation can be made under optimal yawing angle by putting, and this is critically important for operation on the sea system, because I
The size and Orientation of environment force can not possibly accurately be calculated.But can using extended state observer (ESO) come
The direction quadrant of unknown current is obtained, then further according to the suitable circle of geometrically symmetric feature selection of specific observation platform
The heart, it can be thus set to turn bow angle minimum and be optimal bow to having saved time and the energy.
The content of the invention
It is an object of the invention to provide one kind can make control simpler, and oceanographic observation that is efficient and saving the energy is put down
The optimal bow of platform is to control method.
The object of the present invention is achieved like this：
Step 1：Input the desired locations [x of observation platformd yd]；
Step 2：By the derivative of the positional information of observation platformAs extended state observer
Input, judges ocean current force direction βeAffiliated quadrant；
Step 3：The ocean current force direction quadrant obtained according to step 2 carries out the selection in the center of circle；
Step 4：Observation platform is controlled around selected center of circle pρWith the optimal bow of radius ρ motions to position, and to ensure
The center of circle p selected by the bow of observation platform to face all the time in motion processρ。
The present invention can also include：
1st, it is described carry out the center of circle selection specifically chosen foundation for：
(1) when the positive car of propeller used in observation platform is identical with reversing output, as ocean current force direction βe∈[-90
The optimal center of circle is taken as p when 90]ρ=(ρ, 0), as ocean current force direction βe∈ other when the optimal center of circle be taken as pρ=(- ρ, 0)；
When observation platform reaches poised state, ocean current interference power is taken as under satellite coordinate system:
W=[1 0 0]TFe=Φ1Fe,βe∈[-90 90]
W=[- 10 0]TFe=Φ2Fe,βe∈ other；
Wherein w is ocean current interference power, Φ1For direction vector, Φ2For direction vector, FeOcean current power size.
(2) when the positive car of propeller used in observation platform is different with reversing output, as ocean current force direction βe∈[-90
The optimal center of circle is taken as p when 0]ρ=(0, ρ), as ocean current force direction βe∈ other when the optimal center of circle be taken as pρ=(ρ, 0)；
When observation platform reaches poised state, ocean current interference power is taken as under satellite coordinate system:
W=[0 1 0]TFe=Φ3Fe,βe∈[-90 0]
W=[1 0 0]TFe=Φ1Fe,βe∈ other.
Wherein w is ocean current interference power, Φ1For direction vector, Φ3For direction vector, FeOcean current power size.
2nd, the extended state observer is the extended state observer of discrete form, is expressed as：
In formula, h is integration step, β01, β02And β03For gain coefficient, δ is adjustable parameter, and b is compensating factor, z3(t) it is
The disturbance of estimation, fal (e, α, δ) are that power function is expressed as following form：
3rd, the judgement ocean current force direction βeThe specific rules of affiliated quadrant are：
4th, step 4 specifically includes：The control targe is taken to be：Pd=[xd yd ψd]T=[0 0 0]T, error is taken as：E=P-
Pd；Wherein PdFor desired locations, P is observation platform physical location, and e is observation platform physical location and desired locations
Deviation.Because only considering horizontal plane, therefore only consider it is expected lengthwise position xd, it is expected lateral attitude ydWith it is expected bow to position ψd。
Structure decoupling S faces controller, longitudinally, laterally with respectively establish a S faces controller, S faces on three directions of yawing
Controller represents as follows：
F=Ku
Wherein, kpAnd kdFor control parameter, e andDeviation and deviation variation rate are represented for control input, u exports for control, f
It is the power or torque that each free degree needs, K is the maximum, force or torque that propulsion system can provide.
The invention provides a kind of bow of vertically and horizontally symmetrical observation platform to control method.Observation platform is in operation
When sometimes for spot hover, under the ocean current environment of complexity, realize that spot hover needs to use dynamic positioning technology, for
It is of the present invention that holosymmetric observation platform is vertically and horizontally arranged with propeller, can be with when carrying out dynamic positioning
Select optimal bow always to resist the interference effect of ocean current, while turn bow be optimal bow during and can select minimum
Angle.
The characteristics of technical scheme, is embodied in：
1st, whole control process is divided into two stages：
(1) the location observation stage：Establish comprising extended state observer (Extended State Observer, ESO)
(target is taken as observation platform dynamic positioning system：[xd yd ψd]T=[0 0 0]T), the disturbance information exported according to ESO (is only joined
Examine its direction) judge the affiliated quadrant of current direction.
(2) optimal bow to control the stage：The suitable center of circle is selected according to the current direction quadrant of acquisition, behind the selected center of circle
According to the optimal bow that FOSSEN is established to control strategy, S faces controller is introduced, observation platform bow is established to control system, makes to put down
Platform with minimum turn bow angle reach optimal bow to.
2nd, the location observation stage, primarily to judging the quadrant of ocean current disturbance, there is following feature：
" extended state observer " (Extended State Observer, ESO) is introduced into controller design, is used for
Flow disturbance is gone back in observation.The extended state observer of discrete form can be expressed as following form：
In formula, z1(k)、z2(k)、z3(k) it is respectively to be observed the estimated state amount of system, the state velocity of system and add
Speed, y (k) are the quantity of state of system, and e is the quantity of state deviation of system, and h is integration step, β01, β02And β03For gain coefficient,
α01、α02It is adjustable parameter with δ, b is compensating factor, and wherein fal (e, α, δ) is power function, can be expressed as following form：
Ocean current force direction quadrant is carried out according to ESO output results to judge, specific rules are as follows：
3rd, after ESO judges the direction quadrant of unknown disturbance ocean current power, obtained according to the described location observation stage
Ocean current force direction quadrant judged result carries out the selection in the optimal effect center of circle, then moves to optimal bow to position around the selected center of circle
Put, (the optimal center of circle refer to making observation platform to turn bow angle with minimum be optimal bow to the center of circle to be moved in a circle).
Carry out being divided into two kinds of situations when the selection of the optimal center of circle, that is, be divided into the marine positive car of observation platform propeller and reversing output it is identical with
Different two kinds of situations：
(1) when the positive car of propeller used in the observation platform is identical with reversing output, then have：
Now, as ocean current force direction βeThe optimal center of circle is taken as p during ∈ [- 90 90]ρ=(ρ, 0), as ocean current force direction βe∈
Other when the optimal center of circle be taken as pρ=(- ρ, 0).
So when observation platform reaches poised state, ocean current interference power can be taken as under satellite coordinate system:
W=[1 0 0]TFe=Φ1Fe,βe∈[-90 90]
W=[- 10 0]TFe=Φ2Fe,βe∈ other
Wherein w is ocean current interference power, Φ1For direction vector, Φ2For direction vector, FeOcean current power size.
(2) when the positive car of propeller used in the observation platform is different with reversing output, then have：
Now, as ocean current force direction βeThe optimal center of circle is taken as p during ∈ [- 90 0]ρ=(0, ρ), as ocean current force direction βe∈ its
He when the optimal center of circle be taken as pρ=(ρ, 0).
So when observation platform reaches poised state, ocean current interference power can be taken as under satellite coordinate system:
W=[0 1 0]TFe=Φ3Fe,βe∈[-90 0]
W=[1 0 0]TFe=Φ1Fe,βe∈ other
Wherein w is ocean current interference power, Φ1For direction vector, Φ3For direction vector, FeOcean current power size.
4th, it is necessary to which controlling described observation platform to be moved to around the selected center of circle most has after have selected the optimal center of circle
Bow is to position, while, it is necessary to keep the bow of platform as follows to the face center of circle all the time, particular content during motion：
It is P to take control targed=[xd yd ψd]T=[0 0 0]T, error is taken as：E=P-Pd；Wherein PdFor desired locations,
P is observation platform physical location, and e is observation platform physical location and the deviation of desired locations.Because only consider water
Plane, therefore only consider it is expected lengthwise position xd, it is expected lateral attitude ydWith it is expected bow to position ψd。
Because S controller engineering practicabilities are stronger, parameter adjustment is more convenient.Structure decoupling S faces controller, longitudinal direction,
A S faces controller respectively laterally and on three directions of yawing is established, S faces controller can represent as follows：
F=Ku
Wherein, kpAnd kdFor control parameter, e andFor control input, deviation and deviation variation rate are represented respectively, and u is control
Output, f are the power or torque that each free degree needs, and K is the maximum, force or torque that propulsion system can provide.
The present invention mainly designs a kind of dynamic positioning system for being applied to the full symmetric observation platform in direction in length and breadth
For optimal bow in system to control method, it is dynamic that this method can be such that the observation platform is issued in unknown current disturbance situation
The optimal bow that power alignment system defines being optimal bow during to while selecting the suitable center of circle it is turned bow angle
Minimum, reach and save the energy and efficient purpose.
Brief description of the drawings
Fig. 1, observation platform are by ocean current interference power schematic diagram.
Fig. 2, controller architecture figure.
Fig. 3 a- Fig. 3 b, poised state ocean current interference the power schematic diagram under satellite coordinate system.
Fig. 4 a- Fig. 4 b, the positive car of propeller and reversing export the identical bow that is optimal and turn bow angle to minimum.
Fig. 5 a- Fig. 5 b, the positive car of propeller and reversing output difference are optimal bow and turn bow angle to minimum.
Fig. 6, optimal bow are to control schematic diagram.
Fig. 7, the optimal bow of observation platform are to control method flow chart.
Embodiment
Illustrate below and the present invention is described in more detail.
1st, described optimal bow is introduced to definition with reference first to accompanying drawing 1：
(1) assume that ocean current is permanent irrotationality, then it is believed that the perturbed force under ocean current interference is：
W=[wu,wv,wr]T=[wu,wv,0]T
(2) steady motion of a fluid perturbed force FcActive force in different flow to observation platform under satellite coordinate system：
In formula：βeAngle of the flow disturbance under fixed coordinate system is represented, ψ represents current bow to angle.
Then its total power can be expressed as：
Fw=Fc|cos(βe-ψ)|+Fc|sin(βe-ψ)|
From above formula, work as βeFlow disturbance is minimum to the total force of platform during=ψ.Then for observation platform, ring
The optimal bow in border is to the direction of as ocean current perturbed force.
2nd, control strategy is designed, specific controller architecture is divided into two ranks as shown in Figure 2, by whole control process
Section：
(1) the location observation stage：Establish comprising extended state observer (Extended State Observer, ESO)
(target is taken as observation platform dynamic positioning system：[xd yd ψd]T=[0 0 0]T), the disturbance information exported according to ESO (is only joined
Examine its direction) judge the affiliated quadrant of current direction.
(2) optimal bow to control the stage：The suitable center of circle is selected according to the current direction quadrant of acquisition, behind the selected center of circle
According to the optimal bow that FOSSEN is established to control strategy, S faces controller is introduced, observation platform bow is established to control system, makes to put down
Platform with minimum turn bow angle reach optimal bow to.
3rd, the location observation stage, primarily to judging the quadrant of ocean current disturbance, specific features are as follows：
" extended state observer " (Extended State Observer, ESO) is introduced into controller design, is used for
Flow disturbance is gone back in observation.The extended state observer of discrete form can be expressed as following form：
In formula, z1(k)、z2(k)、z3(k) it is respectively to be observed the estimated state amount of system, the state velocity of system and add
Speed, y (k) are the quantity of state of system, and e is the quantity of state deviation of system, and h is integration step, β01, β02And β03For gain coefficient,
α01、α02It is adjustable parameter with δ, b is compensating factor, and wherein fal (e, α, δ) is power function, can be expressed as following form：
Ocean current force direction quadrant is carried out according to ESO output results to judge, specific rules are as follows：
4th, for current direction quadrant judge after the completion of, it is necessary to select the optimal center of circle, make the observation platform around
It is as follows to position, the principle in the specifically chosen optimal center of circle that the selected center of circle reaches optimal bow：
It is divided into two kinds of situations when carrying out optimal center of circle selection, that is, is divided into the positive car of marine observation platform propeller and reversing
Export identical and different two kinds of situations：
(1) when the positive car of propeller used in the observation platform is identical with reversing output, then have：
Now, as ocean current force direction βeThe optimal center of circle is taken as p during ∈ [- 90 90]ρ=(ρ, 0), as ocean current force direction βe∈
Other when the optimal center of circle be taken as pρ=(- ρ, 0).
Propeller arrangement is not considered (i.e. under the interference of different ocean current power as accompanying drawing 4a- Fig. 4 b are shown：Only consider center of circle A)
With consider that observation platform moves to optimal bow to being turned over most during propeller arrangement (while considering center of circle A and center of circle B)
It is small to turn bow angle (original state platform bow to ψ=0).Work as β as can be seen from Fig.eThe center of circle is taken as p during ∈ [- 9090]ρ=(- ρ,
0) can significantly smaller observation platform reach optimal bow to turn bow angle so as to improve efficiency.
So when observation platform reaches poised state, ocean current interference power can be taken as under satellite coordinate system:
W=[1 0 0]TFe=Φ1Fe,βe∈[-90 90]
W=[- 10 0]TFe=Φ2Fe,βe∈ other
Wherein w is ocean current interference power, Φ1For direction vector, Φ2For direction vector, FeOcean current power size.
(2) when the positive car of propeller used in the observation platform is different with reversing output, then have：
Now, as ocean current force direction βeThe optimal center of circle is taken as p during ∈ [- 90 0]ρ=(0, ρ), as ocean current force direction βe∈ its
He when the optimal center of circle be taken as pρ=(ρ, 0).
Propeller arrangement is not considered (i.e. under the interference of different ocean current power as accompanying drawing 5a- Fig. 5 b are shown：Only consider center of circle A)
With consider that observation platform moves to optimal bow to being turned over most during propeller arrangement (while considering center of circle A and center of circle C)
It is small to turn bow angle (original state platform bow to ψ=0).Work as β as can be seen from Fig.eThe center of circle is taken as p during ∈ [- 900]ρ=(0, ρ)
Can significantly smaller observation platform reach optimal bow to turn bow angle so as to improve efficiency.
So when observation platform reaches poised state, ocean current interference power can be taken as under satellite coordinate system:
W=[0 1 0]TFe=Φ3Fe,βe∈[-90 0]
W=[1 0 0]TFe=Φ1Fe,βe∈ other
Wherein w is ocean current interference power, Φ1For direction vector, Φ3For direction vector, FeOcean current power size.
5th, after have selected the optimal center of circle, just observation platform is controlled to move to optimal bow to position around the optimal center of circle,
And, it is necessary to keep the bow of platform as follows to the face center of circle all the time, specific features during motion：
The control targe is taken to be：Pd=[xd yd ψd]T=[0 0 0]T, error is taken as：E=P-Pd；Wherein PdIt is expected position
Put, P is observation platform physical location, and e is observation platform physical location and the deviation of desired locations.Because only consider
Horizontal plane, therefore only consider it is expected lengthwise position xd, it is expected lateral attitude ydWith it is expected bow to position ψd。
Because S controller engineering practicabilities are stronger, parameter adjustment is more convenient.Structure decoupling S faces controller, longitudinal direction,
A S faces controller respectively laterally and on three directions of yawing is established, S faces controller can represent as follows：
F=Ku
Wherein, kpAnd kdFor control parameter, e andFor control input, deviation and deviation variation rate are represented respectively, and u is control
Output, f are the power or torque that each free degree needs, and K is the maximum, force or torque that propulsion system can provide.
6th, a kind of optimal bow of described observation platform can refer to claims to the idiographic flow of control method
Accompanying drawing 7, specific features are as follows：
Step 1：Provide the desired locations [x of observation platformd yd]；
Step 2：By the derivative of the positional information of observation platformAs extended state observer
Input, judges ocean current force direction βeAffiliated quadrant；
Step 3：The selection in the center of circle is carried out according to above-mentioned ocean current force direction quadrant, specific selection gist is as follows：
(1) when the positive car of propeller used in the observation platform is identical with reversing output, as ocean current force direction βe∈
The optimal center of circle is taken as p when [- 90 90]ρ=(ρ, 0), as ocean current force direction βe∈ other when the optimal center of circle be taken as pρ=(- ρ, 0).
(2) when the positive car of propeller used in the observation platform is different with reversing output, as ocean current force direction βe∈
The optimal center of circle is taken as p when [- 90 0]ρ=(0, ρ), as ocean current force direction βe∈ other when the optimal center of circle be taken as pρ=(ρ, 0).
Step 4：The observation platform is controlled around selected center of circle pρWith the optimal bow of radius ρ motions to position, and will
Ensure center of circle p selected by the bow to face all the time of the observation platform in motion processρ。
The present invention mainly proposes a kind of environment in the case where considering revolving body observation platform propeller deployment scenarios most
Excellent bow is to control method, and the realization of optimal location can refer to Fossen correlation technique.
Claims (5)
1. a kind of optimal bow of observation platform is to control method, it is characterized in that：
Step 1：Input the desired locations [x of observation platformd yd]；
Step 2：By the derivative of the positional information of observation platformAs the input of extended state observer,
Judge ocean current force direction βeAffiliated quadrant；
Step 3：The ocean current force direction quadrant obtained according to step 2 carries out the selection in the center of circle；
Step 4：Observation platform is controlled around selected center of circle pρWith the optimal bow of radius ρ motions to position, and to ensure transporting
Center of circle p selected by the bow to face all the time of observation platform during dynamicρ。
2. the optimal bow of observation platform according to claim 1 is to control method, it is characterized in that the carry out center of circle
Selection specifically chosen foundation for：
(1) when the positive car of propeller used in observation platform is identical with reversing output, as ocean current force direction βeDuring ∈ [- 90 90]
The optimal center of circle is taken as pρ=(ρ, 0), as ocean current force direction βe∈ other when the optimal center of circle be taken as pρ=(- ρ, 0)；
When observation platform reaches poised state, ocean current interference power is taken as under satellite coordinate system:
W=[1 0 0]TFe=Φ1Fe,βe∈[-90 90]
W=[- 10 0]TFe=Φ2Fe,βe∈ other；
Wherein w is ocean current interference power, Φ1For direction vector, Φ2For direction vector, FeOcean current power size；
(2) when the positive car of propeller used in observation platform is different with reversing output, as ocean current force direction βeDuring ∈ [- 90 0]
The optimal center of circle is taken as pρ=(0, ρ), as ocean current force direction βe∈ other when the optimal center of circle be taken as pρ=(ρ, 0)；
When observation platform reaches poised state, ocean current interference power is taken as under satellite coordinate system:
W=[0 1 0]TFe=Φ3Fe,βe∈[-90 0]
W=[1 0 0]TFe=Φ1Fe,βe∈ other.
Wherein w is ocean current interference power, Φ1For direction vector, Φ3For direction vector, FeOcean current power size.
3. the optimal bow of observation platform according to claim 2 is to control method, it is characterized in that the expansion state
Observer is the extended state observer of discrete form, is expressed as：
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In formula, z1(k)、z2(k)、z3(k) estimated state amount, the state velocity and acceleration of system of system are respectively observed,
Y (k) is the quantity of state of system, and e is the quantity of state deviation of system, and h is integration step, β01, β02And β03For gain coefficient, α01、
α02It is adjustable parameter with δ, b is compensating factor, and fal (e, α, δ) is that power function is expressed as following form：
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<mn>1</mn>
<mo>-</mo>
<mi>&alpha;</mi>
</mrow>
</msup>
</mfrac>
<mo>,</mo>
<mo>|</mo>
<mi>e</mi>
<mo>|</mo>
<mo>&le;</mo>
<mi>&delta;</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
4. the optimal bow of observation platform according to claim 3 is to control method, it is characterized in that the judgement ocean current
Force direction βeThe specific rules of affiliated quadrant are：
<mrow>
<mi>k</mi>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>w</mi>
<mi>u</mi>
</msub>
<mo>></mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>w</mi>
<mi>v</mi>
</msub>
<mo>></mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>w</mi>
<mi>u</mi>
</msub>
<mo><</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>w</mi>
<mi>v</mi>
</msub>
<mo>></mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>w</mi>
<mi>u</mi>
</msub>
<mo><</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>w</mi>
<mi>v</mi>
</msub>
<mo><</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>w</mi>
<mi>u</mi>
</msub>
<mo>></mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>w</mi>
<mi>v</mi>
</msub>
<mo><</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
5. the optimal bow of observation platform according to claim 4 is to control method, it is characterized in that step 4 is specifically wrapped
Include：The control targe is taken to be：Pd=[xd yd ψd]T=[0 0 0]T, error is taken as：E=P-Pd；Wherein PdFor desired locations, P is
Observation platform physical location, e are observation platform physical location and the deviation of desired locations；Because only consider horizontal
Face, therefore only consider it is expected lengthwise position xd, it is expected lateral attitude ydWith it is expected bow to position ψd；
Structure decoupling S faces controller, longitudinally, laterally with a S faces controller, the control of S faces are respectively established on three directions of yawing
Device represents as follows：
<mrow>
<mi>u</mi>
<mo>=</mo>
<mn>2</mn>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>exp</mi>
<mo>(</mo>
<mrow>
<msub>
<mi>k</mi>
<mi>p</mi>
</msub>
<mi>e</mi>
<mo>+</mo>
<msub>
<mi>k</mi>
<mi>d</mi>
</msub>
<mover>
<mi>e</mi>
<mo>&CenterDot;</mo>
</mover>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
F=Ku
Wherein, kpAnd kdFor control parameter,For deviation variation rate, u exports for control, and f is the power or power that each free degree needs
Square, K are the maximum, force or torque that propulsion system can provide.
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