CN107255919A - A kind of trimaran pitching stabilization decoupling controller and design method - Google Patents

A kind of trimaran pitching stabilization decoupling controller and design method Download PDF

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Publication number
CN107255919A
CN107255919A CN201710443219.2A CN201710443219A CN107255919A CN 107255919 A CN107255919 A CN 107255919A CN 201710443219 A CN201710443219 A CN 201710443219A CN 107255919 A CN107255919 A CN 107255919A
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trimaran
pitching
decoupling
mrow
control device
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朱齐丹
刘娜
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Harbin Engineering University
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Harbin Engineering University
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    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00Automatic controllers
    • G05B11/01Automatic controllers electric
    • G05B11/36Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.

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  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a kind of trimaran pitching stabilization decoupling controller and design method, belong to ship control technical field.Trimaran pitching stabilization decoupling controller includes trimaran, the first PD control device, the second PD control device, decoupling compensator, the first amplitude limit link, the second amplitude limit link, heave measurement module and pitching measurement module.To subtract the heave and pitching influence of shaking the floating body T-shaped wing and wave suppression plate to trimaran, close loop negative feedback control is carried out to system.The T-shaped wing and wave suppression plate point of theory exported according to decoupling controller controls the lift and lifting moment of the T-shaped wing and wave suppression plate, offsets the wave force and wave torque of wave, so as to reduce heave and pitching.The present invention is directed to trimaran pitching stabilization uneoupled control problem, a kind of decoupling method based on feedforward compensation is proposed, the T-shaped wing is realized and wave suppression plate two subtracts the decoupling for shaking floating body, improve its performance in respective action scope, avoid interfering control effect, be optimal anti-rolling effect.

Description

A kind of trimaran pitching stabilization decoupling controller and design method
Technical field
The invention belongs to ship control technical field, and in particular to a kind of trimaran pitching stabilization decoupling controller and design side Method.
Background technology
With the continuous development of scientific technology, and requirement of the every country to "Oceanic" strategy plan, high-performance ship Development is increasingly paid close attention to by people.Trimaran has excellent characteristic, and it has larger inner space and floor space, The reinforcing that bigger space carries out inner facility can be provided for operating personnel, advanced electronic equipment etc. is loaded.Because its is right Claim structure, with more preferable transverse stability, and with good seakeeping characteristics, the area of ship can be increased and ship is not influenceed Rapidity, so the research and development of trimaran also enjoys people to pay close attention to.
Its most of the time is all run at high speeds for high speed multi-hull ship, acutely longitudinal during navigation Athletic meeting is that navigation brings a series of problems, and the excessive lengthwise movement of amplitude can cause ship's staff to produce seasick reaction, reduction The comfort level of ship;Frequently lengthwise movement can also cause instrument and equipment precise decreasing on ship, shipping of green water, etc. it is serious after Really.To solve the longitudinally unstable problem of multi-hull ship, scientific research personnel begins attempt to shake annex mode by installing additional to subtract for hull, comes The lengthwise movement of ship is limited, and achieves certain effect.Subtract that to shake annex be a kind of attachment device outside the hull, relatively The small volume for ship, but if rationally distributed, favourable wave-making interaction can be produced by subtracting to shake between annex and hull, So as to improve the navigation posture of ship.
Conventional mode is to install additional to subtract on trimaran to shake the floating body T-shaped wing and wave suppression plate at present, and the T-shaped wing and wave suppression plate can roots According to the different lift of the difference offer of movement angle and torque, for offsetting influence of the wave to ship, so as to reduce the liter of hull Heavy and pitching.But what the pitching stabilization decoupling controller of current trimaran was used is all single controller, and single control Device processed can not reduce heave and the pitching of trimaran simultaneously, it is impossible to which single change is realized in heave or pitching to trimaran The signal of the control of amount, heave or pitching can produce cross influence when passing through controller to other side.
Trimaran realizes that the thought of uneoupled control is the design by decoupling compensator, makes decoupling compensator and controlled device The transfer function matrix of the generalized ensemble of composition is diagonal matrix, so as to one is turned to by the multi-variable system of coupling influence multiple Non-coupling single-variable system.But Compensating Matrices depend critically upon the accurate mathematical modeling of controlled device in Decoupling design method, and Controlled process is typically time-varying and nonlinear, therefore a linear, permanent decoupling compensation network occurs in controlled process When operating point changes, due to without adaptability, it is difficult to ensure that Control platform, even results in system unstable.
Document Fast Ships Models for Sea keeping Improvement Studies Using Flaps Describe a kind of method of uneoupled control in and T-foil, but weak point be can not be full decoupled by input/output variable, Therefore it is urgently to solve at present to find a kind of trimaran pitching stabilization decoupling mode that multivariable can be converted into unitary variant control Certainly the problem of.
Conventional trimaran pitching stabilization decoupling controller is broadly divided into two large divisions at present, and Part I is controller, the Two parts are decoupling compensators;Controller typically uses PID controller, but this controller can amplify noise link, Er Qiejie Structure is relatively complicated;Decoupling compensator is mainly used in the coupling between deactivation system variable, in research trimaran pitching stabilization decoupling control During method processed, preferable decoupling effect can be just reached with traditional decoupling method, and it is simple in construction, therefore typically all select Traditional decoupling method.So find it is a kind of it is simple in construction, noise can be reduced and can be good fit with conventional decoupling method The problem of controller needs to solve for another.
The content of the invention
It is an object of the invention to provide a kind of coupling that can eliminate the T-shaped wing and wave suppression plate to heave and pitching, and Realize the trimaran pitching stabilization decoupling controller and design method of unitary variant control.
The object of the present invention is achieved like this:
A kind of trimaran pitching stabilization decoupling controller, including trimaran, the first PD control device, the second PD control device, decoupling Compensator, the first amplitude limit link, the second amplitude limit link, heave measurement module and pitching measurement module;First PD control device and Two PD control devices are connected with the first amplitude limit link, the second amplitude limit link respectively by decoupling compensator, the first amplitude limit link with Second amplitude limit link is directly installed on trimaran, and the first amplitude limit link is connected by trimaran with heave measurement module, is heaved Measurement module is connected with the first PD control device again, and the second amplitude limit link is connected by trimaran with pitching measurement module, and pitching is surveyed Amount module is connected with the second PD control device again.
It is preferred that, described trimaran includes the T-shaped wing and wave suppression plate, and the T-shaped wing is loaded on stem, and wave suppression plate is loaded on ship stern.
A kind of trimaran pitching stabilization Decoupling Controller Design method, concrete implementation step includes:
(1) input heave amount gives 0m, and pitching amount is given 0 °;
(2) the heave amount of trimaran is determined by heaving measurement module, the vertical of trimaran is determined by pitching measurement module The amount of shaking;
(3) the heave amount of measure is compared with set-point respectively with pitching amount, difference is sent to respectively as feedback signal First PD control device and the second PD control device are further handled;
(4) first PD control devices, the second PD control device are sent to decoupling using the signal after processing as input variable respectively Compensator, influence of the decoupling compensator by wave suppression plate and the T-shaped wing to heave and pitching is decoupled, and output signal is respectively pressure wave The theory movement angle of plate and the theory movement angle of the T-shaped wing;
(5) the theory movement angle of the theory movement angle of wave suppression plate and the T-shaped wing is sent respectively to by decoupling compensator One amplitude limit link is with the second amplitude limit link as input signal, and the first amplitude limit link is with the second amplitude limit link respectively on trimaran The angle of the wave suppression plate of installation and the T-shaped wing is limited;
(6) first amplitude limit links input the actual motion angle of obtained wave suppression plate and the T-shaped wing with the second amplitude limit link Into trimaran, lift and lifting moment are provided for trimaran;
(7) repeat step (2) arrives step (6), realizes the closed-loop control to the wave suppression plate and the T-shaped wing of trimaran.
It is preferred that, the control of the first PD control device and the second PD control device is adjusted in described step (3) using trial and error procedure Parameter.
It is preferred that, the decoupling compensator described in step (4) uses the decoupling mode of Relative increasing rate, in decoupling mode Middle addition decoupling item, eliminates the T-shaped wing with wave suppression plate to trimaran heave and the coupling of pitching.
It is preferred that, the embodiment of the decoupling compensator described in step (4) is as follows:
(4.1) transmission function is added into decoupling compensator;
(4.2) influence of the heave movement to the second PD control device is eliminated, shadow of the pitching to the first PD control device is eliminated Ring;
(4.3) the first PD control device is made only to correspond to the heave movement of trimaran by the output signal of decoupling compensator, the Two PD control devices only correspond to the pitching of trimaran by the output signal of decoupling compensator.
It is preferred that, the first PD control device and the second PD control device described in step (4.2) eliminate pitching and heave respectively The formula that motion influence is used is as follows:
Wherein, KP1For the first PD control device GC1Gain, KP2For the second PD control device GC2Gain, TD1Controlled for the first PD Device G processedC1Time constant, TD2For the second PD control device GC2Time constant.
The beneficial effects of the present invention are:
The present invention is using two PD control devices and decoupling compensator to having installed the T-shaped wing additional and wave suppression plate two subtracts and shakes floating body Trimaran carries out Feed-forward Compensation Decoupling Control, realizes the T-shaped wing and wave suppression plate two subtracts the decoupling for shaking floating body, improve two and subtract Shake performance of the floating body in respective action scope, it is to avoid interfere control effect, be optimal anti-rolling effect;
The present invention is applied to analyze trimaran pitching stabilization situation under complicated sea situation, can be widely applied to subtract ship Among the control of pitching, decoupling controller can realize the Comprehensive Control to heave and pitching;
A kind of trimaran pitching stabilization decoupling controller disclosed in this invention and design method, control method are simple, structure It is easily achieved, can will subtracts and shake floating body and heave and pitching carries out full decoupled, realize the control of single channel, reach very Good uneoupled control effect.
Brief description of the drawings
Fig. 1 is trimaran pitching stabilization decoupling controller theory of constitution block diagram in the present invention;
Fig. 2 is the closed loop controlling structure exploded view of decoupling controller in the present invention.
Embodiment
The present invention is described further below in conjunction with the accompanying drawings.
Embodiment 1
With reference to Fig. 1, the invention discloses a kind of trimaran pitching stabilization decoupling controller, including trimaran, the first PD control Device, the second PD control device, decoupling compensator, the first amplitude limit link, the second amplitude limit link, heave measurement module and pitching measurement mould Block;First PD control device and the second PD control device by decoupling compensator respectively with the first amplitude limit link, the second amplitude limit link phase Connection, the first amplitude limit link is directly installed on trimaran with the second amplitude limit link, and the first amplitude limit link is by trimaran with rising Heavy measurement module connection, heave measurement module is connected with the first PD control device again, and the second amplitude limit link passes through trimaran and pitching Measurement module is connected, and pitching measurement module is connected with the second PD control device again, so as to realize the closed-loop control of compensated decoupling.
Wherein, trimaran has installed the T-shaped wing additional and wave suppression plate two subtracts and shakes floating body, using two PD control device GC1And GC2With And decoupling compensator carries out Feed-forward Compensation Decoupling Control to it.
The invention discloses a kind of trimaran pitching stabilization Decoupling Controller Design method, its concrete implementation step bag simultaneously Include:
(1) input heave amount gives 0m, and pitching amount is given 0 °;
(2) the heave amount of trimaran is determined by heaving measurement module, the vertical of trimaran is determined by pitching measurement module The amount of shaking;
(3) the heave amount of measure is compared with set-point respectively with pitching amount, difference is sent to respectively as feedback signal First PD control device and the second PD control device are further handled;
(4) first PD control devices, the second PD control device are sent to decoupling using the signal after processing as input variable respectively Compensator, influence of the decoupling compensator by wave suppression plate and the T-shaped wing to heave and pitching is decoupled, and output signal is respectively pressure wave The theory movement angle of plate and the theory movement angle of the T-shaped wing;
(5) the theory movement angle of the theory movement angle of wave suppression plate and the T-shaped wing is sent respectively to by decoupling compensator One amplitude limit link is with the second amplitude limit link as input signal, and the movement angle of wave suppression plate is limited in 0 ° extremely by the first amplitude limit link Between 15 °, the movement angle of the T-shaped wing is limited between -15 ° to 15 ° by the second amplitude limit link;
(6) first amplitude limit links input the actual motion angle of obtained wave suppression plate and the T-shaped wing with the second amplitude limit link Into trimaran, lift and lifting moment are provided for trimaran;
(7) repeat step (2) arrives step (6), realizes the closed-loop control to the wave suppression plate and the T-shaped wing of trimaran.
The control parameter of the first PD control device and the second PD control device is adjusted in described step (3) using trial and error procedure.
Decoupling compensator described in step (4) uses the decoupling mode of Relative increasing rate, is added in decoupling mode Item is decoupled, the T-shaped wing is eliminated with wave suppression plate to trimaran heave and the coupling of pitching.
The embodiment of decoupling compensator described in step (4) is as follows:
(4.1) transmission function is added into decoupling compensator;
(4.2) influence of the heave movement to the second PD control device is eliminated, shadow of the pitching to the first PD control device is eliminated Ring;
(4.3) the first PD control device is made only to correspond to the heave movement of trimaran by the output signal of decoupling compensator, the Two PD control devices only correspond to the pitching of trimaran by the output signal of decoupling compensator.
Wherein, the first PD control device and the second PD control device described in step (4.2) eliminate pitching respectively and heave is transported The formula that dynamic influence is used is as follows:
Wherein, KP1For the first PD control device GC1Gain, KP2For the second PD control device GC2Gain, TD1Controlled for the first PD Device G processedC1Time constant, TD2For the second PD control device GC2Time constant.
With reference to Fig. 1 and Fig. 2, the decoupling compensator that the present invention is used uses Feed-forward Compensation Decoupling method, and concrete mode is:By three The lift and lifting moment that the data obtained in the towing trial of body ship pond and the T-shaped wing and wave suppression plate are provided are updated to ship power Learn in equation, obtain installing additional the trimaran model of the T-shaped wing and wave suppression plate.Equation is as follows:
Wherein, x3For heave amount, x5For pitching amount, m33For heave quality, m55For pitching moment of inertia, aijFor additional matter Amount, bijFor damped coefficient, cijFor recovery coefficient, ω is input Ocean-wave Signal, FiThe power acted on for Ocean-wave Signal on hull, γiThe phase acted on for Ocean-wave Signal on hull.
With reference to Fig. 2, the transmission function of trimaran model is respectively G11、G12、G21、G22, the design philosophy of decoupling compensator For:Influence by u1 to y2, influences of the u2 to y1 is considered as disturbance, and eliminates disturbing influence by the method for feedforward compensation.According to this One thought, calculates the transmission function N in the decoupling compensator described in step (4.1)1And N2, specific implementation is as follows:
Influences of (4.1.1) u1 to y2 be:Y2=u1 (G21+N1G22)
Influences of the u2 to y1 be:Y1=u2 (G12+N2G11)
(4.1.2), in order to eliminate influences of the u1 to y2, influences of the u2 to y1 can obtain the N in decoupling compensator1And N2 For:
Embodiment 2
With reference to Fig. 1, install the T-shaped wing additional and wave suppression plate two subtracts the trimaran for shaking floating body using two PD control device GC1And GC2 And decoupling compensator carries out Feed-forward Compensation Decoupling Control to it.
Decoupling compensator is designed by Fig. 2, and basic thought is:Influence by u1 to y2, influences of the u2 to y1 is considered as Disturbance, and eliminate disturbing influence by the method for feedforward compensation.
Two PD control device G that the present invention is usedC1And GC2In order to eliminate heave and pitching, its expression formula is as follows:
Wherein, KP1For the first PD control device GC1Gain, KP2For the second PD control device GC2Gain, TD1Controlled for the first PD Device G processedC1Time constant, TD2For the second PD control device GC2Time constant.
In fig. 1 and 2, the decoupling compensator that the present invention is used uses Feed-forward Compensation Decoupling method, and specific design step is such as Under:The lift and lifting moment that the data obtained in the towing trial of trimaran pond and the T-shaped wing and wave suppression plate are provided are updated to In ship dynamics equation, equation is as follows:
Wherein, x3For heave amount, x5For pitching amount, m33For heave quality, m55For pitching moment of inertia, aijFor additional matter Amount, bijFor damped coefficient, cijFor recovery coefficient, ω is input Ocean-wave Signal, FiThe power acted on for Ocean-wave Signal on hull, γiThe phase acted on for Ocean-wave Signal on hull.
Obtain installing additional the trimaran model of the T-shaped wing and wave suppression plate, its transmission function is the G in Fig. 211、G12、G21、G22.So Afterwards according to influences of the u1 to y2 is eliminated, the N1 and N2 in influence this design philosophy of u2 to y1, design decoupling compensator are eliminated, Method is as follows:
Influences of the u1 to y2 be:Y2=u1 (G21+N1G22)
Influences of the u2 to y1 be:Y1=u2 (G12+N2G11)
In order to eliminate influences of the u1 to y2, influences of the u2 to y1 can obtain the N in decoupling compensator1And N2For:
It is as follows to trimaran pitching stabilization decoupling controller Close-loop Control System Design procedure:
Step one:Input heave amount and give 0m, pitching amount is given 0 °.
Step 2:To heave the heave amount that collects of measurement module, the pitching amount that pitching measurement module is collected respectively with Set-point compares, input quantity of the difference respectively as two PD control devices.
Step 3:Using the output of PD control device as two input variables of decoupling compensator, decoupling compensator will press unrestrained The influence of plate and the T-shaped wing to heave and pitching is decoupled, and output is respectively the theory movement angle of wave suppression plate and the reason of the T-shaped wing By movement angle.
Step 4:Using the output of decoupling compensator as the input of amplitude limit link, the movement angle of wave suppression plate is limited in Between 0 ° to 15 °, the movement angle of the T-shaped wing is limited between -15 ° to 15 °.
Step 5:The actual motion angle of wave suppression plate and the T-shaped wing is obtained by amplitude limit link, be input to install additional the T-shaped wing and In the trimaran model of wave suppression plate, lift and lifting moment are provided for trimaran, so that trimaran reaches antipitching control effect Really.
Embodiment of above is merely illustrative of the technical solution of the present invention rather than its limitations.It may be noted that all in this hair Any modification and improvement done within bright principle and spirit etc., are all contained in protection scope of the present invention.The present invention For the method for trimaran pitching stabilization Decoupling Controller Design, so being controlled suitable for trimaran pitching stabilization in any case.

Claims (7)

1. a kind of trimaran pitching stabilization decoupling controller, it is characterised in that:Including trimaran, the first PD control device, the 2nd PD controls Device processed, decoupling compensator, the first amplitude limit link, the second amplitude limit link, heave measurement module and pitching measurement module;First PD is controlled Device processed and the second PD control device are connected with the first amplitude limit link, the second amplitude limit link respectively by decoupling compensator, the first limit Width link is directly installed on trimaran with the second amplitude limit link, and the first amplitude limit link is connected by trimaran with heave measurement module Connect, heave measurement module is connected with the first PD control device again, and the second amplitude limit link is connected by trimaran with pitching measurement module, Pitching measurement module is connected with the second PD control device again.
2. a kind of trimaran pitching stabilization decoupling controller according to claim 1, it is characterised in that:Described trimaran bag The T-shaped wing and wave suppression plate are included, the T-shaped wing is loaded on stem, and wave suppression plate is loaded on ship stern.
3. a kind of trimaran pitching stabilization Decoupling Controller Design method, it is characterised in that concrete implementation step includes:
(1) input heave amount gives 0m, and pitching amount is given 0 °;
(2) the heave amount of trimaran is determined by heaving measurement module, the pitching amount of trimaran is determined by pitching measurement module;
(3) the heave amount of measure is compared with set-point respectively with pitching amount, difference is sent to first respectively as feedback signal PD control device and the second PD control device are further handled;
Signal after processing is sent to decoupling compensation by (4) first PD control devices, the second PD control device as input variable respectively Device, influence of the decoupling compensator by wave suppression plate and the T-shaped wing to heave and pitching is decoupled, and output signal is respectively wave suppression plate The theory movement angle of theory movement angle and the T-shaped wing;
(5) the theory movement angle of the theory movement angle of wave suppression plate and the T-shaped wing is sent respectively to the first limit by decoupling compensator Width link is with the second amplitude limit link as input signal, and the first amplitude limit link is with the second amplitude limit link respectively to being installed on trimaran The angle of wave suppression plate and the T-shaped wing limited;
The actual motion angle of obtained wave suppression plate and the T-shaped wing is input to three by (6) first amplitude limit links with the second amplitude limit link In body ship, lift and lifting moment are provided for trimaran;
(7) repeat step (2) arrives step (6), realizes the closed-loop control to the wave suppression plate and the T-shaped wing of trimaran.
4. a kind of trimaran pitching stabilization Decoupling Controller Design method according to claim 3, it is characterised in that:Described The control parameter of the first PD control device and the second PD control device is adjusted in step (3) using trial and error procedure.
5. a kind of trimaran pitching stabilization Decoupling Controller Design method according to claim 3, it is characterised in that:Step (4) decoupling compensator described in uses the decoupling mode of Relative increasing rate, and addition decoupling item, eliminates T in decoupling mode The type wing is with wave suppression plate to trimaran heave and the coupling of pitching.
6. a kind of trimaran pitching stabilization Decoupling Controller Design method according to claim 3, it is characterised in that:Step (4) embodiment of the decoupling compensator described in is as follows:
(4.1) transmission function is added into decoupling compensator;
(4.2) influence of the heave movement to the second PD control device is eliminated, influence of the pitching to the first PD control device is eliminated;
(4.3) the first PD control device is made only to correspond to the heave movement of trimaran, the 2nd PD by the output signal of decoupling compensator Controller only corresponds to the pitching of trimaran by the output signal of decoupling compensator.
7. a kind of trimaran pitching stabilization Decoupling Controller Design method according to claim 6, it is characterised in that:Step (4.2) the first PD control device and the second PD control device described in eliminate pitching and heave movement respectively influences the formula used such as Under:
<mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mn>1.1</mn> <msub> <mi>T</mi> <mrow> <mi>D</mi> <mn>1</mn> </mrow> </msub> <mi>s</mi> </mrow> <mrow> <mn>0.1</mn> <msub> <mi>T</mi> <mrow> <mi>D</mi> <mn>1</mn> </mrow> </msub> <mi>s</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> 1
<mrow> <msub> <mi>G</mi> <mrow> <mi>C</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow> <mi>P</mi> <mn>2</mn> </mrow> </msub> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mn>1.1</mn> <msub> <mi>T</mi> <mrow> <mi>D</mi> <mn>2</mn> </mrow> </msub> <mi>s</mi> </mrow> <mrow> <mn>0.1</mn> <msub> <mi>T</mi> <mrow> <mi>D</mi> <mn>2</mn> </mrow> </msub> <mi>s</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
Wherein, KP1For the first PD control device GC1Gain, KP2For the second PD control device GC2Gain, TD1For the first PD control device GC1Time constant, TD2For the second PD control device GC2Time constant.
CN201710443219.2A 2017-06-13 2017-06-13 A kind of trimaran pitching stabilization decoupling controller and design method Pending CN107255919A (en)

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CN109334892A (en) * 2018-09-20 2019-02-15 江苏大学 A kind of simplification robust adaptive pitching stabilization control method of multi-hull ship
CN109334892B (en) * 2018-09-20 2020-06-26 江苏大学 Simplified robust self-adaptive pitching reduction control method for multi-hull vessel
CN109878633A (en) * 2019-03-14 2019-06-14 哈尔滨工程大学 A kind of high-speed catamaran longitudinal direction stabilization method based on Active Disturbance Rejection Control
CN110083057A (en) * 2019-06-12 2019-08-02 哈尔滨工程大学 PID control method based on hydrofoil athletic posture
CN110083057B (en) * 2019-06-12 2021-12-07 三亚哈尔滨工程大学南海创新发展基地 PID control method based on hydrofoil motion attitude

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