CN107065553A - Many rotation excitations translate oscilator system Non-linear coupling self-adaptation control method - Google Patents
Many rotation excitations translate oscilator system Non-linear coupling self-adaptation control method Download PDFInfo
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Abstract
A kind of many rotation excitation translation oscilator system Non-linear coupling self-adaptation control methods, belong to Underactuated Mechanical Systems automatic control technology field.This method includes：There is unknown parameter and uncertain factor in the system of fully taking into account, introduce coupling terms and construct a kind of new stored-energy function, design a kind of Non-linear coupling self-adaptation control method, enhance the transient performance of system, realize many rotation excitation translation oscillator (Translational Oscillator with Rotational Actuator, TORA) the point stabilization problem of system, can enable many TORA systems given initial position or when being interfered it is quick, equilbrium position is returned to exactly and keeps stable, simultaneously, the influence that more new law can be brought for unknown parameter and uncertain factor to system carries out online compensation.The results show, institute's extracting method has good control performance.
Description
Technical field
It is more particularly to a kind of to be applied to systematic parameter the invention belongs to Underactuated Mechanical Systems automatic control technology field
Unknown and by external interference many rotation excitation translation oscillator (the TranslationalOscillator with of drive lacking
Rotational Actuator, TORA) system Non-linear coupling self-adaptation control method.For simplicity, hereinafter will rotation
Turn excitation translation oscillator and be referred to as TORA.
Background technology
Nowadays, the research for under-actuated systems causes the extensive concern of domestic and international many scholars[1],[2].Drive lacking
The many advantages that system possesses, such as high flexibility, low energy consumption, low cost, mechanical structure are simple etc., are widely used in it
In Mechatronic Systems.But, the controlled quentity controlled variable dimension of under-actuated systems is less than the number of the free degree to be controlled, and this characteristic causes drive lacking
The control problem of system is difficult to solve and full of challenge.Therefore, for under-actuated systems research in theory with it is actually equal
Have very important significance.
Drive lacking TORA systems are a kind of typical under-actuated systems, and it is for studying dual spin spacecraft resonance capture
The baseline system of phenomenon.The structure of single TORA systems can be reduced to a chassis for doing translational motion and one move in a circle
Rotor, its control targe is mainly to realize the point stabilization of chassis displacement and angle of rotor.At present, for the control of single TORA systems
Problem processed, domestic and foreign scholars propose many control methods.According to whether using feedback signal, these control methods can divide
For opened loop control[3]-[7]With closed-loop control[8]-[13]Two classes.However, opened loop control is although simple in construction, without extra sensor
Expected control targe is achieved that, but can not reponse system status signal, and to the uncertain and outer of parameter in real time
The disturbance on boundary is very sensitive.Now, closed-loop control then compensate for the deficiency of opened loop control.Closed-loop control utilizes system Real-time Feedback
Signal carry out On-line Control, therefore in the case where there is external interference, closed-loop control can be obtained compared to opened loop control
Better control effect, while also the robustness of system can be substantially improved.At present, for the calm of single TORA systems
Control problem, researcher utilizes the feedback signal design of feedback controller of system, it is proposed that a variety of closed loop control methods.
On the basis of single TORA systems, many TORA systems being made up of multiple single TORA Cascade Systems are in real life
Also there is application widely.On the one hand, many TORA systems can be used to verify the effective of many advanced non-linear control strategies
Property.On the other hand, many TORA systems can for studying the physical phenomenon that some are important, the motor synchronizing phenomenon of such as Mechatronic Systems,
Chaos phenomenon etc..The electromechanical tool such as electric hand drill operationally produces strong vibration, if at without effective weakening
Reason, will be damaged to the people that it is used for a long time.Therefore, similarly have for many TORA systematic researches theoretical and actual
Double meaning.But compared to single TORA systems, many TORA systems have more complicated dynamics, its control problem
More it is difficult to solve.At this stage, still seldom for many TORA systematic researches, existing research can be divided into two classes.One class is
For analyze motor synchronizing phenomenon generation and the mechanical structure to many TORA systems is studied[14]-[16].It is another kind of to be controlled for design
Strategy, realizes the point stabilization of many TORA systems displacements and corner[17]-[19].However, existing control method deficiency is needs
Accurate system model, or designed controller are discontinuous.On the one hand, system is very easy in actual working environment
Influenceed by various factors, system parameters often have uncertainty, such as chassis quality is unknown, rotor quality is unknown,
Size of components is unknown etc..In this case, the existing method based on accurate system's model is not just applied to.On the other hand, control
Amount processed can discontinuously cause system to produce buffeting, so as to cause damage to equipment.
In summary, to overcome many deficiencies that existing method is present, the control effect of TORA systems is lifted, it would be highly desirable to design
Go out a kind of continuous Closed-loop Control Strategy, can be made full use of in the case of systematic parameter is uncertain, without system linearization
Coupled relation between system mode, realizes the high-performance point stabilization of many TORA systems of drive lacking.
The content of the invention
In place of many TORA system automatic control methods above shortcomings of current drive lacking,
There is provided a kind of drive lacking many TORA mission nonlinears coupling adaptive control methods.
This invention address that proposing a kind of new Non-linear coupling self-adaptation control method, system presence is fully taken into account
Unknown parameter and uncertain factor, introduce a kind of new stored-energy function of Non-linear coupling construction, enhance the temporary of system
State property, while the influence brought in view of unknown parameter and uncertain factor to system, online compensation is carried out using more new law.
Institute's extracting method propose first it is a kind of can make the globally asymptotically stable smooth controller of many TORA systems of unknown parameters, it is real
Showed the point stabilization problem of many TORA systems, can enable many TORA systems given initial position or when being interfered it is fast
Speed, return to equilbrium position exactly, and keep stable, interference has good robustness to control effect significantly and to external world.Most
Afterwards, hardware experiment platform (is made up of) 2 list TORA using double TORA and demonstrates the validity of institute's extracting method and good control
Performance.
The many TORA mission nonlinears coupling adaptive control methods of drive lacking that the present invention is provided include：
1st, control targe is determined
Select each TORA position vector beTarget location vector is
Wherein, for i-th of the TORA, x in many TORA systemsiFor chassis displacement,For machine speed, θiFor the rotor anglec of rotation,
For rotor angular velocity of rotation, θdiFor the angle on target of rotor, list TORA sum is N in system, then i=1,2 ..., N.
2nd, define error signal, parameter vector with can direction finding amount
Define the rotor pivot angle error e of each TORA in many TORA systemsθi(t) it is
eθi=θdi-θi (4)
Wherein, θiFor the rotor anglec of rotation, θdiFor the angle on target of rotor.Define unknown parameter vector
Can direction finding amountWherein, symbol "" representing matrix/vector transposition, vector in element ωi1,ωi2,
ωi3,yi1,yi2,yi3It is expressed as：
yi1=xi cosθi,yi2=-xi-1cosθi,yi3=-xi+1cosθi
Wherein, xiRepresent i-th of TORA chassis displacement, xi-1Represent the i-th -1 TORA chassis displacement, xi+1Represent the
I+1 TORA chassis displacement, θiI-th of TORA rotor pivot angle is represented, cos represents cosine function, Mi,mi,Li,ki,ki+1Point
I-th of TORA chassis quality, rotor quality, rotor radius of turn, the stiffness factor and i+1 bar of i-th spring are not represented
The stiffness factor of spring；x0=xN+1=0.
3rd, controller design
Design Non-linear coupling adaptive controller τiIt is as follows：
Wherein, kE,kpi,kdiIt is positive control gain,Represent ωiOn-line Estimation, its more new lawFor
Wherein, Γi=diag { ri1,ri2,ri3Represent that positive definite diagonally updates gain matrix, rijRepresent that positive definite diagonally updates
Gain matrix ΓiJ-th of element on middle diagonal, meets rij>0, i=1,2 ..., N, j=1,2,3.
4th, control method is realized
Using the sensor installed on chassis, each TORA in many TORA systems being made up of N number of single TORA is measured in real time
Chassis displacement xi, machine speedRotor pivot angle θi, rotor velocityI=1,2 ..., N, utilize formula (16) and formula
(17), calculate and obtain control signal, realize the control of TORA systems many to drive lacking.
The theoretical foundation and derivation of the inventive method：
1st, system model and conversion
The kinetic model of many TORA systems of drive lacking is：
Wherein, for many TORA systems being made up of N number of single TORA systems, xi(t),θi(t),Represent respectively i-th of TORA chassis displacement, machine speed, chassis acceleration, angle of rotor, rotor velocity and
Rotor angular acceleration, xi-1(t) the i-th -1 TORA chassis displacement, x are representedi+1(t) i+1 TORA chassis displacement is represented；
T represents that (t) represents that the variable is the function on the time behind time, variable, for simplicity, omits major part in formula
(t) behind variable；Mi,mi,Li,JiI-th of TORA chassis quality, rotor quality are represented respectively, the rotor radius of gyration, turned
Rotary inertia of the son on pivot；τi(t) it is the control input of system to be mounted in the motor torque on i-th of TORA；
kiRepresent the stiffness factor of i-th spring, ki+1Represent the stiffness factor of i+1 root spring；Wherein, i=1,2 ..., N；This
Outside, x0(t)=xN+1(t)=0.
It is an object of the present invention to design suitable control method, the point stabilization to many TORA systems is realized, makes many TORA
System is in given initial position or equilbrium position can be quickly and accurately returned to when being interfered and keep stable.The target can
It is described as follows：
Wherein, i=1,2 ..., N, θdiRepresent the target location of angle of rotor.
Controller design and stability analysis for convenience, is rewritten as following shape by kinetic model shown in formula (1) first
Formula：
Wherein, for convenience of computing, auxiliary variable is introducedWith
2nd, controller design
To realize the control targe described in formula (2), error signal is defined as follows：
eθi=θdi-θi (4)
In formula, eθi(t) i-th of TORA angular errors, the i.e. current rotational angle theta of rotor are representedi(t) with angle on target θdiBetween
Error.First derivative is asked on the time to it, just like drawing a conclusion：
For convenience of controller design and stability analysis, control targe shown in formula (2) can be equivalent to following form：
Many TORA system capacities function E can be expressed as follows：
Wherein i=1,2 ..., N.
First derivative is sought energy function E, and kinetics equation (1) is substituted into, can be derived from：
Further, Non-linear coupling is introduced in energy function (7)Construct non-negative stored-energy function
V (t), expression formula is as follows：
Wherein i=1,2 ..., N, V (t) are new stored-energy function, kE,kpi∈R+Represent control gain, ΓiFor positive definite
Update matrix and be defined as Γi=diag { ri1,ri2,ri3},rij∈R+, j=1,2,3, rijRepresent that positive definite diagonally updates gain matrix
ΓiJ-th of element on middle diagonal.ωi(t)∈R3For system unknown parameter vector, its expression is：
Respectively system unknown parameter is vectorial, the estimation and parameter vector estimation of unknown parameter vector
Error, meet following relational expression：
By formula (10) on time derivation, it can obtain：
To formula (9) on time derivation, and abbreviation is carried out using formula (8) and (11), following result can be obtained：
Wherein,It is derivatives of the V (t) on the time.To simplify calculating, auxiliary function ψ is definedi(t), expression formula is as follows：
Can direction finding amountUnknown parameter vectorElement in vector
ωi1,ωi2,ωi3,yi1,yi2,yi3For：
Therefore, by formula (11) and formula (13), formula (12) can be rewritten as following form：
To make in formula (15)Anon-normal, designs following Non-linear coupling controller：
Wherein, kE, kpiAnd kdiIt is positive control gain,Represent to unknown parameter ωi(t) On-line Estimation, it is more
New lawExpression formula it is as follows：
Formula (16) and (17) are substituted into formula (15), can be obtained after arrangement：
3rd, stability analysis
This part will illustrate that controller (16) proposed by the present invention and parameter more new law (17) can make by theory analysis
Much TORA systems are in given initial position or equilbrium position can be quickly and accurately returned to when being interfered and keep stable,
I.e. system mode can Asymptotic Stability at equalization point, while fully suppressing and eliminating the residual oscillation of rotor, i.e.,
To prove the conclusion, the special lemma (extended Barbalat ' slemma of Barbara extended below are firstly introduced into
)[20],[21]：
Lemma 1 (the special lemma of the Barbara of extension)：If function f (t):R+→ R has the limitWherein, c ∈
R represents constant, and it can be expressed as on the derivative of timeWherein function f1(t) unanimously connect
It is continuous, and function f2(t) meetThen have
V (t) in selection formula (9) understands V (t) right and wrong as the alternative function of Liapunov by the conclusion in formula (18)
Increase, and the equalization point of closed-loop system is stable under Lyapunov Meaning, therefore, the lower equal bounded of column signal：
In definition (18)Using the conclusion in formula (20), it can derive and knowCause
This, from lemma 1It can be obtained and such as drawn a conclusion by f (t) definition：
Next, controller shown in formula (16) to be substituted into the 1st equation of formula (3), it can be obtained by arrangement：
Wherein, g1(t),g2(t) it is defined as below：
Wherein, auxiliary variableKnown by formula (23)
AndTherefore, it can be obtained and such as drawn a conclusion by lemma 1：
Similarly, controller shown in formula (16) is substituted into the 2nd equation of formula (3), can be obtained：
Wherein, g3And g (t)4(t) it is defined as follows：
From formula (26)Therefore, it can be deduced by lemma 1：
Simultaneous formula (23) and formula (26), using the conclusion in formula (24) and formula (27), arrangement can be obtained：
For ease of calculating, x is utilized0(t)=0, xN+1(t) the 2nd equation=0, in formula (28) is rewritable for following shape
Formula：
Wherein matrix Λ ∈ RN×NWith vector x ∈ RNIt is defined as follows：
Wherein, λi=ki+ki+1, i=1,2 ..., N.It is not difficult to try to achieve, matrix Λ is full rank in formula (30), that is, shows formula
(29) there is following unique solution：
WillIt is rewritten into following form：
WhereinUnderstand(i.e. in formula (20))。g6(t)=0, it is known thatIt can be obtained and such as drawn a conclusion using lemma 1：
By formula (4), formula (28) and formula (31), withUnderstand：
Wherein i=1,2 ..., N.Therefore, convolution (21), (24), (27), (31), (33) and (34), it is known that formula (16)
Shown controller can realize desired control targe.
The advantages of the present invention：
For many rotation excitation translation oscilator systems of drive lacking, it is self-adaptive controlled that the present invention proposes a kind of Non-linear coupling
Method processed.It can be unknown in systematic parameter or in the case of there is uncertain factor, realizes and the translation of many rotation excitations is shaken
The point stabilization of device system is swung, the prospect for having good practical application.
Brief description of the drawings：
Experimental results of the Fig. 1 for institute's extracting method of the present invention in experimental situations 1；
Experimental results of the Fig. 2 for institute's extracting method of the present invention in experimental situations 2；
Experimental results of the Fig. 3 for institute's extracting method of the present invention in experimental situations 3；
Experimental results of the Fig. 4 for institute's extracting method of the present invention in experimental situations 4.
Embodiment：
Embodiment 1：
1st, experimental procedure is described
1.1st, control targe is determined
Select each TORA position vector beTarget location vector is
Wherein, for i-th of the TORA, x in many TORA systemsiFor chassis displacement,For machine speed, θiFor the rotor anglec of rotation,
For rotor angular velocity of rotation, θdiFor the angle on target of rotor, list TORA sum is N in system, then i=1,2 ..., N.
1.2nd, define error signal, parameter vector with can direction finding amount
Define the rotor pivot angle error e of each TORA in many TORA systemsθi(t) it is
eθi=θdi-θi (4)
Wherein, θiFor the rotor anglec of rotation, θdiFor the angle on target of rotor.Define unknown parameter vector
Can direction finding amountWherein, symbol "" representing matrix/vector transposition, vector in element ωi1,ωi2,
ωi3,yi1,yi2,yi3It is expressed as：
yi1=xi cosθi,yi2=-xi-1cosθi,yi3=-xi+1cosθi
Wherein, xiRepresent i-th of TORA chassis displacement, xi-1Represent the i-th -1 TORA chassis displacement, xi+1Represent the
I+1 TORA chassis displacement, θiI-th of TORA rotor pivot angle is represented, cos represents cosine function, Mi,mi,Li,ki,ki+1Point
I-th of TORA chassis quality, rotor quality, rotor radius of turn, the stiffness factor and i+1 bar of i-th spring are not represented
The stiffness factor of spring；x0=xN+1=0.
1.3rd, controller design
Design Non-linear coupling adaptive controller τiIt is as follows：
Wherein, kE,kpi,kdiIt is positive control gain,Represent ωiOn-line Estimation, its more new lawFor
Wherein, Γi=diag { ri1,ri2,ri3Represent that positive definite diagonally updates gain matrix, rijRepresent that positive definite diagonally updates
Gain matrix ΓiJ-th of element on middle diagonal, meets rij>0, i=1,2 ..., N, j=1,2,3.
1.4th, control method is realized
Using the sensor installed on chassis, each TORA in many TORA systems being made up of N number of single TORA is measured in real time
Chassis displacement xi, machine speedRotor pivot angle θi, rotor velocityI=1,2 ..., N, utilize formula (16) and formula
(17), calculate and obtain control signal, realize the control of TORA systems many to drive lacking.
2nd, experimental result is described
In order to verify the validity of method proposed by the invention, according to above-mentioned steps, carried out on double TORA experiment porch
Experiment.In experiment, 2 TORA chassis quality, rotor quality, radius of turn, rotary inertia, the stiffness factor of three springs and
Acceleration of gravity is specifically chosen as follows：
M1=2.70kg, m1=0.31kg, L1=0.12m, M2=3.84kg,
m2=0.50kg, L2=0.12m, J1=0.00446kgm2,J2=0.00720kgm,
k1=602.6Nm, k2=150.7Nm, k3=133.9Nm, g=9.8m/s2
Experiment is divided into 4 kinds of situations, by applying external disturbance and parameter uncertainty, verifies the validity of the inventive method
With robustness.
Situation 1, the interference of non-zero initial condition：By at the beginning of the chassis initial displacement of two TORA in double TORA platforms and rotor
Beginning angle is respectively set to：x1(0)=- 0.14m, x2(0)=- 0.03m, θ1(0)=- 30deg, θ2(0)=45deg；
Situation 2, to chassis translational motion apply external disturbance：In 1.5s, 3.1s, 5.2s or so artificially to two TORA
The translational motion of chassis applies 3 disturbances；
Situation 3, to rotor rotational movement apply external disturbance：In 2.2s, 3.3s, 4.9s, 6.7s or so artificially to two
The rotary motion of individual TORA rotors applies 4 disturbances；
Situation 4, the uncertainty of systematic parameter：Under conditions of situation 1, change the systematic parameter of double TORA platforms, two
Individual TORA chassis quality is by m1=0.31kg, m2=0.5kg is changed to m respectively1=0.314kg, m2=0.317kg.
Control gain value of the institute's extracting method of the present invention in 4 kinds of situations is as follows：
Accompanying drawing 1 to 4 is given in corresponding experimental result, the preceding 3 width subgraph of accompanying drawing 1 to 4, and solid line is carved successively from top to bottom
The 1st TORA chassis displacement, angle of rotor, motor torque are drawn, dotted line features the 2nd TORA platform successively from top to bottom
Parking stall shifting, angle of rotor, motor torque；Accompanying drawing 1 is into Fig. 4 the 4th width subgraph, and solid line, dotted line, dotted line, dotted line are retouched respectively
What is painted is the estimate to system unknown parameterWhat deserves to be explained is, institute's extracting method of the present invention is in 4 kinds of situations
Under experimental result in, to unknown parameter ω12,ω23EstimationIt is 0, then, to make experimental result more concise clear
It is clear,Do not drawn in figure.
By comparing Fig. 1 and Fig. 4, the control effect of method proposed by the invention keeps basic in both cases
Unanimously, it was demonstrated that its good adaptability.From Fig. 2 with can be seen that in Fig. 3, institute's extracting method, which can be eliminated quickly, puts on chassis position
The adverse effect caused with the external interference on angle of rotor to system is moved, with good robustness.Experimental result and theory
Analysis is consistent.
This series of experiments result demonstrates the validity and feasibility of institute's extracting method of the present invention.
Bibliography
[1]E.M.Abdel-Rahman,A.H.Nayfeh,Z.N.Masoud,Dynamics and control of
cranes:A review.Journal of Vibration and Control,9(7):863-908,2003.
[2]J.-X.Xu,Z.-Q.Guo,T.H.Lee,Design and implementation of integral
sliding mode control on an underactuated two-wheeled mobile robot.IEEE
Transactions on Industrial Electronics,61(7):3671-3681,2014.
[3]Q.Quan and K.-Y.Cai,Additive-state-decomposition-based tracking
control for TORA benchmark.Journal of Sound and Vibration,332(20):4829-4841,
2013.
[4]J.-P.Su,Robust control of a class of non-linear cascade systems:A
novel sliding mode approach.IEE Control Theory and Applications,149(2):131-
136,2002.
[5]Y.Jiang and J.Huang,Output regulation for a class of weakly
minimum phase systems and its application to a nonlinear benchmark system.In
Proceedings of the American Control Conference,St.Louis,USA,June 2009:5321-
5326.
[6]F.Celani,Output regulation for the TORA benchmark via rotational
position feedback.Automatica,47(3):584-590,2011.
[7]Z.-P.Jiang and I.Kanellakopoulos,Global output-feedback tracking
for a benchmark nonlinear system.IEEE Transactions on Automatic Control,45
(5):1023-1027,2000.
[8]C.-H.Lee and S.-K.Chang,Experimental implementation of nonlinear
TORA system and adaptive backstepping controller design.Neural Computing&
Applications,21(4):785-800,2012.
[9]R.T.Bupp,D.S.Bernstein,and V.T.Coppola,Experimental implementation
of integrator backstepping and passive nonlinear controllers on the RTAC
testbed.International Journal of Robust and Nonlinear Control,8(4-5):435-457,
1998.
[10]R.Olfati-Saber,Nonlinear control of underactuated mechanical
systems with application to robotics and aerospace
vehicles.Ph.D.dissertation,Massachusetts Institute of Technology,Cambridge,
MA,2001.
[11]S.Dussy and L.E.Ghaoui,Measurement-scheduled control for the RTAC
problem:An LMI approach.International Journal of Robust and Nonlinear
Control,8(4-5):377-400,1998.
[12]R.Adlgostar,H.Azimian,and H.D.Taghirad,Robust H∞,H2/H∞controller
forrotational/translational actuator(RTAC).In Proceedings of the IEEE
International Conference on Control Applications,Munich Germany,Oct.2006:705-
710.
[13]M.Tavakoli,H.D.Taghirad,and M.Abrishamchian,Identification and
robust H∞control of the rotational/translational actuator
system.International Journal of Control,automation,and Systems,3(3):387-396,
2005.
[14]Y.Bonkobara,H.Mori,T.Kondou,and T.Ayabe,Self-synchronized
phenomenon generated in rotor-type oscillators:On the influence of coupling
condition between oscillators.Journal of System Design and Dynamics,2(3):861-
873,2008.
[15]H.Mori,Y.Bonkobara,T.Kondou,and T.Ayabe,Self-synchronized
phenomenon generated in rotor-type oscillators:Investigation using nonlinear
normal modes,Journal of System Design and Dynamics,2(3):874-885,2008.
[16]Y.Bonkobara,T.Ono,and T.Kondou,Development of a generation
mechanism of synchronous vibration suitable for hand-held vibrating tools:
Investigation of an impact model with two oscillators.Journal of System
Design and Dynamics,5(6):1361-1375,2011.
[17]J.M.Avis,S.G.Nersesov,and R.Nathan,Decentralised energy-based
hybrid control for the multi-RTAC system.In Proceedings of the 2009 American
Control Conference,St.Louis,MO,USA,June 2009:895-900.
[18]W.M.Haddad,Q.Hui,V.Chellaboina,and S.Nersesov,Hybrid
decentralized maximum entropy control for large-scale dynamical
systems.Nonlinear Analysis:Hybrid Systems,1(2):244-263,2007.
[19]X.Kong,X.Zhang,X.Chen,B.Wen,and B.Wang,Synchronization analysis
and control of three eccentric rotors in a vibrating system using adaptive
sliding mode control algorithm.Mechanical Systems and Signal Processing,72-
73:432-450,2016.
[20]Y.Fang,W.E.Dixon,D.M.Dawson,and P.Chawda,Homography-based visual
servo regulation of mobile robots.IEEE Transactions on Systems,Man,and
Cybernetics-Part B:Cybernetics,35(5):1041-1050,2005.
[21]N.Sun and Y.Fang,An efficient online trajectory generating method
for crane systems.International Journal of Robust and nonlinear Control,24
(11):1653-1663,2014.
Claims (1)
1. a kind of many rotation excitation translation oscilator system Non-linear coupling self-adaptation control methods, it is characterised in that this method bag
Include：
1st, control targe is determined
The position vector of selected each rotation excitation translation oscillator isTarget location vector isWherein, i-th of the rotation excitation translated for many rotation excitations in oscilator system translates oscillator,
xiFor chassis displacement,For machine speed, θiFor the rotor anglec of rotation,For rotor angular velocity of rotation, θdiFor the target angle of rotor
The sum of rotation excitation translation oscillator is N in degree, system, then i=1,2 ..., N；
2nd, define error signal, parameter vector with can direction finding amount
Define the rotor pivot angle error e that each rotation excitation in many rotation excitation translation oscilator systems translates oscillatorθi(t) it is
eθi=θdi-θi (4)
Wherein, θiFor the rotor anglec of rotation, θdiFor the angle on target of rotor；Define unknown parameter vector
Can direction finding amountWherein, symbolElement ω in representing matrix/vector transposition, vectori1,ωi2,
ωi3,yi1,yi2,yi3It is expressed as：
<mrow>
<msub>
<mi>&omega;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
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yi1=xicosθi,yi2=-xi-1cosθi,yi3=-xi+1cosθi
Wherein, xiRepresent the chassis displacement of i-th of rotation excitation translation oscillator, xi-1Represent that the i-th -1 rotation excitation translation is shaken
Swing the chassis displacement of device, xi+1Represent that i+1 rotation excitation translates the chassis displacement of oscillator, θiRepresent i-th of rotation excitation
The rotor pivot angle of oscillator is translated, cos represents cosine function, Mi,mi,Li,ki,ki+1I-th of rotation excitation translation is represented respectively
The chassis quality of oscillator, rotor quality, rotor radius of turn, the stiffness of the stiffness factor of i-th spring and i+1 bar spring
Coefficient；x0=xN+1=0；
3rd, controller design
Design Non-linear coupling adaptive controller τiIt is as follows：
Wherein, kE,kpi,kdiIt is positive control gain,Represent ωiOn-line Estimation, its more new lawFor
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Wherein, Γi=diag { ri1,ri2,ri3Represent that positive definite diagonally updates gain matrix, rijRepresent the diagonal more new gain of positive definite
Matrix ΓiJ-th of element on middle diagonal, meets rij>0, i=1,2 ..., N, j=1,2,3；
4th, control method is realized
Using the sensor installed on chassis, many rotation excitations that measurement in real time is made up of N number of rotation excitation translation oscillator are put down
Move the chassis displacement x that each rotation excitation in oscilator system translates oscillatori, machine speedRotor pivot angle θi, rotor angle
SpeedI=1,2 ..., N, using formula (16) and formula (17), calculating obtains control signal, realizes and rotation more than drive lacking is swashed
Encourage the control of translation oscilator system.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108319281A (en) * | 2018-01-08 | 2018-07-24 | 南开大学 | Based on time optimal rotor craft lifting system motion planning method |
| CN108508750A (en) * | 2018-05-08 | 2018-09-07 | 重庆大学 | A kind of output feedback ontrol method of TORA systems |
| CN108663937A (en) * | 2018-05-08 | 2018-10-16 | 重庆大学 | A kind of non-minimum phase linear system adjustment control method |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1950222A (en) * | 2004-04-27 | 2007-04-18 | 田纳科自动化操作有限公司 | Model free semi-active vehicle suspension system |
| US20110111718A1 (en) * | 2009-11-09 | 2011-05-12 | Research In Motion Limited | Hysteresis nonlinear state machine with overlapping thresholds for automatic frequency control |
| CN104199291A (en) * | 2014-08-11 | 2014-12-10 | 浙江工业大学 | Dissipative structure theory based TORA (Translation oscillators with a rotating actuator) system self-adaption control method |
-
2017
- 2017-04-20 CN CN201710273827.3A patent/CN107065553B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1950222A (en) * | 2004-04-27 | 2007-04-18 | 田纳科自动化操作有限公司 | Model free semi-active vehicle suspension system |
| US20110111718A1 (en) * | 2009-11-09 | 2011-05-12 | Research In Motion Limited | Hysteresis nonlinear state machine with overlapping thresholds for automatic frequency control |
| CN104199291A (en) * | 2014-08-11 | 2014-12-10 | 浙江工业大学 | Dissipative structure theory based TORA (Translation oscillators with a rotating actuator) system self-adaption control method |
| CN104199291B (en) * | 2014-08-11 | 2017-04-12 | 浙江工业大学 | Dissipative structure theory based TORA (Translation oscillators with a rotating actuator) system self-adaption control method |
Non-Patent Citations (3)
| Title |
|---|
| NING SUN，等: "Adaptive Nonlinear Crane Control With Load Hoisting/Lowering and Unknown Parameters:Design and Experiments", 《IEEE/ASME TRANSACTIONS ON MECHATRONICS》 * |
| 孙宁，方勇纯，陈鹤: "欠驱动桥式吊车消摆跟踪控制", 《控制理论与应用》 * |
| 翟龙军，等: "一类耦合振荡器阵列的有约束条件自适应相位控制方法", 《系统仿真学报》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108319281A (en) * | 2018-01-08 | 2018-07-24 | 南开大学 | Based on time optimal rotor craft lifting system motion planning method |
| CN108319281B (en) * | 2018-01-08 | 2021-02-02 | 南开大学 | Time-optimal-based rotorcraft lifting system motion planning method |
| CN108508750A (en) * | 2018-05-08 | 2018-09-07 | 重庆大学 | A kind of output feedback ontrol method of TORA systems |
| CN108663937A (en) * | 2018-05-08 | 2018-10-16 | 重庆大学 | A kind of non-minimum phase linear system adjustment control method |
| CN108663937B (en) * | 2018-05-08 | 2020-11-13 | 重庆大学 | Non-minimum phase linear system regulation control method |
| CN108508750B (en) * | 2018-05-08 | 2021-05-11 | 重庆大学 | Output feedback control method of TORA system |
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