CN104238365A  Cantilever beam vibration control method on basis of selfadaption neural network control  Google Patents
Cantilever beam vibration control method on basis of selfadaption neural network control Download PDFInfo
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Abstract
The invention discloses a cantilever beam vibration control method on the basis of selfadaption neural network control and is designed on the basis of filtered tracking error. A controller comprises proportional differential items and RBF neural network items. By the cantilever beam vibration control method, with unknown functions of a cantilever beam system of an RBF neural network approach, an updating algorithm of the weight of the RBF neural network is designed on the basis of Lyapunov stability theory, and overall stability of the system is guaranteed. Robust items are added into the updating algorithm, boundedness of control input is guaranteed, and the final tracking error is kept within any small range by the aid of proportional differential control items. Under the conditions of no structural or nonstructural parameters of a cantilever and with external interference, the control method is capable of accurately tracking and controlling the cantilever system, and robustness and reliability of the system are improved.
Description
Technical field
The present invention relates to a kind of semigirder vibration control method based on neural network control, belong to semigirder control technology field.
Background technology
To be one end of fingerboard be semigirder does not produce the holddown support of axis, perpendicular displacement and rotation, and the other end is free end (can produce and be parallel to power axial and perpendicular to axial direction).In engineering mechanics force analysis, more typical simplified model.In Practical Project is analyzed, most of Practical Project stressed member can be reduced to semigirder.
Along with the development of science and technology is maked rapid progress, the develop rapidly of aeronautical and space technology, the expanding day of space operation scale, also more and more stricter to the requirement of aeronautical and space technology and space structure, a large amount of aerospace structures, the trend of flexibility development as all oriented in the space station of large modular, solar energy sailboard, satellite antenna, highprecision optical system and supporting mass structure, space manipulator etc.The use of flexible member not only increases the dirigibility of Spacecraft guidance and control and manufacture, also reduces launch cost simultaneously, and therefore, the extensive employing of flexible member is the trend of a certainty.But flexible member is Shortcomings part also, that is exactly that it easily produces elastic vibration when moving or locate, and at the end of motion, also can produce residual oscillation, caused vibration has very large impact to robust motion and positioning precision.Such as: robot for space and spacecraft flexible appendage as solar array etc. in disturbance cases, its significantly free vibration to continue for a long time, this will affect stability and point to control accuracy, especially when needs accurately control its position and point to.Similar accident was there is in international space in exploring, as the scopic rotating part of Landsat that the U.S. launches, vibrate owing to being subject to the interference of solar energy sailboard drive system, have impact on scopic steady operation, greatly reduce the quality that it transmits image, and for example " seeker No. l " communications satellite of U.S.'s transmitting in 1958, due to a lot of energy of dissipation of vibrations of its four whip antennas, after a period of time that normally worked, there is beyond thought satellite rollover phenomenon, finally cause mission failure.With regard to domestic, along with developing rapidly of China's AeroSpace cause, vibration problem also becomes increasingly conspicuous, as DFH3 communications satellite just produced serious problem because of the vibration of solar energy sailboard.
Tradition suppresses the method for vibration to be by passive vibration isolation, and the method for vibration damping plays the object of vibration damping, and these Measures compare are passive, inflexible, bad adaptability, can not carry out realtime control to changeable extraneous vibration.In order to overcome abovementioned difficulties, Active Vibration Control is suggested, and Active Vibration Control can experience extraneous Vibration Condition in real time, makes suitable reaction, exports control signal, suppresses vibration.The shock resistance of structural system for system functional reliability and precision is smoked to pass wants.A large amount of engineering structures generally bears the excitation of vibration environment in actual motion, is suppressed, will affect serviceability and the lifespan of each parts in structure, can make its disabler time serious if do not take measures to the vibration of these structures.Therefore, in order to improve serviceability and the precision of structure, realtime vibration control must be carried out to structure.
International article has and is applied in the middle of the control of semigirder by various advanced control method, typically has adaptive control and fuzzy control method.These achieve the TRAJECTORY CONTROL to semigirder.But the robustness of adaptive control disturbance is to external world very low, system is easily made to become unstable.As can be seen here, semigirder vibration control obviously still has inconvenience and defect, and is urgently further improved.
Summary of the invention
The object of the invention is to the defect overcoming the existence of existing semigirder vibration control method, particularly improve cantilever beam system having that model is uncertain, under the various disturbed condition such as Parameter Perturbation and external disturbance power, to the tracking performance of ideal trajectory and the robustness of whole system, and provide a kind of semigirder vibration control method based on neural network control.
The present invention solves its technical matters and realizes by the following technical solutions:
Based on the semigirder vibration control method of neural network control, comprise the following steps:
1) the filtering error model based on semigirder is set up;
2) CONTROLLER DESIGN;
3) adopt RBF network to approach the structure function of the semigirder the unknown in semigirder mathematical model, obtain the estimated value of the structure function of semigirder the unknown;
4) based on the update algorithm of Lyapunov stability theory design RBF neural weights;
5) using the control inputs of the control inputs of the controller through RBF network control as semigirder mathematical model, semigirder is controlled, and realtime online upgrades.
Aforesaid step 1) in, the filtering error model based on semigirder is:
Wherein, s is filtering error, and C is the damping term in semigirder kinetic model, and u is the input vector in semigirder kinetic model, and d is the disturbance of semigirder kinetic model, and f (x) represents the structure function of semigirder the unknown.
Aforesaid filtering error s is:
Wherein, Λ is filtering error parameter, and e is tracking error: e=q
_{d}q
Q is semigirder oscillation trajectory, q
_{d}for the desirable oscillation trajectory of semigirder.
The expression formula of structure function f (x) of aforesaid semigirder the unknown is:
Wherein, K is the frequency item in semigirder kinetic model,
for the signal that can measure,
Definition:
Aforesaid step 2) in, the control inputs of controller
exported and proportionplusderivative control item by RBF network
Form:
Wherein,
for RBF network exports, K
_{v}s is proportionplusderivative control item, K
_{v}for linear Feedback Control parameter.
Aforesaid step 3) in, described RBF network is threedecker: input layer, hidden layer and output layer, described input layer in order to accept in system can measuringsignal input x, output after described hidden layer adopts Gaussian bases to calculate Nonlinear Mapping, described output layer obtains the output of whole RBF network by the output of each hidden node of weighting
The output of described RBF network is
be the estimated value of the structure function of semigirder the unknown,
Wherein
for the estimated value of optimal network weights, φ (x) represents that hidden node exports.
Aforesaid step 4) in,
Described Lyapunov function V is chosen for:
Wherein,
for network weight evaluated error, W
^{*}for optimal network weights,
The update algorithm of described RBF network weight is:
Wherein, F=F
^{t}> 0 is the gain matrix of weighed value adjusting, γ be greater than 0 arbitrary value, be called forgetting factor.
In the update algorithm of aforesaid RBF network weight, meet:
Or
Wherein, W
_{b}represent optimal network weights W
^{*}the upper bound, K
_{vmin}for linear Feedback Control parameter K
_{v}smallest real eigenvalue and be greater than zero, ε
_{b}for the upper dividing value of network approximate error ε (x), b
_{d}for the upper dividing value of disturbance d.
Aforesaid step 5) in, semigirder mathematical model is:
Wherein, C is damping term, and K is frequency item, and q is semigirder oscillation trajectory, and u is input vector, and d is disturbance.
Compared with prior art, advantage is in the present invention:
(1) have employed the control method that self_adaptive RBF network and proportionplusderivative control combine, effectively can overcome unknown term and the external interference effect of Flexural cantilever model, greatly can improve tracking accuracy again.
(2) the present invention adopts neural network adaptive algorithm, can online control parameter control system, and adaptive algorithm, based on the design of Lyapunov stability theory, ensure that the global stability of closedloop system.
(3) also add the robust item ensureing weights bounded in the adaptive algorithm of network weight, thus ensure that the boundedness of control inputs, make the present invention be easy to implement in engineering.
(4) the present invention does not need the control of semigirder to be based upon on the basis of object Accurate Model, saves the expense of modeling.
Accompanying drawing explanation
Fig. 1 is the semigirder vibration control principle composition based on neural network control of the present invention;
Fig. 2 is the track following figure after employing the present invention under Static disturbance.
Embodiment
For further setting forth the present invention for the technological means reaching predetermined goal of the invention and take and effect, below in conjunction with accompanying drawing and preferred embodiment, to the detailed description of the invention as rear.
A kind of semigirder vibration control principle based on neural network control of the present invention as shown in Figure 1, comprises following components:
(1) set up based on semigirder filtering error model
The vector form of semigirder kinetic model:
C, K ∈ R in formula
^{i*i}for systematic parameter, wherein C is damping term, and K is frequency item, and q is semigirder oscillation trajectory, and u is input vector, and d is disturbance.
The control objectives of cantilever beam system is that semigirder oscillation trajectory follows the tracks of upper given ideal trajectory, if ideal trajectory q
_{d}for: q
_{d}=[x
_{d1}, x
_{d2}..., x
_{di}]
^{t}, x
_{di}for ideal trajectory ith order component, i represents exponent number.
Definition tracking error e is:
e＝q
_{d}q???(2)
Definition filtering error s expression formula is:
In formula, Λ=Λ
^{t}> 0 is filtering error parameter, and being generally namely taken as element is positive diagonal matrix entirely.Differentiate is carried out to filtering error s, obtains the filtering error model based on semigirder:
In formula,
F (x) represents the structure function of semigirder the unknown, in formula,
for the signal that can measure, as the input of neural network, definition:
(2) CONTROLLER DESIGN
The control inputs of CONTROLLER DESIGN
for:
In formula,
for the estimated value of structure function f (x) of semigirder the unknown, be the output of RBF network, the Nonlinear Mapping utilizing neural network powerful and approximation capability estimate its true value online in real time.
Kv is linear Feedback Control parameter,
be proportionplusderivative control item, wherein
${K}_{v}={K}_{v}^{T}>0.$
By control inputs
control inputs u as the mathematical model of semigirder brings into (4), obtains closedloop system equation to be:
In formula,
for the networkevaluated error of RBF:
Formula (8) is the kinetics equation of filtered tracking error system, and the object of control system makes error s bounded, and converges on a less scope.From formula (3), be a stable wave filter from e to s, if s ultimate boundness, then tracking error e bounded.
For the RBF network in the present invention, select threedecker: input layer, hidden layer and output layer.Input layer accept in system can measuringsignal input x; Output after hidden layer adopts Gaussian bases to calculate Nonlinear Mapping; Output layer obtains the output of whole RBF network by the output of each hidden node of weighting, as follows with mathematical description RBF network model:
φ
_{j}(x)＝exp(xc
_{j}/σ
_{j}),j＝1,2,…n
_{2}
In formula, n
_{2}, n
_{3}represent hidden node number and output layer node number respectively, and the dimension of input signal x is designated as n
_{1}; ω
_{ij}represent network weight; y
_{i}represent that RBF network exports; φ
_{j}x () is hidden node output; c
_{j}, σ
_{j}represent center vector and the sound stage width of each hidden node respectively.Existing document is verified, and RBF network can approach the nonlinear function of arbitrary smooth with arbitrary accuracy.Center vector and the sound stage width of the RBF network in the present invention are determined according to priori, are designed to fixed value, do not change in system operation, and the online realtime update of weights.Based on this, RBF network model is rewritten as:
y＝W
^{T}φ(x)???(11)
In formula, W
^{t}=[ω
_{ij}], φ (x)=[φ
_{j}(x)], due to c
_{j}, σ
_{j}fixing, φ (x) is known signal.
Based on the approximation capability of RBF network, can do to suppose as this: there is one group of optimal network weights W
^{*}, make when the input x of RBF network belong to one compact S time, RBF network can Nonlinear Function Approximation f (x), network approximate error ε (x) bounded under optimal network weights,
f(x)＝W
^{*T}φ(x)+ε(x)???(12)
In formula,  ε (x) ≤ε
_{b},
ε
_{b}for the upper bound of network approximate error ε (x);
Optimal network weights bounded:  W
^{*}
_{f}≤ W
_{b},  
_{f}the F norm of representing matrix, W
_{b}represent optimal network weights W
^{*}the upper bound.
Utilize RBF network to approach f (x), obtain the estimated value of nonlinear function f (x)
for optimal network weights W
^{*}estimated value.
Convolution (7), the control inputs of controller becomes:
By control inputs
control inputs u as the mathematical model of semigirder brings formula (4) into:
In formula,
for network weight evaluated error.
So far, structure and the closedloop error equation of the controller described in invention is obtained.
(3) update algorithm of RBF neural weights is designed
Semigirder vibration control method based on neural network control of the present invention, the update algorithm of its RBF network weight is:
In formula, F=F
^{t}> 0 is the arbitrary value of the gain matrix of weighed value adjusting, γ > 0, is called forgetting factor.
Prove that the network weight update algorithm in formula (16) can ensure tracking error s and network weight estimated value below
ultimate boundness, and respective boundary is as shown in lower inequality (24), (25) right side.Meanwhile, by increasing linear Feedback Control parameter K
_{v}, tracking error s can be made to be maintained to arbitrarily small scope.
A Lyapunov candidate functions V is chosen to the closedloop system of formula (15):
To formula (17) both sides differentiate:
Because
$\stackrel{~}{W}={W}^{*}\hat{W},$ So
$\stackrel{.}{\stackrel{~}{W}=\stackrel{.}{\hat{W}}}$
Network weight update algorithm in formula (16) is brought into formula (18) to obtain:
The character of associate(d) matrix mark and matrix F norm, has:
So,
Wherein, K
_{vmin}for linear Feedback Control parameter K
_{v}smallest real eigenvalue and be greater than zero, ε
_{b}for the upper dividing value of network approximate error ε (x), b
_{d}for the upper dividing value of disturbance d, namely  ε (x) ≤ε
_{b},  d≤b
_{d}.
As can be seen from formula (21), be just such as formula transition formula evaluation in middle bracket, then
be negative, i.e. system stability.
Due to:
It is just that formula (22) is ensured, as long as
Or
In formula, b
_{s}, b
_{w}a just constant of arbitrarily setting.
Comprehensive above analytic process, can reach a conclusion:
negative definite outside the region that formula (23) or (24) describe.According to the standard extension theorem of Lyapunov stability theory, known  s and
ultimate boundedness be guaranteed.Because, once s or
beyond the regional extent that formula (23) and (24) specify, the decline of Lyapunov function V will be caused, this can make again s and
in the scope that two formulas of getting back to limit.So formula (23) and formula (24) have in fact respectively provided  s and
the upper bound.And, can notice from formula (23), larger feedback gain matrix K
_{v}will obtain less  the upper bound of s, therefore tracking error s finally can maintain in arbitrarily small scope.As can be seen from formula (24), the boundedness of RBF network weight, ensure that the boundedness of control inputs, and this point is very important for Practical Project.
As can be seen from analytical proof process above, Section 1 in right value update algorithm in formula (16) is the error back propagation algorithm derived based on lyapunov stability theory, and Section 2 is the robust item added, be used for ensureing the boundedness of weights.
(4) computer simulation experiment
By dynamics, the main contribution of structural vibration in minimum several rank mode, in order to explain the situation and fundamental purpose in the emulation of elastic construction vibration suppression, only select first step mode here.In order to show the validity of the semigirder vibration control method based on neural network control that the present invention proposes more intuitively, perceptive construction on mathematics/SIMULINK is now utilized to carry out computer simulation experiment to this control program.With reference to existing document, choose:
The parameter of semigirder is: damping term C=0.18, frequency item K=56.4.
Desired reference track is set as:
${q}_{d}=0,{\stackrel{.}{q}}_{d}=0,{\stackrel{..}{q}}_{d}=0.$
Linear Feedback Control parameter is taken as K
_{v}=100, filtering error parameter is taken as Λ=1.
The node in hidden layer n of RBF neural
_{2}be taken as 45.
External interference added by emulation experiment is white noise disturbance d=randn (1,1), if disturbance applies all the time, the 10th second time, apply control action Dynamic simulation program, obtain the experimental result of the neural network control system of semigirder as shown in Figure 2.
Fig. 2 illustrates the semigirder oscillation trajectory tracking effect curve under the control method proposed in the present invention, and in figure, solid line is ideal trajectory, and dotted line is actual path.As can be seen from this accompanying drawing, under stable state disturbance, neural network control effect clearly, and after applying control action, external interference decays rapidly in 3s ~ 4s.Control system can make the output of semigirder, when not knowing semigirder parameter and structure and there is external interference effect, can promptly follow the tracks of given ideal trajectory, and tracking error is very little, reaches satisfied effect.
As can be seen from above analogous diagram, the control method that the present invention proposes is followed the tracks of the oscillation trajectory of semigirder good control effects, substantially increase tracking performance and the robustness of cantilever beam system, control to provide theoretical foundation and From Math to the high precision of semigirder oscillation trajectory.
The content be not described in detail in instructions of the present invention belongs to the known technical knowhow of professional and technical personnel in the field.
The above, it is only preferred embodiment of the present invention, not any in form large restriction is done to the present invention, although the present invention discloses as above with preferred embodiment, but and be not used to limit the present invention, any those skilled in the art, do not departing within the scope of technical solution of the present invention, make a little change when the technology contents of abovementioned announcement can be utilized or be modified to the Equivalent embodiments of equivalent variations, in every case be the content not departing from technical solution of the present invention, according to any simple modification that technical spirit of the present invention is done above embodiment, equivalent variations and modification, all still belong in the scope of our bright technical scheme.
Claims (9)
1., based on the semigirder vibration control method of neural network control, it is characterized in that, comprise the following steps:
1) the filtering error model based on semigirder is set up;
2) CONTROLLER DESIGN;
3) adopt RBF network to approach the structure function of the semigirder the unknown in semigirder mathematical model, obtain the estimated value of the structure function of semigirder the unknown;
4) based on the update algorithm of Lyapunov stability theory design RBF neural weights;
5) using the control inputs of the control inputs of the controller through RBF network control as semigirder mathematical model, semigirder is controlled, and realtime online upgrades.
2. the semigirder vibration control method based on neural network control according to claim 1, is characterized in that, described step 1) in, the filtering error model based on semigirder is:
Wherein, s is filtering error, and C is the damping term in semigirder kinetic model, and u is the input vector in semigirder kinetic model, and d is the disturbance of semigirder kinetic model, and f (x) represents the structure function of semigirder the unknown.
3. the semigirder vibration control method based on neural network control according to claim 2, is characterized in that, described filtering error s is:
Wherein, Λ is filtering error parameter, and e is tracking error: e=q
_{d}q
Q is semigirder oscillation trajectory, q
_{d}for the desirable oscillation trajectory of semigirder.
4. the semigirder vibration control method based on neural network control according to claim 2, is characterized in that, the expression formula of structure function f (x) of described semigirder the unknown is:
Wherein, K is the frequency item in semigirder kinetic model,
for the signal that can measure,
Definition:
5. the semigirder vibration control method based on neural network control according to claim 1, is characterized in that, described step 2) in, the control inputs of controller
exported by RBF network and form with proportionplusderivative control item:
Wherein,
for RBF network exports, K
_{v}s is proportionplusderivative control item, K
_{v}for linear Feedback Control parameter.
6. the semigirder vibration control method based on neural network control according to claim 1, it is characterized in that, described step 3) in, described RBF network is threedecker: input layer, hidden layer and output layer, described input layer in order to accept in system can measuringsignal input x, the output after described hidden layer adopts Gaussian bases to calculate Nonlinear Mapping, described output layer obtains the output of whole RBF network by the output of each hidden node of weighting
The output of described RBF network is
be the estimated value of the structure function of semigirder the unknown,
Wherein
for the estimated value of optimal network weights, φ (x) represents that hidden node exports.
7. the semigirder vibration control method based on neural network control according to claim 1, is characterized in that, described step 4) in,
Described Lyapunov function V is chosen for:
Wherein,
for network weight evaluated error, W
^{*}for optimal network weights,
The update algorithm of described RBF network weight is:
Wherein, F=F
^{t}> 0 is the gain matrix of weighed value adjusting, γ be greater than 0 arbitrary value, be called forgetting factor.
8. the semigirder vibration control method based on neural network control according to claim 7, is characterized in that, in the update algorithm of described RBF network weight, meets:
Or
Wherein, W
_{b}represent optimal network weights W
^{*}the upper bound, K
_{vmin}for linear Feedback Control parameter K
_{v}smallest real eigenvalue and be greater than zero, ε
_{b}for the upper dividing value of network approximate error ε (x), b
_{d}for the upper dividing value of disturbance d.
9. the semigirder vibration control method based on neural network control according to claim 1, is characterized in that, described step 5) in, semigirder mathematical model is:
Wherein, C is damping term, and K is frequency item, and q is semigirder oscillation trajectory, and u is input vector, and d is disturbance.
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