CN107608209A - The feedforward of piezoelectric ceramic actuator and closed loop composite control method, system - Google Patents
The feedforward of piezoelectric ceramic actuator and closed loop composite control method, system Download PDFInfo
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Abstract
The present invention relates to a kind of feedforward of piezoelectric ceramic actuator and closed loop composite control method and system, designed to improve control accuracy.The feedforward of piezoelectric ceramic actuator of the present invention and closed loop composite control method and system, utilize any non-linear expression's ability possessed by neutral net, the PID controller of parameter kp, ki, kd self study is established by the study of the performance to piezoelectric ceramics closed-loop control system, piezoelectric ceramic actuator is controlled using feedback displacement closed loop control method using the PID controller adjusted.Running status of the invention according to system, adjust the parameter of PID controller, to reach the optimization of certain performance indications, three adjustable parameters kp, ki, kd that the output state of output layer neuron corresponds to PID controller are made to make neutral net output corresponding to the PID controller parameter under certain optimal control law by the self study of neutral net, weight coefficient adjustment.
Description
Technical field
The present invention relates to a kind of feedforward of piezoelectric ceramic actuator and closed loop composite control method and system.
Background technology
There is error in the Hysteresis Model feedforward compensation of piezoelectric ceramics, the anti-interference of opened loop control is poor, and closed-loop control has
Feedback element can be effective anti-interference.PID controller tries to achieve control deviation e according to set-point r (t) and real output value f (t)
(t), i.e. e (t)=r (t)-f (t), then the ratio of deviation, integration and differential are formed into control variable by linear combination,
Control target is controlled, PID controller is a kind of linear controller, and its control law is：
In formula, kp- proportionality coefficient；TI- integration time constant；TD- derivative time constant；E (t)-deviation signal.
In simple terms, the effect of each correction link of PID controller is as follows.
Proportional component P：Proportionally reflect the deviation signal e (t) of controller system, once producing deviation, controller is stood
Control action is produced, to reduce deviation.
Integral element I：Be mainly used in eliminate static difference, improve system without margin.The power of integral action depends on integration
Time constant TI, TIBigger, integral action is weaker, on the contrary then stronger.
Differentiation element D：Reflect the variation tendency (rate of change) of deviation signal, and can deviation signal become it is too big it
Before, an effective early stage revise signal is introduced in systems, so as to accelerate the responsiveness of system, reduces regulating time.
The control effect of PID controller depends primarily on kp, ki, kdThe regulation of three parameters, therefore how to obtain and most have
The corresponding parameter of effect is the crucial part of PID controller design.The problem of being optimized to pay close attention to for people of PID controller parameter, it
Directly affect the quality of control effect, and safety with system, economical operation have the relation of interwoveness.Pid parameter at present
Optimization method have a lot, such as indirect searching optimization method, gradient method, climbing method etc., and simplex method, expert are whole in heat power engineering system
It is wider to determine rule application.Although these methods all have good optimizing characteristic, there is some drawbacks, simplex method pair
Initial value is more sensitive, is easily trapped into locally optimal solution, causes optimizing to fail.Expert, which adjusts rule, needs too many experience, different
Object function correspond to different experiences, and it is then a prolonged engineering to arrange knowledge base.
In addition, the intrinsic Hysteresis Nonlinear of piezoelectric ceramic actuator is to limit the master of Precision Position Location System control accuracy
Want factor.The Hysteresis Nonlinear characteristic of piezoelectric ceramics is macroscopically shown as：For input voltage, (voltage rose positive stroke
Journey) displacement output and revesal (voltage decline process) displacement output it is misaligned, displacement difference be present, it is more to show as one kind
The mapping relations of value, the sluggish static curve of its input voltage output displacement show as following distinguishing feature：(1) multivalue
Property, i.e., its output is not unique under same input condition；(2) Memorability, the output of actuator subsequent time depend not only on currently
The input and output at moment, it is also relevant with input state before；(3) rate is related, i.e., with the increase of incoming frequency, its is defeated
The sluggish behavior gone out is also strengthened therewith, and displacement output is also different caused by the input voltage of identical amplitude different frequency, and one
As show as frequency get over height output displacement it is smaller.Lagging characteristics cause the output of driver to become unpredictable, reduce
The performance of driver, the stability of high-precision motion alignment system is had a strong impact on.
In order to limit position error caused by the Hysteresis Nonlinear of piezoelectric ceramics, the sluggishness of piezoelectric ceramics is modeled.
Hysteresis Model main at present has Preisach model, PI models, multinomial model, Maxwell models etc..Preisach moulds
There is dual-integration and the more identification difficulty of parameter in type, it is non-linear that multinomial model can accurately describe big ring, but for retouching
State that small ring Hysteresis Nonlinear precision is relatively low, and Maxwell models have physical significance, but be only capable of describing symmetrical sluggish process.PI
Model of the model as more classical description lagging characteristics, it is to be superimposed to obtain by the different sluggish operator of many weights.Through
The PI models of allusion quotation can describe Hysteresis Nonlinear process with less parameter, and will not have error accumulation, but can only also describe pair
The sluggish process of title, but the retardant curve of piezoelectric ceramics is asymmetrical.
In view of the defects of above-mentioned, the design people is actively subject to research and innovation, to found a kind of piezoelectric ceramic actuator
Feedforward and closed loop composite control method, make it with more the value in industry.
The content of the invention
In order to solve the above technical problems, it is an object of the invention to provide the piezoelectric ceramics that a kind of control effect is good, precision is high
The feedforward of driver and closed loop composite control method and system.
To achieve the above object of the invention, the feedforward of piezoelectric ceramic actuator of the present invention and closed loop composite control method, bag
Include：By expectation displacement r (t) inputs of piezoelectric ceramic actuator to feed forward models, feed forward models are according to the expectation shift value r
(t) computing obtains the initial boost voltage u of piezoelectric ceramic actuatorε(t)；With piezoelectric ceramics displacement or piezoelectricity pottery driver position
The feedback signal for PID controller is moved, by PID controller to described initial boost voltage uε(t) error concealment is carried out,
Obtain the driving voltage of piezoelectric ceramic actuator, and the proportion adjustment parameter k using BP neural network to PID controllerp, product
Divide adjustment parameter ki, differential adjustment parameter kdOptimize.
Further, described feed forward models is improve PI sluggishness inversion models, and the improvement PI sluggishness inversion models are by changing
Enter PI Hysteresis Models to invert to obtain；
Wherein, PI Hysteresis Models are improved to be expressed as：The improvement PI Hysteresis Models are divided into rising part and sloping portion,
When input voltage increases, using one group of weights, when the output voltage drops, using another group of weights；Improve PI Hysteresis Models
Represented with below equation,
In formula, z (t) is the displacement of piezoelectric ceramic actuator, wpjRepresent weights when input voltage rises, wqjRepresent defeated
Enter weights when voltage declines, rjFor the threshold value of sluggish operator；Fj() is current sluggish operator displacement function；X (t) is to apply
Voltage on piezoelectric ceramic actuator；I represents the moment；J=1,2......n are sluggish operator number；yj(ti-1) it is previous
The output valve of moment j rank sluggishness operator；
The discrimination method for rising weights and threshold value is identical with the discrimination method of classical PI Hysteresis Models；When input voltage is believed
Number x (t) from maximum be decremented to zero when, then output angle and the relation of input voltage are piezoelectric ceramic actuator sluggishness
The big ring sloping portion of loop line, the weights can that declines of PI Hysteresis Models decline according to the big ring of piezoelectric ceramics lag loop
Partial segmentation slope is tried to achieve；The size of threshold value is tried to achieve according to equation below：
The size for declining weights estimates that estimation formulas is as follows according to the slope value of the big ring sloping portion of retardant curve：
Inverted to improving PI Hysteresis Models, obtain improving PI sluggishness inversion models, the improvement PI sluggishness inversion model formula tables
Show as follows：
The initial boost voltage value of piezoelectricity pottery driver is tried to achieve based on improvement PI sluggishness inversion models.
Further, the proportion adjustment parameter k using BP neural network to PID controllerp, integral adjustment ginseng
Number ki, differential adjustment parameter kdThe method optimized includes：
S1 determines the structure of BP neural network, that is, determines input layer number M and node in hidden layer Q, and provide input
The initial value of layer and hidden layer weight coefficientWithLearning efficiency and inertia coeffeicent are selected, now K=1；
S2 samples to obtain reference input rin (k) and system output yout (k), calculates the moment error e (k)=rin
(k)-your(k)；
S2 calculates the input of each layer neuron of BP neural network, output, and the output of BP neural network output layer is PID
Three adjustable parameter k of controllerp, ki, kd；
S3 calculates the output u (k) of PID controller, classical increment type number according to classical Increment Type Digital Hydraulic pid control algorithm
Word pid control algorithm, is represented with equation below：
In formula, u (k) is the driving voltage of the piezoelectric ceramic actuator of kth time sampling instant, and k is sampling sequence number, k=0,
1,2 ...；E (k) is deviation signal；
S4 carries out neural network learning, on-line tuning input layer and hidden layer weight coefficientWithRealize
The adaptive adjustment of pid parameter；
S5 puts k=k+1, returns to S1.
Further, it is using three layers of BP neural network, the input of network input layer：
In formula,For the j of input layer activation value；
In formula (1), the number M of input variable depends on the complexity of controlled system, network hidden layer it is defeated
Enter, export and be：
In formula (2),For hidden layer neuron i and neuron j connection weight；Superscript (1), (2), (3)
Input layer, hidden layer and output layer are represented respectively；The activation functions of hidden layer neuron take the Sigmoid functions of Symmetrical
For：
The input and output of network output layer are：
Output layer output node corresponds to three adjustable parameter k respectivelyp, ki, kd, due to kp, ki, kdCan not be negative value, so
The negated negative Sigmoid functions of activation functions of output layer neuron are：
The performance index function is taken to be：
According to the weight coefficient of gradient descent method corrective networks, i.e., weight coefficient negative gradient direction is searched for by E (k) and adjusted,
And add an Inertia for making search Fast Convergent global minimal：
In formula (5), η is learning efficiency, and α is inertia coeffeicent；
Due toIt is unknown, so approximation sign functionSubstitution, thus bring and calculate inaccurate shadow
Sound can be compensated by regularized learning algorithm speed, can be obtained by formula (1) and (4)：
Above-mentioned analysis can obtain the learning algorithm that network output layer is weighed：
The learning algorithm of hidden layer weight coefficient can similarly be obtained：
In formula (6) and (7), g ' (x)=g (x) (1-g (x)), f ' (x)=(1-f2(x))/2。
Further, piezoelectricity pottery driver includes platform framework, and piezoelectric ceramics is arranged in the holding part of platform framework,
The piezoelectric ceramics prolonging direction is provided with the flexible hinge of double parallel harden structure, and the flexible hinge is divided into two groups, symmetrical cloth
Put；Dynamic analysis to piezoelectricity pottery driver, obtains the unified dynamics transmission function of piezoelectric ceramics and flexible hinge：
In formula, U (s) is the driving voltage of piezoelectricity pottery driver；Z (s) is the displacement of piezoelectricity pottery driver；meffFor piezoelectricity
The equivalent mass of ceramics, cpIt is K for the damped coefficient of piezoelectric ceramicspThe rigidity of piezoelectric ceramics；M be hinge equivalent mass, cs
For the equivalent damping of hinge, KsFor the equivalent stiffness of hinge.
To achieve the above object of the invention, the feedforward of piezoelectric ceramic actuator of the present invention and closed loop multiplex control system, bag
Include：Feed forward models unit, PID controller, pid parameter optimization unit, Sensor Measurement Unit, piezoelectricity pottery driver, wherein,
The feed forward models unit, pressed for inputting computing according to the expectation displacement r (t) of piezoelectric ceramic actuator
The initial boost voltage u of electroceramics driverε(t)；
The Sensor Measurement Unit, for exporting the displacement of piezoelectricity pottery driver, obtaining piezoelectricity in piezoelectricity pottery driver
The displacement of ceramics, the feedback signal as PID controller closed-loop control；
The PID controller, made pottery for piezoelectricity in the displacement according to described piezoelectricity pottery driver, piezoelectricity pottery driver
The displacement of porcelain is to described initial boost voltage uε(t) error concealment is carried out, and exports the driving electricity of piezoelectric ceramic actuator
Pressure；
BP neural network unit, for the proportion adjustment parameter k to PID controllerp, integral adjustment parameter ki, differential tune
Save parameter kdOn-line tuning is carried out, the carrying out practically process of BP neural network unit includes：
S1 determines the structure of BP neural network, that is, determines input layer number M and node in hidden layer Q, and provide input
The initial value of layer and hidden layer weight coefficientWithLearning efficiency and inertia coeffeicent are selected, now k=1；
S2 samples to obtain reference input rin (k) and system output yout (k), calculates the moment error e (k)=rin
(k)-yout(k)；
S2 calculates the input of each layer neuron of BP neural network, output, and the output of BP neural network output layer is PID
Three adjustable parameter k of controllerp, ki, kd；
S3 calculates the output u (k) of PID controller, classical increment type number according to classical Increment Type Digital Hydraulic pid control algorithm
Word pid control algorithm, is represented with equation below：
In formula, u (k) is that the piezoelectricity of kth time sampling instant is made pottery the driving voltage of driver, and k is sampling sequence number, k=0,1,
2 ...；E (k) is deviation signal；The driving voltage and last moment piezoelectricity of the piezoelectricity pottery driver at Δ u (k) current times
The difference of the driving voltage of pottery driver；
S4 carries out neural network learning, on-line tuning input layer and hidden layer weight coefficientWithRealize
The adaptive adjustment of pid parameter；
S5 puts k=k+1, returns to S1.
Further, the feed forward models unit, described initial driving electricity is obtained using PI sluggishness inversion models are improved
Pressure, wherein the improvement PI sluggishness inversion models formula represents as follows：
Further, piezoelectricity pottery driver includes platform framework, and the appearance of accommodating piezoelectric ceramics is provided with the platform framework
Portion is put, the piezoelectric ceramics is arranged in the piezoelectric ceramics holding part, and the piezoelectric ceramics prolonging direction is provided with double parallel
The flexible hinge of harden structure, described flexible hinge at least four, is divided into two groups, two-by-two relatively, is arranged symmetrically；
Dynamic analysis to piezoelectricity pottery driver, the unified dynamics for obtaining piezoelectric ceramics and flexible hinge transmit letter
Number：
In formula, U (s) is the driving voltage of piezoelectricity pottery driver；Z (s) is the displacement of piezoelectricity pottery driver；meffFor piezoelectricity
The equivalent mass of ceramics, cpIt is K for the damped coefficient of piezoelectric ceramicspThe rigidity of piezoelectric ceramics；M be hinge equivalent mass, cs
For the equivalent damping of hinge, KsFor the equivalent stiffness of hinge；
The Sensor Measurement Unit includes piezoelectric ceramics displacement measurement circuit, piezoelectric ceramic actuator displacement transducer,
Wherein, the piezoelectric ceramics displacement measurement circuit includes four groups of resistance strain gages being attached on piezoelectric ceramics, the resistance-strain
The full-bridge circuit of piece composition measurement piezoelectric ceramics displacement, each bridge arm of the full-bridge circuit are respectively equipped with one group of resistance-strain
Piece.
By such scheme, the feedforward of piezoelectric ceramic actuator of the present invention and closed loop composite control method and system are at least
With advantages below：
Using any non-linear expression's ability possessed by neutral net, by piezoelectric ceramics closed-loop control system
Learning to establish the PID controller of parameter kp, ki, kd self study for performance, makes neutral net output correspond to certain optimal control
PID controller parameter under rule processed, to realize the PID control with best of breed.
Described above is only the general introduction of technical solution of the present invention, in order to better understand the technological means of the present invention,
And can be practiced according to the content of specification, below with presently preferred embodiments of the present invention and coordinate accompanying drawing describe in detail as after.
Brief description of the drawings
Fig. 1 is that the feedforward of piezoelectric ceramic actuator is combined with the feedforward of closed loop composite control method with closed-loop control
Complex controll block diagram；
Fig. 2 is the output of n Play operator；
Fig. 3 is to be initially loaded decline curve figure and the big ring sloping portion of retardant curve；
Fig. 4 is classical PI Hysteresis Models error of fitting；
Fig. 5 is to improve asymmetric PI Hysteresis Models error of fitting.
Fig. 6 is artificial neural network principle figure；
Fig. 7 is PID controller structure of the feedforward with closed loop multiplex control system of piezoelectric ceramic actuator；
Fig. 8 is the pid parameter change curve of the feedforward and the emulation of closed loop composite control method of piezoelectric ceramic actuator.
Embodiment
With reference to the accompanying drawings and examples, the embodiment of the present invention is described in further detail.Implement below
Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
Artificial neural network (Artificial Neural Network) is a kind of active network with topological structure,
It is to a certain degree of imitation of people's cerebral nervous system, arbitrarily complicated non-linear relation can be approached, so as to generate Nonlinear Dynamic
Mechanical system has very strong fault-tolerance and robustness, in the control of nonlinear system to represent the Controlling model of controlled device
In, neutral net with high-precision approximation capability, quick concurrent operation ability and powerful fault-tolerant ability because obtain
It is widely applied.When being modeled with neutral net to Hysteresis Nonlinear, the output of sluggish operator can be inputted with sluggish
Neural network model is established in input together as neutral net.Fig. 6 is the schematic diagram of artificial neural network.
PID control will obtain relatively good control effect, just must be by adjusting three kinds of ratio, integration and differential controls
Make and use, form in controlled quentity controlled variable the relation for not only cooperating but also mutually restricting, this relation is not necessarily simple linear group
Close, can be found out from varied nonlinear combination optimal.Any non-linear table Danone possessed by neutral net
Power, can be by realizing the PID control with best of breed to the study of systematic function.Using BP networks, ginseng can be established
The PID controller of number kp, ki, kd self study.
Embodiment 1
The feedforward of the present embodiment piezoelectric ceramic actuator and closed loop composite control method, including：By piezoelectric ceramic actuator
Expectation displacement r (t) inputs piezoelectric ceramics is obtained according to expectation shift value r (t) computing to feed forward models, feed forward models
The initial boost voltage u of driverε(t)；Using piezoelectric ceramics displacement or piezoelectricity pottery driver displacement as PID controller feedback
Signal, by PID controller to described initial boost voltage uε(t) error concealment is carried out, obtains piezoelectric ceramic actuator
Driving voltage, and the proportion adjustment parameter k using BP neural network to PID controllerp, integral adjustment parameter ki, differential regulation
Parameter kdOptimize.
In the present embodiment, to improve PI sluggishness inversion models, the improvement PI sluggishness inversion models pass through described feed forward models
PI Hysteresis Models are improved to invert to obtain；
Wherein, PI Hysteresis Models are improved to be expressed as：The improvement PI Hysteresis Models are divided into rising part and sloping portion,
When input voltage increases, using one group of weights, when the output voltage drops, using another group of weights；Improve PI Hysteresis Models
Represented with below equation,
In formula, z (t) is the displacement of piezoelectric ceramic actuator, wpjRepresent weights when input voltage rises, wqjRepresent defeated
Enter weights when voltage declines, rjFor the threshold value of sluggish operator；Fj() is current sluggish operator displacement function；X (t) is to apply
Voltage on piezoelectric ceramic actuator；I represents the moment；J=1,2......n are sluggish operator number；yj(ti-1) it is previous
The output valve of moment j rank sluggishness operator；
The discrimination method for rising weights and threshold value is identical with the discrimination method of classical PI Hysteresis Models；When input voltage is believed
Number x (t) from maximum be decremented to zero when, then output angle and the relation of input voltage are piezoelectric ceramic actuator sluggishness
The big ring sloping portion of loop line, the weights can that declines of PI Hysteresis Models decline according to the big ring of piezoelectric ceramics lag loop
Partial segmentation slope is tried to achieve；The size of threshold value is tried to achieve according to equation below：
The size for declining weights estimates that estimation formulas is as follows according to the slope value of the big ring sloping portion of retardant curve：
Inverted to improving PI Hysteresis Models, obtain improving PI sluggishness inversion models, the improvement PI sluggishness inversion model formula tables
Show as follows：
The initial boost voltage value of piezoelectricity pottery driver is tried to achieve based on improvement PI sluggishness inversion models.
Classical PI Hysteresis Models
Hysteresis Nonlinear is regarded as what a series of Play operators linear weighted functions were formed by stacking by classical PI models,
The play operators linear weighted function superposition of multiple different threshold values, Hysteresis Model output is obtained as shown in formula (1), wj
And rjFor the weights and threshold value of play operators, meet 0=r1＜ ... ＜ rn＜+∞, n are the number of play operators.
The parameter identification of classical PI Hysteresis Models
When input voltage signal x (t) be an initial value be zero monotonic increase to maximum signal when, then carry-out bit
Move the big ring rising part as with the relation lag loop of input voltage.When x (t) increases to maximum from zero, n
After Play operator weighted superpositions, you can obtain the PI Hysteresis Models of piezoelectric ceramic actuator, the weights of PI Hysteresis Models can root
Tried to achieve according to the segmentation slope of the big ring rising part of piezoelectric ceramic actuator lag loop.
When input voltage is from zero increase to maximum, the input-output curve of PI Hysteresis Models is referred to as being initially loaded
Curve is risen, can be gone to be fitted the big ring rising part of piezoelectric ceramic actuator lag loop with ascending curve is initially loaded.
The size of threshold value can use formula in the minimum value of input voltage to mean allocation between maximum, threshold value
(2) determine：
Being initially loaded ascending curve can change in every slope after a threshold value, can be according in each section
The slope value of the interior big ring rising part of retardant curve estimates corresponding wjValue, estimation formulas are as follows：
Improve PI Hysteresis Models
In order to describe asymmetrical retardant curve, the present invention is improved PI Hysteresis Models, by PI sluggishness moulds
Type is divided into rising part and sloping portion.When input voltage increases, using one group of weights, when the output voltage drops, use
Another group of weights.Improving PI Hysteresis Models can use formula (4) to represent, the w in formulapjWeights when input voltage rises are represented,
wqjRepresent weights when input voltage declines.
Improve the parameter identification of PI Hysteresis Models
Improving the parameter of PI Hysteresis Models mainly includes rising weight wPjWith decline weight wqj, and threshold value r.Rise power
The discrimination method of value and threshold value is identical with the discrimination method of classical PI Hysteresis Models, and here is omitted.Work as input voltage signal
X (t) from maximum be decremented to zero when, then output angle and the relation of input voltage, which are that piezoelectric ceramic actuator is sluggish, returns
The big ring sloping portion of line, the now output of n Play operator can represent that curve of output is the solid line portion in figure with Fig. 2
Point.
After Fig. 2 n Play operator weighted superposition, you can obtain the PI Hysteresis Models of piezoelectric ceramics, the effect of weights
It is the slope for changing Fig. 2 bends, then the decline weights can of PI Hysteresis Models is according to piezoelectric ceramics lag loop
The segmentation slope of big ring sloping portion is tried to achieve.
When input voltage is decremented to zero from maximum, the input-output curve of PI Hysteresis Models is referred to as being initially loaded down
Curve is dropped, can be gone to be fitted the big ring of piezoelectric ceramic actuator lag loop with decline curve is initially loaded
Sloping portion.It is initially loaded decline curve figure and the big ring sloping portion of retardant curve is as shown in Figure 3.
The size of threshold value can use formula in the minimum value of input voltage to mean allocation between maximum, threshold value
(5) determine：
And the size for declining weights can be estimated according to the slope value of the big ring sloping portion of retardant curve, estimation formulas
It is as follows：
The inversion model of PI sluggishness inversion model models
The feedforward control of piezoelectric ceramic actuator mainly predicts driving according to desired displacement before deviation appearance
Driving voltage value needed for platform, control accuracy is improved with this.It can be estimated according to PI Hysteresis Models are improved by input voltage
Go out the output displacement of piezoelectric ceramic actuator, feed-forward control algorithm needs to try to achieve with this according to improving the inverse of PI Hysteresis Models
The driving voltage value needed for platform is driven, the great advantage of PI models is exactly to be easy to invert, and its inversion model is still a PI mould
Type, only threshold value and weights need to do corresponding conversion, and the inversion model of (4) formula can be designated as shown in Equation 8.
Hysteresis phenomenon has had a strong impact on precision of the piezoelectric ceramics as high-accuracy locating platform, and piezoelectric ceramics is without control
Under the open loop case of system, tracking error caused by its Hysteresis Nonlinear highest is up to 15%, in order to reduce lagging characteristics to positioning
The influence of precision, the PI Hysteresis Models of classics are established based on piezoelectric ceramics hysteresis phenomenon, because classical PI Hysteresis Models can only
The stagnant curve in description center, and actual sluggishness is all asymmetrical, that is, is not had when rising between retardant curve and decline retardant curve
There is symmetry axis.The present invention proposes asymmetrical PI Hysteresis Models, is obtained late using the slope of ascending curve and decline curve
Stagnant rising weights and decline weights, and model emulation is fitted with matlab, the PI Hysteresis Models after improvement are fitted to obtain
More preferable models fitting precision, obtain the inversion model of PI Hysteresis Models, the feedforward compensation for piezoelectric ceramics complex controll.
Classical PI Hysteresis Models contrast with improving PI Hysteresis Models fitting precision
Parametric solution
More than to PI Hysteresis Models description it can be seen from when the Play operators in PI Hysteresis Models take it is more when,
PI Hysteresis Models are better to the degree of fitting of retardant curve, but the complexity in view of being calculated in practical application, selected in the design
25 Play operators.In order to simplify the programming process on identification process and computer, to the input voltage of piezoelectric ceramic actuator
It is normalized with output angle, formula is such as shown in (7).
In formula 7, x (t) is consequently exerted at the voltage on piezoelectric ceramic actuator, x (t)minIt is voltage minimum, x
(t)maxIt is voltage max, z (t) is displacement corresponding to piezoelectric ceramic actuator, z (t)minIt is displacement minimum value, z (t)maxIt is
Displacement maximum, xgAnd z (t)g(t) it is corresponding voltage and displacement after normalizing.X after normalizationg(t) maximum is 1,
The size of 25 threshold values can be obtained according to formula (2), as shown in table 1.
The PI Hysteresis Model threshold values of table 1
To the voltage of piezoelectric ceramic actuator input 0-150-0V change, according to the shift value of output, you can pick out
The weights of classical PI Hysteresis Models and the rising weights and decline weights for improving PI Hysteresis Models.The power of classical PI Hysteresis Models
Value is equal with improving PI Hysteresis Models rising weights, and rising weights can try to achieve according to formula (3), rise the weights such as institute of table 2
Show.Declining weights can try to achieve according to formula (6), decline weights as shown in table 3.
The classical PI Hysteresis Models weights of table 2 and improvement PI Hysteresis Models rise weights
Table 3 improves PI Hysteresis Models and declines weights
Fitting precision contrasts
The angle value of output is fitted come error of fitting is as shown in Figure 4, Figure 5 according to the magnitude of voltage of input.It will fit
The data come are contrasted with actually measured data, carry out data processing to error, the result after processing is as shown in table 4.
The error amount data processing of table 4
Data in Fig. 4, Fig. 5 and table 4 are analyzed, it can be seen that the fitting precision for improving PI Hysteresis Models is obvious
Improve.As seen from Figure 4, the fitting angle value of classical PI Hysteresis Models is smaller in the error of voltage ascent stage, and in electricity
The error of drops section is larger, then observes Fig. 5 figures and can be seen that the match value for improving PI Hysteresis Models in decline stage fitting
Error is small, rises weights because the weights for improving PI Hysteresis Models are divided into and declines weights, matched curve is asymmetric
, retardant curve can be described preferably, and the weights of classical PI Hysteresis Models only include rising weights, matched curve is pair
Claim, in the retardant curve decline stage, error of fitting is larger.
The present embodiment, the introducing of the feedforward control based on improved PI inversion models can improve Hysteresis Nonlinear characteristic, and
Improve its dynamic characteristic.And PID control method has preferable robustness and the characteristics of without Accurate Model, in precision positioning
Had a wide range of applications in control system.According to classical control theory, suitable feedforward control link can improve the sound of system
Should be able to power, but do not influence the control accuracy of system.PID/feedback control is combined based on the feedforward of improved PI inversion models using one kind
The control strategy of system.Its control principle drawing is as shown in Fig. 5, and wherein system passes through the mould that feedovers first according to shift value r (t) it is expected
Type it is expected voltage u corresponding to obtainingε(t) error concealment then, is carried out to it by PID/feedback control.
Embodiment 2
The feedforward of the present embodiment piezoelectric ceramic actuator and closed loop composite control method, on the basis of embodiment 1, institute
The proportion adjustment parameter k using BP neural network to PID controller statedp, integral adjustment parameter ki, differential adjustment parameter kdEnter
The method of row optimization includes：
S1 determines the structure of BP neural network, that is, determines input layer number M and node in hidden layer Q, and provide input
The initial value of layer and hidden layer weight coefficientWithLearning efficiency and inertia coeffeicent are selected, now K=1；
S2 samples to obtain reference input rin (k) and system output yout (k), calculates the moment error e (k)=rin
(k)-yout(k)；
S2 calculates the input of each layer neuron of BP neural network, output, and the output of BP neural network output layer is PID
Three adjustable parameter k of controllerp, ki, kd；
S3 calculates the output u (k) of PID controller, classical increment type number according to classical Increment Type Digital Hydraulic pid control algorithm
Word pid control algorithm, is represented with equation below：
In formula, u (k) is the driving voltage of the piezoelectric ceramic actuator of kth time sampling instant, and k is sampling sequence number, k=0,
1,2 ...；E (k) is deviation signal；
S4 carries out neural network learning, on-line tuning input layer and hidden layer weight coefficientWithRealize
The adaptive adjustment of pid parameter；
S5 puts k=k+1, returns to S1.
In the present embodiment, using three layers of BP neural network, the input of network input layer is：
In formula,For the j of input layer activation value；
In formula (1), the number M of input variable depends on the complexity of controlled system, network hidden layer it is defeated
Enter, export and be：
In formula (2),For hidden layer neuron i and neuron j connection weight；Superscript (1), (2), (3)
Input layer, hidden layer and output layer are represented respectively；The activation functions of hidden layer neuron take the Sigmoid functions of Symmetrical
For：
The input and output of network output layer are：
Output layer output node corresponds to three adjustable parameter k respectivelyp, ki, kd, due to kp, ki, kdCan not be negative value, so
The negated negative Sigmoid functions of activation functions of output layer neuron are：
The performance index function is taken to be：
According to the weight coefficient of gradient descent method corrective networks, i.e., weight coefficient negative gradient direction is searched for by E (k) and adjusted,
And add an Inertia for making search Fast Convergent global minimal：
In formula (5), η is learning efficiency, and α is inertia coeffeicent；
Due toIt is unknown, so approximation sign functionSubstitution, thus bring and calculate inaccurate shadow
Sound can be compensated by regularized learning algorithm speed, can be obtained by formula (1) and (4)：
Above-mentioned analysis can obtain the learning algorithm that network output layer is weighed：
The learning algorithm of hidden layer weight coefficient can similarly be obtained：
In formula (6) and (7), g ' (x)=g (x) (1-g (x)), f ' (x)=(1-f2(x))/2。
The present embodiment is based on the PID control system structure of BP networks as shown in fig. 7, controller is made up of two parts：It is classical
PID controller, directly to controlled device closed-loop control, and three parameters kp, ki, kd are on-line tuning mode.Nerve net
Network adjusts the parameter of PID controller, to reach the optimization of certain performance indications, makes output according to the running status of system
The output state of layer neuron correspond to three adjustable parameters kp, ki, kd of PID controller by the self study of neutral net,
Weight coefficient adjusts, the PID controller parameter for making neutral net output correspond under certain optimal control law.By this implementation
The feedforward of example piezoelectric ceramic actuator understands to follow the mistake of curve and input curve with the simulation curve of closed loop composite control method
Poor very little, as can be seen from Figure 8 kp, ki, kd value adjust in real time, so that tracking error is minimum.
Embodiment 3
The feedforward of the present embodiment piezoelectric ceramic actuator and closed loop multiplex control system, including：Feed forward models unit, PID
Controller, pid parameter optimization unit, Sensor Measurement Unit, piezoelectricity pottery driver, wherein,
The feed forward models unit, pressed for inputting computing according to the expectation displacement r (t) of piezoelectric ceramic actuator
The initial boost voltage u of electroceramics driverε(t)；
The Sensor Measurement Unit, for exporting the displacement of piezoelectricity pottery driver, obtaining piezoelectricity in piezoelectricity pottery driver
The displacement of ceramics, the feedback signal as PID controller closed-loop control；
The PID controller, made pottery for piezoelectricity in the displacement according to described piezoelectricity pottery driver, piezoelectricity pottery driver
The displacement of porcelain is to described initial boost voltage uε(t) error concealment is carried out, and exports the driving electricity of piezoelectric ceramic actuator
Pressure；
BP neural network unit, for the proportion adjustment parameter k to PID controllerp, integral adjustment parameter ki, differential tune
Save parameter kdOn-line tuning is carried out, the carrying out practically process of BP neural network unit includes：
S1 determines the structure of BP neural network, that is, determines input layer number M and node in hidden layer Q, and provide input
The initial value of layer and hidden layer weight coefficientWithLearning efficiency and inertia coeffeicent are selected, now k=1；
S2 samples to obtain reference input rin (k) and system output yout (k), calculates the moment error e (k)=rin
(k)-yout(k)；
S2 calculates the input of each layer neuron of BP neural network, output, and the output of BP neural network output layer is PID
Three adjustable parameter k of controllerp, ki, kd；
S3 calculates the output u (k) of PID controller, classical increment type number according to classical Increment Type Digital Hydraulic pid control algorithm
Word pid control algorithm, is represented with equation below：
In formula, u (k) is that the piezoelectricity of kth time sampling instant is made pottery the driving voltage of driver, and k is sampling sequence number, k=0,1,
2 ...；E (k) is deviation signal；The driving voltage and last moment piezoelectricity of the piezoelectricity pottery driver at Δ u (k) current times
The difference of the driving voltage of pottery driver；
S4 carries out neural network learning, on-line tuning input layer and hidden layer weight coefficientWithRealize
The adaptive adjustment of pid parameter；
S5 puts k=k+1, returns to S1.
In the present embodiment, the feed forward models unit, described initial driving electricity is obtained using PI sluggishness inversion models are improved
Pressure, wherein the improvement PI sluggishness inversion models formula represents as follows：
The specific control method of the present embodiment system is same as Example 1, will not be repeated here.
In the various embodiments described above, piezoelectricity pottery driver includes platform framework, and piezoelectric ceramics is arranged on the accommodating of platform framework
In portion, the piezoelectric ceramics prolonging direction is provided with the flexible hinge of double parallel harden structure, and the flexible hinge is divided into two groups,
It is arranged symmetrically；Dynamic analysis to piezoelectricity pottery driver, the unified dynamics for obtaining piezoelectric ceramics and flexible hinge transmit letter
Number：
In formula, U (s) is the driving voltage of piezoelectricity pottery driver；Z (s) is the displacement of piezoelectricity pottery driver；meffFor piezoelectricity
The equivalent mass of ceramics, cpIt is K for the damped coefficient of piezoelectric ceramicspThe rigidity of piezoelectric ceramics；M be hinge equivalent mass, cs
For the equivalent damping of hinge, KsFor the equivalent stiffness of hinge.
In the various embodiments described above, the Sensor Measurement Unit includes piezoelectric ceramics displacement measurement circuit, piezoelectric ceramics drives
Dynamic device displacement transducer, the piezoelectric ceramics displacement measurement circuit include four groups of resistance strain gages being attached on piezoelectric ceramics, institute
The full-bridge circuit of resistance strain gage composition measurement piezoelectric ceramics displacement is stated, each bridge arm of the full-bridge circuit is respectively equipped with one
Group resistance strain gage；The piezoelectric ceramic actuator displacement transducer capaNCDT6300 single channel Series of High Accuracies displacement passes
Sensor.Piezoelectric ceramics displacement of the Sensor Measurement Unit suitable for above-described embodiment 1, embodiment 2 described in the embodiment
Acquisition and piezoelectric ceramic actuator displacement acquisition.
System described in above-described embodiment 3 is using the method operation described in embodiment 1,2.
Described above is only the preferred embodiment of the present invention, is not intended to limit the invention, it is noted that for this
For the those of ordinary skill of technical field, without departing from the technical principles of the invention, some improvement can also be made
And modification, these improvement and modification also should be regarded as protection scope of the present invention.
Claims (8)
1. a kind of feedforward of piezoelectric ceramic actuator and closed loop composite control method, it is characterised in that including：
By expectation displacement r (t) inputs of piezoelectric ceramic actuator to feed forward models, feed forward models are according to the expectation shift value r
(t) computing obtains the initial boost voltage u of piezoelectric ceramic actuatorε(t)；With piezoelectric ceramics displacement or piezoelectricity pottery driver displacement
For the feedback signal of PID controller, by PID controller to described initial boost voltage uε(t) error concealment is carried out, is obtained
The driving voltage of piezoelectric ceramic actuator, and the proportion adjustment parameter k using BP neural network to PID controllerp, integral adjustment
Parameter ki, differential adjustment parameter kdOptimize.
2. the feedforward of piezoelectric ceramic actuator according to claim 1 and closed loop composite control method, it is characterised in that institute
The feed forward models stated to improve PI sluggishness inversion models, by improving PI Hysteresis Models inverted by the improvement PI sluggishnesses inversion model
Arrive；
Wherein, PI Hysteresis Models are improved to be expressed as：The improvement PI Hysteresis Models are divided into rising part and sloping portion, work as input
When voltage increases, using one group of weights, when the output voltage drops, using another group of weights；PI Hysteresis Models are improved with following
Formula expression,
In formula, z (t) is the displacement of piezoelectric ceramic actuator, wpjRepresent weights when input voltage rises, WijRepresent input voltage
Weights during decline, rjFor the threshold value of sluggish operator；Fj() is current sluggish operator displacement function；X (t) is consequently exerted at piezoelectricity pottery
Voltage on porcelain driver；I represents the moment；J=1,2......n are sluggish operator number；yj(ti-1) it is that previous moment j ranks are slow
The output valve of stagnant operator；
The discrimination method for rising weights and threshold value is identical with the discrimination method of classical PI Hysteresis Models；As input voltage signal x (t)
When being decremented to zero from maximum, then output angle and the relation of input voltage are the big of piezoelectric ceramic actuator lag loop
Ring sloping portion, PI Hysteresis Models decline segmentation of the weights can according to the big ring sloping portion of piezoelectric ceramics lag loop
Slope is tried to achieve；The size of threshold value is tried to achieve according to equation below：
The size for declining weights estimates that estimation formulas is as follows according to the slope value of the big ring sloping portion of retardant curve：
Inverted to improving PI Hysteresis Models, obtain improving PI sluggishness inversion models, the improvement PI sluggishness inversion models formula represents such as
Under：
The initial boost voltage value of piezoelectricity pottery driver is tried to achieve based on improvement PI sluggishness inversion models.
3. the feedforward of piezoelectric ceramic actuator according to claim 1 and closed loop composite control method, it is characterised in that institute
The proportion adjustment parameter k using BP neural network to PID controller statedp, integral adjustment parameter ki, differential adjustment parameter kdEnter
The method of row optimization includes：
S1 determines the structure of BP neural network, that is, determine input layer number M and node in hidden layer Q, and provide input layer and
The initial value of hidden layer weight coefficientWithLearning efficiency and inertia coeffeicent are selected, now K=1；
S2 samples to obtain reference input rin (k) and system output yout (k), calculates the moment error e (k)=rin (k)-yout
(k)；
S2 calculates the input of each layer neuron of BP neural network, output, and the output of BP neural network output layer is PID controller
Three adjustable parameter kp, ki, kd；
S3 calculates the output u (k), classical Increment Type Digital Hydraulic PID of PID controller according to classical Increment Type Digital Hydraulic pid control algorithm
Control algolithm, represented with equation below：
In formula, u (k) is the driving voltage of the piezoelectric ceramic actuator of kth time sampling instant, and k is sampling sequence number, k=0,1,
2 ...；E (k) is deviation signal；
S4 carries out neural network learning, on-line tuning input layer and hidden layer weight coefficientWithRealize PID
The adaptive adjustment of parameter；
S5 puts k=k+1, returns to S1.
4. the feedforward of piezoelectric ceramic actuator according to claim 3 and closed loop composite control method, it is characterised in that adopt
With three layers of BP neural network, the input of network input layer is：
In formula,For input layer activation value；
In formula (1), the number M of input variable depends on the complexity of controlled system, input, the output of network hidden layer
For：
In formula (2),For hidden layer neuron i and neuron j connection weight；Superscript (1), (2), (3) difference
Represent input layer, hidden layer and output layer；The activation functions of hidden layer neuron take the Sigmoid functions of Symmetrical to be：
The input and output of network output layer are：
Output layer output node corresponds to three adjustable parameter k respectivelyp, ki, kd, due to kp, ki, kdCan not be negative value, so output
Layer neuron the negated negative Sigmoid functions of activation functions be：
The performance index function is taken to be：
According to the weight coefficient of gradient descent method corrective networks, i.e., weight coefficient negative gradient direction is searched for by E (k) and adjusted, and it is attached
Add an Inertia for making search Fast Convergent global minimal：
In formula (5), η is learning efficiency, and α is inertia coeffeicent；
Due toIt is unknown, so approximation sign functionSubstitution, thus bring the inaccurate influence of calculating can
To be compensated by regularized learning algorithm speed, can be obtained by formula (1) and (4)：
Above-mentioned analysis can obtain the learning algorithm that network output layer is weighed：
The learning algorithm of hidden layer weight coefficient can similarly be obtained：
In formula (6) and (7), g ' (x)=g (x) (1-g (x)), f ' (x)=(1-f2(x))/2。
5. the feedforward of piezoelectric ceramic actuator according to claim 1 and closed loop composite control method, it is characterised in that pressure
Electricity pottery driver includes platform framework, and piezoelectric ceramics is arranged in the holding part of platform framework, the piezoelectric ceramics prolonging direction
The flexible hinge of double parallel harden structure is provided with, the flexible hinge is divided into two groups, is arranged symmetrically；Piezoelectricity pottery driver is moved
Mechanical analysis, obtain the unified dynamics transmission function of piezoelectric ceramics and flexible hinge：
In formula, U (s) is the driving voltage of piezoelectricity pottery driver；Z (s) is the displacement of piezoelectricity pottery driver；meffFor piezoelectric ceramics
Equivalent mass, cpIt is K for the damped coefficient of piezoelectric ceramicspThe rigidity of piezoelectric ceramics；M be hinge equivalent mass, csFor hinge
The equivalent damping of chain, KsFor the equivalent stiffness of hinge.
6. a kind of feedforward of piezoelectric ceramic actuator and closed loop multiplex control system, it is characterised in that including：Feed forward models list
Member, PID controller, pid parameter optimization unit, Sensor Measurement Unit, piezoelectricity pottery driver, wherein,
The feed forward models unit, piezoelectric ceramics is obtained for inputting computing according to the expectation displacement r (t) of piezoelectric ceramic actuator
The initial boost voltage u of driverε(t)；
The Sensor Measurement Unit, for exporting the displacement of piezoelectricity pottery driver, obtaining piezoelectric ceramics in piezoelectricity pottery driver
Displacement, the feedback signal as PID controller closed-loop control；
The PID controller, the position for piezoelectric ceramics in the displacement according to described piezoelectricity pottery driver, piezoelectricity pottery driver
Move to described initial boost voltage uε(t) error concealment is carried out, and exports the driving voltage of piezoelectric ceramic actuator；
BP neural network unit, for the proportion adjustment parameter k to PID controllerp, integral adjustment parameter ki, differential adjustment parameter
kdOn-line tuning is carried out, the carrying out practically process of BP neural network unit includes：
S1 determines the structure of BP neural network, that is, determine input layer number M and node in hidden layer Q, and provide input layer and
The initial value of hidden layer weight coefficientWithLearning efficiency and inertia coeffeicent are selected, now k=1；
S2 samples to obtain reference input rin (k) and system output yout (k), calculate the moment error e (k)==rin (k)-
your(k)；
S2 calculates the input of each layer neuron of BP neural network, output, and the output of BP neural network output layer is PID controller
Three adjustable parameter kp, ki, kd；
S3 calculates the output u (k), classical Increment Type Digital Hydraulic PID of PID controller according to classical Increment Type Digital Hydraulic pid control algorithm
Control algolithm, represented with equation below：
In formula, u (k) is that the piezoelectricity of kth time sampling instant is made pottery the driving voltage of driver, and k is sampling sequence number, k=0,1,
2 ...；E (k) is deviation signal；The driving voltage and last moment piezoelectricity of the piezoelectricity pottery driver at Δ u (k) current times
The difference of the driving voltage of pottery driver；
S4 carries out neural network learning, on-line tuning input layer and hidden layer weight coefficientWithRealize PID
The adaptive adjustment of parameter；
S5 puts k=k+1, returns to S1.
7. the feedforward of piezoelectric ceramic actuator according to claim 6 and closed loop multiplex control system, it is characterised in that institute
Feed forward models unit is stated, described initial boost voltage is obtained using PI sluggishness inversion models are improved, wherein the improvement PI is sluggish
Inversion model formula represents as follows：
8. the feedforward of piezoelectric ceramic actuator according to claim 6 and closed loop multiplex control system, it is characterised in that pressure
Electricity pottery driver includes platform framework, and the holding part of accommodating piezoelectric ceramics is provided with the platform framework, and the piezoelectric ceramics is set
Put in the piezoelectric ceramics holding part, the piezoelectric ceramics prolonging direction is provided with the flexible hinge of double parallel harden structure, institute
Flexible hinge at least four is stated, is divided into two groups, two-by-two relatively, is arranged symmetrically；
Dynamic analysis to piezoelectricity pottery driver, obtains the unified dynamics transmission function of piezoelectric ceramics and flexible hinge：
In formula, U (s) is the driving voltage of piezoelectricity pottery driver；Z (s) is the displacement of piezoelectricity pottery driver；meffFor piezoelectric ceramics
Equivalent mass, cpIt is K for the damped coefficient of piezoelectric ceramicspThe rigidity of piezoelectric ceramics；M be hinge equivalent mass, csFor hinge
The equivalent damping of chain, KsFor the equivalent stiffness of hinge；
The Sensor Measurement Unit includes piezoelectric ceramics displacement measurement circuit, piezoelectric ceramic actuator displacement transducer, wherein,
The piezoelectric ceramics displacement measurement circuit includes four groups of resistance strain gages being attached on piezoelectric ceramics, the resistance strain gage composition
The full-bridge circuit of piezoelectric ceramics displacement is measured, each bridge arm of the full-bridge circuit is respectively equipped with one group of resistance strain gage.
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| CN112835295B (en) * | 2021-01-22 | 2022-07-19 | 武汉工程大学 | Piezoelectric ceramic actuator parameter identification and composite control method based on PI model |
| CN112906875A (en) * | 2021-04-29 | 2021-06-04 | 常州高凯电子有限公司 | Control system and method for precise gas flow valve |
| CN113268002A (en) * | 2021-05-31 | 2021-08-17 | 苏州大学 | Piezoelectric driving feedforward control method, device, equipment and storage medium |
| CN113110038A (en) * | 2021-05-31 | 2021-07-13 | 苏州大学 | Piezoelectric-driven closed-loop control method, device, equipment and storage medium |
| CN113359421A (en) * | 2021-06-28 | 2021-09-07 | 上海师范大学 | Composite control system and method for piezoelectric precision gas flow valve |
| CN113487016A (en) * | 2021-07-07 | 2021-10-08 | 华中科技大学鄂州工业技术研究院 | Neural network-based displacement control method and equipment for scanning device and storage medium |
| CN114237310A (en) * | 2021-11-29 | 2022-03-25 | 北京控制工程研究所 | Multi-mode flow regulating system and method based on displacement flow double closed loop |
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