CN108696176B - A kind of piezoelectric ceramic actuator control method based on particle swarm algorithm - Google Patents
A kind of piezoelectric ceramic actuator control method based on particle swarm algorithm Download PDFInfo
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Abstract
A kind of piezoelectric ceramic actuator control method based on particle swarm algorithm, the following steps are included: S1. carries out mathematical modeling to piezoelectric ceramic actuator with the non-linear total parameter kinetic model of mechanical-electric coupling, obtain the kinetic model of piezoelectric ceramic actuator are as follows: S2. carries out discrete processes with kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, converts nonlinear programming problem for optimal control problem；S3. the fitness function of particle swarm algorithm is obtained based on nonlinear programming problem；S4. fitness function is solved using particle swarm algorithm, obtains globally optimal solution.The present invention can eliminate very well the lagging characteristics of piezoelectric ceramic actuator, and improve the positioning accuracy of piezoelectric ceramic actuator.
Description
Technical field
The present invention relates to piezoelectric actuator control technology fields, and in particular to a kind of piezoelectric ceramics based on particle swarm algorithm
Driver control method.
Background technique
Piezoelectric ceramic actuator is one of the critical elements of precision positioning Yu Precision Manufacturing Technology field, fast with response,
High resolution, rigidity headlight advantage, and do not generate heat, without magnetic disturbance, noiseless, easily controllable, it is ideal driving, locator
Part is widely used among sophisticated manufacturing.But since the physical property of itself has sluggish, compacted property, vibration etc. is non-
Linear characteristic causes to bring certain influence to precision positioning precision in practical applications.Currently, controlling piezoelectric ceramics both at home and abroad
The model of driver has very much, such as Preisach model, Maxwell model, Prandtle-Ishlinskii model etc..This
The deficiencies of a little models are due to that inverse cannot parse, and form is complicated, and parameter is more and is not easy to determine, computationally intensive, brings to practical operation
It is difficult.The existing Compensation Control based on model is the method for mainstream, and this method requires to establish sluggish positive inversion model, then
It is added in inversion model as feedforward compensation link on control access, carries out the compensation to hysteresis.But it is correctly inverse establishing
Model is highly difficult and computationally intensive, is unfavorable for the control of precision, it is difficult to meet required precision.
Therefore new mathematical model is established to piezoelectric ceramic actuator, the effective control method of modelling, is pressed improving accordingly
Electroceramics driver positioning accuracy is necessary.
Summary of the invention
Present invention aims to overcome that the shortcomings that prior art and deficiency, provide a kind of piezoelectricity based on particle swarm algorithm
Ceramic driver control method can eliminate the lagging characteristics of piezoelectric ceramic actuator very well, improve piezoelectric ceramic actuator
Positioning accuracy.
To achieve the above object, The technical solution adopted by the invention is as follows:
A kind of piezoelectric ceramic actuator control method based on particle swarm algorithm, comprising the following steps:
S1. mathematical modeling is carried out to piezoelectric ceramic actuator with mechanical-electric coupling non-linear total parameter kinetic model, obtained
The kinetic model of piezoelectric ceramic actuator are as follows:
Wherein x is reality output displacement, and y is expectation displacement, and u is control variable, uTFor the transposed matrix of u, Q and R are power
Matrix, q are the linear segment charge for flowing through non-linear hysteresis submodel total electrical charge, and w is the input electricity of non-linear hysteresis submodel
Pressure, b are damped coefficient, and k is spring rate, and m is the equivalent mass of piezoelectric stack, T1、T2、T3、S1、C1、C2And C3It is normal system
Number, T4For the proportionality coefficient of motor converter, C4For the linear capacitance of motor converter；
S2. discrete processes are carried out with kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, by optimal control problem
It is converted into nonlinear programming problem；
S3. the fitness function of particle swarm algorithm is obtained based on nonlinear programming problem；
S4. fitness function is solved using particle swarm algorithm, obtains globally optimal solution.
From the foregoing, it will be observed that the present invention carries out discrete processes using kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, make
The calculation amount for solving kinetic model is reduced, and solving precision is higher, converts Non-Linear Programming for optimal control problem equivalence
Problem simplifies optimal control problem, and nonlinear programming problem is easier to solve its approximate solution, finally uses particle swarm algorithm
Nonlinear programming problem is solved, globally optimal solution is obtained.The present invention can eliminate the slow of piezoelectric ceramic actuator very well
Stagnant characteristic, and improve the positioning accuracy of piezoelectric ceramic actuator.
Further, the step S2 " carries out discrete place with kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator
Reason, converts nonlinear programming problem for optimal control problem " detailed process includes following sub-step:
S21. a variable replacement is done to the time firstSo that integral domain from [0 ,+∞) become [- 1,1), note
S22. section [- 1,1) on consider Gaussian node τ1, τ2……τn, and wherein τ0=-1 is corresponding for initial time
T=0, τn+1=1 it is corresponding for terminal time t=+ ∞, n be node number；
S23. for state variableWith n rank lagrange polynomial come approximate,
Then
Then its component form are as follows:
WhereinFor the matrix of a n* (n+1)；
S24. approximation is carried out with Gauss integration for secondary system type performance indicator J, obtained:
Wherein ωiTo integrate weight,
And obtain nonlinear programming problem:
Further, the step S3 " fitness function of particle swarm algorithm is obtained based on nonlinear programming problem " is specific
Process includes following sub-step:
S31. equation group is tieed up using formula (1), (2) and (4) composition n, joint solves available u (τi) and x (τi) relationship
Formula: x (τi)=f (u (τi))；
S32. by x (τi)=f (u (τi)) it is updated to objective function:
Obtain the fitness function of particle swarm algorithm:
Further, the step S4 " solves nonlinear programming problem using particle swarm algorithm, obtains the overall situation most
Excellent solution " detailed process includes following sub-step:
S41., Population Size, that is, particle number i is set, and initializes all particles, initializes their speedWith positionAnd the history optimum position Pbest of particle is set as working as
Front position, and particle optimal in group is as current global optimum position Gbest；
S42. the fitness function value of each particle is calculated；
S43. judge whether the fitness function value of particle is better than its current history optimum position Pbest, if it is
Current history optimum position Pbest is replaced with the fitness function value of particle, and selects particle optimal in group as new
Global optimum position Gbest；
Speed and position to the n-th dimension of i-th of particle are updated by following equation:
Wherein ω is inertia weight, is generally initialized as 0.9, then as evolutionary process linear decrease to 0.4, then ωt
=(0.9-0.4) (tmax-t)/tmax+0.4, tmax are maximum number of iterations, and t is current iteration number, c1And c2To accelerate system
Number, takes fixed value 2,WithIt is the random number on [0,1] section；
S44. if meeting objective function requirement or terminate if reaching maximum update times and export:
Otherwise it re-execute the steps S42.
Compared with prior art, the invention has the following advantages that
The present invention carries out discrete processes using kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, makes to solve dynamics
The calculation amount of model is reduced, and solving precision is higher, converts nonlinear programming problem for optimal control problem equivalence, simplifies
Optimal control problem is easier to nonlinear programming problem to solve its approximate solution, finally using particle swarm algorithm to non-linear rule
The problem of drawing is solved, and globally optimal solution is obtained；The present invention can eliminate very well the lagging characteristics of piezoelectric ceramic actuator, and mention
The positioning accuracy of high-voltage electricity ceramic driver.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the piezoelectric ceramic actuator control method of particle swarm algorithm；
Fig. 2 is the decomposition diagram of the kinetic model of piezoelectric ceramic actuator of the present invention.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.It is understood that tool described herein
Body embodiment is used only for explaining the present invention rather than limiting the invention.It also should be noted that for the ease of retouching
It states, only some but not all contents related to the present invention are shown in the drawings.
Embodiment
Referring to FIG. 1, a kind of piezoelectric ceramic actuator control method based on particle swarm algorithm, comprising the following steps:
S1. mathematical modeling is carried out to piezoelectric ceramic actuator with mechanical-electric coupling non-linear total parameter kinetic model, obtained
The kinetic model of piezoelectric ceramic actuator are as follows:
Wherein x is reality output displacement, and y is expectation displacement, and u is control variable, uTFor the transposed matrix of u, Q and R are power
Matrix, q are the linear segment charge for flowing through non-linear hysteresis submodel total electrical charge, and w is the input electricity of non-linear hysteresis submodel
Pressure, b are damped coefficient, and k is spring rate, and m is the equivalent mass of piezoelectric stack, T1、T2、T3、S1、C1、C2And C3It is normal system
Number, T4For the proportionality coefficient of motor converter, C4For the linear capacitance of motor converter.
Referring to FIG. 2, theoretical based on layered modeling, the kinetic model of piezoelectric ceramic actuator of the present invention can be divided into three
Submodel: (1) based on the non-linear hysteresis submodel of piezoelectric stack physical characteristic；(2) based on Piezoelectric Ceramic pattern etc.
Imitate driving circuit submodel；(3) based on the mass-spring-damper submodel of piezoelectric ceramic actuator dynamic characteristic.
Wherein QtFor the charge for flowing through motor converter, Qt=T4*x,QcFor the charge for flowing through linear capacitance, Qc=T4*E,
T4For the proportionality coefficient of motor converter, C4For the linear capacitance parallel with motor converter, E is the anti-electronic of mechanical part
Gesture, U are total input voltage of piezoelectric ceramic actuator, FtFor the conversion power that electric part generates, m is the equivalent matter of piezoelectric stack
Amount, b are damped coefficient, and k is spring rate, and x is the output displacement of piezoelectric stack, and w is the input electricity of non-linear hysteresis submodel
Pressure, q1To flow through non-linear hysteresis submodel total electrical charge.It that is to say that the kinetic model of piezoelectric ceramic actuator of the present invention is abundant
The sluggishness of piezoelectric ceramic actuator, compacted property are considered, the nonlinear characteristics factor such as vibration can eliminate Piezoelectric Ceramic very well
The lagging characteristics of device.
S2. discrete processes are carried out with kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, by optimal control problem
Nonlinear programming problem is converted into,
Specifically, the step S2 " carry out discrete processes with kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator,
Nonlinear programming problem is converted by optimal control problem " detailed process includes following sub-step:
S21. a variable replacement is done to the time firstSo that integral domain from [0 ,+∞) become [- 1,1), note
S22. section [- 1,1) on consider Gaussian node τ1, τ2……τn, and wherein τ0=-1 is corresponding for initial time
T=0, τn+1=1 it is corresponding for terminal time t=+ ∞, n be node number；
S23. for state variableWith n rank lagrange polynomial come approximate,
Then
Then its component form are as follows:
WhereinFor the matrix of a n* (n+1)；
S24. approximation is carried out with Gauss integration for secondary system type performance indicator J, obtained:
Wherein ωiTo integrate weight,
And obtain nonlinear programming problem:
S3. the fitness function of particle swarm algorithm is obtained based on nonlinear programming problem,
Specifically, the specific mistake of the step S3 " fitness function of particle swarm algorithm is obtained based on nonlinear programming problem "
Journey includes following sub-step:
S31. equation group is tieed up using formula (1), (2) and (4) composition n, joint solves available u (τi) and x (τi) relationship
Formula: x (τi)=f (u (τi))；
S32. by x (τi)=f (u (τi)) it is updated to objective function:
Obtain the fitness function of particle swarm algorithm:
S4. fitness function is solved using particle swarm algorithm, obtains globally optimal solution,
Specifically, the step S4 " solves nonlinear programming problem using particle swarm algorithm, obtains global optimum
Solution " detailed process includes following sub-step:
S41., Population Size, that is, particle number i is set, and initializes all particles, initializes their speedWith positionAnd the history optimum position Pbest of particle is set as working as
Front position, and particle optimal in group is as current global optimum position Gbest；
S42. the fitness function value of each particle is calculated；
S43. judge whether the fitness function value of particle is better than its current history optimum position Pbest, if it is
Current history optimum position Pbest is replaced with the fitness function value of particle, and selects particle optimal in group as new
Global optimum position Gbest；
Speed and position to the n-th dimension of i-th of particle are updated by following equation:
Wherein ω is inertia weight, is generally initialized as 0.9, then as evolutionary process linear decrease to 0.4, then ωt
=(0.9-0.4) (tmax-t)/tmax+0.4, tmax are maximum number of iterations, and t is current iteration number, c1And c2To accelerate system
Number, takes fixed value 2,WithIt is the random number on [0,1] section；
S44. if meeting objective function requirement or terminate if reaching maximum update times and export:
Otherwise it re-execute the steps S42.
From the foregoing, it will be observed that the present invention carries out discrete processes using kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, make
The calculation amount for solving kinetic model is reduced, and solving precision is higher, converts Non-Linear Programming for optimal control problem equivalence
Problem simplifies optimal control problem, and nonlinear programming problem is easier to solve its approximate solution, finally uses particle swarm algorithm
Nonlinear programming problem is solved, globally optimal solution is obtained.The present invention can eliminate the slow of piezoelectric ceramic actuator very well
Stagnant characteristic, and improve the positioning accuracy of piezoelectric ceramic actuator.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (4)
1. a kind of piezoelectric ceramic actuator control method based on particle swarm algorithm, it is characterised in that the following steps are included:
S1. mathematical modeling is carried out to piezoelectric ceramic actuator with mechanical-electric coupling non-linear total parameter kinetic model, obtains piezoelectricity
The kinetic model of ceramic driver are as follows:
Wherein x is reality output displacement, and y is expectation displacement, and u is control variable, uTFor the transposed matrix of u, Q and R are weight matrix, q
For the linear segment charge for flowing through non-linear hysteresis submodel total electrical charge, w is the input voltage of non-linear hysteresis submodel, and b is
Damped coefficient, k are spring rate, and m is the equivalent mass of piezoelectric stack, T1、T2、T3、S1、C1、C2And C3It is constant coefficient, T4For
The proportionality coefficient of motor converter, C4For the linear capacitance of motor converter；
S2. discrete processes are carried out with kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, optimal control problem is converted
For nonlinear programming problem；
S3. the fitness function of particle swarm algorithm is obtained based on nonlinear programming problem；
S4. fitness function is solved using particle swarm algorithm, obtains globally optimal solution.
2. the piezoelectric ceramic actuator control method according to claim 1 based on particle swarm algorithm, it is characterised in that: institute
Step S2 is stated " to carry out discrete processes with kinetic model of the pseudo- spectrometry to piezoelectric ceramic actuator, optimal control problem is turned
Turning to nonlinear programming problem " detailed process includes following sub-step:
S21. a variable replacement is done to the time firstSo that integral domain from [0 ,+∞) become [- 1,1), note
S22. section [- 1,1) on consider Gaussian node τ1, τ2……τn, and wherein τ0=-1 it is corresponding be initial time t=0,
τn+1=1 it is corresponding for terminal time t=+ ∞, n be node number；
S23. for state variableWith n rank lagrange polynomial come approximate,
Then
Then its component form are as follows:
WhereinFor the matrix of a n* (n+1)；
S24. approximation is carried out with Gauss integration for secondary system type performance indicator J, obtained:
Wherein ωiTo integrate weight,
And obtain nonlinear programming problem:
3. the piezoelectric ceramic actuator control method according to claim 2 based on particle swarm algorithm, it is characterised in that: institute
Stating step S3 " fitness function of particle swarm algorithm is obtained based on nonlinear programming problem " detailed process includes following sub-step:
S31. equation group is tieed up using formula (1), (2) and (4) composition n, joint solves available u (τi) and x (τi) relational expression: x
(τi)=f (u (τi))；
S32. by x (τi)=f (u (τi)) it is updated to objective function:
Obtain the fitness function of particle swarm algorithm:
4. the piezoelectric ceramic actuator control method according to claim 3 based on particle swarm algorithm, it is characterised in that: institute
State step S4 " nonlinear programming problem is solved using particle swarm algorithm, obtain globally optimal solution " detailed process include with
Lower sub-step:
S41., Population Size, that is, particle number i is set, and initializes all particles, initializes their speedWith positionAnd the history optimum position Pbest of particle is set as working as
Front position, and particle optimal in group is as current global optimum position Gbest；
S42. the fitness function value of each particle is calculated；
S43. judge whether the fitness function value of particle is better than its current history optimum position Pbest, if it is use grain
The fitness function value of son replaces current history optimum position Pbest, and selects particle optimal in group as newly complete
Office optimal location Gbest；
Speed and position to the n-th dimension of i-th of particle are updated by following equation:
Wherein ω is inertia weight, is initialized as 0.9, then as evolutionary process linear decrease to 0.4, then ωt=(0.9-
0.4) (tmax-t)/tmax+0.4, tmax are maximum number of iterations, and t is current iteration number, c1And c2For accelerator coefficient, take solid
Definite value 2,WithIt is the random number on [0,1] section；
S44. if meeting objective function requirement or terminate if reaching maximum update times and export:
Otherwise it re-execute the steps S42.
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| CN109343467B (en) * | 2018-11-02 | 2021-02-05 | 南京航空航天大学 | Elliptical trajectory error control system of non-resonance EVC device |
| CN109739085A (en) * | 2018-12-21 | 2019-05-10 | 广东工业大学 | A kind of piezoelectric ceramic actuator optimum displacement control method based on improvement Gauss puppet spectrometry |
| CN110376452B (en) * | 2019-06-14 | 2020-12-25 | 中国科学院西安光学精密机械研究所 | Piezoelectric ceramic actuator electrical noise index determination method based on coupled electromechanical analysis |
| CN110308650B (en) * | 2019-06-27 | 2023-01-20 | 广东工业大学 | Piezoelectric ceramic driver control method based on data driving |
| CN111368400B (en) * | 2020-02-17 | 2021-09-21 | 华南理工大学 | Modeling identification method for piezoelectric micro-drive variable-frequency positioning platform based on PSO algorithm |
| CN112487693B (en) * | 2020-11-23 | 2021-10-26 | 国网浙江省电力有限公司杭州供电公司 | Curve magnetic valve type controllable reactor harmonic wave optimization method, system and application |
| CN114460847A (en) * | 2022-01-28 | 2022-05-10 | 哈尔滨理工大学 | Piezoelectric ceramic driver driven by asymmetric voltage |
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