CN107093962A - Second order known to partial parameters does not know the self-adaptation control method of lag structure - Google Patents
Second order known to partial parameters does not know the self-adaptation control method of lag structure Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
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Abstract
The present invention relates to the self-adaptation control method that second order known to a kind of partial parameters does not know lag structure, pedestal and the supersonic motor being provided thereon are provided, supersonic motor side output shaft is connected with photoelectric encoder, opposite side output shaft is connected with flywheel inertia load, the output shaft of flywheel inertia load is connected through shaft coupling with torque sensor, and photoelectric encoder, the signal output part of torque sensor are respectively connected to control system.The control system is made up of Backstepping Controller and motor, and the system of whole controller is set up on the basis of contragradience calculating, so as to obtain more preferable controlled efficiency.Not only control accuracy is high by the present invention, and apparatus structure is simple, compact, and using effect is good.
Description
Technical field
The present invention relates to the self-adaptation control method that second order known to a kind of partial parameters does not know lag structure.
Background technology
There is a discontinuous function sgn (z in the design of existing supersonic motor contragradience adaptive servo control systemn)
Control is participated in, this may result in flutter.In order to avoid such case, our currently proposed improved contragradience Self Adaptive Control sides
Case.This control system can effectively promote the controlled efficiency of system, and further reduce system for probabilistic influence journey
Degree.Therefore the Position And Velocity control of motor can obtain preferable dynamic characteristic.
The content of the invention
In view of this, oneself of lag structure is not known it is an object of the invention to provide second order known to a kind of partial parameters
Adaptive control method, not only control accuracy is high, and simple in construction, compact, and using effect is good.
To achieve the above object, the present invention is adopted the following technical scheme that：
Second order known to a kind of partial parameters does not know the self-adaptation control method of lag structure there is provided pedestal and located at base
Supersonic motor on seat, it is characterised in that：Supersonic motor side output shaft is connected with photoelectric encoder, opposite side
Output shaft is connected with flywheel inertia load, and the output shaft of the flywheel inertia load is connected through shaft coupling with torque sensor
Connect, the signal output part of the photoelectric encoder, the signal output part of the torque sensor are respectively connected to control system；It is described
Control system is set up on the basis of Reverse Step Control, estimates to be related to the knot of hysteresis effect and external disturbance using law is updated
Really, the anglec of rotation of controlled motor rotor is carried out using contragradience algorithm, then by calculating the anglec of rotation indirect control motor of rotor
Speed, so as to obtain more preferable controlled efficiency.
Further, the control system includes supersonic motor drive control circuit, the supersonic motor driving control
Circuit processed includes control chip circuit and driving chip circuit, the signal output part of the photoelectric encoder and the control chip
The respective input of circuit is connected, the output end of the control chip circuit and the respective input of the driving chip circuit
It is connected, to drive the driving chip circuit, the driving frequency Regulate signal output end of the driving chip circuit and driving
Respective input of the half-bridge circuit Regulate signal output end respectively with the supersonic motor is connected.
Further, concrete methods of realizing is as follows：
The dynamical equation of piezoelectric motor drive system can be written as：
Wherein m is unknown positive parameter, and c is uncertain parameter, and Φ represents nonlinear component, and f (t) is that unknown outside is done
Disturb, u (t) is control input；In structural system, m and c are respectively quality and damped coefficient, and restoring force Φ represents piezoelectric
Delayed behavior, x is position, and u (t) is the active controlling force provided by appropriate actuator f (t), its be described as f (t)=-
Ma (t), wherein a (t) are vibration accelerations；
Restoring force Φ is described with following form:
Φ (x, t)=α kx (t)+(1- α) Dkz (t) (5-4)
Wherein, x and z represent position and restoring force, are respectively acting on piezoelectric, there is lagged relationship between x and z,
Length, width and the size in hysteresis interval of parameter A, β and λ control hysteresis curve, n is an integer, is determined by experimental data；
The model represents restoring force Φ (x, t) by component of elasticity α kx (t) and lagging component (1- α) Dkz superposition, its
Middle D>0 produces constant displacement, and α is pre- production ratio；Lagging portion is related to auxiliary variable z, and it is that non-linear first rank is non-linear
The solution of equation (5-5)；
From dynamical system (5-5), have
Construct a positive Liapunov function Vz=z (t)2/2；Consider A>0 situation, there is following three kinds of possibilities：
*P1:β+λ ＞ 0 and β-λ >=0
*P2:β+λ ＞ 0 and β-λ ＜ 0
(5-7)
*P3:β+λ≤0
Concern situation P1, is setAnd by VQ1It is expressed as Lyapunov functions V in set Q1Z's
The expression formula of derivative, hasTherefore,Similarly, for | z | >=z0,
WhereinSet in additionWithIn the case of, draw
Same conclusion；
ForAll possible sign and z, have | z | >=z0；Draw a conclusion：Z (t) is the segmentation letter of each bounded
Number x and each primary condition z (0)；Z (t) boundary can draw as follows：
If z primary condition is | z (0) |≤z0, then | z |≤z0, t >=0；
If z primary condition is z (0) >=z0, then | z |≤z (0), t >=0；
By consideringRegion inTo turn to situation
According to similar argument, it can be shown that for meeting | z (0) |≤z1Original state z (0),For feelings
Condition P1 carries out identical analysis, it can be seen that z can be limited to some functions with right and wrongMean the region of bounded, in such case
Under, z (t) is sky；
For A<0 and A=0 and a situation, can carry out similar analysis, and the conclusion drawn from analysis is summarised in following
Lemma：
Consider Kind of Nonlinear Dynamical System (5-5), then for any piecewise continuous signals x andOutput z (t) is global
Bounded, only when the parameter of system (5-5) meets inequality β ＞ | λ | when, control targe is that one contragradience of design is self-adaptive controlled
System rule；
Closed loop bounded
In transient process, tracking error x (t)-yr(t) all it is that arbitrarily small cycle and stable state are set by clearly selecting
Count parameter, wherein yr(t) it is known bounded reference signal；
Some prior informations of hypothesized model parameter are available, therefore, further make use of the mould in controller design
Type structure improves systematic function；
Nonlinear restoring force Φ (x, t) can parameterize as follows：
Φ (t)=θ1x(t)+θ2z(t)
Wherein θ1=α k and θ2=(1- α) DK are uncertain parameters；
Assuming that parameter A, β, D, λ are in some known intervals, by above-mentioned it is assumed that equation can be used to generate signal
Wherein A0,β0,D0,λ0In known spacings, for thisBy Φ (x, t) withIt is approximately
It can proveIt is bounded；Due toSoIt is also bounded, estimation
Then, with following form rewrite equation
Wherein x1=x,It is the constant vector of uncertain parameter,
Output control method given below：
Wherein c1, c2, γ and γ f are positive parameter, and Γ is a positive definition, design matrixIt is θ, m and F with F
Estimation；
It is all bounded that x, x, θ, m, F, which can be determined,；The result that the stability of a system and performance can be obtained is as follows：
Consider uncertain nonlinear system (1)；With controller and parameter updating method, following condition needs to have：
Produced closed-loop system is the global unified limit；
Asymptotic tracking is realized, i.e.,
Transient Displacements tracking error performance is given by
Instantaneous velocity tracking error performance is given by
Due to using some available structural informations in the design, and delayed residual effect is considered as with Unknown Bound
The Bounded Perturbations of limit, are estimated to be related to the result of hysteresis effect and external disturbance using law is updated, are controlled using contragradience algorithm
The anglec of rotation of rotor processed, then pass through the speed for the anglec of rotation indirect control motor for calculating rotor.
The present invention has the advantages that compared with prior art：Effectively promote present invention uses innovatory algorithm and be
The controlled efficiency of system, and system is further reduced for probabilistic influence degree, the accuracy of control is improved, can be obtained
Obtain preferable dynamic characteristic.In addition, device is reasonable in design, simple in construction, compact, manufacturing cost is low, with very strong practicality
With wide application prospect.
Brief description of the drawings
Fig. 1 is the structural representation of one embodiment of the invention.
Fig. 2 is the control circuit theory diagrams of the present invention.
In figure：1- photoelectric encoders, 2- photoelectric encoder fixed supports, 3- supersonic motor output shafts, 4- ultrasonic waves electricity
Machine, 5- supersonic motor fixed supports, 6- supersonic motor output shafts, 7- flywheel inertia loads, the output of 8- flywheels inertia load
Axle, 9- yielding couplings, 10- torque sensors, 11- torque sensor fixed supports, 12- pedestals, 13- control chip circuits,
14- driving chip circuits, 15,16,17- photoelectric encoders output A, B, Z phase signals, 18,19,20,21- driving chip circuits
The driving frequency Regulate signal of generation, 22- driving chips circuit produce driving half-bridge circuit Regulate signal, 23,24,25,26,
27th, the signal for the driving chip circuit that 28- control chips circuit is produced, 29- supersonic motor drive control circuits.
Embodiment
Below in conjunction with the accompanying drawings and embodiment the present invention will be further described.
The present invention provides the self-adaptation control method that second order known to a kind of partial parameters does not know lag structure, refer to
Supersonic motors 4 of the Fig. 1 there is provided pedestal 12 and on pedestal 12, the side output shaft 3 of supersonic motor 4 is compiled with photoelectricity
Code device 1 is connected, and opposite side output shaft 6 is connected with flywheel inertia load 7, and the output shaft 8 of the flywheel inertia load 7 is through bullet
Property shaft coupling 9 is connected with torque sensor 10, the signal output part of the photoelectric encoder 1, the torque sensor 10
Signal output part is respectively connected to control system.The control system is set up on the basis of Reverse Step Control, uses renewal law
Estimation is related to the result of hysteresis effect and external disturbance, the anglec of rotation of controlled motor rotor is carried out using contragradience algorithm, then pass through
The speed of the anglec of rotation indirect control motor of rotor is calculated, so as to obtain more preferable controlled efficiency.
Above-mentioned supersonic motor 4, photoelectric encoder 1, torque sensor 10 are respectively through supersonic motor fixed support 5, light
Photoelectric coder fixed support 2, torque sensor fixed support 11 are fixed on the pedestal 12.
As shown in Fig. 2 above-mentioned control system includes supersonic motor drive control circuit 29, the supersonic motor driving
Circuit 29 is controlled to include control chip circuit 13 and driving chip circuit 14, the signal output part of the photoelectric encoder 1 and institute
The respective input for stating control chip circuit 13 is connected, output end and the driving chip electricity of the control chip circuit 13
The respective input on road 14 is connected, to drive the driving chip circuit 14, the driving frequency of the driving chip circuit 14
The respective input phase of Regulate signal output end and driving half-bridge circuit Regulate signal output end respectively with the supersonic motor 4
Connection.The driving chip circuit 14 produces driving frequency Regulate signal and driving half-bridge circuit Regulate signal, to ultrasonic wave electricity
Frequency, phase and the break-make of machine output A, B two phase PWM are controlled.Ultrasound is controlled by opening and turning off the output of PWM ripples
The startup of ripple motor and out of service；By adjust output PWM ripples frequency and two-phase phase difference come regulation motor most
Good running status.
We carry out the anglec of rotation of controlled motor rotor using Backstepping Controller.Obtained by liapunov's theorem of stability
The robustness learning rule of Reverse Step Control parameter.As described above, in the present embodiment, the hardware circuit of the control system includes
Supersonic motor drive control circuit, the supersonic motor drive control circuit includes control chip circuit and driving chip electricity
Road, the Backstepping Controller is located in the control chip circuit.
Supersonic motor contragradience adaptive servo control system, contragradience is adaptively by using estimating the unknown of control system
, the stability of designed control system is ensured with Liapunov function.
The concrete methods of realizing of this method is as follows：
The dynamical equation of piezoelectric motor drive system can be written as：
Wherein m is unknown positive parameter, and c is uncertain parameter, and Φ represents nonlinear component, and f (t) is that unknown outside is done
Disturb.U (t) is control input.In structural system, m and c are respectively quality and damped coefficient, and restoring force Φ represents piezoelectric
Delayed behavior, x is position, and u (t) is the active controlling force provided by appropriate actuator f (t), this be described as f (t)=-
Ma (t), wherein a (t) are vibration accelerations.It is delayed
Power Φ is described with following form:
Φ (x, t)=α kx (t)+(1- α) Dkz (t) (5-4)
Wherein, x and z represent position and restoring force, are respectively acting on piezoelectric, there is lagged relationship between x and z,
Length, width and the size in hysteresis interval of parameter A, β and λ control hysteresis curve, n is an integer, is determined by experimental data；
The model represents restoring force Φ (x, t) by component of elasticity α kx (t) and lagging component (1- α) Dkz superposition, its
Middle D>0 produces constant displacement, and α is pre- production ratio；Lagging portion is related to auxiliary variable z, and it is that non-linear first rank is non-linear
The solution of equation (5-5)；
From dynamical system (5-5), have
Construct a positive Liapunov function Vz=z (t)2/2.Consider A>0 situation.There are three kinds of possibilities.
*P1:β+λ ＞ 0 and β-λ >=0
*P2:β+λ ＞ 0 and β-λ ＜ 0 (5-7)
*P3:β+λ≤0
We are focusing on situation P1.In fact, settingAnd by VQ1It is expressed as in set Q1
Lyapunov functions VZDerivative expression formula, haveTherefore,Similarly, for
|z|≥z0,WhereinSet in additionWith
In the case of, draw same conclusion.
ForAll possible sign and z, we have | z | >=z0.We conclude that：Z (t) is each bounded
Piecewise function x and each primary condition z (0).Z (t) boundary can draw as follows：
If z primary condition is | z (0) |≤z0, then | z |≤z0, t >=0；
If z primary condition is z (0) >=z0, then | z |≤z (0), t >=0
We are now by considering's
In regionTo turn to situation
According to similar argument, we are it can be shown that for meeting | z (0) |≤z1Original state z (0),
Identical analysis is carried out for situation P3, it may be seen that z can be limited to some functions with right and wrongMean have
The region on boundary, in this case, z (t) are sky.
For A<0 and A=0 and a situation, can carry out similar analysis, and the conclusion drawn from analysis is summarised in following
Lemma.
Consider Kind of Nonlinear Dynamical System (5-5).So for any piecewise continuous signals x andOutput z (t) is global
Bounded, only when the parameter of system (5-5) meets inequality β ＞ | λ | when, control targe is that one contragradience of design is self-adaptive controlled
System rule.
Closed loop bounded
In transient process, tracking error x (t)-yr(t) all it is that arbitrarily small cycle and stable state are set by clearly selecting
Count parameter, wherein yr(t) it is known bounded reference signal.
Some prior informations of hypothesized model parameter are available.Therefore, it further make use of the mould in controller design
Type structure improves systematic function.
Nonlinear restoring force Φ (x, t) can parameterize as follows：
Φ (t)=θ1x(t)+θ2z(t)
Wherein θ1=α k and θ2=(1- α) DK are uncertain parameters.
Assuming that parameter A, β, D, λ are in some known intervals, by above-mentioned it is assumed that equation can be used to generate signal
Wherein A0,β0,D0,λ0In known spacings.For thisWe by Φ (x, t) withIt is approximately
It can proveIt is bounded.Due toSoIt is also bounded.Estimation
Then, with following form rewrite equation
Wherein x1=x,It is the constant vector of uncertain parameter,
Output control method given below：
Wherein c1, c2, γ and γ f are designed to positive parameter, and Γ is a positive definition.Design matrixIt is θ, m with F
With F estimation.
It is all bounded that x, x, θ, m, F, which can be determined,.The result that the stability of a system and performance can be obtained is as follows：
Consider uncertain nonlinear system (1).With controller and parameter updating method, following condition needs to have：
Produced closed-loop system is the global unified limit.
Asymptotic tracking is realized, i.e.,
Transient Displacements tracking error performance is given by
Instantaneous velocity tracking error performance is given by
Due to using some available structural informations in the design, and delayed residual effect is considered as with Unknown Bound
The Bounded Perturbations of limit.Estimate to be related to the result of hysteresis effect and external disturbance using law is updated.Controlled using contragradience algorithm
The anglec of rotation of rotor processed, then pass through the speed for the anglec of rotation indirect control motor for calculating rotor.
The foregoing is only presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with
Modification, should all belong to the covering scope of the present invention.
Claims (3)
1. second order known to a kind of partial parameters does not know the self-adaptation control method of lag structure there is provided pedestal and located at pedestal
On supersonic motor, it is characterised in that：Supersonic motor side output shaft is connected with photoelectric encoder, and opposite side is defeated
Shaft is connected with flywheel inertia load, and the output shaft of the flywheel inertia load is connected through shaft coupling with torque sensor,
The signal output part of the photoelectric encoder, the signal output part of the torque sensor are respectively connected to control system；The control
System processed is set up on the basis of Reverse Step Control, estimates to be related to the result of hysteresis effect and external disturbance using law is updated,
Carry out the anglec of rotation of controlled motor rotor using contragradience algorithm, then pass through the speed for the anglec of rotation indirect control motor for calculating rotor
Degree, so as to obtain more preferable controlled efficiency.
2. second order known to partial parameters according to claim 1 does not know the self-adaptation control method of lag structure, its
It is characterised by：The control system includes supersonic motor drive control circuit, the supersonic motor drive control circuit bag
Include control chip circuit and driving chip circuit, the phase of the signal output part of the photoelectric encoder and the control chip circuit
Input is answered to be connected, the output end of the control chip circuit is connected with the respective input of the driving chip circuit,
To drive the driving chip circuit, the driving frequency Regulate signal output end and driving half-bridge circuit of the driving chip circuit
Respective input of the Regulate signal output end respectively with the supersonic motor is connected.
3. second order known to partial parameters according to claim 1 does not know the self-adaptation control method of lag structure, its
It is characterised by：Concrete methods of realizing is as follows：
The dynamical equation of piezoelectric motor drive system can be written as：
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Wherein m is unknown positive parameter, and c is uncertain parameter, and Φ represents nonlinear component, and f (t) is unknown external disturbance, u
(t) it is control input；In structural system, m and c are respectively quality and damped coefficient, and restoring force Φ represents the stagnant of piezoelectric
Behavior afterwards, x is position, and u (t) is the active controlling force provided by appropriate actuator f (t), and it is described as f (t)=- ma
(t), wherein a (t) is vibration acceleration；
Restoring force Φ is described with following form:
Φ (x, t)=α kx (t)+(1- α) Dkz (t) (5-4)
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Wherein, x and z represent position and restoring force, are respectively acting on piezoelectric, there is lagged relationship, parameter between x and z
Length, width and the size in hysteresis interval of A, β and λ control hysteresis curve, n is an integer, is determined by experimental data；
The model represents restoring force Φ (x, t), wherein D by component of elasticity α kx (t) and lagging component (1- α) Dkz superposition>0
Constant displacement is produced, α is pre- production ratio；Lagging portion is related to auxiliary variable z, and it is non-linear first rank nonlinear equation
The solution of (5-5)；
From dynamical system (5-5), have
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Construct a positive Liapunov function Vz=z (t)2/2；Consider A>0 situation, there is following three kinds of possibilities：
*P1:β+λ ＞ 0 and β-λ >=0
*P2:β+λ ＞ 0 and β-λ ＜ 0
(5-7)
*P3:β+λ≤0
Concern situation P1, is setAnd by VQ1It is expressed as Lyapunov functions V in set Q1ZDerivative
Expression formula, hasTherefore,Similarly, for | z | >=z0,WhereinSet in additionWithIn the case of, draw same
The conclusion of sample；
ForAll possible sign and z, have | z | >=z0；Draw a conclusion：Z (t) be each bounded piecewise function x and
Each primary condition z (0)；Z (t) boundary can draw as follows：
If z primary condition is | z (0) |≤z0, then | z |≤z0, t >=0；
If z primary condition is z (0) >=z0, then | z |≤z (0), t >=0；
By consideringRegion inCome
Steering situation
According to similar argument, it can be shown that for meeting | z (0) |≤z1Original state z (0),For situation P1
Carry out identical analysis, it can be seen that z can be limited to some functions with right and wrongMean the region of bounded, in this case, z
(t) it is sky；
For A<0 and A=0 and a situation, can carry out similar analysis, and the conclusion drawn from analysis is summarised in following lemma：
Consider Kind of Nonlinear Dynamical System (5-5), then for any piecewise continuous signals x andIt is global bounded to export z (t)
, only when the parameter of system (5-5) meets inequality β ＞ | λ | when, control targe is one contragradience Self Adaptive Control of design
Rule；
Closed loop bounded
In transient process, tracking error x (t)-yr(t) all it is arbitrarily small cycle and stable state by clearly selecting design to join
Number, wherein yr(t) it is known bounded reference signal；
Some prior informations of hypothesized model parameter are available, therefore, further make use of the model knot in controller design
Structure improves systematic function；
Nonlinear restoring force Φ (x, t) can parameterize as follows：
Φ (t)=θ1x(t)+θ2z(t)
Wherein θ1=α k and θ2=(1- α) DK are uncertain parameters；
Assuming that parameter A, β, D, λ are in some known intervals, by above-mentioned it is assumed that equation can be used to generate signal
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Wherein A0,β0,D0,λ0In known spacings, for thisBy Φ (x, t) withIt is approximately
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It can proveIt is bounded；Due toSoIt is also bounded, estimation
Then, with following form rewrite equation
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2
Wherein x1=x,It is the constant vector of uncertain parameter,
Output control method given below：
Wherein c1, c2, γ and γ f are positive parameter, and Γ is a positive definition, design matrixIt is θ, m and F estimation with F；
It is all bounded that x, x, θ, m, F, which can be determined,；The result that the stability of a system and performance can be obtained is as follows：
Consider uncertain nonlinear system (1)；With controller and parameter updating method, following condition needs to have：
Produced closed-loop system is the global unified limit；
Asymptotic tracking is realized, i.e.,
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Due to using some available structural informations in the design, and delayed residual effect is considered as with unknown boundary
Bounded Perturbations, estimate to be related to the result of hysteresis effect and external disturbance using law is updated, electricity are controlled using contragradience algorithm
The anglec of rotation of machine rotor, then pass through the speed for the anglec of rotation indirect control motor for calculating rotor.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102722136A (en) * | 2012-06-29 | 2012-10-10 | 沈阳工业大学 | Device and method for controlling XY working platform of ultrasonic motor based on neural network |
| CN103513181A (en) * | 2013-07-10 | 2014-01-15 | 闽江学院 | Ultrasonic wave motor transient characteristic testing device and control system thereof |
| US20150270790A1 (en) * | 2014-03-24 | 2015-09-24 | Vital Biomedical Technologies Inc. | Ultrasonic motor control system and method |
| US20160268928A1 (en) * | 2013-11-27 | 2016-09-15 | Murata Manufacturing Co., Ltd. | Driving device |
| CN106877774A (en) * | 2017-04-21 | 2017-06-20 | 闽江学院 | Supersonic motor servo adaptive control system and method under input saturation conditions |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102722136A (en) * | 2012-06-29 | 2012-10-10 | 沈阳工业大学 | Device and method for controlling XY working platform of ultrasonic motor based on neural network |
| CN103513181A (en) * | 2013-07-10 | 2014-01-15 | 闽江学院 | Ultrasonic wave motor transient characteristic testing device and control system thereof |
| US20160268928A1 (en) * | 2013-11-27 | 2016-09-15 | Murata Manufacturing Co., Ltd. | Driving device |
| US20150270790A1 (en) * | 2014-03-24 | 2015-09-24 | Vital Biomedical Technologies Inc. | Ultrasonic motor control system and method |
| CN106877774A (en) * | 2017-04-21 | 2017-06-20 | 闽江学院 | Supersonic motor servo adaptive control system and method under input saturation conditions |
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