CN107093962B - 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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- 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 methods that second order known to a kind of partial parameters does not know lag structure, the supersonic motor that pedestal is provided and is provided thereon, supersonic motor side output shaft is connect with photoelectric encoder, other side output shaft is connect with flywheel inertia load, the output shaft of flywheel inertia load is connect through shaft coupling with torque sensor, photoelectric encoder, torque sensor signal output end be respectively connected to control system.The control system is established by Backstepping Controller and motor form, the system of entire controller on the basis of contragradience calculates, so as to obtain better controlled efficiency.Not only control accuracy is high by the present invention, but also apparatus structure is simple, compact, and using effect is good.
Description
Technical field
The present invention relates to the self-adaptation control methods that second order known to a kind of partial parameters does not know lag structure.
Background technique
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 be further reduced system for probabilistic influence journey
Degree.Therefore the Position And Velocity control of motor can obtain preferable dynamic characteristic.
Summary of the invention
In view of this, the purpose of the present invention is to provide second orders known to a kind of partial parameters not to know oneself of lag structure
Adaptive control method, not only control accuracy is high, but also structure is simple, compact, and using effect is good.
To achieve the above object, the present invention adopts the following technical scheme:
Second order known to a kind of partial parameters does not know the self-adaptation control method of lag structure, provides pedestal and is set to base
Supersonic motor on seat, it is characterised in that: supersonic motor side output shaft is connected with photoelectric encoder, the other 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 end of the photoelectric encoder, the torque sensor signal output end be respectively connected to control system；It is described
Control system is established on the basis of Reverse Step Control, estimates to be related to the knot of hysteresis effect and external disturbance using law is updated
Fruit controls the rotation angle of rotor using contragradience algorithm, then the rotation angle by calculating rotor indirectly controls motor
Speed, to obtain better controlled efficiency.
Further, the control system includes supersonic motor drive control circuit, the supersonic motor driving control
Circuit processed includes controlling chip circuit and driving chip circuit, the signal output end 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 adjustment signal output end of the driving chip circuit and driving
Half-bridge circuit adjustment signal output end is connected with the respective input of the supersonic motor respectively.
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 indicates that nonlinear component, f (t) are that unknown outside is dry
It disturbs, u (t) is control input；In structural system, m and c are respectively quality and damped coefficient, and restoring force Φ indicates piezoelectric material
Lag behavior, x is position, and u (t) is the active controlling force provided by actuator f (t) appropriate, be 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)
Wherein, x and z indicates position and restoring force, is respectively acting on piezoelectric material, there is lagged relationship between x and z,
Parameter A, β and λ control length, the size of width and hysteresis section of hysteresis curve, and n is an integer, is determined by experimental data；
The model represents restoring force Φ (x, t) by the superposition of component of elasticity α kx (t) and lagging component (1- α) Dkz,
Middle D > 0 generates constant displacement, and α is pre- production ratio；Lagging portion is related to auxiliary variable z, 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；The case where considering A > 0, there is following three kinds of possibilities:
* P1: β+λ > 0 and-λ >=0 β
* P2: β+λ > 0 and β-λ < 0
(5-7)
*P3:β+λ≤0
Pay close attention to situation P1, settingAnd by VQ1It is expressed as Lyapunov function V in set Q1Z's
The expression formula of derivative, hasTherefore,Similarly, for | z | >=z0,
WhereinIn addition it is arrangedWithIn the case where, it obtains
Same conclusion；
ForAll possible sign and z, have | z | >=z0；Conclude that z (t) is the segmentation letter of each bounded
Number x and each primary condition z (0)；The boundary of z (t) is it can be concluded that as follows:
If the primary condition of z is | z (0) |≤z0, then | z |≤z0, t >=0；
If the primary condition of z is z (0) >=z0, then | z |≤z (0), t >=0；
Pass through considerationRegion 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 certain functions with right and wrongThe region for meaning bounded, in this feelings
Under condition, z (t) is sky；
The case where for A < 0 and A=0 and a, can carry out similar analysis, and the conclusion obtained 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 target is that one contragradience of design is self-adaptive controlled
System rule；
Closed loop bounded
In transient process, tracking error x (t)-yrIt (t) is all to be set by clearly selection in arbitrarily small period and stable state
Parameter is counted, wherein yrIt (t) is known bounded reference signal；
Certain prior informations of hypothesized model parameter are available, and therefore, the mould in controller design are further utilized
Type structure improves system performance；
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 is uncertain parameter；
Assuming that parameter A, β, D, λ be in some known intervals, by above-mentioned it is assumed that equation, which can be used, generates 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,Result control method is 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 can determine that x, x, θ, m, F are bounded；The result of available system stability and performance is as follows:
Consider uncertain nonlinear system (1)；With controller and parameter updating method, the following conditions need to have:
Generated closed-loop system is the global unified limit；
Realize asymptotic tracking, 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 the residual effect lagged is considered as with Unknown Bound
The Bounded Perturbations of limit, estimate to be related to using law is updated hysteresis effect and external disturbance as a result, being controlled using contragradience algorithm
The rotation angle of rotor processed, then the rotation angle by calculating rotor indirectly control the speed of motor.
Compared with the prior art, the invention has the following beneficial effects: effectively promoting present invention uses innovatory algorithm and being
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 design is rationally, structure is simple, compact, and manufacturing cost is low, has very strong practicability
With wide application prospect.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of one embodiment of the invention.
Fig. 2 is control circuit schematic diagram of the invention.
In figure: 1- photoelectric encoder, the fixed bracket of 2- photoelectric encoder, 3- supersonic motor output shaft, 4- ultrasonic wave electricity
Machine, the fixed bracket of 5- supersonic motor, 6- supersonic motor output shaft, 7- flywheel inertia load, the output of 8- flywheel inertia load
Axis, 9- yielding coupling, 10- torque sensor, the fixed bracket of 11- torque sensor, 12- pedestal, 13- control chip circuit,
14- driving chip circuit, 15,16,17- photoelectric encoder output A, B, Z phase signals, 18,19,20,21- driving chip circuit
The driving frequency adjustment signal of generation, 22- driving chip circuit generate driving half-bridge circuit adjustment signal, 23,24,25,26,
27,28- controls the signal for the driving chip circuit that chip circuit generates, 29- supersonic motor drive control circuit.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
The present invention provides the self-adaptation control method that second order known to a kind of partial parameters does not know lag structure, please refers to
Fig. 1, provides pedestal 12 and the supersonic motor 4 on pedestal 12, and the 4 side output shaft 3 of supersonic motor is compiled with photoelectricity
Code device 1 is connected, and other 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 end of the photoelectric encoder 1, the torque sensor 10
Signal output end is respectively connected to control system.The control system is established on the basis of Reverse Step Control, and update law is used
It is that estimation is related to hysteresis effect and external disturbance as a result, control the rotation angle of rotor using contragradience algorithm, then pass through
The rotation angle for calculating rotor indirectly controls the speed of motor, to obtain better controlled efficiency.
Above-mentioned supersonic motor 4, photoelectric encoder 1, torque sensor 10 are respectively through supersonic motor fixed bracket 5, light
Photoelectric coder is fixed the fixed bracket 11 of bracket 2, torque sensor and is 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
Control circuit 29 includes control chip circuit 13 and driving chip circuit 14, the signal output end of the photoelectric encoder 1 and institute
The respective input for stating control chip circuit 13 is connected, the output end and 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
Adjustment signal output end and the driving half-bridge circuit adjustment signal output end respective input phase with the supersonic motor 4 respectively
Connection.The driving chip circuit 14 generates driving frequency adjustment signal and driving half-bridge circuit adjustment signal, to ultrasonic wave electricity
Frequency, phase and the on-off of machine output A, B two phase PWM are controlled.Ultrasound is controlled by opening and turning off the output of PWM wave
Wave motor starts and stops operation；Motor is adjusted most by the phase difference of the frequency and two-phase that adjust the PWM wave of output
Good operating status.
We control the rotation angle of rotor using Backstepping Controller.It is 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 include control chip circuit and driving chip electricity
Road, the Backstepping Controller are set in the control chip circuit.
Supersonic motor contragradience adaptive servo control system, contragradience adaptively estimate the unknown of control system for using
, 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 indicates that nonlinear component, f (t) are that unknown outside is dry
It disturbs.U (t) is control input.In structural system, m and c are respectively quality and damped coefficient, and restoring force Φ indicates piezoelectric material
Lag behavior, x is position, and u (t) is the active controlling force provided by actuator f (t) appropriate, this be described as f (t)=-
Ma (t), wherein a (t) is vibration acceleration.Lag
Power Φ is described with following form:
Φ (x, t)=α kx (t)+(1- α) Dkz (t) (5-4)
Wherein, x and z indicates position and restoring force, is respectively acting on piezoelectric material, there is lagged relationship between x and z,
Parameter A, β and λ control length, the size of width and hysteresis section of hysteresis curve, and n is an integer, is determined by experimental data；
The model represents restoring force Φ (x, t) by the superposition of component of elasticity α kx (t) and lagging component (1- α) Dkz,
Middle D > 0 generates constant displacement, and α is pre- production ratio；Lagging portion is related to auxiliary variable z, 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.The case where considering A > 0.There are three types of possibilities.
* P1: β+λ > 0 and-λ >=0 β
* 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 function VZDerivative expression formula, haveTherefore,Similarly, for
|z|≥z0,WhereinIn addition it is arrangedWithIn the case where, obtain 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).The boundary of z (t) is it can be concluded that as follows:
If the primary condition of z is | z (0) |≤z0, then | z |≤z0, t >=0；
If the primary condition of z is z (0) >=z0, then | z |≤z (0), t >=0
We pass through consideration now'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 certain functions with right and wrongMean have
The region on boundary, in this case, z (t) are sky.
The case where for A < 0 and A=0 and a, can carry out similar analysis, and the conclusion obtained 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 target is that one contragradience of design is self-adaptive controlled
System rule.
Closed loop bounded
In transient process, tracking error x (t)-yrIt (t) is all to be set by clearly selection in arbitrarily small period and stable state
Parameter is counted, wherein yrIt (t) is known bounded reference signal.
Certain prior informations of hypothesized model parameter are available.Therefore, the mould in controller design is further utilized
Type structure improves system performance.
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 is uncertain parameter.
Assuming that parameter A, β, D, λ be in some known intervals, by above-mentioned it is assumed that equation, which can be used, generates 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,Result control method is given below:
Wherein c1, c2, γ and γ f are designed the parameter that is positive, and Γ is a positive definition.Design matrixIt is θ, m with F
With the estimation of F.
It can determine that x, x, θ, m, F are bounded.The result of available system stability and performance is as follows:
Consider uncertain nonlinear system (1).With controller and parameter updating method, the following conditions need to have:
Generated closed-loop system is the global unified limit.
Realize asymptotic tracking, 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 the residual effect lagged 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.It is controlled using contragradience algorithm
The rotation angle of rotor processed, then the rotation angle by calculating rotor indirectly control the speed of motor.
The foregoing is merely presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with
Modification, is all covered by the present invention.
Claims (2)
1. second order known to a kind of partial parameters does not know the self-adaptation control method of lag structure, pedestal is provided and is set to pedestal
On supersonic motor, it is characterised in that: supersonic motor side output shaft is connected with photoelectric encoder, and the other 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 end of the photoelectric encoder, the torque sensor signal output end be respectively connected to control system；The control
System processed is established on the basis of Reverse Step Control, estimate to be related to using law is updated hysteresis effect and external disturbance as a result,
The rotation angle of rotor is controlled using contragradience algorithm, then the rotation angle by calculating rotor indirectly controls the speed of motor
Degree, to obtain better controlled efficiency；Concrete methods of realizing is as follows:
The dynamical equation of supersonic motor drive system can be written as:
Wherein m is unknown positive parameter, and c is uncertain parameter, and Φ indicates nonlinear component, and f (t) is unknown external disturbance, u
It (t) is control input；In structural system, m and c are respectively quality and damped coefficient, and restoring force Φ indicates the stagnant of piezoelectric material
Behavior afterwards, x are position, and u (t) is the active controlling force provided by actuator f (t) appropriate, are 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)
Wherein, x indicates position, and z indicates lagging portion auxiliary variable, is respectively acting on piezoelectric material, has between x and z stagnant
Relationship afterwards, parameter A, β and λ control length, the size of width and hysteresis section of hysteresis curve, and n is an integer, by experiment number
According to determination；
The model represents restoring force Φ (x, t) by the superposition of component of elasticity α kx (t) and lagging component (1- α) Dkz, wherein D > 0
Constant displacement is generated, α is pre- production ratio；K indicates the coefficient of elasticity of component of elasticity, and lagging portion is related to auxiliary variable z, it is
The solution of non-linear first rank nonlinear equation (5-5)；
From non-linear first rank nonlinear equation (5-5), have
Construct a positive Liapunov function Vz=z (t)2/2；The case where considering A > 0, there is following three kinds of possibilities:
* P1: β+λ > 0 and-λ >=0 β
* P2: β+λ > 0 and β-λ < 0
(5-7)
*P3:β+λ≤0
Situation P1 is paid close attention to, is arranged Q1:={ x >=0 and z >=0 }, and by VQ1It is expressed as Lyapunov function V in set Q1ZDerivative
Expression formula, haveTherefore,Similarly, for | z | >=z0,WhereinIn addition it is arrangedWithIn the case where, it has obtained same
The conclusion of sample；ForAll possible sign and z, have | z | >=z0；Conclude that z (t) is the segmentation letter of each bounded
Number x and each primary condition z (0)；The boundary of z (t) is it can be concluded that as follows:
If the primary condition of z is | z (0) |≤z0, then | z |≤z0, t >=0；
If the primary condition of z is z (0) >=z0, then | z |≤z (0), t >=0；
Pass through considerationRegion inCome
Turn to situation
According to similar argument, it can be shown that for meeting | z (0) |≤z1Original state z (0), Vz≤0；For situation P1
Carrying out identical analysis, it can be seen that z is greater than 0, if x means the region of bounded, in this case, z (t) is sky；
The case where for A < 0 and A=0 and a, can carry out similar analysis, and the conclusion obtained from analysis is summarised in following lemma:
Consider non-linear first rank nonlinear equation (5-5), then for any piecewise continuous signals x andIt is complete for exporting z (t)
Office's bounded, only when the parameter of non-linear first rank nonlinear equation (5-5) meets inequality β > | λ | when, control target is
Design a contragradience adaptive control laws；
Closed loop bounded
In transient process, tracking error x (t)-yrIt (t) is all to pass through clearly selection design ginseng in arbitrarily small period and stable state
It counts, wherein yrIt (t) is known bounded reference signal；
The prior information of hypothesized model parameter is available, and therefore, the model structure being further utilized in controller design is come
Improve system performance；
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 is uncertain parameter；
Assuming that parameter A, β, D, λ be in some known intervals, by above-mentioned it is assumed that equation, which can be used, generates 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,
Result control method is given below:
Wherein c1, c2, γ and γfFor positive parameter to be designed, Γ is a positive definite matrix to be designed,It is wait set
Matrix is counted,It is the estimation of θ, m, F；It isFirst derivative；U is control input；
It is control intermediate variable, sign () is sign function,Be the given tracking error with output valve,It is given and virtual controlling
Error, α1It is the intermediate variable of virtual controlling,It is the second dervative of known bounded reference signal, yrIt (t) is known bounded
Reference signal；
It can determineX, θ, m, F are bounded；The result of available system stability and performance is as follows:
Consider uncertain dynamical equation (1)；With controller and parameter updating method, the following conditions need to have:
Generated closed-loop system is the global unified limit；
Realize asymptotic tracking, 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 the residual effect lagged is considered as having unknown boundary
Bounded Perturbations, estimate to be related to using law is updated hysteresis effect and external disturbance as a result, controlling electricity using contragradience algorithm
The rotation angle of machine rotor, then the rotation angle by calculating rotor indirectly control the speed of motor.
2. second order known to partial parameters according to claim 1 does not know the self-adaptation control method of lag structure,
Be characterized in that: the control system includes supersonic motor drive control circuit, the supersonic motor drive control circuit packet
Include control chip circuit and driving chip circuit, the phase of the signal output end of the photoelectric encoder and the control chip circuit
Input terminal 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 adjustment signal output end and driving half-bridge circuit of the driving chip circuit
Adjustment signal output end is connected with the respective input of the supersonic motor respectively.
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| 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 |
| 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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