CN107257211B - The stable piezoelectric motor self-adaptation control method in gap under partial parameters known conditions - Google Patents
The stable piezoelectric motor self-adaptation control method in gap under partial parameters known conditions Download PDFInfo
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Abstract
The present invention relates to the piezoelectric motor self-adaptation control methods that gap under a kind of partial parameters known conditions is stable.There is provided a piezoelectric motor adaptive control system includes pedestal and the piezoelectric motor on pedestal, piezoelectric motor side output shaft is connected with photoelectric encoder, other side output shaft is connected with flywheel inertia load, 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 is established on the basis of contragradience calculates, so as to obtain better controlled efficiency.The method of the present invention makes piezoelectric motor self adaptive control obtain better controlled efficiency.
Description
Technical Field
The invention relates to a self-adaptive control method for a piezoelectric motor with stable clearance under the condition of known partial parameters.
Background
The design of the existing piezoelectric motor backstepping self-adaptive servo control system has a discontinuous function sgn (z)n) Taking part in the control, this may lead to chattering. To avoid this, we now propose an improved back-stepping adaptive control scheme. The control system can effectively improve the control efficiency of the system and further reduce the influence degree of the system on the uncertainty. Therefore, the position and speed control of the motor can obtain better dynamic characteristics.
Disclosure of Invention
The invention aims to provide a piezoelectric motor self-adaptive control method with stable clearance under the condition of known partial parameters, which enables the piezoelectric motor self-adaptive control to obtain better control efficiency.
In order to achieve the purpose, the technical scheme of the invention is as follows: a piezoelectric motor self-adaptive control method with stable gap under the condition of known partial parameters provides a piezoelectric motor self-adaptive control system which comprises a base and a piezoelectric motor arranged on the base, wherein an output shaft on one side of the piezoelectric motor is connected with a photoelectric encoder, an output shaft on the other side of the piezoelectric motor is connected with a flywheel inertial load, an output shaft of the flywheel inertial load is connected with a torque sensor through a coupler, a signal output end of the photoelectric encoder and a signal output end of the torque sensor are respectively connected to the control system, and the control system is established on the basis of backstepping calculation, so that better control efficiency can be obtained.
In an embodiment of the present invention, the control system includes a piezoelectric motor driving control circuit, the piezoelectric motor driving control circuit includes a control chip circuit and a driving chip circuit, a signal output end of the photoelectric encoder is connected to a corresponding input end of the control chip circuit, an output end of the control chip circuit is connected to a corresponding input end of the driving chip circuit to drive the driving chip circuit, and a driving frequency adjusting signal output end and a driving half-bridge circuit adjusting signal output end of the driving chip circuit are respectively connected to corresponding input ends of the piezoelectric motor; the control system adopts a back-stepping self-adaptive controller which is arranged in the control chip circuit.
In one embodiment of the present invention, the method is implemented as follows,
the dynamic equation for a piezoelectric motor drive system can be written as:
where m is an unknown positive parameter, c is an uncertain parameter, Φ represents a nonlinear component, f (t) is an unknown external disturbance, u (t) is a control input, in the structural architecture, m and c are mass and damping coefficients, respectively, the restoring force Φ represents the hysteresis behavior of the piezoelectric material, x is the position, u (t) is the active control force provided by a suitable actuator f (t), described as f (t) ═ ma (t), where a (t) is the vibration acceleration;
the restoring force Φ is described in the following form
Φ(x,t)＝αkx(t)+(1-α)Dkz(t) (2)
The parameters A, β and lambda control the length, width and size of hysteresis curve, n is an integer and is determined by experimental data;
the model represents the restoring force Φ (x, t) by the superposition of an elastic component α kx (t) and a hysteresis component (1- α) Dkz, where D >0 produces a constant displacement, α is the pre-yield ratio, the hysteresis component relates to the auxiliary variable z, which is a solution of the nonlinear first order nonlinear equation (3);
in the background step, the following coordinate transformation is performed
Wherein,is the virtual control at the q step of the i cycle; the specific virtual control process is as follows,
step 1: from stable errorIs obtained from equations (4) and (5)
Virtual control rateIs designed as
Wherein,andis a positive design parameter that is,is thetaiIs estimated by the estimation of (a) a, (ii) an estimate of (d);
the influencing subsystem designed to compensate for the interaction of other subsystems or its own unmodeled part in equation (8); from formulae (6) and (7):
wherein,order to
Considering the Lyapunov function
Assume an uncertain parameter piAnd thetaiWithin the internally known compact set, a priori information may then be used as follows:
due to uncertain parameter piAnd thetaiInternally known compact setsIn the adaptive control law adopted by the back-stepping adaptive controller, smooth projection operation is used to ensure that all time belonging to a compact set is estimated; the projection operation ensures that all t's estimated parametersAnd estimating the parameter vectorThus, the limitation guarantees all tAndthe inverse step adaptive controller thus obtained adopts the adaptive control law and the parameter update law as follows:
adaptive control law:
parameter updating law:
estimating the results relating to hysteresis effects and external disturbances using a parameter update law; and controlling the rotation angle of the motor rotor by using an adaptive control law, and indirectly controlling the speed of the motor by calculating the rotation angle of the rotor.
Compared with the prior art, the invention has the following beneficial effects: the method adopts an improved backstepping self-adaptive controller to replace a traditional backstepping controller, and the traditional backstepping controller has discontinuous functions to participate in control, which may cause flutter; in order to reduce the occurrence of chatter, the invention uses an improved algorithm to effectively improve the control efficiency of the system, further reduce the influence degree of the system on uncertainty, improve the control accuracy and obtain better dynamic characteristics.
Drawings
Fig. 1 is a schematic structural diagram of an embodiment of the present invention.
Fig. 2 is a schematic diagram of a control circuit of an embodiment of the invention.
In the figure, 1-a photoelectric encoder, 2-a photoelectric encoder fixing support, 3-a piezoelectric motor output shaft, 4-a piezoelectric motor, 5-a piezoelectric motor fixing support, 6-a piezoelectric motor output shaft, 7-a flywheel inertial load, 8-a flywheel inertial load output shaft, 9-an elastic coupling, 10-a torque sensor, 11-a torque sensor fixing support, 12-a base, 13-a control chip circuit, 14-a driving chip circuit, 15, 16 and 17-A, B, Z phase signals output by the photoelectric encoder, 18, 19, 20 and 21-driving frequency adjusting signals generated by the driving chip circuit, 22-driving half-bridge circuit adjusting signals generated by the driving chip circuit, and 23, 24, 25, 26, 27 and 28-signals generated by the driving chip circuit, 29-piezoelectric motor drive control circuit.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The invention provides a piezoelectric motor self-adaptive control method with stable clearance under the condition of known partial parameters, and provides a piezoelectric motor self-adaptive control system which comprises a base 12 and a piezoelectric motor 4 arranged on the base 12, wherein an output shaft 3 at one side of the piezoelectric motor 4 is connected with a photoelectric encoder 1, an output shaft 6 at the other side of the piezoelectric motor 4 is connected with a flywheel inertial load 7, an output shaft 8 of the flywheel inertial load 7 is connected with a torque sensor 10 through an elastic coupling 9, and a signal output end of the photoelectric encoder 1 and a signal output end of the torque sensor 10 are respectively connected to the control system.
The piezoelectric motor 4, the photoelectric encoder 1 and the torque sensor 10 are fixed on the base 12 through a piezoelectric motor fixing support 5, a photoelectric encoder fixing support 2 and a torque sensor fixing support 11 respectively.
As shown in fig. 2, the control system includes a piezoelectric motor driving control circuit 29, the piezoelectric motor driving control circuit 29 includes a control chip circuit 13 and a driving chip circuit 14, a signal output end of the photoelectric encoder 1 is connected to a corresponding input end of the control chip circuit 13, an output end of the control chip circuit 13 is connected to a corresponding input end of the driving chip circuit 14 to drive the driving chip circuit 14, and a driving frequency adjusting signal output end and a driving half-bridge circuit adjusting signal output end of the driving chip circuit 14 are respectively connected to corresponding input ends of the piezoelectric motor 4. The driving chip circuit 14 generates a driving frequency adjusting signal and a driving half-bridge circuit adjusting signal to control the frequency, the phase and the on-off of A, B two-phase PWM output by the piezoelectric motor. Controlling the starting and stopping of the piezoelectric motor by switching on and off the output of the PWM wave; the optimal operation state of the motor is adjusted by adjusting the frequency of the output PWM wave and the phase difference of the two phases.
The invention relates to a piezoelectric motor self-adaptive control method with stable clearance under the condition of part of parameters, which uses a backstepping self-adaptive controller to control the rotation angle of a motor rotor. The robust learning rule of the backstepping control parameter is obtained by the Lyapunov stability theorem. The reverse step self-adaptive controller of the control system is arranged in the control chip circuit. The whole system of the backstepping self-adaptive controller is established on the basis of backstepping control, and the backstepping is also taken as an adjusting function of the backstepping self-adaptive controller in the design of a robust controller, so that better control efficiency can be obtained. The method is realized in the following concrete way,
the dynamic equation for a piezoelectric motor drive system can be written as:
where m is an unknown positive parameter, c is an uncertain parameter, Φ represents a nonlinear component, f (t) is an unknown external disturbance, u (t) is a control input, in the structural architecture, m and c are mass and damping coefficients, respectively, the restoring force Φ represents the hysteresis behavior of the piezoelectric material, x is the position, u (t) is the active control force provided by a suitable actuator f (t), described as f (t) ═ ma (t), where a (t) is the vibration acceleration;
the restoring force Φ is described in the following form
Φ(x,t)＝αkx(t)+(1-α)Dkz(t) (2)
The parameters A, β and lambda control the length, width and size of hysteresis curve, n is an integer and is determined by experimental data;
the model represents the restoring force Φ (x, t) by the superposition of an elastic component α kx (t) and a hysteresis component (1- α) Dkz, where D >0 produces a constant displacement, α is the pre-yield ratio, the hysteresis component relates to the auxiliary variable z, which is a solution of the nonlinear first order nonlinear equation (3);
in the background step, the following coordinate transformation is performed
Wherein,is the virtual control at the q step of the i cycle; the specific virtual control process is as follows,
step 1: from stable errorIs obtained from equations (4) and (5)
Virtual control rateIs designed as
Wherein,andis a positive design parameter that is,is thetaiIs estimated by the estimation of (a) a,is that(ii) an estimate of (d);
the influencing subsystem designed to compensate for the interaction of other subsystems or its own unmodeled part in equation (8); from formulae (6) and (7):
wherein,order to
Considering the Lyapunov function
Assume an uncertain parameter piAnd thetaiWithin the internally known compact set, a priori information may then be used as follows:
due to uncertain parameter piAnd thetaiInternally known compact setsIn the adaptive control law adopted by the back-stepping adaptive controller, smooth projection operation is used to ensure that all time belonging to a compact set is estimated; the projection operation ensures that all t's estimated parametersAnd estimating the parameter vectorThus, the limitation guarantees all tAndthe inverse step adaptive controller thus obtained adopts the adaptive control law and the parameter update law as follows:
adaptive control law:
parameter updating law:
estimating the results relating to hysteresis effects and external disturbances using a parameter update law; and controlling the rotation angle of the motor rotor by using an adaptive control law, and indirectly controlling the speed of the motor by calculating the rotation angle of the rotor.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (1)
1. The utility model provides a piezoelectric motor self-adaptation control method of clearance stability under the condition is known to part parameter, provides a piezoelectric motor self-adaptation control system and includes the base and locates the piezoelectric motor on the base, its characterized in that: an output shaft at one side of the piezoelectric motor is connected with a photoelectric encoder, an output shaft at the other side of the piezoelectric motor is connected with a flywheel inertial load, an output shaft of the flywheel inertial load is connected with a torque sensor through a coupler, a signal output end of the photoelectric encoder and a signal output end of the torque sensor are respectively connected to a control system, and the control system is established on the basis of backstepping calculation, so that better control efficiency can be obtained; the control system comprises a piezoelectric motor drive control circuit, the piezoelectric motor drive control circuit comprises a control chip circuit and a drive chip circuit, the signal output end of the photoelectric encoder is connected with the corresponding input end of the control chip circuit, the output end of the control chip circuit is connected with the corresponding input end of the drive chip circuit so as to drive the drive chip circuit, and the drive frequency adjusting signal output end and the drive half-bridge circuit adjusting signal output end of the drive chip circuit are respectively connected with the corresponding input end of the piezoelectric motor; the control system adopts a back-stepping self-adaptive controller which is arranged in the control chip circuit; the method is realized in the following concrete way,
the dynamic equation for a piezoelectric motor drive system can be written as:
where Φ represents the nonlinear component, f (t) is unknown external disturbance, u (t) is the control input, m and c are the mass and damping coefficients, respectively, the restoring force Φ represents the hysteresis behavior of the piezoelectric material, x is the position, u (t) is the active control force provided by a suitable actuator f (t), described as f (t) ═ ma (t), where a (t) is the vibration acceleration;
the restoring force Φ is described in the following form
Φ(x,t)＝αkx(t)+(1-α)Dkz(t) (2)
The parameters A, β and lambda control the length, width and size of hysteresis curve, n is an integer and is determined by experimental data;
the restoring force Φ (x, t) represents the restoring force Φ (x, t) by the superposition of an elastic component α kx (t) and a hysteresis component (1- α) Dkz, where D >0 produces a constant displacement, α is the pre-yield ratio, the hysteresis component relates to the auxiliary variable z, which is the solution of the nonlinear first-order nonlinear equation (3);
in the background step, the following coordinate transformation is performed
Wherein,is the virtual control at the q step of the i cycle; the specific virtual control process is as follows,
step 1: from stable errorIs obtained from equations (4) and (5)
Virtual control rateIs designed as
Wherein,andis a positive design parameter that is,is thetaiIs estimated by the estimation of (a) a,is that(ii) an estimate of (d);
the influencing subsystem designed to compensate for the interaction of other subsystems or its own unmodeled part in equation (8); from formulae (6) and (7):
wherein,order to
Considering the Lyapunov function
Wherein, ГiIs a positive definite design matrix sumIs a positive design parameter;
assume an uncertain parameter piAnd thetaiWithin the internally known compact set, a priori information may then be used as follows:
due to uncertain parameter piAnd thetaiInternally known compact setsIn the adaptive control law adopted by the back-stepping adaptive controller, smooth projection operation is used to ensure that all time belonging to a compact set is estimated; the projection operation ensures that all t's estimated parametersAnd estimating the parameter vectorThus, the limitation guarantees all tAndthe inverse step adaptive controller thus obtained adopts the adaptive control law and the parameter update law as follows:
adaptive control law:
parameter updating law:
estimating the results relating to hysteresis effects and external disturbances using a parameter update law; and controlling the rotation angle of the motor rotor by using an adaptive control law, and indirectly controlling the speed of the motor by calculating the rotation angle of the rotor.
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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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| US9513620B2 (en) * | 2014-03-24 | 2016-12-06 | Vital Biomedical Technologies Inc. | Ultrasonic motor control system and method |
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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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