CN107276455B - Piezoelectric motor dead band control system and method based on output feedback Reverse Step Control - Google Patents
Piezoelectric motor dead band control system and method based on output feedback Reverse Step Control Download PDFInfo
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- CN107276455B CN107276455B CN201710518972.3A CN201710518972A CN107276455B CN 107276455 B CN107276455 B CN 107276455B CN 201710518972 A CN201710518972 A CN 201710518972A CN 107276455 B CN107276455 B CN 107276455B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
- H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
- H02N2/14—Drive circuits; Control arrangements or methods
- H02N2/142—Small signal circuits; Means for controlling position or derived quantities, e.g. speed, torque, starting, stopping, reversing
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Abstract
The present invention relates to a kind of piezoelectric motor dead band control systems and method based on output feedback Reverse Step Control, the system includes: pedestal and the piezoelectric motor that is provided thereon, piezoelectric 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 method includes: that one adaptive Backstepping Controller of carrying, the system of entire controller are established on the basis of feeding back calculating, so as to obtain better controlled efficiency in the controls.A kind of piezoelectric motor dead band control system and control method based on output feedback Reverse Step Control proposed by the invention, not only control accuracy is high, but also structure is simple, compact, and using effect is good.
Description
Technical Field
The invention relates to a piezoelectric motor dead zone control system and method based on output feedback backstepping control.
Background
The existing piezoelectric motor servo control system has detection errors of output signals in design, which may cause estimation errors of control variables. To avoid this, we now propose a feedback 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 dead zone control system and method based on output feedback backstepping control, so as to overcome the defects in the prior art.
In order to achieve the purpose, the technical scheme of the invention is as follows: a piezoelectric motor dead zone control system based on output feedback backstepping control comprises a base and a piezoelectric motor arranged on the base; an output shaft at one side of the piezoelectric motor is connected with a photoelectric encoder, and an output shaft at the other side of the piezoelectric motor is connected with a flywheel inertial load; the output shaft of the flywheel inertial load is connected with a torque sensor through a coupler; the signal output end of the photoelectric encoder, the signal output end of the torque sensor and the input end of the piezoelectric motor are respectively connected with a control system.
In an embodiment of the present invention, the control system includes a piezoelectric motor driving control circuit; the piezoelectric motor driving control circuit comprises a control chip circuit and a driving chip circuit; the signal output end of the photoelectric encoder is connected with the corresponding input end of the control chip circuit, and the output end of the control chip circuit is connected with the corresponding input end of the driving chip circuit so as to drive the driving chip circuit; and the driving frequency adjusting signal output end of the driving chip circuit and the driving half-bridge circuit adjusting signal output end are respectively connected with the corresponding input ends of the piezoelectric motor.
In an embodiment of the present invention, the coupling is an elastic coupling.
In an embodiment of the present invention, the piezoelectric motor, the photoelectric encoder, and the torque sensor are respectively fixed on the base through a piezoelectric motor fixing bracket, a photoelectric encoder fixing bracket, and a torque sensor fixing bracket.
The control system is internally provided with a reverse step self-adaptive controller, the rotating angle of a motor rotor is controlled through a reverse step control method, the speed of the motor is indirectly controlled through calculating the rotating angle of the rotor, and a robustness method for obtaining feedback control parameters through a Lyapunov stability function is used for ensuring the stability of the system.
In an embodiment of the present invention, the boundary of the total set uncertainty is known, | d (t) | is less than or equal to ρ, ρ is a preset normal number, and the system is servo-controlled by feedback control:
note the nonlinear system as follows:
wherein, YiIs known as continuous linear nonlinear distortion, d (t) represents a bounded external perturbation, parameter aiIs not constant, control gain b is constant, v is control input, u (v) represents a dead-zone nonlinear function;
wherein, br≥0,blLess than or equal to 0 and m>0 is a constant, v is an input, u is an output;
u(t)＝mv(t)+d1(v(t))
wherein,
then d1(v (t)) is bounded;
recording:
wherein β is bm andthe influence of d (t) is due to both external perturbations and bd1(v (t)) let D (t) be the interference term and use D to represent its bounds;
then:
wherein,a＝[-a1,-a2,…,-ar]T，Y＝[Y1，Y2，…，Yr]T；
the reverse step self-adaptive control method comprises the following steps:
α1＝-c1z1
the parameter updating method comprises the following steps:
where the uncertainty parameters b and m are such that β > 0, the desired trajectory yr(t) and its (n-1) order derivatives are known and bounded; the closed loop is stable and uniform in all signals in the loop and finally bounded; tracking error x (t) -yr(t) is adjustable during transient periods;
limt→∞x(t)-yr(t) 0 or limt→∞|x(t)-yr(t)|-δ10 for an arbitrarily specified boundary δ1＝0；
For ciWhere i is 1, …, n is a positive design parameter, γ and η are two positive design parameters, Γ is a positive definite matrix,andis an estimate of e 1/β, a and D, δi(i ═ 1, …, n) is the positive design parameter, q ═ round { (n-i +2)/2}, round { x } denotes the elements of x to the nearest integer.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a piezoelectric motor dead zone control system and method based on output feedback backstepping control, which uses a motor servo system of an improved backstepping controller. 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. In addition, the device has the advantages of reasonable design, simple and compact structure, low manufacturing cost, strong practicability and wide application prospect.
Drawings
Fig. 1 is a schematic structural diagram in an embodiment of the present invention.
Fig. 2 is a schematic diagram of a control circuit in an embodiment of the invention.
[ numbering description ]: 1-photoelectric encoder, 2-photoelectric encoder fixed support, 3-piezoelectric motor output shaft, 4-piezoelectric motor, 5-piezoelectric motor fixed support, 6-piezoelectric motor output shaft, 7-flywheel inertial load, 8-flywheel inertial load output shaft, 9-elastic coupling, 10-torque sensor, 11-torque sensor fixed support, 12-base, 13-control chip circuit, 14-drive chip circuit, 15, 16, 17-A, B, Z phase signal line output by photoelectric encoder, 18, 19, 20, 21-drive frequency regulation signal line generated by drive chip circuit, 22-drive half-bridge circuit regulation signal line generated by drive chip circuit, 23, 24, 25, 26, 27, 28-signal line of drive chip circuit generated by control 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 dead zone control system based on output feedback backstepping control, 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 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, a signal output end of the torque sensor 10 and an input end of the piezoelectric motor are respectively connected to the control system, as shown in figure 1.
Further, 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.
Further, as shown in fig. 2, the control system includes a piezoelectric motor drive control circuit 29, and the piezoelectric motor drive control circuit 29 includes a control chip circuit 13 and a drive chip circuit 14; the signal output end of the photoelectric encoder 1 is connected with the corresponding input end of the control chip circuit 13, the output end of the control chip circuit 13 is connected with the corresponding input end of the driving chip circuit 14 so as to drive the driving chip circuit 14, and the driving frequency adjusting signal output end and the driving half-bridge circuit adjusting signal output end of the driving chip circuit 14 are respectively connected with the corresponding input end 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.
Furthermore, the piezoelectric motor dead zone control system based on output feedback backstepping control is a piezoelectric motor backstepping controller servo control system and consists of a backstepping controller and a motor; in order to avoid unpredictable uncertainty items in the motor, a backstepping control method is used for controlling the system.
In this embodiment, the boundaries of the aggregate uncertainty term are assumed to be known, e.g., | D (t) | ≦ ρ, ρ being a given normal number term. To avoid unpredictable uncertainties in the motor, the system is servo-controlled using feedback control.
The nonlinear system with unknown regions is denoted as:
wherein, YiIs known as continuous linear nonlinear distortion, d (t) represents a bounded external perturbation, parameter aiIs an unknown constant and the control gain b is an unknown constant, v is the control input, u (v) represents a dead-zone nonlinear function;
wherein, br≥0,blLess than or equal to 0 and m>0 is a constant, v is an input, and u is an output.
u(t)＝mv(t)+d1(v(t)) (2.3)
Wherein,
obviously, d1(v (t)) is bounded.
From the structure (2.3), (2.1) of the model (2.2) to
Wherein β is bm andthe influence of d (t) is due to both external perturbations and bd1(v (t)). I amWe refer to D (t) as the simple representation of the "interference" term and to D as its limit.
Further, the formula (2.5) is rewritten in the following form:
wherein,a＝[-a1,-a2,…,-ar]Tand Y ═ Y1，Y2，…，Yr]T。
Further, in order to make a control law, the following assumption is made.
Suppose 1. uncertain parameters b and m are such that β > 0.
Assumption 2. desired trajectory yr(t) and its (n-1) order derivatives are known and bounded.
In this embodiment, the control objective is to design a feedback adaptive control law:
the final bounding that all signals of the closed loop in the loop are stable and uniform;
the tracking error x (t) -yr(t) is adjustable during the transient period.
In the present embodiment, the design parameters and lim are explicitly selectedt→∞x(t)-yr(t) 0 or limt→∞|x(t)-yr(t)|-δ10 for an arbitrarily specified boundary δ1＝0。
In this example, c in Table 2.1iWhere i is 1, …, n is a positive design parameter, γ and η are two positive design parameters, Γ is a positive definite matrix,andis e 1/β, an estimate of a and D, δi(i ═ 1, …, n) is the positive design parameter, q ═ round { (n-i +2)/2}, round { x } denotes the elements of x to the nearest integer.
In this embodiment, the adaptive control law is as follows:
α1＝-c1z1 (2.7)
in this embodiment, the parameter updating method is as follows:
furthermore, a reverse step adaptive controller adopts a reverse step control algorithm to control the rotation angle of the motor rotor, and the rotation angle of the rotor is calculated to indirectly control the speed of the motor. The robust learning rule of the feedback control parameters is obtained by the Lyapunov stability theorem. Feedback adaptation will be used to estimate the output term of the control system, ensuring the stability of the designed control system with the Lyapunov function.
In this embodiment, the hardware circuit of the control system includes a piezoelectric motor drive control circuit, the piezoelectric motor drive control circuit includes a control chip circuit and a driver chip circuit, and the back-stepping adaptive controller is mounted on the control chip circuit.
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 (4)
1. A piezoelectric motor dead zone control system based on output feedback backstepping control comprises a base and a piezoelectric motor arranged on the base; an output shaft at one side of the piezoelectric motor is connected with a photoelectric encoder, and an output shaft at the other side of the piezoelectric motor is connected with a flywheel inertial load; the output shaft of the flywheel inertial load is connected with a torque sensor through a coupler; the signal output end of the photoelectric encoder, the signal output end of the torque sensor and the input end of the piezoelectric motor are respectively connected with a control system; the control system is internally provided with a backstepping self-adaptive controller, the rotation angle of a motor rotor is controlled by a backstepping control method, the speed of the motor is indirectly controlled by calculating the rotation angle of the rotor, and a robustness method of feedback control parameters is obtained by a Lyapunov stability function to ensure the stability of the system, and the control system is characterized in that the boundary of an uncertain item of a total set is recorded as known, | D (t) | is less than or equal to rho, rho is a preset normal number item, and the servo control is performed on the system by adopting feedback control:
note the nonlinear system as follows:
wherein, YiIs known as continuous linear or non-linear distortion, d (t) represents a bounded external perturbation, parameter aiIs an unknown constant, the control gain b is a constant, v is the control input, u (v) represents a dead-zone nonlinear function;
wherein, br≥0,blLess than or equal to 0 and m>0 is a constant, v is an input, u is an output;
u(t)＝mv(t)+d1(v(t))
wherein,
then d1(v (t)) is bounded;
recording:
wherein β is bm andthe influence of d (t) is due to bothExternal disturbance and bd1(v (t)) let D (t) be the interference term and use D to represent its bounds;
then:
wherein,a＝[-a1,-a2,…,-ar]T，Y＝[Y1，Y2，L，Yr]T(ii) a x represents a position signal;
the reverse step self-adaptive control method comprises the following steps:
α1＝-c1z1
the parameter updating method comprises the following steps:
where the uncertainty parameters b and m are such that β > 0, the desired trajectory yr(t) and its (n-1) order derivatives are known and bounded; the closed loop is stable and uniform in all signals in the loop and finally bounded; tracking error x (t) -yr(t) is adjustable during transient periods; x (t) represents a position signal at time t;
limt→∞x(t)-yr(t) 0 or limt→∞|x(t)-yr(t)|-δ10 for an arbitrarily specified boundary δ1＝0；
For ci,i＝1,L,n，ciAre positive design parameters, γ and η are two positive design parameters, Γ is a positive definite matrix,andis an estimate of e 1/β, a and D, δi(i ═ 1, L, n) is a positive design parameter, q ═ round { (n-i +2)/2}, round { x } denotes the elements of x to the nearest integer.
2. The piezoelectric motor dead-zone control system based on output feedback backstepping control according to claim 1, wherein the control system comprises a piezoelectric motor drive control circuit; the piezoelectric motor driving control circuit comprises a control chip circuit and a driving chip circuit; the signal output end of the photoelectric encoder is connected with the corresponding input end of the control chip circuit, and the output end of the control chip circuit is connected with the corresponding input end of the driving chip circuit so as to drive the driving chip circuit; and the driving frequency adjusting signal output end of the driving chip circuit and the driving half-bridge circuit adjusting signal output end are respectively connected with the corresponding input ends of the piezoelectric motor.
3. The piezoelectric motor dead zone control system based on output feedback backstepping control according to claim 1, wherein the coupling is an elastic coupling.
4. The piezoelectric motor dead zone control system based on output feedback backstepping control according to claim 1, wherein the piezoelectric motor, the photoelectric encoder and the torque sensor are fixed on the base through a piezoelectric motor fixing support, a photoelectric encoder fixing support and a torque sensor fixing support, respectively.
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