CN107276455B - Piezoelectric motor dead band control system and method based on output feedback Reverse Step Control - Google Patents

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

Piezoelectric Motor Dead Zone Control System and Method Based on Output Feedback Backstep Control

technical field

The invention relates to a piezoelectric motor dead zone control system and method based on output feedback backstepping control.

Background technique

The design of the existing piezoelectric motor servo control system has the detection error of the output signal, which may lead to the estimation error of the control variable. To avoid this situation, we now propose a feedback adaptive control scheme. The control system can effectively improve the control efficiency of the system and further reduce the degree of influence of the system on uncertainty. Therefore, the position and speed control of the motor can obtain better dynamic characteristics.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a piezoelectric motor dead zone control system and method based on output feedback backstepping control, so as to overcome the defects existing in the prior art.

In order to achieve the above purpose, the technical scheme of the present invention is: a piezoelectric motor dead zone control system based on output feedback backstepping control, comprising a base and a piezoelectric motor arranged on the base; the piezoelectric motor motor One output shaft is connected with a photoelectric encoder, and the other output shaft is connected with a flywheel inertial load; the output shaft of the flywheel inertial load is connected with a torque sensor through a coupling; the photoelectric encoder The signal output end of the torque sensor, the signal output end of the torque sensor and the input end of the piezoelectric motor are respectively connected to a control system.

In an embodiment of the present invention, the control system includes a piezoelectric motor drive control circuit; the piezoelectric motor drive control circuit includes a control chip circuit and a drive chip circuit; the signal output end of the photoelectric encoder is connected to the The corresponding input terminals of the control chip circuit are connected, and the output terminals of the control chip circuit are connected with the corresponding input terminals of the driving chip circuit to drive the driving chip circuit; the driving frequency of the driving chip circuit is adjusted The signal output terminal and the driving half-bridge circuit adjustment signal output terminal are respectively connected with the corresponding input terminals 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 via a piezoelectric motor fixing bracket, a photoelectric encoder fixing bracket, and a torque sensor fixing bracket.

Further, a control method of a piezoelectric motor dead-zone control system based on output feedback backstepping control is also provided. The control system is equipped with a backstepping adaptive controller, and the rotation of the motor rotor is controlled by the backstepping control method. Angle, and then indirectly control the speed of the motor by calculating the rotation angle of the rotor, and obtain the robust method of feedback control parameters through the Lyapunov stability function to ensure the stability of the system.

In an embodiment of the present invention, the boundary of the uncertainty item of the total set is known, |D(t)|≤ρ, ρ is a preset constant term, and feedback control is used to perform servo control on the system:

Note the nonlinear system as follows:

where Y _i is the known continuous linear nonlinear distortion, d(t) represents the bounded external disturbance, the parameter a _i is not constant, the control gain b is constant, v is the control input, and u(v) represents the dead zone nonlinear function;

Among them, b _r ≥0, b _l ≤0 and m>0 are constants, v is the input, and u is the output;

u(t)=mv(t)+d ₁ (v(t))

in,

Then d ₁ (v(t)) is bounded;

remember:

where β=bm and The effect of d(t) is due to both external disturbances and bd ₁ (v(t)), let d(t) be the disturbance term, and use D to denote its bounds;

but:

in, a=[-a ₁ ,-a ₂ ,...,-ar ] ^T , Y=[Y ₁ , Y ₂ ,...,Y _r ] ^T _;

The backstepping adaptive control method is as follows:

α ₁ =-c ₁ z ₁

The parameter update method is as follows:

where the uncertain parameters b and m are such that β>0; the desired trajectory y _r (t) and its (n-1) derivative are known and bounded; the closed loop is stable and uniform for all signals in the loop Ultimately bounded; tracking error x(t) _-yr (t) is adjustable during transient periods;

lim _t→∞ x(t)-y _r (t)=0 or lim _t→∞ |x(t)-y _r (t)|-δ ₁ =0 for an arbitrarily specified boundary δ ₁ =0;

For c _i , i=1,...,n are positive design parameters, γ and η are two positive design parameters, Γ is a positive definite matrix, and is the estimate of e=1/β, a and D, δ _i (i=1,...,n) is the positive design parameter, q=round{(n-i+2)/2}, round{x} represents the element to the nearest integer.

Compared with the prior art, the present invention has the following beneficial effects: a piezoelectric motor dead zone control system and method based on output feedback backstep control proposed by the present invention, a motor servo system using an improved backstep controller, traditional Backstepping controllers have discontinuous functions involved, which can lead to chattering. In order to reduce the occurrence of flutter, the present invention uses an improved algorithm to effectively improve the control efficiency of the system, further reduces the degree of influence of the system on uncertainty, improves the control accuracy, and can obtain better dynamic characteristics. In addition, the device has reasonable design, simple and compact structure, low manufacturing cost, strong practicability and broad application prospect.

Description of 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 in an embodiment of the present invention.

[Numbering description]: 1-photoelectric encoder, 2-photoelectric encoder fixing bracket, 3-piezoelectric motor output shaft, 4-piezoelectric motor, 5-piezoelectric motor fixing bracket, 6-piezoelectric motor output shaft, 7 -Flywheel inertial load, 8-Flywheel inertial load output shaft, 9-Elastic coupling, 10-Torque sensor, 11-Torque sensor fixing bracket, 12-Base, 13-Control chip circuit, 14-Drive chip circuit, 15 , 16, 17 - A, B, Z phase signal lines output by photoelectric encoder, 18, 19, 20, 21 - Drive frequency adjustment signal lines generated by driver chip circuit, 22 - Drive half-bridge circuit adjustment generated by driver chip circuit Signal lines, 23, 24, 25, 26, 27, 28—signal lines for driving the chip circuit generated by the control chip circuit, 29—piezoelectric motor drive control circuit.

Detailed ways

The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings.

The present invention proposes a piezoelectric motor dead zone control system based on output feedback back-step control. As shown in FIG. 1 , it includes a base 12 and a piezoelectric motor 4 arranged on the base 12, and one side of the piezoelectric motor 4 outputs an output. The shaft 3 is connected with the photoelectric encoder 1, the output shaft 6 on the other side is connected with the flywheel inertial load 7, the output shaft 8 of the flywheel inertial load 7 is connected with the torque sensor 10 through the elastic coupling 9, and the output shaft 8 of the photoelectric encoder 1 is connected. The signal output end, the signal output end of the torque sensor 10 and the input end of the piezoelectric motor are respectively connected to the control system.

Further, the piezoelectric motor 4 , the photoelectric encoder 1 , and the torque sensor 10 are respectively fixed on the base 12 via the piezoelectric motor fixing bracket 5 , the photoelectric encoder fixing bracket 2 , and the torque sensor fixing bracket 11 .

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 and the control chip circuit 13 is connected to the corresponding input terminal, and the output terminal of the control chip circuit 13 is connected to the corresponding input terminal of the driving chip circuit 14 to drive the driving chip circuit 14, the driving frequency adjustment signal output terminal of the driving chip circuit 14 and the driving half-bridge circuit. The adjustment signal output terminals are respectively connected with the corresponding input terminals of the piezoelectric motor 4 . The driving chip circuit 14 generates a driving frequency adjustment signal and a driving half-bridge circuit adjustment signal, and controls the frequency, phase and on-off of the A and B two-phase PWM output by the piezoelectric motor. By turning on and off the output of the PWM wave to control the start and stop of the piezoelectric motor; by adjusting the frequency of the output PWM wave and the phase difference between the two phases to adjust the best running state of the motor.

Further, the piezoelectric motor dead zone control system based on output feedback backstepping control is a piezoelectric motor backstepping controller servo control system, which is composed of a backstepping controller and a motor; in order to avoid unpredictable uncertainties in the motor term, the system is controlled using the backstepping control method.

In this embodiment, it is assumed that the boundary of the uncertainty item of the total set is known, such as |D(t)|≤ρ, where ρ is a given constant term. In order to avoid unpredictable uncertain items in the motor, feedback control is used to servo control the system.

Denote a nonlinear system with unknown region as:

where Y _i is the known continuous linear nonlinear distortion, d(t) represents a bounded external disturbance, parameter a _i is an unknown constant and control gain b is an unknown constant, v is the control input, and u(v) represents the dead area nonlinear function;

where b _r ≥ 0, b _l ≤ 0 and m > 0 are constants, v is the input, and u is the output.

u(t)=mv(t)+d ₁ (v(t)) (2.3)

in,

Obviously, d ₁ (v(t)) is bounded.

From the structure (2.3) of the model (2.2), (2.1) becomes

where β=bm and The effect of d(t) is due to both external perturbations and bd ₁ (v(t)). We call d(t) a simple representation of the "disturbance" term and use D to denote its bounds.

Further, rewrite equation (2.5) in the following form:

in, a=[-a ₁ ,-a ₂ ,...,- _ar ] ^T and Y=[Y ₁ , Y ₂ ,...,Y _r ] ^T .

Further, in order to formulate the control law, the following assumptions are made.

Assumption 1. Uncertain parameters b and m such that β>0.

Assumption 2. The desired trajectory yr( _t ) and its (n-1) derivative are known and bounded.

In this embodiment, the control objective is to design a feedback adaptive control law:

Closed-loop All signals in the loop are stable and uniform and eventually bounded;

• The tracking error x(t) _-yr (t) is adjustable during transient periods.

In this example, by explicitly choosing the design parameters and lim _t→∞ x(t)-y _r (t)=0 or lim _t→∞ |x(t)-y _r (t)|-δ ₁ =0 δ ₁ =0 for an arbitrarily specified boundary.

In this embodiment, c _i , i=1,...,n in Table 2.1 are positive design parameters, γ and η are two positive design parameters, Γ is a positive definite matrix, and is e=1/β, estimates of a and D, δ _i (i=1,...,n) are positive design parameters, q=round{(n-i+2)/2}, round{x} represents the element to the nearest integer.

In this embodiment, the adaptive control law is as follows:

α ₁ =-c ₁ z ₁ (2.7)

In this embodiment, the parameter update method is as follows:

Further, the backstep control algorithm is used by the backstep adaptive controller to control the rotation angle of the rotor of the motor, and then the speed of the motor is indirectly controlled by calculating the rotation angle of the rotor. Robust learning law for feedback control parameters obtained from Lyapunov stability theorem. Feedback adaptation will be used to estimate the output terms of the control system, using the Lyapunov function to ensure the stability of the designed control system.

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 drive chip circuit, and the backstepping adaptive controller is mounted in the control chip circuit.

The above are the preferred embodiments of the present invention, all changes made according to the technical solutions of the present invention, when the resulting functional effects do not exceed the scope of the technical solutions 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, Y_iIs known as continuous linear or non-linear distortion, d (t) represents a bounded external perturbation, parameter a_iIs an unknown constant, the control gain b is a constant, v is the control input, u (v) represents a dead-zone nonlinear function;

wherein, b_r≥0,b_lLess 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,…,-a_r]^T，Y＝[Y₁，Y₂，L，Y_r]^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 y_r(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) -y_r(t) is adjustable during transient periods; x (t) represents a position signal at time t;

lim_t→∞x(t)-y_r(t) 0 or lim_t→∞|x(t)-y_r(t)|-δ₁0 for an arbitrarily specified boundary δ₁＝0；

For c_i,i＝1,L,n，c_iAre 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, δ_i(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.