CN103346692A - Frequency domain compensation method for piezoelectric actuator hysteresis nonlinearity in vibration active control - Google Patents

Abstract

The invention discloses a frequency domain compensation method for piezoelectric actuator hysteresis nonlinearity in the vibration active control, and belongs to the field of vibration control of a nonlinearity system. The method comprises the steps that through introduction of high order harmonic wave input, a linear harmonic wave steady state control method is adopted, compensation is conducted on a high order harmonic wave component caused by the piezoelectric actuator hysteresis nonlinearity in control response, and the purpose of compensation of hysteresis nonlinearity in a control channel is achieved. The method is simple in system and avoids building a complex hysteresis nonlinearity model, a control system can be suitable for conditions of single frequency disturbance and multi-frequency disturbance, and the nonlinearity influence of the piezoelectric laminated actuator is effected reduced; the method that the frequency domain outputs feedback to control the time domain input is adopted, and the frequency domain compensation of the piezoelectric actuator hysteresis nonlinearity in the vibration active control is achieved.

Description

Piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method in the Active Vibration Control

Technical field

The invention discloses piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method in the Active Vibration Control, belong to the technical field of Control of Nonlinear Systems.

Background technology

Piezoelectric actuator utilizes the inverse piezoelectric effect of piezoelectric, realizes that electric energy is converted to mechanical energy output, and it has advantages such as power output is big, quality is little, response speed is fast, operating frequency is wide, is widely used in structural vibration and radiated noise ACTIVE CONTROL.But in control system, the Hysteresis Nonlinear properties influence control performance that piezoelectric actuator is intrinsic becomes the major obstacle that the restriction control performance further improves.The structural vibration response and the radiated noise that with the rotating parts are driving source show as cyclophysis, require actuator with the input that is used as power frequently, control controlled structural vibrations and respond and radiated noise.Because the Hysteresis Nonlinear characteristic of piezoelectric actuator will be followed high order harmonic component response output under control harmonic wave input stimulus, reduce the control effect.

In order to reduce the piezoelectric actuator Hysteresis Nonlinear to the influence of control effect, existing multiple compensation policy can be divided into two classes generally: directly electric charge control and application inversion model carry out pseudo-linear compensation.Electric charge control utilizes the displacement output of piezoelectric and the electric charge that acts on above it to be the better linearity relation, can effectively reduce the hysteretic and nonlinear influence.But this method needs complicated control electric charge multiplying arrangement, and good linearty is just arranged when only working in lower frequency range.The application inversion model carries out pseudo-linear compensation method and uses the Hysteresis Nonlinear model that Maxwell gliding model, Preisach model, artificial neural net etc. are set up piezoelectric actuator usually, realize the pseudo-linearisation of control system by the inversion model of in control channel, introducing the Hysteresis Nonlinear model, another approach is in feedfoward control, reference signal through the pre-filtering of Hysteresis Nonlinear model, is used the compensation that the nonlinear adaptive control method realizes the influence of piezoelectric actuator Hysteresis Nonlinear.The Hysteresis Nonlinear model of setting up piezoelectric actuator is complicated and is difficult to accurate process, needs great deal of experiment data usually.

Summary of the invention

Technical problem to be solved by this invention is the deficiency at the above-mentioned background technology, and piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method in the Active Vibration Control is provided.

The present invention adopts following technical scheme for achieving the above object:

Piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method comprises the steps: in the Active Vibration Control

Step 1 is determined the high-order harmonic wave signal that need compensate;

Step 2, the high-order harmonic wave signal that the needs of determining according to step 1 compensate, the time domain that obtains the current period is controlled the input harmonics signal;

Step 3 is imported as the control of the control channel of piezoelectric actuator driving with the time domain control input harmonics signal of current period, gathers the departure response signal in measurement point;

Step 4, the departure response signal of gathering in the treatment step 3, in the controlled error responses signal to cosine coefficient, sinusoidal coefficient in requisition for the higher order signal of compensation;

Step 5, cosine coefficient, sinusoidal coefficient that linear harmonic wave stable state controller utilizes step 4 to obtain, the coefficient of Correction and Control input harmonics signal determines that the time domain of next period is controlled the input harmonics signal, returns step 3.

In the piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method, step 5 comprises the steps: in the described Active Vibration Control

Steps A, according in the described departure response signal of step 4 in requisition for the higher order signal of compensation cosine harmonics coefficient, multifrequency sinusoid coefficient, utilize linear harmonic wave frequency domain control method calculate in next period control input of piezoelectric actuator in requisition for the higher order signal of compensation harmonic constant;

Step B, in next period control input of piezoelectric actuator of being determined by steps A in requisition for the higher order signal of compensation harmonic constant obtain the time domain control input harmonics signal of next period of piezoelectric actuator.

In the described Active Vibration Control in the piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method, step 1 utilizes following method need to determine the high-order harmonic wave signal of compensation: the control channel that piezoelectric actuator is driven applies the simple harmonic quantity input signal identical with the disturbance driving frequency, gather the start response signal of the control channel of piezoelectric actuator driving, the start response signal is done the high-order harmonic wave signal that discrete Fourier transform needing to obtain compensation.

The present invention adopts technique scheme, has following beneficial effect: avoided setting up complicated Hysteresis Nonlinear model, be applicable to single-frequency disturbance and multifrequency disturbance situation, reduced the non-linear effects of laminated piezoelectric actuator effectively; Utilize the method for frequency domain output FEEDBACK CONTROL time domain input, realized piezoelectric actuator hysteretic and nonlinear frequency domain compensation in the Active Vibration Control.

Description of drawings

Fig. 1 is piezoelectric actuator input and output figure.

Fig. 2 is multiple-harmonic control input piezoelectric actuator Hysteresis Nonlinear compensation principle figure.

Fig. 3 is the block diagram of control system.

Fig. 4 is the acceleration responsive spectrogram that has or not control and have or not nonlinear compensation.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

As shown in Figure 1, the control channel of piezoelectric actuator driving is exported under the excitation of simple harmonic quantity input signal and is made dynamic response.

As Fig. 2, shown in Figure 3, piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method comprises the steps in the Active Vibration Control.

Step 1, definite high-order harmonic wave signal that needs compensation, the control channel that piezoelectric actuator is driven applies the simple harmonic quantity input signal u identical with the disturbance driving frequency ₁(t)=sin (ω ₁T), gather the start response signal of the control channel of piezoelectric actuator driving, the start response signal is done discrete Fourier transform, analyze because the high-order harmonic wave start response intensity that the piezoelectric actuator Hysteresis Nonlinear causes, require higher the compensating of selection intensity according to control precision, exponent number is N.

Step 2, the high-order harmonic wave signal that the needs of determining according to step 1 compensate, the time domain that obtains the current period is controlled input harmonics signal u ⁰(t):

$u^0\left(t\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{x}_n\left(0\right)\cos \left({\mathrm{\ω}}_{n}t\right)+y_n\left(0\right)\sin \left({\mathrm{\ω}}_{n}t\right)---\left(1\right)$

In the formula (1), x _n(0) and y _n(0) is the cosine of the n order harmonics of control input and the sinusoidal coefficient value at initial time.

Step 3 is with the time domain control input harmonics signal u of current period ⁰(t) T is waited in the control input of the control channel that drives as piezoelectric actuator _w(generally get 1～3 fundamental frequency cycles T _s) after, gather departure response signal e (t), T in measurement point _sBe departure response signal fundamental frequency cycles, departure response signal e (t) is the difference of disturbance response d (t) and control response, and the expression formula of departure response signal e (t) is:

$e\left(t\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{a}_n\cos \left({\mathrm{\ω}}_{n}t\right)+b_n\sin \left({\mathrm{\ω}}_{n}t\right)---\left(2\right)$

Step 4, the departure response signal of gathering in the discrete Fourier transform step 3, in the controlled error responses signal to cosine coefficient, the sinusoidal coefficient of higher order signal in requisition for compensation, for n order harmonic signal in the departure response signal, its cosine coefficient, sinusoidal coefficient are respectively a _n, b _n

Step 5, linear harmonic wave stable state controller are utilized cosine coefficient, the sinusoidal coefficient of the departure response signal that step 4 obtains, and the coefficient of Correction and Control input harmonics signal is determined the time domain control input harmonics signal of next period to return step 3:

Steps A according to the cosine coefficient of the described departure response signal of step 4, sinusoidal coefficient, utilizes linear harmonic wave frequency domain control method to calculate piezoelectric actuator T _w+ T _sThe control input harmonics coefficient of period,

$x_n(i+1)=x_n\left(i\right)-{\mathrm{\μ}}_n\·\mathrm{Re}\left({\hat{G}}^H\left({\mathrm{\ω}}_n\right)\·E_n\left(i\right)\right)---\left(3a\right),$

$y_n(i+1)=y_n\left(i\right)-{\mathrm{\μ}}_n\·\mathrm{Im}\left({\hat{G}}^H\left({\mathrm{\ω}}_n\right)\·E_n\left(i\right)\right)---\left(3b\right),$

Formula (3a) (3b) in, E _n(i)=a _n(i)+jb _n(i), μ _nFor revising step-length, i is step correction time; Re represents to get real, and Im represents to get the imaginary part of plural number;

Because the Hysteresis Nonlinear factor need be identified in the value at each order frequency place one by one to transfer function: at first import fundamental frequency harmonics voltage, the transfer function values at identification fundamental frequency place

At the n rank high-order harmonic wave of needs compensation, incoming frequency is ω then _nHarmonic voltage u _n(t), identify the transfer function values at n order harmonic frequency place

Step B, the coefficient of each frequency component obtains the time domain control input harmonics signal of next period of piezoelectric actuator in next period control input of piezoelectric actuator of being determined by steps A:

$u^{i+1}\left(t\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_n(i+1)\cos \left({\mathrm{\&omega;}}_{n}t\right)+y_n(i+1)\sin \left({\mathrm{\&omega;}}_{n}t\right),$ i(T _w+T _s)<t≤(i+1)(T _w+T _s)（4）。

Have or not the acceleration responsive time history at controlled point place under the nonlinear compensation as shown in table 1:

Table 1

Shown in Figure 4 is to have or not control and have or not the acceleration responsive spectrogram of nonlinear compensation, shows that equally the control response that has after the nonlinear compensation obviously reduces.It is worthy of note that the inventive method can be used for compensating magnetostrictive actuator, marmem actuator and other presents the compensation of the system of small nonlinearity.

In sum, the present invention has following beneficial effect:

(1) system is simple, has avoided setting up complicated Hysteresis Nonlinear model, and control system reduces the non-linear effects of laminated piezoelectric actuator effectively applicable to single-frequency disturbance and multifrequency disturbance situation;

(2) method of utilizing frequency domain output FEEDBACK CONTROL time domain to import has realized piezoelectric actuator hysteretic and nonlinear frequency domain compensation in the Active Vibration Control.

Claims (3)

1. piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method in the Active Vibration Control is characterized in that, comprises the steps:

Step 1 is determined the high-order harmonic wave signal that need compensate;

Step 2, the high-order harmonic wave signal that the needs of determining according to step 1 compensate, the time domain that obtains the current period is controlled the input harmonics signal;

Step 3 is imported as the control of the control channel of piezoelectric actuator driving with the time domain control input harmonics signal of current period, gathers the departure response signal in measurement point;

Step 4, the departure response signal of gathering in the treatment step 3, in the controlled error responses signal to cosine coefficient, sinusoidal coefficient in requisition for the higher order signal of compensation;

Step 5, cosine coefficient, sinusoidal coefficient that linear harmonic wave stable state controller utilizes step 4 to obtain ,The coefficient of Correction and Control input harmonics signal determines that the time domain of next period is controlled the input harmonics signal, returns step 3.

2. piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method in the Active Vibration Control according to claim 1 is characterized in that step 5 comprises the steps:

Steps A, according in the described departure response signal of step 4 in requisition for the higher order signal of compensation cosine harmonics coefficient, multifrequency sinusoid coefficient, utilize linear harmonic wave frequency domain control method calculate in next period control input of piezoelectric actuator in requisition for the higher order signal of compensation harmonic constant;

Step B, in next period control input of piezoelectric actuator of being determined by steps A in requisition for the higher order signal of compensation harmonic constant obtain the time domain control input harmonics signal of next period of piezoelectric actuator.

3. piezoelectric actuator Hysteresis Nonlinear frequency domain compensating method in the Active Vibration Control according to claim 1 and 2, it is characterized in that, step 1 utilizes following method need to determine the high-order harmonic wave signal of compensation: the control channel that piezoelectric actuator is driven applies the simple harmonic quantity input signal identical with the disturbance driving frequency, gather the start response signal of the control channel of piezoelectric actuator driving, the start response signal is done the high-order harmonic wave signal that discrete Fourier transform needing to obtain compensation.

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