CN101977034B - Backlash self-adaptive filter and method for modeling and compensating hysteresis thereof - Google Patents

Abstract

The invention relates to a Backlash self-adaptive filter and a method for modeling and compensating the hysteresis thereof, belonging to the technical field of modeling and control of hysteresis non-linear systems. The filter comprises a summator module, an error calculating module, a plurality of self-adaptive weighting modules and a plurality of Backlash operator modules with the same width. The whole designing scheme avoids using a hysteresis item and is only related with current inputs, meanwhile, the hysteresis non-linearity can be reflected, and the modeling effect is more precise; and the self-adaptive inverse control of the filter can effectively compensate the hysteresis non-linearity of a piezoelectric ceramic actuator. The self-adaptive filter and the modeling and self-adaptive inverse control method based on the filter can be applied to systems having the characteristics of hysteresis non-linearity, such as intelligent materials of magnetostrictive materials, excitation motors, piezoelectric chips, piezoelectric ceramics, and the like.

Description

Backlash sef-adapting filter and to the modeling and the compensation method of sluggishness

Technical field

The present invention relates to a kind of Backlash sef-adapting filter and, belong to Hysteresis Nonlinear system modelling and control technology field the modeling and the compensation method of sluggishness.

Background technology

The Hysteresis Nonlinear phenomenon is present in the middle of a lot of reality systems, like magnetostrictive material, and excitation electromotor, systems such as piezoelectric chip and piezoelectric ceramic.The existence of nonlinear characteristic reduces these system's repeatability, and transient response speed is slack-off, the controllability variation.Sluggishness has many mapping property and Memorability, and this makes that classical control theory and modern control theory all are difficult to it is implemented effectively control.So need to propose the problem in specific modeling and this field of control method solution.

To compensate to realize the accurate control of Hysteresis Nonlinear system sluggishness, at first need set up accurately sluggish model, on model based, propose the control compensation method then.

For the Hysteresis Nonlinear object; Multiple sluggish modeling methods such as Krasnoselskii-Pokrovskii (KP) model, Jiles-Atherton (JA) model, Preisach model, Duhem model, Prandtl-Ishlinskii (PI) model have been suggested at present; The modeling method that exists at present mostly realizes complicated, is unfavorable for practical application.The PI model superposes with the sluggish unit of ramp function characteristic and approaches lagging characteristics, because it is simple in structure, that can resolve inverts, and is applied to real-time control morely.Sluggish model based on the sluggish operator of Backlash belongs to the PI model, and this model is made up of a series of Backlash operator weighted superposition.For compensating sluggish harmful effect, the sluggish compensation method of the present Backlash that proposes is mostly through setting up sluggish Backlash inversion model and it being connected with hysteresis system to offset Hysteresis Nonlinear.The affirmation of the Backlash operator lagging characteristics parameter that these class methods adopted lacks effective means, and model structure adopts similar neural network structure, realizes more complicated, and there is the local optimum problem in e-learning.

A kind of Adaptive Signal Processing and control method that Adaptive inverse control is at first proposed by the B.Widrow of Stanford Univ USA; This method adopts transverse filter structure commonly used in the Digital Signal Processing, is made up of the tapped delay line of variable weighting, an adder and an adaptive process.The input signal of these weight coefficients is exactly to postpone the signal on tap line at each, with the signal plus of an adder after with these weightings, searches these weight coefficients of adjusting automatically by a LMS adaptive process again.It comes the dynamic characteristic of system is done open-loop compensation as series controller with the contrary of controlled device, and the instability problem of having avoided feedback to cause has been realized the separate processes of dynamic characteristic control with disturbance compensation simultaneously.This method is simple in structure, and computational speed is fast, and adaptive ability is strong, is convenient to very much computer simulation and hardware and realizes.But the precision of the Hysteresis Nonlinear object being carried out modeling and control is relatively poor.For this reason, on linear Filter Structures basis, add quadratic term and constitute non-linear transversal filter, but its Structure Calculation is complicated, is not easy to realize, sluggish modeling accuracy improves little.

Summary of the invention

The objective of the invention is to be the modeling of the non-linear hysteresis system of solution piezoelectricity and the technical problem of control; Sluggish modeling and compensating control method precision and the not enough problems of realizability such as nonlinear filter to time delay line transversal filter, adding quadratic term; In conjunction with the simple adaptable advantage of transverse filter structure of sluggish modeling characteristic of Backlash and Adaptive inverse control, a kind of Backlash sef-adapting filter is proposed and to the modeling and the compensation method of sluggishness.

The Backlash sef-adapting filter is formed the Backlash operator module that comprises adder Module, error calculating module, a plurality of adaptive weighted modules and a plurality of same widths.Wherein, the Backlash operator module of a plurality of same widths forms cascaded structure, and the signal input part of filter links to each other with first Backlash operator module; Signal between adjacent two Backlash operator module of series connection is drawn, and is connected to the input of an adaptive weighted module; The output of each adaptive weighted module connects the input of adder Module; The output of adder Module links to each other with an input of error calculating module as the output of whole filter simultaneously, and another input of error calculating module is that the desired output signal of filter is an echo signal; The output of error calculating module is connected to each adaptive weighted module.

The function of adder Module obtains filter output for the weighted value stack with each operator:

P _RiThe output of i operator in [x (k)] expression series connection Backlash operator structure, w _iThe value of representing i weighting block.The width of each Backlash operator is r.X (k) expression k is the input signal of filter constantly.

The function of error calculating module is that calculation expectation output y (k) exports y ' error e (k)=y (k)-y ' (k) (k) with practical filter, and the adaptive weight that its result supplies to adjust adaptive weighted module uses.

Adaptive weighted module has a plurality of.The adaptive weight of each weighting block is according to the error of desired output and practical filter output, i.e. the output of error calculating module is adjusted in real time.The adjustment principle is lowest mean square (LMS) adaptive algorithm, and its detailed process is: calculating filter output y ' (k) with the error of desired output y (k)

Minimum Mean Square Error ξ=E [e ²(k)].LMS can utilize the gradient of performance curved surface to seek its minimum value; Each step on the weight vector changes the negative value that all is proportional to gradient vector:

and is gradient vector; Scalar parameter μ is a convergence factor; It has controlled stability and adaptation rate, and μ is big more, and convergence rate is fast more.Get ε ²(k) as mean square error E [ε ²(k)] estimated value can get the recursive expression of weight vector at this moment:

W(k+1)＝W(k)+2·μ·e(k)P _r(k)

Wherein, W (k+1), W (k) are respectively (k+1) moment and (k) weight vector constantly, W (k)=[w ₀(k), w ₁(k) ... w _n(k)].μ is a convergence factor, P _r(k) be Backlash operator cascaded structure output vector, P _r(k)=[P _R0(k), P _R1(k) ... P _Rn(k)].

This filter adopts the structure of the Backlash operator series connection of several same width, realizes laying a good foundation for hardware, avoids the complexity of Backlash operator when hardware is realized of different in width.The input of whole filter carried out the normalization processing, exported under the situation of carrying out anti-normalization processing, the width r of each Backlash operator is determined by the number n of the Backlash operator of being selected for use: the computational methods of the output of each Backlash operator module are in cascaded structure:

K constantly the input signal x (k) of filter through the output P of the width Backlash operator module that is r _R1[x (k)] is:

$P_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000338380100041.png,HSA00000338380100042.png"\; state="\{\{state\}\}">r</figure-callout>}1}=\left[x\left(k\right)\right]=\left\{\begin{array}{cc}x\left(k\right)-r& x\left(k\right)>x(k-1)\&P_{r1}\left[x(k-1)\right]\&le;x(k-1)-r\\ x\left(k\right)+r& x\left(k\right)<x(k-1)\&P_{r1}\left[x(k-1)\right]\&GreaterEqual;x(k-1)+r\\ P_{r1}\left[x(k-1)\right]& \mathrm{others}\end{array}\right.---\left(1\right)$

Output P behind the Backlash operator module cascaded structure that i width of input x (k) process of k moment filter is r _Ri[x (k)] is:

$P_{\mathrm{ri}}\left[x\left(k\right)\right]=\left\{\begin{array}{cc}x\left(k\right)-r\&CenterDot;i& x\left(k\right)>x(k-1)\mathrm{and}{P}_{\mathrm{ri}}\left[x(k-1)\right]\&le;x(k-1)-r\&CenterDot;i\\ x\left(k\right)+r\&CenterDot;i& x\left(k\right)<x(k-1)\mathrm{and}{P}_{\mathrm{ri}}\left[x(k-1)\right]\&GreaterEqual;x(k-1)+r\&CenterDot;i\\ P_{\mathrm{ri}}\left[x(k-1)\right]& \mathrm{others}\end{array}\right.---\left(2\right)$

Utilize Backlash sef-adapting filter of the present invention to be to the modeling method of sluggishness:

Step 1, the adaptive modeling system of building hysteresis system.The modeling signal is connected the input of actual Hysteresis Nonlinear system and the signal input part of Backlash sef-adapting filter simultaneously.To have the actual Hysteresis Nonlinear system of disturbing signal input and the output signal of Backlash sef-adapting filter and import subtracter respectively.The output of subtracter is connected to the desired output signal input part of Backlash sef-adapting filter after adaptive algorithm is calculated.

Step 2, put up modeling after, the value W of given weighting block (0)=[w at random ₀(0), w ₁(0) ... w _n(0)], with first modeling signal input adaptive modeling, the Backlash operator cascaded structure output vector of Backlash sef-adapting filter: P _r(0)=[P _R0(0), P _R1(0) ... P _Rn(0)], the output e (0) of corresponding subtracter=y (0)-y ' (0) is used to regulate according to the LMS algorithm weights of weighting block: W (0)=W (0)+2 μ e (0) P _r[y (0)].

Step 3; Import next modeling signal; According to the real-time output of the Backlash operator cascaded structure of Backlash sef-adapting filter and this moment subtracter output e (k)=y (k)-y ' (k), on the basis of a last moment weighting block, according to LMS algorithm refreshing weight; Repeat this process, k update method constantly is: W (k+1)=W (k)+2 μ e (k) P _r[y (k)]

Step 4; Repeating step 3 no longer descends and keeps a period of time until error; Make for same input signal; The output of Backlash sef-adapting filter of the present invention approaches the output of actual Hysteresis Nonlinear system as much as possible, can simulate actual Hysteresis Nonlinear system accurately to guarantee Backlash sef-adapting filter of the present invention.

Utilize Backlash sef-adapting filter of the present invention to be to the compensation method of sluggishness:

Step 1, the Adaptive inverse control system of building hysteresis system.Command input signals links to each other with the filtering signal input of Backlash sef-adapting filter; The output of Backlash sef-adapting filter links to each other with actual Hysteresis Nonlinear system, and the output signal of command input signals and actual Hysteresis Nonlinear system is imported subtracter respectively.The output of subtracter is connected to the desired output signal input part of Backlash sef-adapting filter after adaptive algorithm.

Step 2, on the basis of the Adaptive inverse control system that step 1 is built, the value W of given weighting block (0)=[w at random ₀(0), w ₁(0) ... w _n(0)], with the contrary control system of first command input signals input adaptive, the Backlash operator cascaded structure output vector of Backlash sef-adapting filter: P _r(0)=[P _R0(0), P _R1(0) ... P _Rn(0)], the output e (0) of corresponding subtracter=v (0)-v ' (0), v (0), v ' (0) is respectively the output signal of initial given signal and non linear system.Be used to regulate the value of weighting block: W (0)=W (0)+2 μ e (0) P according to the LMS algorithm _r[v (0)].

Step 3; Input next instruction signal; According to the output vector of the Backlash operator cascaded structure of Backlash sef-adapting filter this moment and this moment subtracter output e (k)=v (k)-v ' (k), on the basis of a last moment weighting block, according to LMS algorithm refreshing weight; Repeat this process, k update method constantly is: W (k+1)=W (k)+2 μ e (k) P _r[v (k)].

Step 4, repeating step 3 no longer descends and keeps a period of time until error, makes the output signal follow given input signal with less error, realizes accurate tracking Control.

Beneficial effect

Backlash sef-adapting filter of the present invention improves on horizontal linear Filter Structures, adds the Backlash operator, and method for designing is simple.Filter of the present invention avoids the use of and postpones item, and is only relevant with current input, can embody the non-linear of sluggishness simultaneously.Compare with transversal filter and the linear filter of branch that added quadratic term, the Backlash sef-adapting filter has more accurate modeling effect.Can effectively compensate the Hysteresis Nonlinear of piezoelectric ceramic actuator based on the Adaptive inverse control of Backlash sef-adapting filter.

Backlash sef-adapting filter of the present invention and the system that can be applied to have the Hysteresis Nonlinear characteristic, for example piezoelectric ceramic actuator, magnetostrictive actuator and excitation electromotor etc. based on the modeling and the adaptive inverse control of this filter.The present invention can carry out modeling and control to the system with lagging characteristics, accurately describes the lagging characteristics of non linear system, and offsets non-linear effectively.

Description of drawings

Fig. 1 is a Backlash sef-adapting filter structural representation of the present invention;

Fig. 2 is two Backlash operator series connection equivalents sketch mapes in the embodiment;

Fig. 3 is the modeling sketch map of Backlash sef-adapting filter of the present invention;

Fig. 4 is the Adaptive inverse control system schematic of Backlash sef-adapting filter of the present invention;

Fig. 5 is the structural representation of the piezoelectric ceramic actuator experiment porch of embodiment;

Fig. 6 is a Backlash Adaptive inverse control algorithm flow in the DSP interrupt routine of embodiment

Fig. 7 is for being used for two kinds of Filter Structures sketch mapes of effect comparison in the embodiment, wherein (a) is the structural representation of linear forward-direction filter, (b) is the structural representation that has added the nonlinear filter of quadratic term;

Fig. 8 is the modeling design sketch of Backlash sef-adapting filter and other filters in the embodiment; Wherein, (a) modeling situation and the error when having adopted linear forward-direction filter; (b) modeling situation and the error when having adopted the nonlinear filter that adds quadratic term, (c) modeling situation and the error when having adopted Backlash sef-adapting filter of the present invention.

Fig. 9 follows the tracks of situation and error design sketch when being the adaptive inverse control that adopts in the embodiment based on the Backlash sef-adapting filter;

Figure 10 is the input-output curve figure after the compensation of Backlash sef-adapting filter in the embodiment.

Embodiment

Further specify objects and advantages of the present invention in order better to explain below in conjunction with accompanying drawing and embodiment.

Backlash sef-adapting filter structure of the present invention is as shown in Figure 1, comprises the Backlash operator module of adder Module, error calculating module, a plurality of adaptive weighted modules and a plurality of same widths.Calculate the output of each series connection Backlash operator link according to formula (2).The validity proof of formula (2) is drawn by following theorem.

Theorem: the width for series connection as shown in Figure 2 is respectively r ₁And r ₂Two Backlash operators, can be equivalent to a width is r ₁+ r ₂The Backlash operator.

Proof: be respectively r for width ₁And r ₂Two Backlash operators, the transmission characteristic of its discrete form is respectively:

$y_1\left(k\right)=P_{r_1}\left[x_1\left(k\right)\right]\left(k\right)=\left\{\begin{array}{cc}{x}_1\left(k\right)-r_1& x_1\left(k\right)>x_1(k-1)\mathrm{and}{P}_{r_1}\left[x_1(k-1)\right]\&le;x_1(k-1)-r_1\\ x_1\left(k\right)+r_1& x_1\left(k\right)<x_1(k-1)\mathrm{and}{P}_{r_1}\left[x_1(k-1)\right]\&GreaterEqual;x_1(k-1)+r_1\\ P_{r_1}\left[x_1(k-1)\right]& \mathrm{others}\end{array}\right.$

With:

$y_2\left(k\right)=P_{r_2}\left[x_2\left(k\right)\right]\left(k\right)=\left\{\begin{array}{cc}{x}_2\left(k\right)-r_2& x_2\left(k\right)>x_2(k-1)\mathrm{and}{P}_{r_2}\left[x_2(k-1)\right]\&le;x_2(k-1)-r_2\\ x_2\left(k\right)+r_2& x_2\left(k\right)<x_2(k-1)\mathrm{and}{P}_{r_2}\left[x_2(k-1)\right]\&GreaterEqual;x_2(k-1)+r_2\\ P_{r_2}\left[x_2(k-1)\right]& \mathrm{others}\end{array}\right.$

X in the formula ₁And x ₂Being respectively width is r ₁And r ₂The input of Backlash operator, y ₁And y ₂Be respectively output.

When two operators such as Fig. 2 are connected in series, x is arranged ₁(k)=and x (k), y ₁(k)=x ₂(k), y (k)=y ₂(k), in order to calculate the output y (k) of series connection post-operator, can divide following three kinds of situation to discuss:

(1) works as x ₁(k-1)＜x ₁(k) time:

If y ₁(k)≤x ₁(k-1)-r ₁, then have y ₁(k)=x ₁(k)-r ₁

Because the Backlash function is non-strictly monotone increasing, and x ₁(k-1)＜x ₁(k)

So y ₁(k-1)＜y ₁(k) be x ₂(k-1)＜x ₂(k)

If y ₂(k-1)≤x ₂(k-1)-r ₂=x ₁(k-1)-r ₁-r ₂=x ₁(k-1)-(r ₁+ r ₂)

Y then ₂(k)=x ₂(k)-r ₂=x ₁(k)-(r ₁+ r ₂)

(2) x ₁(k-1)＞x ₁(k) time:

If y ₁(k)>=x ₁(k-1)-r ₁, then have y ₁(k)=x ₁(k)-r ₁

Because the Backlash function is non-strictly monotone increasing, and x ₁(k-1)＞x ₁(k)

So y ₁(k-1)＞y ₁(k) be x ₂(k-1)＞x ₂(k)

If y ₂(k-1)>=x ₂(k-1)-r ₂=x ₁(k-1)-r ₁-r ₂=x ₁(k-1)-(r ₁+ r ₂)

Y then ₂(k)=x ₂(k)-r ₂=x ₁(k)-(r ₁+ r ₂)

(3) during other situation: y (k)=y (k-1)

Card is finished

By above theorem, if the Backlash operator width of two series connection equates r ₁=r ₂=r, the Backlash operator that then to be equivalent to a width be 2r.And the like, i the Backlash operator series connection that width is r, being equivalent to like next width is the operator of ir

The output of Backlash operator module of the present invention can be adopted the output P in the summary of the invention _RiThe computing formula of [x] is represented.

Present embodiment is superior to prior art through on piezoelectric ceramic actuator nanometer positioning system experimental platform, experimentizing with modeling and the compensation effect of verifying the Backlash sef-adapting filter that the present invention proposes.

It is as shown in Figure 3 to utilize Backlash sef-adapting filter of the present invention that the Hysteresis Nonlinear system is carried out the system for modeling sketch map.Wherein, " non linear system " in the model of present embodiment foundation is piezoelectric ceramic.When setting up model; Modeling signal for input; The output displacement of piezoelectric ceramic actuator nanometer positioning system and the output of Backlash sef-adapting filter are tried to achieve error through subtracter,, adopt LMS algorithm refreshing weight according to the output vector of the Backlash operator cascaded structure of Backlash sef-adapting filter; Finally try to achieve one group and make Backlash sef-adapting filter of the present invention can approach the sluggish weights of piezoelectric ceramic actuator more accurately, modeling process finishes.Make convergence rate comparatively fast and not can cause convergence factor μ=0.01 of dispersing and number n=60 of connecting the Backlash operator through experimental selection, promptly width

parameter at this moment is that modeling result is comparatively accurate.

It is as shown in Figure 4 to adopt Backlash sef-adapting filter of the present invention to carry out the system configuration sketch map of Adaptive inverse control.Backlash sef-adapting filter of the present invention is series at the front of piezoelectric ceramic Hysteresis Nonlinear system as controller, and the error of the output of given instruction input and piezoelectric ceramic actuator nanometer positioning system is used to the adaptive weight according to LMS algorithm real-time update Backlash sef-adapting filter.Adaptive inverse control based on the Backlash sef-adapting filter of the present invention can be adjusted weight function in real time, makes non-linear output more accurately follow the instruction input.

Piezoelectric ceramic actuator nanometer positioning system experimental platform according to Fig. 4 builds is as shown in Figure 5, and the piezoelectric ceramic model is PST150/7/40VS12, and withstand voltage scope is-30～150V, and the output displacement range is 0-12 μ m.Power amplification and differential amplification are realized by HPV series drive power supply for piezoelectric ceramics.Dsp controller is done control device with TI company's T MS320LF2407, and digital-to-analogue and analog-to-digital conversion are respectively 16 AD669 and AD976, and controller is passed to host computer to the data that collect through serial ports.Backlash sef-adapting filter and Adaptive inverse control are all accomplished in DSP.The program circuit of Adaptive inverse control is as shown in Figure 6 in the DSP interrupt service routine.

The effect that utilization Backlash sef-adapting filter carries out modeling is shown in Fig. 8 (c), and the actual output of exporting displacement and Backlash sef-adapting filter of piezoelectric ceramic has been carried out relatively and listed error.The modeling effect that adopts the modeling effect of linear forward-direction filter (shown in Fig. 7 (a)) and the nonlinear filter (shown in Fig. 7 (b)) that employing has added quadratic term is respectively shown in Fig. 8 (a) and Fig. 8 (b).

Different input signals is carried out the modeling experiment, chooses four groups of signal input piezoelectric ceramic actuators, measure its actual displacement output, compare under the various signals input condition average absolute value error of modeling during the utilization different model | e| _AveAnd all square MSE is poor.When calculating mean square deviation, carry out beginning after a period of time from adaptive process, after this maximum value error basically no longer reduces.Table 1 has been listed the error under the different situations.

Modeling error under table 1 varying input signal

It is thus clear that the Backlash sef-adapting filter that proposes can reach higher precision, modeling average absolute value error is reduced to below the 0.13 μ m.

When Fig. 9 is given sinusoidal signal, adopted the situation of following of the Adaptive inverse control of Backlash sef-adapting filter.After the adjusting through five cycles, the maximum value error drops to 0.202 micron.

Figure 10 is under the attenuation sinusoidal wave signal input condition, and the situation of given displacement is followed in the output displacement after compensation, can find out, after overcompensation, the output displacement can be followed given displacement basically, and Hysteresis Nonlinear has been compensated effectively.

Can find out that by above experimental result the Backlash sef-adapting filter that the present invention proposes can reach modeling preferably and compensation control effect.

Claims (7)

1.Backlash sef-adapting filter is characterized in that: the Backlash operator module that comprises adder Module, error calculating module, a plurality of adaptive weighted modules and a plurality of same widths; Wherein, the Backlash operator module of a plurality of same widths forms cascaded structure, and the signal input part of filter links to each other with first Backlash operator module; Signal between adjacent two Backlash operator module of series connection is drawn, and is connected to the input of an adaptive weighted module; The output of each adaptive weighted module connects the input of adder Module; The output of adder Module links to each other with an input of error calculating module as the output of whole filter simultaneously, and another input of error calculating module is that the desired output signal of filter is an echo signal; The output of error calculating module is connected to each adaptive weighted module.

2. Backlash sef-adapting filter according to claim 1 is characterized in that: the function of described adder Module obtains filter output for the weighted value stack with each operator:

P _RiThe output of i operator in [x (k)] expression series connection Backlash operator structure, w _iThe value of representing i weighting block; N is selected Backlash operator number, and the width of each Backlash operator is r; X (k) expression k is the input signal of filter constantly.

3. Backlash sef-adapting filter according to claim 1; It is characterized in that: described error calculating module calculation expectation output y (k) exports y ' error e (k)=y (k)-y ' (k) (k) with practical filter, and the adaptive weight that its result supplies to adjust adaptive weighted module uses.

4. Backlash sef-adapting filter according to claim 1 is characterized in that: described adaptive weighted module has a plurality of; The adaptive weight of each weighting block is according to the error of desired output and practical filter output, i.e. the output of error calculating module is adjusted in real time; The adjustment principle is a lms adaptive algorithm.

5. Backlash sef-adapting filter according to claim 1 is characterized in that: the Backlash operator cascaded structure of described several same width, and normalization is carried out in the input of filter handled, carry out anti-normalization during output and handle; The width r of each Backlash operator is determined by the number n of the Backlash operator of being selected for use: The computational methods of the output of each Backlash operator module are in the cascaded structure: the output P behind the Backlash operator module cascaded structure that i width of input x (k) process of k moment filter is r _Ri[x (k)] is:

6. Backlash sef-adapting filter according to claim 1 is characterized in that: utilize the Backlash sef-adapting filter to the modeling method of sluggishness to be:

Step 1, the adaptive modeling system of building hysteresis system; The modeling signal is connected the input of actual Hysteresis Nonlinear system and the signal input part of Backlash sef-adapting filter simultaneously; To have the actual Hysteresis Nonlinear system of disturbing signal input and the output signal of Backlash sef-adapting filter and import subtracter respectively; The output of subtracter is connected to the desired output signal input part of Backlash sef-adapting filter after adaptive algorithm is calculated;

Step 2, put up modeling after, the value W of given weighting block (0)=[w at random ₀(0), w ₁(0) ... w _n(0)], with first modeling signal input adaptive modeling, the Backlash operator cascaded structure output vector of Backlash sef-adapting filter: P _r(0)=[P _R0(0), P _R1(0) ... P _Rn(0)], the output e (0) of corresponding subtracter=y (0)-y ' (0) is used to regulate according to lms adaptive algorithm the weights of weighting block: W (0)=W (0)+2 μ e (0) P _r[y (0)]; Wherein, n is selected Backlash operator number, and the width of each Backlash operator is r; Y (0) is the initial time desired output, and y ' (0) is the output of initial time practical filter;

Step 3; Import next modeling signal; According to the real-time output of the Backlash operator cascaded structure of Backlash sef-adapting filter and this moment subtracter output e (k)=y (k)-y ' (k), y (k) be a k desired output constantly, y ' be that k moment practical filter is exported (k); On the basis of a last moment weighting block, according to the lms adaptive algorithm refreshing weight, repeat this process, k update method constantly is: W (k+1)=W (k)+2 μ e (k) P _r[y (k)];

Step 4; Repeating step 3 no longer descends and keeps a period of time until error; Make for same input signal; The output of Backlash sef-adapting filter of the present invention approaches the output of actual Hysteresis Nonlinear system as much as possible, can simulate actual Hysteresis Nonlinear system accurately to guarantee Backlash sef-adapting filter of the present invention.

7. Backlash sef-adapting filter according to claim 1 is characterized in that: utilize the Backlash sef-adapting filter to the compensation method of sluggishness to be:

Step 1, the Adaptive inverse control system of building hysteresis system; Command input signals links to each other with the filtering signal input of Backlash sef-adapting filter; The output of Backlash sef-adapting filter links to each other with actual Hysteresis Nonlinear system, and the output signal of command input signals and actual Hysteresis Nonlinear system is imported subtracter respectively; The output of subtracter is connected to the desired output signal input part of Backlash sef-adapting filter after adaptive algorithm;

Step 2, on the basis of the Adaptive inverse control system that step 1 is built, the value W of given weighting block (0)=[w at random ₀(0), w ₁(0) ... w _n(0)], with the contrary control system of first command input signals input adaptive, the Backlash operator cascaded structure output vector of Backlash sef-adapting filter: P _r(0)=[P _R0(0), P _R1(0) ... P _Rn(0)], wherein, n is selected Backlash operator number, and the width of each Backlash operator is r; The output e (0) of corresponding subtracter=v (0)-v ' (0), v (0), v ' (0) is respectively the output signal of initial given signal and non linear system; Be used to regulate the value of weighting block: W (0)=W (0)+2 μ e (0) P according to lms adaptive algorithm _r[v (0)];

Step 3; Input next instruction signal; According to the output vector of the Backlash operator cascaded structure of Backlash sef-adapting filter this moment and this moment subtracter output e (k)=v (k)-v ' (k); Wherein, v (k), v ' (k) are respectively k given signal and non linear system constantly and export signal; On the basis of a last moment weighting block, according to the lms adaptive algorithm refreshing weight, repeat this process, k update method constantly is: W (k+1)=W (k)+2 μ e (k) P _r[v (k)];

Step 4, repeating step 3 no longer descends and keeps a period of time until error, makes the output signal follow given input signal with less error, realizes accurate tracking Control.

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