CN102270007B - Feed-forward open-loop linear controlling method of delay characteristics of piezoelectric ceramic actuator and implementing circuit thereof - Google Patents

Abstract

The invention discloses a feed-forward open-loop linear controlling method of delay characteristics of a piezoelectric ceramic actuator and an implementing circuit thereof. The feed-forward open-loop linear controlling method comprises the following steps: constructing a delay component observer to observe delay components of the piezoelectric ceramic actuator under the action of a control voltage by establishing a mathematical model of the piezoelectric ceramic actuator; calculating a compensation voltage for compensating the delay components; and overlapping the compensation voltage and the control voltage to obtain an actual drive voltage for acting on the piezoelectric ceramic actuator to cause the piezoelectric ceramic actuator to generate displacement output. A feed-forward open-loop linear controller comprises a control signal generator, an analog-to-digital converter, the feed-forward open-loop linear controller, a digital-to-analog converter and a power amplifier. According to the invention, the delay non-linear relationship between the output displacement and control voltage of the piezoelectric ceramic actuator is linearized; the control algorithm of the piezoelectric ceramic actuator is greatly simplified, and the positioning precision is improved.

Description

The feedforward open loop linearization method of controlling of piezoelectric ceramic actuator lagging characteristics and realize circuit

Technical field

The invention belongs to the LINEARIZED CONTROL technical field, particularly the linearizing linearization method of controlling of a kind of piezoelectric ceramic actuator lagging characteristics.The invention still further relates to a kind of circuit of realizing of the method.

Background technology

Piezoelectric ceramic actuator has the advantages such as volume is little, energy density is high, positioning precision is high, resolution is high, frequency response is fast, is widely applied in the fields such as precision positioning, MEMS (micro electro mechanical system), micro-nano manufacturing technology, nano biological engineering.But the Hysteresis Nonlinear characteristic of the output displacement of piezoelectric ceramic actuator and control voltage has been brought very large difficulty to the positioning control of piezoelectric ceramic actuator.

At present, the method that realizes the piezoelectric ceramic actuator positioning control mainly contains three major types:

The first kind is to use electric charge to drive to substitute the method that general voltage drives.Newcomb and Flinn (Electronics Letters, Vol.18, No.11,442-444,1982) find the hysteresis phenomenon that adopts electric charge to drive piezoelectric ceramic actuator has obvious reduction than adopting voltage to drive.On this basis, Kaizuka and Sui (Japanese Journal of Applied Physics, Vo1.27, No.5,773-776,1988) adopt the method for a building-out capacitor of series connection to make voltage drive and produce the effect that electric charge drives.But electric charge drives the sensitivity that can reduce piezoelectric ceramic actuator, and range of application is very limited.

Equations of The Second Kind is to use simple closed loop displacement control method.The method is regarded the sluggishness of piezoelectric ceramic actuator as the disturbance of control system, adopts closed-loop control to eliminate sluggish impact.But, because the hysteresis phenomenon of piezoelectric ceramic actuator is more serious, will produce larger disturbance to closed-loop control system, control system probably is in transient process for a long time, can not enter the steady state (SS) of expectation, and its control accuracy is not high yet.

The 3rd class is the tracing control method that adopts based on Hysteresis Model.At first the method obtains the Hysteresis Model of piezoelectric ceramic actuator by modeling, utilize the contrary of this Hysteresis Model to form feedforward control to compensate the output displacement tracking expectation displacement of piezoelectric ceramic actuator.Because inevitably there is model error in Hysteresis Model, also can bring error in the process that Hysteresis Model is inverted, therefore many scholars introduce closed-loop control to make up model error and opposing external interference, the control algolithm more complicated, and need high-precision displacement transducer, cost is very high, and is also very high to the environmental requirement of application.

In sum, up to the present, do not have special effective method piezoelectric ceramic actuator is carried out precise Positioning Control.

Summary of the invention

Can't carry out the problem of precise Positioning Control effectively to piezoelectric ceramic actuator for solving prior art, the invention provides a kind of feedforward open loop linearization method of controlling of piezoelectric ceramic actuator and realize circuit, adopt this linearization method of controlling and realize that circuit can make the output displacement of piezoelectric ceramic actuator and the Hysteresis Nonlinear between control voltage concern linearization, simplify the control algolithm of piezoelectric ceramic actuator, improve its positioning precision.

The application is specifically by the following technical solutions:

The feedforward linearized control method of a kind of piezoelectric ceramic actuator lagging characteristics, the control voltage (referring to u (t)) that will input piezoelectric ceramic actuator by feedforward open loop LINEARIZED CONTROL is converted to driving voltage and (refers to be converted into u by u (t) _b(t)) acting on piezoelectric ceramic actuator makes it produce displacement output, the output displacement of piezoelectric ceramic actuator becomes linear approximate relationship with control voltage (referring to u (t)) after feedforward open loop LINEARIZED CONTROL, said method comprising the steps of:

(1) output displacement of piezoelectric ceramic actuator and the sluggishness between driving voltage are the stack of linear component and sluggish component, utilize the described sluggish component of the sluggish operator simulation of Bouc-Wen, and the Bouc-Wen model that obtains piezoelectric ceramic actuator is

$x\left(t\right)=k_v{u}_b\left(t\right)+x_0+h\left(t\right)---\left(1\right)$

$\stackrel{\·}{h}\left(t\right)=A{\stackrel{\·}{u}}_b\left(t\right)-\mathrm{\β}|{\stackrel{\·}{u}}_b\left(t\right)|{\left|h\left(t\right)\right|}^{n-1}h\left(t\right)-\mathrm{\γ}{\stackrel{\·}{u}}_b\left(t\right){\left|h\left(t\right)\right|}^n---\left(2\right)$

Wherein, t is the time;

X (t) is the output displacement of piezoelectric ceramic actuator;

k _vFor output displacement and driving voltage ratio constant;

u _b(t) be driving voltage;

x ₀For the displacement that exists under original state;

H (t) is the sluggish component of piezoelectric ceramic actuator;

(t) be the first order derivative of driving voltage to the time;

() is the first order derivative of sluggish component to the time;

A, β, γ and n are the parameter of model;

(2) because sluggish component h (t) can not obtain by sensor measurement, therefore must utilize the sluggish operator of Bouc-Wen of formula (2) expression to build the sluggish component h (t) of online sluggish component observer with the On-line Estimation piezoelectric ceramic actuator, but due to driving voltage u _b(t) unknowable, can only replace driving voltage u with controlling voltage u (t) _b(t), obtain the estimated value of sluggish component h (t)

(t), the expression formula of sluggish component observer is:

$\stackrel{\stackrel{\·}{^}}{h}\left(t\right)=A\stackrel{\·}{u}\left(t\right)-\mathrm{\β}\left|\stackrel{\·}{u}\left(t\right)\right|{\left|\hat{h}\left(t\right)\right|}^{n-1}h\left(t\right)-\mathrm{\γ}\stackrel{\·}{u}\left(t\right){\left|\hat{h}\left(t\right)\right|}^n---\left(3\right)$

Wherein, u (t) is the control voltage of piezoelectric ceramic actuator;

(t) for controlling the first order derivative of voltage to the time;

(t) be the estimated value of sluggish component;

(t) be the first order derivative of sluggish component estimated value to the time;

(3) utilize the estimated value of the sluggish component that obtains Order

The output displacement that can obtain piezoelectric ceramic actuator can be expressed as with the relation of controlling voltage:

$x\left(t\right)=k_{v}u\left(t\right)+x_0+[h\left(t\right)-\hat{h}\left(t\right)]---\left(4\right)$

Estimated value due to sluggish component

Very little with sluggish component h (t) error, therefore, after adopting feedforward open loop linearization method of controlling involved in the present invention, the piezoelectric ceramic actuator output displacement becomes linear approximate relationship with controlling between voltage.The sluggish operator of the Bouc-Wen of the relation for the sluggish component of describing piezoelectric ceramic actuator and driving voltage that the method adopts also can replace with other sluggish operator representations (such as the sluggish operator of Dahl, Jiles-Atherton operator etc.), equally can be with the lagging characteristics linearization of piezoelectric ceramic actuator.

the invention also discloses a kind of circuit of realizing based on feedforward open loop linearization method of controlling of the present invention, describedly realize that circuit comprises control signal generator (1), analog to digital converter (2), feedforward open loop LINEARIZED CONTROL device (3), digital to analog converter (4) and power amplifier (5), described control signal generator (1), analog to digital converter (2), feedforward open loop LINEARIZED CONTROL device (3), digital to analog converter (4) is connected 5 with power amplifier) connect in turn, wherein control signal generator (1) produces analog control voltage, adopt analog to digital converter (2) to convert analog control voltage to digital controlled signal and send into feedforward open loop LINEARIZED CONTROL device (3), feedforward open loop LINEARIZED CONTROL device (3) the nonlinear compensation signal that superposes on digital controlled signal according to linearization method of controlling obtains digital drive signals and sends into digital to analog converter (4), digital to analog converter (4) is converted to analog drive voltage with digital drive signals and sends into power amplifier (5), be used for driving piezoelectric ceramic actuator (6) after the analog drive voltage that power amplifier (5) will be inputted is amplified and produce displacement output.When the digital control voltage of control signal generator (1) generation is, can directly sends into feedforward open loop LINEARIZED CONTROL device (3), and not need through analog to digital converter (2).

Described feedforward open loop LINEARIZED CONTROL device (3) comprises sluggish component observer (3-1), multiplier (3-2) and totalizer (3-3), sluggish component observer (3-1), multiplier (3-2) are connected 3-3 with totalizer) connection in turn, sluggish component observer (3-1) obtains the digital estimated value of sluggish component

Multiplier (3-2) is with the digital estimated value of sluggish component

With the driving voltage ratio constant k after output displacement and compensation _vReciprocal multiplication, totalizer (3-3) is subtracted each other the output valve of digital control voltage u (kT) and multiplier (3-2), obtains digital drive voltage u _b(kT).

Based on feedforward open loop linearization method of controlling of the present invention and realize that circuit is equally applicable to the lagging characteristics linearization of electrostriction ceramics actuator.

Beneficial effect of the present invention:

1, compare with the control method of existing piezoelectric ceramic actuator, feedforward open loop linearization method of controlling involved in the present invention is after the mathematical model that obtains piezoelectric ceramic actuator, do not need this mathematical model is inverted, the error of having avoided inversion process to introduce;

2, adopt the present invention the Hysteresis Nonlinear between piezoelectric ceramic actuator output displacement and driving voltage can be concerned linearization, can be with piezoelectric ceramic actuator when linear actuator use, greatly simplify the control algolithm of piezoelectric ceramic actuator, improve its positioning precision;

3, of the present inventionly realize that circuit structure is simple, can greatly reduce controlling cost of piezoelectric ceramic actuator, be convenient to microminiaturization, integrated.

Description of drawings

The invention will be further described below in conjunction with the drawings and specific embodiments.

Fig. 1 is the hardware composition diagram of realizing circuit of the feedforward open loop linearization method of controlling that in specific embodiment one, the present invention proposes;

Fig. 2 is the algorithm flow chart of the feedforward open loop linearization method of controlling that in specific embodiment one, the present invention proposes;

Fig. 3 is the concrete enforcement block diagram of the feedforward open loop linearization method of controlling that in specific embodiment one, the present invention proposes;

Fig. 4 is linearization result that in specific embodiment one, the present invention draws and the contrast figure of actual retardant curve;

Fig. 5 is the hardware composition diagram of the feedforward open loop LINEARIZED CONTROL device that in specific embodiment two, the present invention proposes;

Fig. 6 is the hardware composition diagram of the feedforward open loop LINEARIZED CONTROL device that in specific embodiment three, the present invention proposes.

Embodiment

Specific embodiment one:

As shown in Figure 1, the hardware of realizing circuit of the feedforward open loop linearization method of controlling of the present embodiment forms and comprises control signal generator (1), analog to digital converter (2), feedforward open loop LINEARIZED CONTROL device (3), digital to analog converter (4) and power amplifier (5).The open loop LINEARIZED CONTROL that wherein feedovers device is realized by chip or the system that dsp chip, single-chip microcomputer, CPLD/FPGA chip and ARM chip etc. have digital signal processing function.Comprise sluggish component observer (3-1) in feedforward open loop LINEARIZED CONTROL device (3), multiplier (3-2) and totalizer (3-3), be used for completing the piezoelectric ceramic actuator linearization technique that this specific embodiment proposes.The mathematic(al) representation of realizing piezoelectric ceramic actuator lagging characteristics feedforward open loop LINEARIZED CONTROL is:

$\left\{\begin{array}{c}{u}_b\left(t\right)=u\left(t\right)-\frac{\hat{h}\left(t\right)}{k_v}\\ \stackrel{\·}{\hat{h}}\left(t\right)=A\stackrel{\·}{u}\left(t\right)-\mathrm{\β}\left|\stackrel{\·}{u}\left(t\right)\right|{\left|\hat{h}\left(t\right)\right|}^{n-1}h\left(t\right)-\mathrm{\γ}\stackrel{\·}{u}\left(t\right){\left|\hat{h}\left(t\right)\right|}^n\end{array}\right.---\left(5\right)$

U wherein _b(t) be the driving voltage after compensation;

k _vFor output displacement and the ratio constant of controlling voltage;

U (t) is the control voltage of piezoelectric ceramic actuator;

Estimated value for sluggish component;

For controlling the first order derivative of voltage to the time;

For the first order derivative of sluggish component estimated value to the time;

A, β, γ and n are undetermined parameter, n=1 in the present embodiment.

Because the present embodiment adopts digital circuit piezoelectric ceramic actuator linearization technique, therefore must be with formula (5) discretize.As shown in Figure 1, the digital drive voltage u of piezoelectric ceramic actuator _b(kT) (wherein T is the discrete periodic of control signal, and k is positive integer.) be by the digital control voltage u (kT) of piezoelectric ceramic actuator and the estimated value of sluggish component Determine.Specific algorithm can be described below:

Under original state, establish

U (kT-2T)=0 and u (kT-T)=u (T).As kT〉0 the time, order

U (kT-2T)=u (kT-T) and u (kT-T)=u (kT).

1) set

U (kT-2T)=0 and u (kT-T)=u (kT);

2) if u (kT-T) 〉=u (kT-2T) makes $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1+(\mathrm{\β}+\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]};$

If a)

, u (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

B) otherwise, the order $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1+(\mathrm{\β}-\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]},\hat{h}(\mathrm{kT}-T)=\hat{h}\left(\mathrm{kT}\right),$ U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

3) if u (kT-T)＜u (kT-2T) makes $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1-(\mathrm{\β}-\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]};$

If a)

U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

B) otherwise, the order $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1-(\mathrm{\β}+\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]},\hat{h}(\mathrm{kT}-T)=\hat{h}\left(\mathrm{kT}\right),$ U (kT-2T)=u (kT-T) and u (KT-T)=u (kT);

4) will calculate

Substitution

Try to achieve the digital drive voltage u of piezoelectric ceramic actuator _b(kT);

5) adopt digital to analog converter (4) with digital drive voltage u _b(kT) be converted to analog drive voltage u _b(t), power amplifier (5) is with analog drive voltage u _b(t) amplify and be used for driving piezoelectric ceramic actuator (6);

6) after completing the processing of this secondary data, enter 2), the next numerical value of cycle calculations.

In the present embodiment, the software program flow process of feedforward open loop LINEARIZED CONTROL device as shown in Figure 2.By shown in Figure 2, owing to relating to many control modules in the LINEARIZED CONTROL device, thereby initial period need to arrange various control registers; Simultaneously, in feedforward open loop LINEARIZED CONTROL device, defined multiple variable, need to define and initialization it.Adopt cycle interruption to carry out acquisition and processing to data point in this specific embodiment.After the timer initialization, start this timer, wait for down trigger.When interrupting triggering, obtain the control voltage signal, and will control voltage signal and process by above-mentioned control algolithm, and the result after processing is converted to analog drive signal by D/A converter, should drive the signal input power amplifier drives piezoelectric ceramic actuator, after completing this process, wait for the triggering again of interrupting, realize the processing to next data point.

The concrete enforcement block diagram of the present embodiment as shown in Figure 3.As shown in Figure 3, in the present embodiment, control signal generator (1) adopts function synthesized signal generator (1 '), the model of analog to digital converter (2) is ADS8328 (2 '), what feedforward open loop LINEARIZED CONTROL device (3) was selected is that model is the dsp chip (3 ') of TMS320F2812, the model of digital to analog converter (4) is DAC715 (4 '), the model of power amplifier (5) is P﹠I-1 (5 ') (Wang Daihua, the fourth civilization, the patent No.: ZL20061005458.1).This embodiment adopts the cycle interruption of the CPU-Timer0 of dsp chip to gather data point.When the down trigger of CPU-Timer0 timer, obtain the control voltage signal, and should control after voltage signal is processed and send into D/A converter and be converted to analog drive signal, should drive the signal input power amplifier drives piezoelectric ceramic actuator, after completing this process, wait for the triggering again of interrupting, realize the processing to next data point.

Solid line in Fig. 4 is for the piezoelectric ceramic actuator that records in this example without the output displacement of controlling and the actual retardant curve of controlling voltage, and dotted line is the output displacement of piezoelectric ceramic actuator after LINEARIZED CONTROL and the curve of driving voltage.As seen from Figure 4, after adopting this method, piezoelectric ceramic actuator output displacement and the Hysteresis Nonlinear Relationship Change of controlling between voltage are linear approximate relationship.

Specific embodiment two:

As shown in Figure 5, the present embodiment and embodiment one difference are, the signal that control signal generator (1) produces is digital control voltage u (kT), can directly send into feedforward open loop LINEARIZED CONTROL device (3), and not need analog to digital converter (2).

Specific embodiment three:

As shown in Figure 6, the present embodiment and embodiment one difference be, the hardware of this feedforward open loop LINEARIZED CONTROL device forms and comprises at least: control signal generator (1), signal preprocessor (7), analog to digital converter (2), feedforward open loop LINEARIZED CONTROL device (3), digital to analog converter (4) and power amplifier (5).The user not only can produce digital controlled signal by feedforward open loop LINEARIZED CONTROL device (3), can also pass through any analog control voltage u that signal preprocessor (7) produces control signal generator (1) _r(t) be converted to analog control signal and send into analog to digital converter (2), analog to digital converter (2) converts analog control signal to digital controlled signal and sends into feedforward open loop LINEARIZED CONTROL device (3), to realize the LINEARIZED CONTROL of the analog control voltage that outside is inputted arbitrarily.

Need to prove finally, above embodiment is only unrestricted in order to technical scheme of the present invention to be described, although with reference to preferred embodiment, the present invention is had been described in detail, those of ordinary skill in the art is to be understood that, can modify or be equal to replacement technical scheme of the present invention, and not breaking away from aim and the scope of technical solution of the present invention, it all should be encompassed in the middle of claim scope of the present invention.

The lagging characteristics linearization of the applicable equally electrostriction ceramics actuator of this method.

The present patent application people has done detailed explanation and description in conjunction with Figure of description to embodiments of the invention; but those skilled in the art should understand that; above embodiment is only the preferred embodiments of the invention; detailed explanation is just in order to help the reader to understand better spirit of the present invention; and be not limiting the scope of the invention; on the contrary, any any improvement of doing based on spirit of the present invention or modify and all should drop on protection scope of the present invention within.

Claims (8)

1. the feedforward open loop linearization method of controlling of a piezoelectric ceramic actuator lagging characteristics is characterized in that: the control voltage u (t) that will input piezoelectric ceramic actuator by feedforward open loop LINEARIZED CONTROL is converted to driving voltage u _b(t) act on piezoelectric ceramic actuator and make it produce displacement output, the output displacement of piezoelectric ceramic actuator becomes linear approximate relationship with control voltage u (t) after feedforward open loop LINEARIZED CONTROL, said method comprising the steps of:

(1) output displacement of piezoelectric ceramic actuator and the sluggishness between driving voltage are the stack of linear component and sluggish component, utilize the described sluggish component of the sluggish operator simulation of Bouc-Wen, and the Bouc-Wen model that obtains piezoelectric ceramic actuator is

x(t)＝k _vu _b(t)+x ₀+h(t)

$\stackrel{\·}{h}\left(t\right)=A{\stackrel{\·}{u}}_b\left(t\right)-\mathrm{\β}\left|{\stackrel{\·}{u}}_b\left(t\right)\right|{\left|h\left(t\right)\right|}^{n-1}h\left(t\right)-\mathrm{\γ}{\stackrel{\·}{u}}_b\left(t\right){\left|h\left(t\right)\right|}^n$

Wherein, t is the time;

X (t) is the output displacement of piezoelectric ceramic actuator;

k _vFor output displacement and driving voltage ratio constant;

u _b(t) be driving voltage;

x ₀For the displacement that exists under original state;

H (t) is the sluggish component of piezoelectric ceramic actuator;

For the first order derivative of driving voltage to the time;

For the first order derivative of sluggish component to the time;

A, β, γ and n are the parameter of model;

(2) utilize the sluggish operator of Bouc-Wen to build the sluggish component h (t) of online sluggish component observer with the On-line Estimation piezoelectric ceramic actuator, due to driving voltage u _b(t) unknowable, replace driving voltage u with controlling voltage u (t) _b(t), obtain the estimated value of sluggish component h (t)

The expression formula of sluggish component observer is:

$\stackrel{\·}{\hat{h}}\left(t\right)=A\stackrel{\·}{u}\left(t\right)-\mathrm{\β}\left|\stackrel{\·}{u}\left(t\right)\right|{\left|\hat{h}\left(t\right)\right|}^{n-1}h\left(t\right)-\mathrm{\γ}\stackrel{\·}{u}\left(t\right){\left|\hat{h}\left(t\right)\right|}^n$

Wherein, u (t) is the control voltage of piezoelectric ceramic actuator;

For controlling the first order derivative of voltage to the time;

Estimated value for sluggish component;

For the first order derivative of sluggish component estimated value to the time;

A, β, γ and n are the parameter of model;

(3) utilize the estimated value of the sluggish component that obtains

Order

The output displacement that can obtain piezoelectric ceramic actuator with the relation of controlling voltage can approximate representation be:

x(t)＝k _vu(t)+x ₀

Wherein, x (t) is the output displacement of piezoelectric ceramic actuator;

k _vFor output displacement and driving voltage ratio constant;

U (t) is the control voltage of piezoelectric ceramic actuator;

x ₀For the displacement that exists under original state;

Described piezoelectric ceramic actuator linearization technique adopts digital circuit, the digital drive voltage u of piezoelectric ceramic actuator _b(kT) be by the digital control voltage u (kT) of piezoelectric ceramic actuator and the estimated value of sluggish component Determine, wherein T is the discrete periodic of control signal, and k is positive integer, and specific algorithm is as follows:

1) under original state, set

U (kT-2T)=0 and u (kT-T)=u (kT); When kT＞0, order

U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

2) if u (kT-T) 〉=u (kT-2T) makes $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1+(\mathrm{\β}+\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]};$

If 1.

U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

2. otherwise, the order $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1+(\mathrm{\β}-\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]},$ $\hat{h}(\mathrm{kT}-T)=\hat{h}\left(\mathrm{kT}\right),$ U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

3) if u (kT-T)＜u (kT-2T) makes $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1-(\mathrm{\β}-\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]};$

If 1. U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

2. otherwise, the order $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1-(\mathrm{\β}+\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]},$ $\hat{h}(\mathrm{kT}-T)=\hat{h}\left(\mathrm{kT}\right),$ U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

4) will calculate

Substitution

Try to achieve the digital drive voltage u of piezoelectric ceramic actuator _b(kT);

5) adopt digital to analog converter (4) with digital drive voltage u _b(kT) be converted to analog drive voltage u _b(t), power amplifier (5) is with analog drive voltage u _b(t) amplify and be used for driving piezoelectric ceramic actuator (6);

6) after completing the processing of this secondary data, enter 2), the next numerical value of cycle calculations;

Wherein,

u _b(kT) be the digital drive voltage of piezoelectric ceramic actuator;

T is the discrete periodic of control signal;

K is positive integer;

U (kT) is the digital control voltage of piezoelectric ceramic actuator;

It is the estimated value of sluggish component;

A, β and γ are the parameter of model;

k _vFor output displacement and driving voltage ratio constant.

2. the feedforward open loop linearization method of controlling of piezoelectric ceramic actuator lagging characteristics according to claim 1, it is characterized in that: A, β and γ are undetermined parameter, the inputoutput data on-line identification by the piezoelectric ceramic actuator that records obtains.

3. the feedforward open loop linearization method of controlling of piezoelectric ceramic actuator lagging characteristics according to claim 1, it is characterized in that: the sluggish component of piezoelectric ceramic actuator and the relation of driving voltage can also be described with other sluggish operators, and described sluggish operator comprises the sluggish operator of Dahl, Jiles-Atherton operator.

4. the feedforward open loop linearization method of controlling of piezoelectric ceramic actuator lagging characteristics according to claim 1, it is characterized in that: this control method is equally applicable to the lagging characteristics linearization of electrostriction ceramics actuator.

piezoelectric ceramic actuator lagging characteristics feedforward open loop linearization method of controlling realize circuit, described circuit comprises control signal generator (1), analog to digital converter (2), feedforward open loop LINEARIZED CONTROL device (3), digital to analog converter (4) and power amplifier (5), it is characterized in that: described control signal generator (1), analog to digital converter (2), feedforward open loop LINEARIZED CONTROL device (3), digital to analog converter (4) is connected 5 with power amplifier) connect in turn, control signal generator (1) produces analog control voltage, adopt analog to digital converter (2) to convert analog control voltage to digital controlled signal and send into feedforward open loop LINEARIZED CONTROL device (3), feedforward open loop LINEARIZED CONTROL device (3) obtains digital drive signals and sends into digital to analog converter (4) according to the feedforward open loop linearization method of controlling nonlinear compensation signal that superposes on digital controlled signal, digital to analog converter (4) is converted to analog drive voltage with digital drive signals and sends into power amplifier (5), be used for driving piezoelectric ceramic actuator (6) after the analog drive voltage that power amplifier (5) will be inputted is amplified and produce displacement output,

The digital drive voltage u of piezoelectric ceramic actuator _b(kT) be by the digital control voltage u (kT) of piezoelectric ceramic actuator and the estimated value of sluggish component

Determine, wherein T is the discrete periodic of control signal, and k is positive integer, and specific algorithm is as follows:

7) under original state, set U (kT-2T)=0 and u (kT-T)=u (kT); When kT＞0, order

U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

8) if u (kT-T) 〉=u (kT-2T) makes $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1+(\mathrm{\β}+\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]};$

If 1.

U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

2. otherwise, the order $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1+(\mathrm{\β}-\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]}\text{,}$ $\hat{h}(\mathrm{kT}-T)=\hat{h}\left(\mathrm{kT}\right),$ U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

9) if u (kT-T)＜u (kT-2T) makes $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1-(\mathrm{\β}-\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]};$

If 1.

U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

2. otherwise, the order $\hat{h}\left(\mathrm{kT}\right)=\frac{A[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]+\hat{h}(\mathrm{kT}-T)}{1-(\mathrm{\β}+\mathrm{\γ})[u(\mathrm{kT}-T)-u(\mathrm{kT}-2T)]},$ $\hat{h}(\mathrm{kT}-T)=\hat{h}\left(\mathrm{kT}\right),$ U (kT-2T)=u (kT-T) and u (kT-T)=u (kT);

10) will calculate

Substitution

Try to achieve the digital drive voltage u of piezoelectric ceramic actuator _b(kT);

11) adopt digital to analog converter (4) with digital drive voltage u _b(kT) be converted to analog drive voltage u _b(t), power amplifier (5) is with analog drive voltage u _b(t) amplify and be used for driving piezoelectric ceramic actuator (6);

12) after completing the processing of this secondary data, enter 8), the next numerical value of cycle calculations;

Wherein,

u _b(kT) be the digital drive voltage of piezoelectric ceramic actuator;

T is the discrete periodic of control signal;

K is positive integer;

U (kT) is the digital control voltage of piezoelectric ceramic actuator;

It is the estimated value of sluggish component;

A, β and γ are the parameter of model;

k _vFor output displacement and driving voltage ratio constant.

6. piezoelectric ceramic actuator lagging characteristics according to claim 5 feedforward open loop linearization method of controlling realizes circuit, it is characterized in that: feedforward open loop LINEARIZED CONTROL device (3) uses the chip or the system that have digital signal processing function to realize, described chip or system comprise dsp chip, single-chip microcomputer, CPLD/FPGA chip, ARM chip, computing machine.

7. piezoelectric ceramic actuator lagging characteristics according to claim 6 feedforward open loop linearization method of controlling realizes circuit, it is characterized in that: when control signal generator (1) produces digital control voltage, also can not need through analog to digital converter (2), directly send into feedforward open loop LINEARIZED CONTROL device (3), if described control signal is fit to be directly inputted to feedforward open loop LINEARIZED CONTROL device (3), control signal generator (1) and analog to digital converter (2) can not adopt.

8. according to claim 5 or 6 described piezoelectric ceramic actuator lagging characteristics feedforward open loop linearization method of controlling realizes circuit, it is characterized in that: described feedforward open loop LINEARIZED CONTROL device (3) comprises sluggish component observer (3-1), multiplier (3-2) and totalizer (3-3), sluggish component observer (3-1), multiplier (3-2) are connected 3-3 with totalizer) connection in turn, sluggish component observer (3-1) obtains the digital estimated value of sluggish component

Multiplier (3-2) is with the digital estimated value of sluggish component

With the driving voltage ratio constant k after output displacement and compensation _vReciprocal multiplication, totalizer (3-3) is subtracted each other the output valve of digital control voltage u (kT) and multiplier (3-2), obtains digital drive voltage u _b(kT).

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