CN105068564B - A kind of displacement control method of piezoelectric ceramic actuator - Google Patents

Abstract

The invention discloses the displacement control method of a kind of piezoelectric ceramic actuator.Use the present invention can offset the Hysteresis Nonlinear of servo platform, possess good control effect, and simple in construction, easily build enforcement.Dynamic hysteresis behavior is modeled by the present invention initially with static Hysteresis Model, controlled device is carried out hysteresis compensation, then by the dynamic error, modeling error and other interference not modeled that are brought by static Hysteresis Model by disturbance estimator On-line Estimation out, and disturbance estimated result is fed back to sliding mode controller, improve the robustness that control system is disturbed to external world, the control effect of the device that tightens control；Finally utilize sliding mode controller that piezoelectric ceramic actuator is carried out Bit andits control.The present invention is by static Hysteresis Model and the cooperation of sliding mode controller based on disturbance estimation so that the sluggish strong nonlinearity of piezoelectric ceramic actuator is weakened step by step, and can keep good tracking accuracy and robustness, and simple in construction, enforcement are conveniently.

Description

A kind of displacement control method of piezoelectric ceramic actuator

Technical field

The present invention relates to technical field of electromechanical control, be specifically related to the displacement control method of a kind of piezoelectric ceramic actuator.

Background technology

In recent years, along with the development of science and technology, increasing field proposes demand to high-precision location technique.? The key technology having a general character in hardware equipped is exactly to need to solve object stage or the High Precision Automatic survey of its relevant device Amount and precision positioning technology positioning precision and resolving power requirement.The type of drive being conventionally used to micro-displacement location is typically Use frictional drive, lead screw transmission etc., but its nonlinear characteristic is strong, and structure is complex, it is difficult to reach volume little, high The control requirement of precision.Utilize the piezoelectric ceramic actuator (Piezoelectric Actuator, PEA) that inverse piezoelectric effect is made Overcome the deficiency of conventional actuators, there is the advantages such as control accuracy height, fast response time, displacement resolution height, High power output, But the nonlinear characteristics such as its intrinsic sluggishness, creep limit its actual application.Such non-linear meeting causes piezoelectric ceramics Positioning precision is very poor, affects system stability.And it is the most difficult that its modeling is especially set up dynamic model, the non-thread commonly used Property control method can not efficiently solve braking problems.

At present research worker modeling to Hysteresis Nonlinear proposes multiple method, substantially may be summarized to be two classes:

A kind of is the Hysteresis Model set up by sluggish physics principle.At present, there is research worker for ferromagnetic Class material establishes Hysteresis Model, also has the research worker physical principle according to piezoelectric, carries out reasonable analysis and is deduced Hysteresis Model between output displacement and input voltage.

Another kind is the Hysteresis Model set up hysteresis phenomenon by mathematical model.Model based on hysteresis phenomenon is compared Simpler based on physical model form, therefore obtain wider application.

The lagging characteristics of piezoelectric actuator generally can be divided into two classes: static lagging characteristics and dynamic hysteresis behavior.At present, exist In some documents, research worker is typically to enter the static lagging characteristics of piezoelectric ceramics displacement platform with dynamic hysteresis behavior simultaneously Row modeling, the advantage so modeled is that model can more fully reflect defeated at different frequency of piezoelectric ceramics locating platform Enter the individual features under signal excitation, but have the disadvantage that in Controlling model and comprise the parameter more needing identification, more complicated Identification process.

In order to solve non-linear hysteretic characteristic, impact, the control of scientific research personnel's design are brought for precision piezoelectric servo platform System processed can be largely divided into three classes: based on feedforward compensate control, compensation based on feedback controls and is simultaneously based on feedforward and anti- The control system of feedback.Wherein, for control system based on feedforward and feedback, the feedforward can utilize laboratory facilities to obtain The data taking controlled device carry out the compensator of design compensation Hysteresis Nonlinear, offset the Hysteresis Nonlinear of servo platform, it is possible to decrease The difficulty of subsequent design feedback controller；Feedback controller can solve compensator and do not compensate dry on the basis of feedforward controller Clean lagging characteristics and some other uncertainty not modeled.Therefore, control system based on feedforward and feedback is due to feedforward Control and the combination of feedback control, complementary advantage and receive and be widely applied.But, due to this control system simultaneously Have employed feedforward controller and feedback controller, generally also can there is control system complicated, the shortcoming such as the most readily understood, utilization.

Summary of the invention

In view of this, the invention provides the displacement control method of a kind of piezoelectric ceramic actuator, it is possible to offset servo and put down The Hysteresis Nonlinear of platform, possesses good control effect, and simple in construction, easily builds enforcement.

The displacement control method of the piezoelectric ceramic actuator of the present invention, comprises the steps:

Step 1, uses the hysteresis compensation device based on the static Hysteresis Model dynamic hysteresis behavior to piezoelectric ceramic actuator Carry out the hysteresis compensation that feedovers；

Step 2, with the interference of the compensation error of hysteresis compensation device, the model error setting up Hysteresis Model and the unknown it With for total disturbance Ψ (t), disturbance estimator is utilized total disturbance Ψ (t) to be estimated, and by total disturbance estimated result Ψ_estimatedT () feeds back to sliding mode controller；

Step 3, utilizes sliding mode controller that the piezoelectric ceramic actuator after step 1 feedovers hysteresis compensation is carried out displacement control System.

Further, in described step 1, static Hysteresis Model is Bouc-Wen static state Hysteresis Model.

Further, first with Bouc-Wen static state Hysteresis Model, the dynamic hysteresis behavior of piezoelectric ceramic actuator is entered Row modeling, then utilizes particle swarm optimization algorithm that the model parameter of Bouc-Wen static state Hysteresis Model is carried out identification, it is thus achieved that Bouc-Wen static state Hysteresis Model.

Further, in described step 3, the sliding-mode surface s of described sliding mode controller is proportional integral type, i.e.

$s=\stackrel{\·}{e}+ce---\left(1\right)$

Wherein, e is the displacement expected value x of piezoelectric ceramic actuator_dWith the difference of actual value x, c is controller ratio ginseng Number, for empirical parameter, c > 0；

First in the case of not considering total disturbance Ψ (t), obtain the dynamic of sliding-mode surface

$\stackrel{\·}{s}=-ks-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)---\left(2\right)$

Wherein, k and ε is controller parameter；K is empirical value；Sgn () is switch function；

Then in the case of having total disturbance Ψ (t), sliding-mode surface is dynamically

$\stackrel{\·}{s}=-ks-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)+{\mathrm{\Ψ}}_{actual}\left(t\right)-{\mathrm{\Ψ}}_{estimated}\left(t\right)---\left(3\right)$

Wherein, Ψ_actualT () is actual disturbance term, Ψ_estimatedT () is the disturbance term estimated；

Then control rate u of sliding mode controller based on disturbance estimator is:

$u=-\frac{1}{c}\{\frac{1}{k}\[-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)-c\stackrel{\·}{e}-\stackrel{\·\·}{e}\]-\stackrel{\·}{e}\}+e\left(t\right)+u(t-T)$

Wherein, t is for currently to control the moment, and u (t-T) is the controlled quentity controlled variable in previous control cycle.

Beneficial effect:

(1) displacement of piezoelectric ceramic actuator is controlled, first by the control system that the present invention uses feedforward to add feedback Use static Hysteresis Model that dynamic hysteresis behavior is modeled, controlled device is carried out hysteresis compensation, then will be slow by static state Dynamic error, modeling error and other interference not modeled that stagnant model brings are estimated by disturbance estimator, and utilization is disturbed Dynamic estimator realizes the On-line Estimation to disturbance, and disturbance estimated result feeds back to sliding mode controller, and can to improve control system external The robustness of boundary's interference, the control effect of the device that tightens control；Finally utilize sliding mode controller that piezoelectric ceramic actuator is carried out position Move and control；By static Hysteresis Model and the cooperation of sliding mode controller based on disturbance estimation so that piezoelectric ceramics start The sluggish strong nonlinearity of device is weakened step by step, and can keep good tracking accuracy and robustness, and simple in construction, embodiment party Just.

(2) Bouc-Wen static state Hysteresis Model has simple in construction, parameter is few, realization is simple and convenient advantage of inverting, Hysteresis compensation device simple in construction based on Bouc-Wen static state Hysteresis Model, easily implement.

(3) disturbance estimator is combined by the present invention with traditional sliding mode controller, brings two benefits: one is removable Tradition sliding mode controller is it is to be appreciated that the requirement of perturbating upper bound；Two is owing to disturbance estimator has estimated the letter that system is unknown Breath, controller can provide controlled quentity controlled variable more accurately according to these information.

(4) use particle cluster algorithm that the parameter of Bouc-Wen static state Hysteresis Model carries out parameter identification, identification result essence Spending the highest, the identification time is short, is conducive to quickly, obtains Bouc-Wen static state Hysteresis Model accurately.

Accompanying drawing explanation

Fig. 1 is the structural representation of hysteresis compensation device based on Bouc-Wen static state Hysteresis Model.

Fig. 2 is Control system architecture schematic diagram of the present invention.

Fig. 3 is analogue system overall design drawing.

Fig. 4 is the maximum absolute error comparison diagram that different unifrequency sinusoidal signal inputs lower two kinds of methods.

Fig. 5 is under composite input signal, the actual displacement of the hysteresis compensation of the present invention+sliding formwork control and Error Graph thereof.

Fig. 6 is under composite input signal, the actual displacement of hysteresis compensation+proportional plus integral control and Error Graph thereof.

Detailed description of the invention

Develop simultaneously embodiment below in conjunction with the accompanying drawings, describes the present invention.

The invention provides the displacement control method of a kind of piezoelectric ceramic actuator, use feedforward to add the control system of feedback Displacement to piezoelectric ceramic actuator is controlled, and wherein, feedforward controller uses based on Bouc-Wen static state Hysteresis Model Hysteresis compensation device, feedback controller uses sliding mode controller based on disturbance estimator.In control system of the present invention, it is positioned at forward direction The hysteresis compensation device of path (i.e. feedforward path) is responsible for nonlinear systems with hysteresis about subtracts into a linear system.But, due to Hysteresis loop can change along with the difference of frequency input signal, and therefore the system after hysteresis compensation device compensates exists one Compensate error.The present invention this is compensated error and some other not modeling, uncertain error leaves on feedback network Sliding mode controller solve.Sliding mode controller based on disturbance estimator, can by disturbance estimator above-mentioned compensation by mistake Difference and modeling error, some other Interference Estimation not modeled out and introduce in sliding formwork control law, effectively improve and watch Take precision so that whole system has good robustness.Owing to having properly selected Bouc-Wen static state Hysteresis Model, design The simple in construction of the compensator gone out, it is easy to implement.Meanwhile, sliding mode controller based on disturbance estimator also have simple in construction, Regulation parameter is few, the advantage of easy enforcement.Therefore, whole control system is while possessing good control effect, it may have knot Structure simply, easily builds the advantage of enforcement, solves the problem that some existing control systems are complicated, be difficult to implement.

The cardinal principle of hysteresis compensation is first lagging characteristics according to controlled device, obtains the inverse characteristic of lagging characteristics, And inverse characteristic is modeled, the most inverse Hysteresis Model.To be connected on before through path is positioned at controlled device against Hysteresis Model, enter And reach to offset controlled device Hysteresis Nonlinear, nonlinear system is changed into the purpose of linear system.As shown in Figure 1.High-precision The controlled device that degree servo-positioning platform can be abstracted into a Systems with Hysteresis H and a linear system is in series, will Hysteresis compensation device is placed on forward path, before being positioned at controlled device.Input signal u (t) exports after hysteresis compensation device Signal v (t), after signal v (t) enters controlled device, can first pass through Systems with Hysteresis, due to sluggish inversion model H^-1Work With, signal v (t) is reduced into again u (t), the result before therefore hysteresis compensation device being connected on controlled device be non-linear late Stagnant system balance becomes a linear system.

The lagging characteristics of piezoelectric actuator is divided into static lagging characteristics and dynamic hysteresis behavior, and current research worker is typically The static lagging characteristics of piezoelectric ceramics displacement platform is modeled with dynamic hysteresis behavior simultaneously, have employed dynamic hysteresis model The dynamic hysteresis behavior of controlled system is modeled, uses static Hysteresis Model that the static lagging characteristics of controlled system is carried out Modeling；Although the model that this modeling method is set up can more fully reflect that piezoelectric ceramics locating platform is at different frequency Individual features under input signal excitation, but its shortcoming is the parameter, more complicated comprising in Controlling model and more needing identification Identification process.In order to solve this problem, the present invention selects to use static Hysteresis Model to be modeled dynamic hysteresis behavior, When frequency input signal increases, the compensation error of compensator based on static Hysteresis Model can be gradually increased, this compensation error Estimate with the most available disturbance estimator below not modeled of other system, be finally introducing sliding mode controller. Therefore, this sluggish strong nonlinearity is to be weakened by these links rather than only rely on a certain link to solve step by step. Compensator based on Bouc-Wen static state Hysteresis Model and sliding mode controller based on disturbance estimator are by reasonably both coordinating Good tracking accuracy and robustness can be kept to make again whole control system maintain simple in construction, implement spy easily Point.Wherein, Bouc-Wen model nonlinear differential equation describes hysteresis phenomenon, by selecting suitable equation parameter group Close, it is possible to obtain variously-shaped retardant curve, so that Bouc-Wen model has simple in construction, parameter is few, realization is simple List and convenient advantage of inverting.

Disturbance estimator needs to know with removing sliding mode controller for improving the control system robustness for external interference The requirement of road perturbating upper bound, these interference include the uncertainty of model parameter, unknown external disturbance and controll plant Some is non-linear, and these disturbances all it is assumed to be bounded.Disturbance estimator can realize the On-line Estimation to disturbance, can improve control The robustness of system external circle processed interference, the control effect of the device that tightens control.The present invention is by disturbance estimator and tradition sliding formwork control Device processed combines, and brings two benefits: one is removable tradition sliding mode controller it is to be appreciated that the requirement of perturbating upper bound.Two be by Having estimated, in disturbance estimator, the information that system is unknown, controller can provide controlled quentity controlled variable more accurately according to these information. It should be noted that the control cycle of sliding mode controller based on disturbance estimator to be faster than system dynamics to a certain extent Just can play preferably performance.Hysteresis compensation device based on Bouc-Wen model and sliding mode controller based on disturbance estimator The structural representation of control system is as shown in Figure 2.The design object of this control system is to be provided that good control effect Meanwhile, make control system simple as much as possible.

It is described in detail below:

The system input and output mathematical model that Bouc-Wen model describes is as follows:

$\left\{\begin{array}{c}y=du-h\\ \stackrel{\·}{h}=\mathrm{\α}d\stackrel{\·}{u}-\mathrm{\β}\left|\stackrel{\·}{u}\right|{\left|h\right|}^{n-1}h-\mathrm{\γ}\stackrel{\·}{u}{\left|h\right|}^n\end{array}\right.---\left(1\right)$

Wherein, u is input voltage signal, and y is system output displacement signal, and h is sluggish item, and d is proportional gain, α, beta, gamma For determining the model parameter of hysteresis loop shape, n is the exponent number of model.From formula (1), this model needs the parameter one of identification Have four, be respectively as follows: d, α, beta, gamma.Identification of Model Parameters is after types of models and model structure determine, according to experiment number One group of parameter value is determined so that number is tested in matching that can be best by the calculated numerical result of model according to the model set up According to.For the parameter that these are to be estimated, space, referred to as a parameter space can be defined.Parameter identification is exactly empty from sample Between to the mapping of parameter space.Parameter identification the most important thing is to select suitable parameter identification method.Particle cluster algorithm is owing to intending Closing precision the highest, fit time is the shortest, and therefore employing particle swarm optimization algorithm is carried out identification of Model Parameters by the present invention.

Particle cluster algorithm (Particle Swarm Optimization, PSO) is suggested as far back as nineteen ninety-five, due to it Algorithm simply, easily realize, so the most substantial amounts of research worker has carried out research and has achieved particle swarm optimization algorithm The biggest progress.In fact, parameter identification process can be understood from being one and constantly seeks obtaining the process of optimal solution.Each particle represents One group model parameter, sets a formula being referred to as constraint function and calculates the distance of particle and optimal solution, and which particle is from The distance of excellent solution is the nearest, just illustrates that this group model parameter more can preferably simulate the characteristic of practical object.Constraint function such as formula (2) Shown in, constraint function is the form of mean square deviation, can reflect the average level of models fitting error.Population location updating formula is such as Shown in formula (3).

$J=\sqrt{\frac{1}{N}{\mathrm{\Σ}}_{i=1}^N{\left(x_{\exp }\right(i)-x_{mdl}(i\left)\right)}^2}---\left(2\right)$

$\left\{\begin{array}{c}{v}_{id}^{k+1}=w\·v_{id}^k+c_1\·r_1\·\[p_{id}\·x_{id}^x\]+c_2\·r_2\·\[p_{gd}-x_{id}^k\]\\ x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1}\end{array}\right.---\left(3\right)$

In formula (3), x_idRepresent the position of particle, v_idRepresent the speed of particle.p_i=(p_i1,p_i2,…,p_id,…,p_iD) it is The history desired positions of individual particles, p_i=(p_g1,p_g2,…,p_gd,…,p_gD) it is global history desired positions, k is iteration time Number, r₁,r₂∈ (0,1) is random number, and the two parameter is used for keeping the multiformity of colony.c₁, c₂For Studying factors, w is inertia Weight.

Parameter identification completes under MATLAB environment, and particle cluster algorithm workflow is approximately as several steps:

1) initialization of program: include the importing of experimental data and the initialization of particle cluster algorithm.Studying factors c₁And c₂ 2 are all elected as through repeatedly debugging.Inertia weight w is chosen for 0.7.System is input to the gain amplifier of output and is determined by parameter d.As Fruit ignores the impact of lagging characteristics of system, then the input-output curve of locating platform can be approximately straight line, i.e. 0～ Corresponding 0～100 μm of 100V, the general interval of the estimated value that thus can estimate parameter d is [0,2 × 10^-6].It is carried out simple Change so that it is easy to programming.When writing equation, parameter d is amplified 10⁶Times, it is then engage in identification process, afterwards by identification Result reduces 10 again⁶Times, it is ensured that will not make mistakes.Parameter alpha, the span of β, γ is typically between [0,1].

Table 1 PSO algorithm parameter

In table 1, maxDT is maximum iteration time, and D is particle dimension, and N is particle scale, and eps is constraint function threshold.

2) calculating fitness (i.e. the value of constraint function): the value of each particle brought in formula (2), computation model exports, Fourth order Runge-Kutta is used to realize differential equation.The output of calculated model is utilized formula with actual data point (2) fitness minimum in current all particles is calculated.

3) judge whether the model parameter that picks out meets precision: the minimum fitness calculated by second step and constraint letter Number threshold value eps value compares, if more than eps, carries out particle shown in location updating such as formula (3), if less than eps, terminating to distinguish Know.

4) repeat above-mentioned circulation, if arriving maximum iteration time, exiting circulation, terminating identification.

After identification of Model Parameters, so that it may set up based on Bouc-Wen static state Hysteresis Model.Formula (1) gives displacement x, Input voltage u, the relation of sluggish item h, according to above-mentioned thinking, in order to be compensated the algorithm of device, input voltage u is proposed, depending on Sluggish item h is the function of input u, is designated as h (u), x is written as x_d, regard the u function as displacement x, during n=1, hysteresis compensation simultaneously The mathematic(al) representation of device is as follows:

$\left\{\begin{array}{c}u\left(t\right)=\frac{1}{d}(x_d+h(u\left(t\right)\left)\right)\\ \stackrel{\·}{h}=\mathrm{\α}d\stackrel{\·}{u}-\mathrm{\β}\left|\stackrel{\·}{u}\right|h-\mathrm{\γ}\stackrel{\·}{u}\left|h\right|\end{array}\right.---\left(4\right)$

System is represented by after compensation based on Bouc-Wen static state sluggishness hysteresis compensation device:

X (t)=u (t)-Ψ (t) (5)

In formula, x (t) is piezoelectric actuator actual displacement, and u (t) is input voltage, and Ψ (t) is all uncompensated sluggishnesses The summation of characteristic, Unmarried pregnancy and interference.

To formula (5) application disturbance estimator observational variable Ψ (t), then

Ψ_estimated(t)=-x (t)+u (t-T) (6)

Wherein, u (t-T) is the controlled quentity controlled variable of previous moment.

In order to design sliding mode controller, definition error term e (t) is as follows:

E (t)=x_d(t)-x(t) (7)

In formula, x_dT () is the desired trajectory that system is followed the tracks of.E (t) is desired trajectory signal and piezoelectric actuator actual displacement Difference e (t).

The sliding-mode surface of one proportional integral type of definition:

$s=\stackrel{\·}{e}+ce---\left(8\right)$

In formula, c (c ＞ 0) is a controller parameter needing experience to debug.

In the case of not considering disturbance term Ψ (t), one meets lim_t→∞E (t)=0 and attraction rateSliding-mode surface DynamicallyFor:

$\stackrel{\·}{s}=-ks-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)---\left(9\right)$

K and ε is the parameter needing design, and sgn () is switch function.

In the case of having disturbance term Ψ (t), formula (9) can be rewritten as:

$\begin{array}{c}\stackrel{\·}{s}=-ks-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)+{\mathrm{\Ψ}}_{actual}\left(t\right)-{\mathrm{\Ψ}}_{estimated}\left(t\right)\\ =-ks-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)+\widetilde{\mathrm{\Ψ}}\left(t\right)\end{array}---\left(10\right)$

In formula,Represent actual disturbance term Ψ_actual(t) and the disturbance term Ψ estimated_estimatedMistake between (t) Difference.

Composite type (9) and formula (10), sliding formwork control rate u is as follows:

$u=-\frac{1}{c}\{\frac{1}{k}\[-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)-c\stackrel{\·}{e}-\stackrel{\·\·}{e}\]-\stackrel{\·}{e}\}+x_d+{\mathrm{\Ψ}}_{estimated}---\left(11\right)$

By variable Ψ_estimatedT () substitutes into formula (11) has:

$u=-\frac{1}{c}\{\frac{1}{k}\[-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)-c\stackrel{\·}{e}-\stackrel{\·\·}{e}\]-\stackrel{\·}{e}\}+e\left(t\right)+u(t-T)---\left(12\right)$

Formula (12) is the control rate of sliding mode controller based on disturbance estimator.

The stability analysis of controller is as follows:

Define a positive definite Lyapunov function:

$V=\frac{1}{2}{s}^2---\left(13\right)$

So, its first derivative is:

$\stackrel{\·}{V}=s\stackrel{\·}{s}---\left(14\right)$

Wushu (10) substitutes into above formula, has

$\begin{array}{c}\stackrel{\·}{V}=s\stackrel{\·}{s}=s(-ks-\mathrm{\ϵ}\mathrm{sgn}(s)+\widetilde{\mathrm{\Ψ}})\\ =-{\mathrm{ks}}^2-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)s+\widetilde{\mathrm{\Ψ}}s\\ \≤-{\mathrm{ks}}^2-\mathrm{\ϵ}\left|s\right|+\widetilde{\mathrm{\Ψ}}\left|s\right|\end{array}---\left(15\right)$

Therefore, if it is desired to allow controller stably must be fulfilled for following condition:

$\mathrm{\&epsiv;}>\widetilde{\mathrm{\&Psi;}}\&RightArrow;\stackrel{\&CenterDot;}{V}<0---\left(16\right)$

I.e. controller parameter ε should be more than error term

The method proposed in the present invention is verified below in semi-matter simulating system.

HWIL simulation is a kind of emulation technology that computer is connected with material object, is a kind of closer to actual emulation, It is referred to as Hardware-in-the-loop simu-lation.In Practical Project field, emulation is widely used for it, and these fields include electromechanics, connect Mouth, hydraulic pressure and control technical field.The application process of HWIL simulation is object of study to be difficult to model in emulation experiment Part directly with material object replace, easily with rule describe characteristic mathematical model replace.Owing to access in kind is imitative In true loop so that the emulation that other forms are compared in HWIL simulation is truer, owing to the complex characteristics of object can be reflected, Therefore simulation result is closer to reality, the most also has higher credibility, provides Reliable guarantee for checking designed system.Herein By configuration semi-physical emulation platform based on the iHawk system and piezoelectric actuator of Concurrent company, to this paper institute The control system of design carries out HWIL simulation experiment.

It is roughly divided into iHawk HWIL simulation computer, interface board based on iHawk precision piezoelectric semi-physical emulation platform Card, driver, 4 parts in kind.Computer receives feedback signal, then carries out data process, provides control signal；Interface board Card uses PMC-16AIO board, and it is 16 simulation input/output boards, and simulation computer passes through it and driver communication；Drive Dynamic device is that piezoelectric ceramics locating platform matching used E-709Digital Piezo Controller controls driver, and it props up Hold Analog control and analog feedback, carry out upstream communication with computer card, and directly drive locating platform；Simulation For piezoelectric ceramic actuator.Analogue system master-plan is as shown in Figure 3.

As it can be seen, system is divided into four parts: iHawk simulation computer, interface board, E-709 Digital Piezo Controller, piezoelectric ceramics locating platform.Board is equipped with A/D, D/A conversion completing 300,000 conversions per second Device.Simulation input and output voltage range of signal is configurable on ± 2.5V, ± 5V, ± 10V.

E-709 digitial controller is responsible for amplifying control signal and the collecting sensor feedback signal that computer provides.It connects Receive from iHawk simulation computer 0～10V voltage signal, and be translated into-30～130V voltage signal driving pressure starts Device.On feedback channel, 0～100 μm position signallings of piezoelectric actuator are converted into 0～10V voltage signal and send back to iHawk Computer.

Owing to the output voltage range of board is 0～10V, corresponding to driving voltage is-30～130V, and relation is as follows:

Piezoelectric actuator required voltage scope is 0～100V, from formula (17), works as U_DriveSpan be [0, 100] time (V), U_BoardSpan be [1.875,8.125], and the output area of emulation controller is also [0,10], so Make such as down conversion:

U_Board=0.625U_con+1.875 (18)

Then having, when controller output scope is [0,10], corresponding driving voltage is [0,100] (V).

Piezoelectric ceramics locating platform is the P-611.2s High Precision Piezoelectric Ceramic of physik instrumente company of Germany Locating platform, full stroke is 100 μm, and driving voltage is-20～120 (V), and general load is+15/-5 (N), and built-in resistor strains Sheet type sensor, can be converted into the voltage signal of 0～10V by the displacement signal of 0～100 μm.

Controller parameter: first determine control cycle T, disturbance estimator estimates that the effective premise of disturbance is to control frequency Rate system dynamics to be faster than, this just requires that the control cycle is the least, but on the other hand, sensor, with noise, is being asked During differential signal, the less control cycle can cause bigger error, causes controlling effect and is deteriorated, comprehensive above 2 considerations, Selecting herein to control frequency is 10kHz, meanwhile, is filtered sensor signal processing.Remaining controls parameter through the most whole Surely it is listed in table.Hysteresis compensation+proportional plus integral control is the matched group in order to contrast experiment effect of the present invention.

Table 2 controller parameter

Fig. 4,5,6 are experimental result picture.Wherein, Fig. 4 is the maximum that different unifrequency sinusoidal signal inputs lower two kinds of methods Absolute error comparison diagram.Fig. 5,6 it is under composite input signal, the actual displacement of two kinds of methods and Error Graph thereof.Wherein, Dark grey Representing expectation displacement, black represents actual displacement, and light gray represents displacement error.Abscissa represents the time, and unit is the second.Vertical seat Being designated as the error of displacement or displacement, unit is μm.Under composite signal encourages, both maximum absolute displacement errors are respectively It is 3.1 μm and 28 μm.Meanwhile, the controlling curve of proportional plus integral control system has obvious Phase delay.

Shown in Fig. 4,5,6, control system control accuracy proposed by the invention is high, and the change to system lagging characteristics has Well adapting to property, still has the strongest tracking ability to changing fast signal.

In sum, these are only presently preferred embodiments of the present invention, be not intended to limit protection scope of the present invention. All within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. made, should be included in the present invention's Within protection domain.

Claims (4)

1. the displacement control method of a piezoelectric ceramic actuator, it is characterised in that comprise the steps:

Step 1, uses hysteresis compensation device based on static Hysteresis Model to carry out the dynamic hysteresis behavior of piezoelectric ceramic actuator Feedforward hysteresis compensation；

Step 2, with the interference sum of the compensation error of hysteresis compensation device, the model error setting up Hysteresis Model and the unknown be Total disturbance Ψ (t), utilizes disturbance estimator total disturbance Ψ (t) to be estimated, and by total disturbance estimated result Ψ_estimated(t) Feed back to sliding mode controller；

Step 3, utilizes sliding mode controller that the piezoelectric ceramic actuator after step 1 feedovers hysteresis compensation is carried out Bit andits control.

2. the displacement control method of piezoelectric ceramic actuator as claimed in claim 1, it is characterised in that in described step 1, quiet State Hysteresis Model is Bouc-Wen static state Hysteresis Model.

3. the displacement control method of piezoelectric ceramic actuator as claimed in claim 2, it is characterised in that in described step 1, first First with Bouc-Wen static state Hysteresis Model, the dynamic hysteresis behavior of piezoelectric ceramic actuator is modeled, then utilizes particle Colony optimization algorithm carries out identification to the model parameter of Bouc-Wen static state Hysteresis Model, it is thus achieved that Bouc-Wen static state Hysteresis Model.

4. the displacement control method of piezoelectric ceramic actuator as claimed in claim 1 or 2, it is characterised in that described step 3 In, the sliding-mode surface s of described sliding mode controller is proportional integral type, i.e.

$s=\stackrel{\&CenterDot;}{e}+ce---\left(1\right)$

Wherein, e is the displacement expected value x of piezoelectric ceramic actuator_dWith the difference of actual value x, c is controller scale parameter, for warp Test parameter, c > 0；

First in the case of not considering total disturbance Ψ (t), obtain the dynamic of sliding-mode surface

$\stackrel{\&CenterDot;}{s}=-ks-\mathrm{\&epsiv;}\mathrm{sgn}\left(s\right)---\left(2\right)$

Wherein, k and ε is controller parameter；K is empirical value；Sgn () is switch function；

Then in the case of having total disturbance Ψ (t), sliding-mode surface is dynamically

$\stackrel{\&CenterDot;}{s}=-ks-\mathrm{\&epsiv;}\mathrm{sgn}\left(s\right)+{\mathrm{\&Psi;}}_{actual}\left(t\right)-{\mathrm{\&Psi;}}_{estimated}\left(t\right)---\left(3\right)$

Wherein, Ψ_actualT () is actual disturbance term, Ψ_estimatedT () is the disturbance term estimated；

Then control rate u of sliding mode controller based on disturbance estimator is:

$u=-\frac{1}{c}\{\frac{1}{k}\&lsqb;-\mathrm{\&epsiv;}\mathrm{sgn}\left(s\right)-c\stackrel{\&CenterDot;}{e}-\stackrel{\&CenterDot;\&CenterDot;}{e}\&rsqb;-\stackrel{\&CenterDot;}{e}\}+e\left(t\right)+u(t-T)$

Wherein, t is for currently to control the moment, and u (t-T) is the controlled quentity controlled variable in previous control cycle.