A piezoelectric positioning platform noise reduction control method based on interference observation

Abstract

The application provides a piezoelectric positioning platform noise reduction control method based on disturbance observation, comprising the following steps: S1: establishing a transfer function model of a positioning platform driven by a piezoelectric driver; S2: combining the obtained transfer function model and a desired model to design a disturbance observer, and giving a parameter expression of a nominal model embedded in the disturbance observer; S3: designing a filter in a main feedback loop to reduce the response of the main loop to high-frequency measurement noise and modeling errors, and designing an anti-interference controller based on the disturbance observer; S4: giving conditions to be met for system stability, and selecting control parameters in combination with the anti-interference controller and the desired model. The application mainly aims at the influence of high-frequency modeling errors, environmental disturbances and measurement noise on piezoelectric positioning platform control, can improve the servo accuracy and robustness of the piezoelectric positioning platform, and is suitable for engineering application.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of precision tracking and precision motion control, and particularly relates to a piezoelectric positioning platform noise reduction control method based on disturbance observation, which is mainly used for servo tracking control with high bandwidth and high precision requirements. BACKGROUND

[0002] The piezoelectric positioning platform is a platform that completes precise displacement by the deformation of the piezoelectric actuator driving the mechanical part. In recent years, it has attracted extensive attention in the application fields of micro-nano manipulation, micro-robot and microscope scanning. The piezoelectric actuator has the advantages of fast dynamic response, large torque output and ultra-high resolution, and is therefore often used to drive the piezoelectric positioning platform. However, in the face of increasingly complex working conditions in the application field, the piezoelectric positioning platform is difficult to maintain its high bandwidth and high precision characteristics. The piezoelectric actuator is faced with the problem of mechanical resonance caused by weak damping, which not only affects the control accuracy but also shortens the service life of the system. Moreover, the bandwidth of the piezoelectric positioning platform is often limited to less than 0.1 times the first-order resonance frequency, which cannot quickly and precisely track high-frequency signals, limiting the improvement of the overall system dynamic performance.

[0003] The control system can coordinate the driving, sensing and mechanical parts of the piezoelectric positioning platform, and is the key to the performance limit of the whole platform. The existing resonance control method designs a damping controller based on an accurate model to reconfigure the system poles, which greatly depends on the accuracy of the system model. When the dynamic characteristics of the system change, the original control strategy cannot make the piezoelectric positioning platform have the desired performance. In addition, the piezoelectric positioning platform is also affected by multiple sources of disturbance such as high-frequency modeling error, environmental disturbance torque and piezoelectric nonlinear dynamics, which reduces the servo positioning accuracy. The measurement noise of the sensor in actual application also has a great influence on the control performance. SUMMARY

[0004] The present application mainly aims at the problems of weak damping, model uncertainty and measurement noise in the precise servo control of the piezoelectric positioning platform, and proposes a piezoelectric positioning platform noise reduction control method based on disturbance observation. In order to overcome the above technical problems, the present application first identifies the system parameters by the method of frequency sweep, and establishes the transfer function model of the positioning platform driven by the piezoelectric actuator; thereafter, according to the transfer function model obtained by identification and the expected model, a disturbance observer is designed, and the expected model is embedded into the disturbance observer, so as to simultaneously suppress the influence of weak damping and multiple sources of disturbance on the control performance and improve the robustness; on this basis, an active disturbance rejection tracking controller is designed to minimize the tracking error of the piezoelectric positioning platform, and a filter is designed in the main feedback loop to reduce the response of the system to high-frequency noise and modeling error; finally, the conditions that need to be met for the stability of the system are analyzed, and the parameters of the expected model and the variable gain controller are optimized.

[0005] To achieve the above object, the technical scheme adopted by the present application is as follows:

[0006] A piezoelectric positioning platform noise reduction control method based on disturbance observation, comprising the following steps:

[0007] S1: establishing a transfer function model of a positioning platform driven by a piezoelectric actuator;

[0008] S2: combining the identified transfer function model with the expected model to design a disturbance observer, and giving a parameter expression of the expected model embedded in the disturbance observer;

[0009] S3: designing a filter in the main feedback loop to reduce the response of the main loop to high-frequency measurement noise and modeling errors, and designing an anti-disturbance controller based on the disturbance observer;

[0010] S4: giving the conditions to be met for system stability, and selecting control parameters in combination with the anti-disturbance controller and the expected model.

[0011] (1) Specifically, the specific modeling process of S1 step is as follows:

[0012] A small-amplitude sinusoidal scanning signal of 0-10000 Hz is input to the input end of the piezoelectric positioning platform to excite the piezoelectric positioning platform, and the output displacement of the piezoelectric positioning platform corresponding to the input signal at each time is recorded. Due to the increasing complexity of calculation with the increase of model order, the piezoelectric positioning platform can be identified as a three-order continuous system transfer function model based on the input and output signals:

[0013]

[0014] Where s is the Laplace operator, G(s) is the transfer function model identified by the piezoelectric positioning platform, which can be regarded as a series connection of an inertia element and a two-order system, Y(s) is the Laplace transform of the output displacement, U(s) is the Laplace transform of the input voltage, a is the real pole of the model, ζ1 is the damping ratio of the two-order system, ω1 is the natural frequency of the two-order system, b0, b1, b2 are parameters related to the zero point in the system model. The upper and lower bounds of all parameters in G(s) are known, and the sign of b2 is determined. The weak damping dynamic characteristics of the piezoelectric positioning platform are mainly caused by the extremely small damping ratio ζ1 in the two-order system.

[0015] (2) Further, the specific design of the disturbance observer of step S2 is as follows:

[0016] The disturbance observer regards the external disturbance, model uncertainty and nonlinear dynamic characteristics of the controlled object as total disturbance, and realizes the observation and compensation of the disturbance by embedding the expected dynamic model and designing a low-pass filter. First, according to the three-order continuous system transfer function model identified in step S1, the expected model Gn (s) should be in the form of:

[0017]

[0018] a n ζ is the real pole of the desired model, n ω is the damping ratio of the second order system part of the desired model, n b is the natural frequency of the second order system part of the desired model, n0 b n1 b n2 is a parameter related to the zero of the desired model, where b n2 has the same sign as b2. On this basis, a filter Q(s) with low-pass characteristics is designed, which is in the form of:

[0019]

[0020] where τ represents the filter constant of the low-pass filter, N Q (s,τ) is the numerator of Q(s), D Q (s,τ) is the denominator of Q(s). The relative order of Q(s) is not less than the relative order of G n (s). The observation of the total disturbance can be expressed as:

[0021]

[0022] where, is the inverse of the desired model G n (s) embedded in the disturbance observer, y represents the displacement output measured by the sensor, and u represents the input of the piezoelectric positioning platform. Therefore, the compensated input of the positioning platform can be further expressed as:

[0023]

[0024] where u0 is the control output of the anti-disturbance controller.

[0025] (3) The specific design of the main feedback loop filter of step S3 and the anti-disturbance controller is as follows:

[0026] The displacement output y measured by the sensor is obtained by sensor measurement, which necessarily contains high-frequency measurement noise n, and the relationship between them can be expressed in the form of:

[0027] y = y r + n

[0028] where y r ​The displacement output of the actual system. In addition, the high frequency unmodeled dynamics of the system also affect the control performance, in order to avoid the excitation of the main loop controller to the high frequency part of the error between the measured output and the expected model output, a filter is designed to remove the high frequency part of the feedback signal. Therefore, the processed displacement output signal y l Can be expressed as:

[0029] y l = y - (1 - Q(s)) (y - uG n (s))

[0030] On the basis of the above processing, the input of the anti-interference controller C(s) is the tracking error e which can be expressed as:

[0031] e = r - y l

[0032] Where r is the reference input signal. The anti-interference controller should make the error have the following expected dynamics:

[0033]

[0034] e (i) Represents the i-th derivative of e. The part deviating from the above expected dynamics in the system is regarded as disturbance, which can be estimated in real time by the extended state observer. The above dynamics should be embedded in the observer. First, the above dynamics can be expressed in the following extended state space form:

[0035]

[0036] Where ω c Is the controller parameter to be determined, z1 represents e, z2 represents e (1) , z3 represents e (2) , z4 represents g, In turn, z1, z2, z3, z4, g is the derivative of g, which is the difference between the actual dynamics and the expected dynamics of the tracking error e, which can be expressed as:

[0037]

[0038] I = 0, 1, 2, j = 0, 1, 2

[0039] Where f is the dynamics of the tracking error e obtained according to G n (s), Contains the remaining disturbance after S2 compensation and the equivalent control amount caused by the reference input r.

[0040] Further write the above extended state space as an extended state observer as follows:

[0041]

[0042] are the observed values of z1, z2, z3, z4, respectively, and l1, l2, l3, l4 are the gain parameters of the observer, and the output of the disturbance controller is:

[0043]

[0044] Based on the above expression of the extended state observer, the characteristic equation of the observer can be derived as:

[0045]

[0046] Therefore, the gain parameters l1, l2, l3, l4 of the observer should be selected according to the following formula:

[0047] l1+3ω c = 4ω o

[0048]

[0049]

[0050]

[0051] where ω o is another parameter of the disturbance controller. Therefore, the output of the disturbance controller can be represented as:

[0052]

[0053] The transfer function of the disturbance controller C(s) can be represented as:

[0054]

[0055] The system stability condition of the step S4 and the selection of the controller and disturbance observer parameters are as follows:

[0056] From the perspective of the entire closed-loop control system, the stability condition is derived, and each part of the parameter needs to satisfy the following conditions:

[0057] 1) G n (s) is stable, that is, all its poles have negative real parts;

[0058] 2) is stable, and there is no zero-pole cancellation when calculating G n (s)C(s);

[0059] 3) G(s) is a minimum phase system;

[0060] 4) All zeros of p(s) generated by G(s) have negative real parts.

[0061] Where p(s) is G n b in (s) n2 b2 in G(s) and D in Q(s) Q (s,τ) and N Q (s,τ) is generated, where τ=1, and its specific form is shown below:

[0062]

[0063] Based on the stability conditions of the closed-loop system described above, the parameters of each component are determined to ensure G. n (s) Under the premise of stability, increase the damping ratio ζ of the second-order component. n The filter constant τ should be determined based on the resonant frequency of the piezoelectric positioning platform and the frequency band of the ambient noise. The anti-interference controller parameter ω... c The choice should be as large as possible, making it consistent with G. n ω in (s) n Similarly, the other parameter ω of the anti-interference controller is finally adjusted based on the control effect of the closed-loop system. o .

[0064] The beneficial effects of this invention are as follows:

[0065] 1. The method of the present invention can realize ultra-precision control of a type of system with weakly damped dynamic characteristics, represented by a piezoelectric positioning platform. It suppresses system oscillations by using an interference observer and an anti-interference controller, and reduces the impact of noise and high-frequency modeling errors on the overall control performance by adding a processing step for the measurement output.

[0066] 2. Compared with traditional PID control and resonant control methods, this invention addresses the weak damping problem and modeling error problem of the system by embedding the desired model into the disturbance observer. For residual disturbances that the disturbance observer cannot handle, an anti-interference controller is designed based on the error to further suppress the error caused by unknown dynamics and disturbances.

[0067] 3. Compared with ordinary robust control, this invention addresses high-frequency noise and high-frequency modeling errors by eliminating the high-frequency components of the measurement output that deviate from the expected model output, thereby suppressing the excitation of these high-frequency components by the main control loop. This invention primarily solves the problems of weak damping, multi-source interference, and measurement noise faced by systems such as piezoelectric positioning platforms. The proposed control method is more suitable for practical applications and exhibits stronger robustness and noise reduction effects. Attached Figure Description

[0068] Figure 1The flow chart of noise reduction control of the piezoelectric positioning platform based on disturbance observation of the present application.

[0069] Figure 2 The overall control block diagram of the present application.

[0070] Figure 3 The tracking effect diagram of the piezoelectric positioning platform on the step signal after inputting the step signal.

[0071] Figure 4 The relationship diagram of the reference signal and the output displacement after inputting the sine signal.

[0072] Figure 5 The relationship diagram of the reference signal and the output displacement after inputting the triangular wave signal.

[0073] Figure 6 The relationship diagram of the reference signal, the output displacement of the original system and the output displacement of the perturbed model G2 after the model of the piezoelectric positioning platform is perturbed.

[0074] Figure 7 The relationship diagram between the output displacement of the original system and the measured output. DETAILED DESCRIPTION

[0075] In order to make the objectives, technical solutions and advantages of the present application clearer and more comprehensible, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0076] As shown in Figure 1 The present application proposes a noise reduction control method of a piezoelectric positioning platform based on disturbance observation, which comprises the following steps:

[0077] Step S1: establishing a transfer function model of the positioning platform driven by the piezoelectric actuator.

[0078] A small-amplitude sine scanning signal of 1-10000 Hz is inputted to the input end of the piezoelectric positioning platform to excite the piezoelectric positioning platform. The output displacement corresponding to the input signal at each moment of the piezoelectric positioning platform is recorded. Since the calculation complexity will increase with the increase of the model order, the piezoelectric positioning platform can be identified as the following three-order continuous system transfer function model based on the input and output signals:

[0079]

[0080] where s is Laplace operator, G(s) is the transfer function model identified from the piezoelectric positioning platform, which can be regarded as a series connection of an inertia element and a second-order system, Y(s) is the Laplace transform of the output displacement, U(s) is the Laplace transform of the input voltage, a is the real pole of the model, ζ1 is the damping ratio of the second-order system, ω1 is the natural frequency of the second-order system, b0, b1, b2 are parameters related to the zero of the system model. The upper and lower bounds of all parameters in G(s) are known, and the sign of b2 is determined. The weak damping dynamic characteristics of the piezoelectric positioning platform are mainly caused by the extremely small damping ratio ζ1 in the second-order system.

[0081] Step S2: Design the disturbance observer combined with the identified transfer function model and the desired model, and give the parameter expression of the desired model embedded in the disturbance observer. The specific design steps are as follows:

[0082] The disturbance observer regards the external disturbance, model uncertainty and nonlinear dynamic characteristics of the controlled object as total disturbance, and realizes the observation and compensation of the disturbance by embedding the desired dynamic model and designing a low-pass filter. First, according to the third-order system model identified in step S1, the desired model G n (s) embedded in the disturbance observer should be as follows:

[0083]

[0084] a n is the real pole of the desired model, ζ n is the damping ratio of the second-order system part of the desired model, ω n is the natural frequency of the second-order system part of the desired model, b n0 , b n1 , b n2 are parameters related to the zero of the desired model, wherein b n2 has the same sign as b2. On this basis, a filter Q(s) with low-pass characteristics is designed, and the specific form is as follows:

[0085]

[0086] Where τ represents the filter constant of the low-pass filter, N Q (s, τ) is the numerator of Q(s), D Q (s, τ) is the denominator of Q(s). The relative order of Q(s) is not less than the relative order of G n (s). Then the observation of the total disturbance can be expressed as:

[0087]

[0088] Where G n-1(s) represents the desired model G in the embedded interference observer. n The reciprocal of (s), where y represents the displacement output measured by the sensor, and u represents the input of the piezoelectric positioning platform. Therefore, the input of the compensated positioning platform can be further expressed as:

[0089]

[0090] Where u0 is the control quantity output by the anti-interference controller.

[0091] Step S3: Design a filter in the main feedback loop to reduce the main loop's response to high-frequency measurement noise and modeling errors, and design an anti-interference controller based on the interference observer. The specific design steps are as follows:

[0092] The displacement output y measured by the sensor is obtained through sensor measurement, which inevitably contains high-frequency measurement noise n. The relationship between the two can be expressed as follows:

[0093] y = y r +n

[0094] Among them, y r This represents the displacement output of the actual system. In addition, unmodeled high-frequency dynamics of the system can also affect control performance. To avoid the excitation of high-frequency components in the error between the measured output and the desired model output by the main loop controller, a filter is designed to remove the high-frequency components from the feedback signal. Therefore, the processed displacement output signal y in the feedback path... l It can be represented as:

[0095] y l =y-(1-Q(s))(y-uG n (s))

[0096] Based on the above processing, the input of the anti-interference controller C(s), the tracking error e, can be expressed as:

[0097] e = ry l

[0098] Where r is the reference input signal. The anti-interference controller should ensure that the error has the following desired dynamics:

[0099]

[0100] e (i) Let represent the i-th derivative of e. Treating the deviations from the desired dynamics in the system as disturbances, these disturbances can be estimated in real time using an extended state observer. The dynamics described above should be embedded in the observer. Firstly, the dynamics can be expressed in the following extended state space form:

[0101]

[0102] where ω c is the controller parameter to be determined, z1 represents e, z2 represents e (1) , z3 represents e (2) , and z4 represents g, g is the difference between the actual dynamics of the tracking error e and the expected dynamics, which can be expressed as:

[0103]

[0104] i = 0, 1, 2, j = 0, 1, 2

[0105] where f is the dynamics of the tracking error e obtained according to G n (s), and contains the residual disturbance after S2 compensation and the equivalent control amount caused by the reference input r.

[0106] The above extended state space is further written in the form of an extended state observer as follows:

[0107]

[0108] are the observation values of z1, z2, z3, and z4, respectively, and l1, l2, l3, and l4 are the gain parameters of the observer, and the output of the anti-disturbance controller is:

[0109]

[0110] Based on the expression of the above extended state observer, the characteristic equation of the observer can be derived as:

[0111]

[0112] Therefore, the gain parameters l1, l2, l3, and l4 of the observer can be converted to the selection of a single parameter according to the following formula:

[0113] l1+ 3ω c = 4ω o

[0114]

[0115]

[0116]

[0117] where ω o is another parameter of the anti-disturbance controller. Therefore, the output of the anti-disturbance controller can be expressed as:

[0118]

[0119] The transfer function of the anti-interference controller C(s) can be expressed as:

[0120]

[0121] According to the above steps, the overall control block diagram can be obtained as Figure 2 .

[0122] Step S4: The conditions to be met for system stability are given, and the control parameters are selected in combination with the anti-interference controller and the desired model. The specific design steps are as follows:

[0123] The stability conditions are derived from the perspective of the entire closed-loop control system, and the parameters of each part need to meet the following conditions:

[0124] 1) G n (s) is stable, that is, all its poles have negative real parts;

[0125] 2) is stable, and there is no zero-pole pair cancellation when calculating G n (s)C(s);

[0126] 3) G(s) is a minimum phase system;

[0127] 4) All zeros of p(s) generated by G(s) have negative real parts.

[0128] Among them, p(s) is generated by b n 1 in G n2 (s), b2 in G(s) and D Q (s, τ) and N Q (s, τ) in Q(s), where τ = 1, and the specific form is as follows:

[0129]

[0130] Based on the stability conditions of the above closed-loop system, the parameters of each link are determined, and under the premise of ensuring the stability of G n (s), the damping ratio ζ n of the second-order link part is improved. The filter constant τ should be determined according to the resonant frequency of the piezoelectric positioning platform and the frequency band range of the environmental noise, the selection of the anti-interference controller parameter ω c should be as large as possible, which is the same as ω n in G n (s), and finally the other parameter ω o of the anti-interference controller is adjusted according to the control effect of the closed-loop system.

[0131] The simulation experiment of the application includes the following steps:

[0132] (1) Simulation setup:

[0133] In this example, the simulation step is set to 0.0001s (i.e. the sampling frequency is 10 kHz), and the total simulation time is 0.1s. The transfer function model of the piezoelectric positioning platform obtained by identification is After factorizing the characteristic polynomial, we can get According to the object model information, the parameters a of the desired model are selected n = -1.285 x 10 4 , ζ n = 0.881, ω n = 5.367 x 10 3 , b n0 = b0= 9.462 x 10 10 , b n1 = 1.149 x 10 6 , b n2 = 2379.7, then The filter constant of the filter is Then the transfer function is On this basis, the anti-interference controller parameters are selected as ω o = 9684, ω c = 8254.6. Then set the actual controlled object when the parameter perturbation occurs as The noise is generated by a random number module with a mean of 0 and a variance of 0.1 and a 10th order Butterworth high-pass filter with a cutoff frequency of 50000 rad / s.

[0134] (2) Step signal tracking

[0135] The input unit step signal is used as the tracking trajectory signal. The simulation is carried out to obtain the tracking effect of the piezoelectric positioning platform under this condition. Figure 3 The tracking effect of the piezoelectric positioning platform on the step signal after inputting the step signal.

[0136] (3) Sine reference signal tracking:

[0137] First, the amplitude of the sine wave signal is 1 μrad, and the frequency is 50 Hz. The sine wave signal is used as the tracking trajectory signal. The simulation is carried out to obtain the tracking effect of the piezoelectric positioning platform under this condition. Figure 4 The tracking effect diagram of the reference signal and the output displacement.

[0138] (4) Triangle wave signal tracking and noise and interference suppression effect;

[0139] The amplitude of the triangle wave signal is 2 μrad, and the frequency is 50 Hz. The triangle wave signal is used as the tracking trajectory signal. The simulation is carried out to obtain the tracking effect of the piezoelectric positioning platform under this condition. Figure 5The tracking effect diagram of the reference signal and the output displacement.

[0140] Figure 6 The relationship diagram of the reference signal, the output displacement of the original system and the output displacement of the perturbed model G2 after the parameter perturbation of the piezoelectric positioning platform model, and the relative error is not more than 1.7%.

[0141] Figure 7 The relationship diagram of the output displacement of the original system and the measured output. It has a very strong noise suppression capability.

[0142] Those skilled in the art will easily understand that the above description is only a preferred embodiment of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A piezoelectric positioning platform noise reduction control method based on interference observation, characterized in that, The method comprises the following steps: S1: establishing a transfer function model of a piezoelectric actuator driven positioning platform; S2: combining the identified transfer function model with a desired model to design a disturbance observer, and giving a parameter expression of the desired model embedded in the disturbance observer; S3: designing a filter in a main feedback loop to reduce the response of the main loop to high-frequency measurement noise and modeling errors, and designing an anti-disturbance controller based on the disturbance observer; S4: giving conditions to be met for system stability, and selecting control parameters in combination with the anti-disturbance controller and the desired model; The specific modeling process of the S1 step is as follows: A small-amplitude sinusoidal scanning signal of 0-10000 Hz is input to the input end of the piezoelectric positioning platform to excite the piezoelectric positioning platform, and the output displacement of the piezoelectric positioning platform corresponding to the input signal at each time is recorded. Due to the increasing complexity of calculation with the increase of the model order, the piezoelectric positioning platform can be identified as a three-order continuous system transfer function model based on the input and output signals as follows: where s is the Laplace operator, The transfer function model identified for the piezoelectric positioning stage can be considered as a series connection of an inertia element and a second-order system, is the Laplace transform of the output displacement, is the Laplace transform of the input voltage, are the real poles of the model, is the damping ratio of the second-order system, is the natural frequency of the second-order system, , , are the parameters related to the zeros of the system model, The upper and lower bounds of all the parameters in are known, and The sign of is determined, and the weakly damped dynamic characteristics of the piezoelectric positioning stage are caused by the small damping ratio of the second-order system. The specific design of the disturbance observer of the step S2 is as follows: The disturbance observer regards the external disturbance, the model uncertainty and the nonlinear dynamic characteristics of the controlled object as total disturbance, and realizes the observation and compensation of the total disturbance by embedding the expected dynamic model and designing a low-pass filter. First, according to the three-order continuous system transfer function model identified in the S1 step, the expected model embedded in the disturbance observer should be Should be as follows: a real pole of the desired model, a damping ratio of the second order system part of the desired model, a natural frequency of the second order system part of the desired model, , , a parameter related to a zero of the desired model, where has the same sign as , on the basis of which a filter having a low-pass characteristic is designed, which has the following specific form: wherein the filter constant representing this low-pass filter, is the numerator of is the denominator of the relative order of the relative order of the observation of the total interference can be expressed as: wherein, is the inverse of the desired model embedded in the disturbance observer is the inverse of the desired model embedded in the disturbance observer represents the displacement output of the sensor measurement, represents the input to the piezoelectric positioning stage, thus, the input to the positioning stage can be further expressed as: wherein is the control quantity output by the disturbance rejection controller; The specific design of the main feedback loop filter and the anti-disturbance controller of the step S3 is as follows: The displacement output measured by the sensor is obtained by the sensor measurement, which inevitably contains high-frequency measurement noise The relationship between the two can be expressed as follows: wherein, The displacement output of the actual system, in addition to this, the system high frequency unmodeled dynamics will also affect the control performance, in order to avoid the excitation of the main loop controller to the high frequency part of the error between the measured output and the expected model output, a filter is designed to remove the high frequency part in the feedback signal, therefore, the processed displacement output signal in the feedback channel Can be expressed as: On the basis of the above processing, the anti-interference controller The input of the anti-interference controller may be expressed as: wherein, is the reference input signal, the anti-jamming controller should make the error has the following desired dynamics: representing the first derivative, the part of the system deviating from the above desired dynamics is regarded as disturbance, which can be estimated in real time by the extended state observer. The above dynamics should be embedded in the observer. First, the above dynamics can be expressed in the following extended state space form: wherein is the controller parameter to be determined, represents , represents , represents , represents , , , , , in turn are , , , , the derivative of is the difference between the actual dynamics and the desired dynamics of the tracking error , which can be expressed in particular as wherein is obtained by subtracting the estimated disturbance from the reference input and the dynamic of the tracking error contains the residual disturbance after compensation in step S2 and the equivalent control resulting from the reference input ​ Further, the above extended state space is written as an extended state observer as follows: 、 、 、 are the observation values of 、 、 、 、 、 、 is the gain parameter of the observer, and the output of the disturbance rejection controller is​ Based on the expression of the above extended state observer, the characteristic equation of the observer can be derived as follows: Therefore, the gain parameters l1, l2, l3, l4 of the observer should be selected according to the following formula: wherein, is another parameter of the anti-interference controller, and thus the output of the anti-interference controller can be expressed as: Anti-jamming controller The transfer function of the anti-jamming controller can be represented as: 。 2. The piezoelectric positioning stage noise reduction control method based on disturbance observation according to claim 1, wherein, The system stability conditions, controller and disturbance observer parameter selection of the step S4 are as follows: From the perspective of the entire closed-loop control system, the stability conditions are derived, and the parameters of each part need to meet the following conditions: 1) is stable, i.e. all its poles have negative real parts; 2) is stable and does not have a zero-pole cancellation situation when calculating the transfer function 3) is a minimum phase system; 4) by generated All zeros have negative real parts; wherein from in , in and in and wherein , in particular, as follows: Based on the stability condition of the closed loop system, parameters of each link are determined, under the premise of ensuring the stability, the damping ratio of the second order link part is improved , the filter constant should be determined according to the resonant frequency of the piezoelectric positioning platform and the frequency band range of the environmental noise, the selection of the anti-interference controller parameter should be as large as possible, so that it is the same as in , and finally the other parameter of the anti-interference controller is adjusted according to the control effect of the closed loop system .

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