CN111172196A - Precise extraction and injection method of micro-injection system based on micro-vision improved self-adaptive control - Google Patents

Precise extraction and injection method of micro-injection system based on micro-vision improved self-adaptive control Download PDF

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CN111172196A
CN111172196A CN202010019969.9A CN202010019969A CN111172196A CN 111172196 A CN111172196 A CN 111172196A CN 202010019969 A CN202010019969 A CN 202010019969A CN 111172196 A CN111172196 A CN 111172196A
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方勇纯
樊志
孙明竹
赵新
武毅男
刘存桓
王超
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Abstract

A microscopic injection system accurate extraction and injection method based on microscopic vision improved adaptive control is disclosed. The method comprises the steps of firstly, considering the characteristics of all parts including an image algorithm, an air pump, operated cells and manipulated microneedles in a system, and establishing a corresponding mathematical model for the whole system; secondly, because each parameter in the model is difficult to accurately and conveniently obtain, the invention is assisted with track tracking, designs an adaptive control algorithm for improving the updating law, completes the high-efficiency control of microinjection, has better robustness to the uncertainty of the parameters in the whole experimental process, has no overshoot of the system, and effectively inhibits the damage to the operated object. Compared with the traditional adaptive control and high-frequency robust control, the method of the invention has the advantages of higher convergence rate and shorter regulation time than the controller. Finally, the stability of the method is proved by the Lyapunov stability theory and the Lassel invariance principle.

Description

Precise extraction and injection method of micro-injection system based on micro-vision improved self-adaptive control
Technical Field
The invention belongs to a control system-microinjection system in the field of micro-nano science and technology, and mainly relates to the establishment of an integral mathematical model of the system and the design of a corresponding controller.
Background
Nuclear transfer is considered one of the most prominent achievements in biological experiments, and microinjection and extraction (IE) are the most critical steps in the process [1-4 ]. In order to improve the efficiency of microinjection and extraction and increase the survival rate of cells, many researchers have put great efforts into the field. These efforts have been largely achieved so far, for example, some automated operations such as cell positioning [5-6], cell alignment [7], cell pose adjustment [8-11], etc. have been introduced into the IE process. However, as of today, the most critical start and stop steps of the IE procedure are still manually operated by researchers [12], often exhibiting the disadvantages of low precision, high repetition error, long training time required, etc. Therefore, it is highly desirable to introduce automation into the IE process, particularly precise control of injection and extraction, which will help improve the success of the experiment, facilitate cell nucleus transplantation-based bio-cloning techniques, and also enhance human understanding [13 ]. In addition, the control time of the IE process should be as short as possible to ensure that the whole IE process is completed quickly enough to ultimately ensure sufficient cellular biological activity, which is extremely important for a successful cloning experiment.
Recently, a great deal of research has been conducted on the aforementioned problems [14 ]. These studies have focused on improvements in hardware facilities in systems including system architecture optimization [15-19], better-performing physical devices [20-21] and sensors [22-23], and the like, to ensure more accurate state measurements by the system. Obviously, such hardware adjustments generally imply greater expense and greater difficulty of installation. At the same time, advanced control algorithms that improve system performance have been relatively less studied [24-25 ]. In fact, the variants of proportional-integral-derivative (PID), proportional-integral (PI), proportional-derivative (PD) and PID remain the most prevalent control methods in IE systems today, and the performance of such controllers is difficult to guarantee in the presence of uncertainty in the system. Based on these considerations, it is important to design various advanced control algorithms such as sliding mode control, adaptive control, learning control, etc. for the IE system.
Disclosure of Invention
The present invention aims to solve the above problems of course in IE procedures and proposes a precise extraction and injection method with improved adaptive control using microscopic vision as feedback. Specifically, the characteristics of links such as micro-needles, cells, an air pump, a stepping motor and the like in the system are fully considered, and a comprehensive mathematical model is constructed for the system. By noticing the requirement of no overshoot in the control process, the invention designs a smooth track for tracking control. After that, in order to solve the uncertainty presented in the IE process, an adaptive controller for improving the updating law is designed, and the global asymptotic convergence control is completed when the uncertainty exists in the system parameters. The performance of the controller is fully proved by theory, simulation and actual experiment, and has better performance than the traditional adaptive control and high-frequency robust control.
Technical scheme of the invention
The precise extraction and injection method of the micro-injection system based on the micro-vision improved self-adaptive control comprises the following specific implementation steps:
1, respectively researching the characteristics of each component of a microinjection system, respectively establishing a mathematical model of input and output relations, and finally converging and summarizing the mathematical models into an air pressure driven injection microneedle damping model;
the whole microinjection system is composed of a plurality of submodules and links, and will act on cells. In these links, there is a part that can be easily modeled by existing theories, for example, a theoretical model can be created for a pneumatic pump according to the Boyed theorem and the characteristics of incompressible gas; there are also unknown portions, such as the relationship between the intracellular pressure and the amount of change in cell volume. Therefore, corresponding mathematical models are respectively established by adopting a reasonable method aiming at different links in the system; finally converging and summarizing into an air pressure driven injection microneedle damping model;
1.1, determining the relationship between intracellular pressure and the amount of change in cell volume:
since the relationship between intracellular pressure and cell volume is not clear, it is difficult to obtain a very accurate model; however, since intracellular pressure is closely related to cell volume, which continuously changes with intracellular pressure, it can be assumed that intracellular pressure PcellIs a continuous non-linear function P of the cell volumecell=f(V0+ Δ V), where f (·) is a non-linear function, V0Is the initial volume of the cell and Δ V is the amount of change in cell volume. P can be obtained by Taylor expansioncell=a0+a1ΔV+a2(ΔV)2+a3(ΔV)3+ … wherein, a0,a1,a2,a3… are constant coefficients, i.e., the intracellular pressure can be approximated using a higher order polynomial of the amount of change in cell volume.
1.2, determining the dynamic characteristic characterization of liquid in the injection microneedle:
fully considering the action of the liquid to be injected in the injection microneedle, including the pressure exerted by a pneumatic pump/intracellular fluid, the capillary force, the elastic force exerted by the microneedle wall and the viscous resistance of the liquid, and constructing a dynamic model of the liquid in the microneedle by using the classical Newtonian mechanics,
Figure BDA0002360340330000031
wherein
Figure BDA0002360340330000032
1.3, establishing a relation between the rotating speed input and the output pressure of a motor of the pneumatic pump:
in the designed microinjection control system, the expected air pressure cannot be directly applied, but the position of a piston in the air pressure pump is controlled by a stepping motor, so that the applied air pressure is indirectly controlled; the speed n of the stepper motor can therefore be obtained by reasonable simplification, based on the assumption of incompressible air, using Boyed's lawnWith change of air pressure Δ p and displacement Δ l of crescent surface3The relationship between them satisfies:
Figure BDA0002360340330000033
wherein k isp,kxP is the pump air pressure, a constant coefficient closely related to the system.
1.4, an air pressure driven injection microneedle damping model:
the sub-models obtained in sections 1.1, 1.2 and 1.3 are summarized to obtain an air pressure driven injection microneedle damping model, which is as follows:
Figure BDA0002360340330000034
2, designing an adaptive control method for improving an updating law based on the air pressure driven injection microneedle damping model of the microinjection system, and realizing efficient and stable control of the whole system;
2.1, determining a smooth tracking track:
in order to increase the robustness of the microinjection system, avoid the overshoot phenomenon of the system in the control process and accurately control the injection speed in the whole operation process, a smooth tracking track is introduced in the design of the controller; the mathematical expression is
Figure BDA0002360340330000035
Where v is the desired injection velocity, xfIs the final desired position, b0,b1,b2Is a parameter of a second order curve; specifically, at [ t0,t1]During a period of time, according to the desired injection rateSolving to obtain the moving speed of the crescent surface at (t)1,t2) Using a smooth second-order curve to make the crescent surface from t in the time period1Velocity of time of day
Figure BDA00023603403300000410
Slowly varying transition to t2At time t2And thereafter, the tracking trajectory is located at the desired position and the velocity is kept at zero; from the tracking trajectory at t1And t2The displacement and speed at the moment can be continuously solved to obtain t2And coefficients in the second order curve.
2.2, improving the adaptive controller design of the update law:
in the pneumatic driving injection microneedle damping model, known or easily-measured parameters exist, and parameters which are difficult to measure or even cannot be measured exist, so that the corresponding parameters are estimated by using an adaptive controller; in addition, in order to improve the response speed of the system, the update law of the system is correspondingly improved. In particular, the pneumatically driven injection microneedle damping model is abbreviated as
Figure BDA0002360340330000041
The adaptive controller for improving the update law and the corresponding update law are designed as follows:
and (3) improving self-adaptation:
Figure BDA0002360340330000042
Figure BDA0002360340330000043
Figure BDA0002360340330000044
wherein the symbols are defined as follows, except for the symbols already given definitions herein before:
p, k η are normal numbers and are used for adjusting the performance of the system,
Figure BDA0002360340330000049
gamma updated gain matrix
The first derivative is a uniformly continuous function with the global existence of
Y is a row vector consisting of known functions in the mathematical model of the system,
Figure BDA0002360340330000045
theta is a column vector composed of unknown constants in the mathematical model of the system,
θ=[c,ξ,an,an-1,…,a1,a0]T
Figure BDA0002360340330000046
estimation of theta
The stability and global convergence of the adaptive controller for improving the update law can be improved by selecting the Lyapunov candidate function as
Figure BDA0002360340330000047
The principle of Lassel invariance is combined to prove that, among them,
Figure BDA0002360340330000048
the invention has the advantages and beneficial effects that:
1. firstly, the dynamic characteristics of an air pump are analyzed, the dynamic characteristics and the rest parts of the system are taken into consideration, and a system air pressure driven injection microneedle damping model is established, so that the model is high in precision and provides a good basis for the design of a controller later;
2. based on trajectory tracking, an adaptive controller for improving the updating law is designed, the volume of injected cells can be accurately controlled when the parameters of a system model are uncertain, and the convergence speed is fast enough, so that the adaptive controller plays an important role in maintaining the activity of the cells. Moreover, the controller can inhibit the overshoot of the system, thereby avoiding unnecessary damage to the cells subjected to the nucleus removing operation and improving the survival rate of the cells;
3. the theory, simulation and computer experiment verify the good performance of the controller.
Description of the drawings:
FIG. 1 is a diagram of a microinjection control system and the relationship between each part, which is applied in the present invention, and includes the steps of firstly obtaining the state of an injection microneedle through a microscope camera, then calculating a corresponding control quantity through the method of the present invention, and applying the control quantity to an air pressure pump to control the injection microneedle, and finally indirectly controlling a target cell;
FIG. 2 is a schematic view of the structure of the injection microneedle and the air pump used in the present invention, and the overall result can be divided into three parts, wherein1Corresponding to the chamber portion of the pneumatic pump,/2Corresponding to the central airway segment,/3Corresponding to the injection microneedle portion;
FIG. 3 is a left graph of a tracking trajectory used in a simple piecewise function and a right graph of a smoothed tracking trajectory used in the present invention;
fig. 4 is a flow chart of the algorithm of the control software in the present invention.
FIG. 5 is a simulation output of the system in the present invention when the initial estimation error is small; wherein, (a) is the tracking situation of the traditional adaptive control, the improved adaptive control and the high-frequency robust control to the track, (b) is the tracking error of the three controllers, and (c) is the tracking error of the improved adaptive controller
Figure BDA0002360340330000051
The variation of (2).
FIG. 6 is a simulation output of the system when the initial estimation error is large in the present invention; wherein, (a) is the tracking situation of the traditional adaptive control, the improved adaptive control and the high-frequency robust control to the track, (b) is the tracking error of the three controllers, and (c) is the tracking error of the improved adaptive controller
Figure BDA0002360340330000052
The variation of (2).
FIG. 7 is a gray image obtained by a CCD in an on-machine experiment according to the present invention; wherein, (1) is the object to be manipulated, (2) is the crescent surface, (3) is the microneedle used for injection;
FIG. 8 is a vision algorithm used in the present invention; the image processing method comprises the steps of (a) obtaining an original image, (b) obtaining a result after binarization, and (c) enabling the upper part to be an interested area extracted from the (b) and the lower part to be foreground pixels of a corresponding column;
FIG. 9 is a graph showing the results of the on-machine experiment of the present invention; where (a) is the tracking of the track and (b) is the corresponding tracking error map.
Detailed Description
The experimental environment is Windows 7, the used programming language is C + +, and the integrated development environment is Visual Studio 2010; the experimental platform hardware part consists of a Nikon Tie microscope, a CCD of German BaslerAG series, a Beijing Weinsi stepper motor, a Japanese metallocene IM9B injector and a self-made micro-needle group, and the software part consists of a corresponding SDK and an independently written program code and completes the real-time control of the injection and extraction processes together.
Example 1
The accurate extraction and injection method of the micro-injection system based on the micro-vision improved self-adaptive control is shown in the figure 4.
The method comprises the following specific steps:
1, respectively researching the characteristics of each component of a microinjection system, respectively establishing a mathematical model of input and output relations, and finally converging and summarizing the mathematical models into an air pressure driven injection microneedle damping model;
as shown in FIG. 1, the entire microinjection system is composed of many submodules and segments, and will act on cells. In these links, there is a part that can be easily modeled by existing theories, for example, a theoretical model can be created for a pneumatic pump according to the Boyed theorem and the characteristics of incompressible gas; there are also unknown portions, such as the relationship between the intracellular pressure and the amount of change in cell volume. Therefore, corresponding mathematical models are respectively established by adopting a reasonable method aiming at different links in the system; finally converging and summarizing into an air pressure driven injection microneedle damping model;
1.1, determining the relationship between intracellular pressure and the amount of change in cell volume:
since the relationship between intracellular pressure and cell volume is not clear, it is difficult to obtain a very accurate model; however, since intracellular pressure is closely related to cell volume, which continuously changes with intracellular pressure, it can be assumed that intracellular pressure PcellIs a continuous non-linear function P of the cell volumecell=f(V0+ Δ V), where f (·) is a non-linear function, V0Is the initial volume of the cell and Δ V is the amount of change in cell volume. P can be obtained by Taylor expansioncell=a0+a1ΔV+a2(ΔV)2+a3(ΔV)3+ … wherein, a0,a1,a2,a3… are constant coefficients, i.e., the intracellular pressure can be approximated using a higher order polynomial of the amount of change in cell volume.
1.2, determining the dynamic characteristic characterization of liquid in the injection microneedle:
fully considering the action to which the liquid to be injected in the injection microneedle shown in fig. 2 includes the pressure exerted by the pneumatic pump/intracellular fluid, the capillary force, the elastic force exerted by the microneedle wall, and the viscous resistance to which the liquid is subjected, and constructing a dynamic model of the liquid in the microneedle by using the classical newton mechanics,
Figure BDA0002360340330000071
wherein
Figure BDA0002360340330000072
1.3, establishing a relation between the rotating speed input and the output pressure of a motor of the pneumatic pump:
in the designed microinjection control system, the desired air pressure cannot be directly applied, but the air pressure pump is controlled by the stepping motorThe position of the middle piston, thereby indirectly controlling the applied air pressure; the speed n of the stepper motor can therefore be obtained by reasonable simplification, based on the assumption of incompressible air, using Boyed's lawmWith change of air pressure Δ p and displacement Δ l of crescent surface3The relationship between them satisfies:
Figure BDA0002360340330000073
wherein k isp,kxP is the pump air pressure, a constant coefficient closely related to the system.
1.4, an air pressure driven injection microneedle damping model:
the sub-models obtained in sections 1.1, 1.2 and 1.3 are summarized to obtain an air pressure driven injection microneedle damping model, which is as follows:
Figure BDA0002360340330000074
2, designing an adaptive controller for improving an updating law based on the air pressure driven injection microneedle damping model of the microinjection system, and realizing an efficient and stable control scheme for the whole system;
2.1, determining a smooth tracking track:
in order to increase the robustness of the system, avoid the overshoot phenomenon of the system in the control process and accurately control the injection speed in the whole operation process, a smooth tracking track as shown in fig. 3 is introduced in the design of the controller; the mathematical expression is
Figure BDA0002360340330000081
Where v is the desired injection velocity, xfIs the final desired position, b0,b1,b2Is a parameter of a second order curve; specifically, at [ t0,t1]During the time period, the moving speed of the crescent surface is obtained by solving according to the expected injection speed, and the moving speed is (t)1,t2) Using a smooth second-order curve to make the crescent surface from t in the time period1Of time of daySpeed of rotation
Figure BDA0002360340330000088
Slowly varying transition to t2At time t2And thereafter, the tracking trajectory is located at the desired position and the velocity is kept at zero; from the tracking trajectory at t1And t2The displacement and speed at the moment can be continuously solved to obtain t2And coefficients in the second order curve.
2.2, improving the adaptive controller design of the update law:
in the system model, known or easily-measured parameters exist, and the parameters are difficult to measure or even cannot be measured, so that the corresponding parameters are estimated by using an adaptive controller; in addition, in order to improve the response speed of the system, the update law of the system is correspondingly improved. In particular, the pneumatically driven injection microneedle damping model is abbreviated as
Figure BDA0002360340330000082
The adaptive controller for improving the update law and the corresponding update law are designed as follows:
and (3) improving self-adaptation:
Figure BDA0002360340330000083
Figure BDA0002360340330000084
Figure BDA0002360340330000085
wherein the symbols are defined as follows, except for the symbols already given definitions herein before:
p, k, η are normal numbers and are used for adjusting the performance of the system,
Figure BDA0002360340330000086
gamma updated gain matrix
Satisfies χ (e) e ≧ 0, and the first derivative exists globally and is consistent and continuous
χ(e)
Function(s)
Y is a row vector consisting of known functions in the mathematical model of the system,
Figure BDA0002360340330000087
theta is a column vector composed of unknown constants in the mathematical model of the system,
θ=[c,ξ,an,an-1,…,a1,a0]T
Figure BDA0002360340330000091
estimation of theta
The stability and global convergence of the adaptive controller for improving the update law can be improved by selecting the Lyapunov candidate function as
Figure BDA0002360340330000092
The principle of Lassel invariance is combined to prove that, among them,
Figure BDA0002360340330000093
no. 3, control method implementation
As shown in fig. 8, an open source OpenCV library is used to binarize an acquired image, and the number of pixels belonging to the foreground is counted in columns, where a step point exists, that is, the position x of the corresponding crescent surface can be obtained; the corresponding speed can be obtained by passing the position through a differentiator with a low-pass filter
Figure BDA0002360340330000094
Incorporating a known tracking trajectory xdAnd derivatives thereof
Figure BDA0002360340330000095
Figure BDA0002360340330000096
And the estimated value of the initial setting
Figure BDA0002360340330000097
Equivalently, generating corresponding control output u according to the control algorithm given in the steps 1 and 2, and updating corresponding parameter estimation
Figure BDA0002360340330000098
A good control result can be achieved.
4, description of simulation and experiment effects
4.1 th simulation results
This section has performed simulation verification of the improved adaptive control of the present invention. Selecting the cell volume change of 4.1 × 10-12L, the corresponding shift position of the crescent surface is 6.56 multiplied by 10-4And m, constructing a corresponding tracking track, estimating the relation between the intracellular pressure and the cell volume change by using a third-order polynomial, and estimating all parameters and estimation in an air pressure driven injection microneedle damping model for improving adaptive control as follows:
Figure BDA0002360340330000099
the simulation result is shown in fig. 5, and it can be seen that in (a), the crescent surface position completely coincides with the position of the tracking track in about 1.8s, and thereafter the moving speed coincides with the expected track, and no overshoot occurs in the whole control process; (b) is a corresponding tracking error map; (c) and (3) for the variation trend of the estimated value of one parameter, after the tracking track is static, the tracking error is zero, and the parameter estimation is stopped to update. To further verify the reliability of the method of the present invention, an initial estimate was further selected as
Figure BDA0002360340330000101
The simulation results are shown in fig. 6, and the same analysis results as those in fig. 5 can be obtained.
4.2, results of the experiment
In an actual experiment, an image acquired from the CCD is as shown in fig. 7, and the required position and speed information can be obtained according to the method in step 3; and selecting each initial estimation and control parameter as:
Figure BDA0002360340330000102
the obtained control result is shown in fig. 9, in the experimental result diagram, the crescent surface reaches the designated position in about 5.5s, the designed control system can well inhibit overshoot, the response speed of the system is high, and the designed control system can flexibly adjust the control speed of the system by adjusting the tracking track.
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Claims (1)

1. The precise extraction and injection method of the micro-injection system based on the micro-vision improved self-adaptive control comprises the following specific implementation steps:
1, respectively researching the characteristics of each component of a microinjection system, respectively establishing a mathematical model of input and output relations, and finally converging and summarizing the mathematical models into an air pressure driven injection microneedle damping model;
the whole microinjection system is composed of a plurality of submodules and links and finally acts on cells, and in the links, a part which can be easily modeled through the existing theory and a part which has unknown mechanism exist, so that corresponding mathematical models are respectively established on the basis of physical laws aiming at different links in the system;
1.1, determining the relationship between intracellular pressure and the amount of change in cell volume:
since the relationship between intracellular pressure and cell volume is not clear, it is difficult to obtain a very accurate model; however, since intracellular pressure is closely related to cell volume, which continuously changes with intracellular pressure, it is assumed that intracellular pressure PcellIs a continuous non-linear function P of the cell volumecell=f(V0+ Δ V), where f (·) is a non-linear function, V0Is the initial volume of the cell, Δ V is the amount of change in cell volume; then P is obtained by Taylor expansioncell=a0+a1ΔV+a2(ΔV)2+a3(ΔV)3+ … wherein, a0,a1,a2,a3,.. is a constant coefficient, i.e. the intracellular pressure can be approximately fitted using a high order polynomial of the cell volume change;
1.2, determining the dynamic characteristic characterization of liquid in the injection microneedle:
fully considering the action of the liquid to be injected in the injection microneedle, including the pressure exerted by a pneumatic pump/intracellular fluid, the capillary force, the elastic force exerted by the microneedle wall and the viscous resistance of the liquid, and constructing a dynamic model of the liquid in the microneedle by using the classical Newtonian mechanics,
Figure FDA0002360340320000011
wherein
Month of xPosition of tooth surface
Figure FDA0002360340320000012
Speed and acceleration of crescent surface
m (x) liquid mass in microneedle c viscosity coefficient of culture
Pcell(x) Pressure exerted by intracellular fluid σ surface tension of the culture fluid
R (x) micro-needle radius β crescent surface contact angle with micro-needle wall at x
u pressure pi circumference ratio exerted by the pneumatic pump;
1.3, establishing a relation between the rotating speed input and the output pressure of a motor of the pneumatic pump:
in the designed microinjection system, the expected air pressure cannot be directly applied, but the position of a piston in the air pressure pump is controlled by a stepping motor, so that the applied air pressure is indirectly controlled; the speed n of the stepping motor is thus obtained by simplification using Boyed's law based on the assumption of incompressible airmWith change of air pressure Δ p and displacement Δ l of crescent surface3The relationship between them satisfies:
Figure FDA0002360340320000021
wherein k isp,kxIs a constant coefficient closely related to the system, p is the air pressure in the pump;
1.4, an air pressure driven injection microneedle damping model:
the sub-models obtained in sections 1.1, 1.2 and 1.3 are summarized to obtain an air pressure driven injection microneedle damping model, which is as follows:
Figure FDA0002360340320000022
2, designing an adaptive control method for improving an updating law based on the air pressure driven injection microneedle damping model of the microinjection system, and realizing efficient and stable control of the whole system;
2.1, determining a smooth tracking track:
in order to increase the robustness of the microinjection system, avoid the overshoot phenomenon of the system in the control process and accurately control the injection speed in the whole operation process, a smooth tracking track is introduced in the design of the controller, and the mathematical expression of the smooth tracking track is
Figure FDA0002360340320000023
Where v is the desired injection velocity, xfIs the final desired position, b0,b1,b2Is a parameter of a second order curve; specifically, at [ t0,t1]During the time period, the moving speed of the crescent surface is obtained by solving according to the expected injection speed, and the moving speed is (t)1,t2) Using a smooth second-order curve to make the crescent surface from t in the time period1Velocity of time of day
Figure FDA0002360340320000024
Slowly varying transition to t2At time t2And thereafter, the tracking trajectory is located at the desired position and the velocity is kept at zero; from the tracking trajectory at t1And t2The displacement and speed at the moment can be continuously solved to obtain t2And coefficients in the second order curve;
2.2, improving the adaptive controller design of the update law:
in the pneumatic driving injection microneedle damping model, known or easily-measured parameters exist, and parameters which are difficult to measure or even cannot be measured exist, so that the corresponding parameters are estimated by using an adaptive controller; in addition, in order to improve the response speed of the system, the update law of the system is correspondingly improved, and the pneumatic-driven injection microneedle damping model is abbreviated as
Figure FDA0002360340320000031
The adaptive controller for improving the update law and the corresponding update law are designed as follows:
and (3) improving self-adaptation:
Figure FDA0002360340320000032
Figure FDA0002360340320000033
Figure FDA0002360340320000034
wherein the symbols are defined as follows, except for the symbols already given definitions herein before:
p, k η are normal numbers and are used for adjusting the performance of the system,
r
Figure FDA00023603403200000310
the gain matrix is updated by the gamma value,
satisfying the requirement of chi (e) e being more than or equal to 0, the first derivative exists globally and is consistent and continuous function,
y a row vector consisting of a known function in a pneumatically driven injection microneedle damping model,
Figure FDA0002360340320000035
theta is a column vector composed of unknown constants in the air pressure driven injection microneedle damping model,
θ=[c,ξ,an,an-1,…,a1,a0]T
Figure FDA0002360340320000036
estimation of theta
The stability and global convergence of the adaptive controller for improving the update law are improved by selecting the Lyapunov candidate function as
Figure FDA0002360340320000037
Figure FDA0002360340320000038
The principle of Lassel invariance is combined to prove that, among them,
Figure FDA0002360340320000039
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