Three-dimensional permanent magnet closed-loop control system

Abstract

The invention discloses a three-dimensional permanent magnet closed-loop control system, which is used for an XY plane-Z direction decoupling type single-magnetic-pole single-magnetic-bead, and comprises a guide permanent magnet driving module, an image acquisition and processing module, a motion control module and a controller, the controller, the motion control module and the guide permanent magnet driving module are connected in sequence, and the image acquisition and processing module is connected with the output end of the guide permanent magnet driving module and the input end of the controller; and the controller controls the motion control module to calculate and guide the permanent magnet driving module to output a new position point of the magnetic bead according to the received actual position and expected path point of the magnetic bead so as to drive the magnetic bead to move. By means of feedback linearization control, control errors caused by non-linear terms in traditional PID control are avoided, and the magnetic bead motion control capacity of the system is improved. The one-dimensional, two-dimensional and three-dimensional path tracking capability of the system is proved, and the magnetic bead can be controlled to perform cable-free and contact-free high-precision control in a complex three-dimensional narrow space.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic bead motion control, specifically to a three-dimensional permanent magnet closed-loop control system, and more specifically to an XY plane - Z direction decoupled single-magnet-pole and single-magnetic-bead three-dimensional motion control system. Background Art

[0002] Magnetic micro-robots have the advantages of small size, cable-free driving, and high controllability. They can enter the interior of complex human tissues (such as extracellular fluid, lymphatic fluid, cerebrospinal fluid, synovial fluid, aqueous humor, etc.) where existing invasive medical devices and traditional surgical robots are difficult to reach. It is expected to minimally or non-invasively enter the human tissue interior through complex and narrow cavity-type spaces (zones) to carry out biomedical applications such as targeted delivery and in-situ diagnosis and treatment.

[0003] However, the high-precision and high-reliability requirements of biomedical applications pose various demands on the driving system of magnetic micro-robots, including but not limited to driving ability, stability, real-time performance, and accuracy. Among them, the driving ability is mainly related to the driving magnetic field distribution, mainly including parameters such as magnetic field strength, magnetic field gradient, and working space size, as well as the spatial and temporal variation characteristics of the three. Stability, real-time performance, and accuracy are mainly related to the hardware composition and control algorithm of the driving system. In addition, how to improve the energy and cost efficiency during the manufacturing and use processes of the magnetic micro-robot system, and the mass of the micro-robot that can be driven (i.e., the load capacity of the driving magnetic field) are important considerations.

[0004] The driving methods of magnetic micro-robots can be divided into permanent magnet driving and / or electromagnetic driving. Among them, electromagnetic driving uses programmed current to achieve a controllable time-varying spatial distribution of the external magnetic field. Generally, a multi-mode spatial combination of Helmholtz and Maxwell coils can be used to achieve a magnetic field distribution with uniform magnetic field intensity / gradient, and a multi-mode spatial combination of solenoid coils (soft magnetic excitation materials can be embedded inside) can be used to achieve a time-varying gradient magnetic field distribution. The electromagnetic driving method has the advantages of simple magnetic field distribution modeling and high control precision, and can realize the closing and opening of the driving magnetic field. However, the magnetic field generated by its excitation is 2-3 orders of magnitude weaker than that of permanent magnet driving in terms of the core parameters of magnetic field intensity and magnetic field gradient. The size of the working space is also limited to the central area surrounded by the spatially combined coils, which limits its driving ability and applicable scenarios. In addition, compared with permanent magnet driving, electromagnetic driving consumes more energy by using programmed current to supply power and convert it into magnetic field energy. Especially to obtain a stronger magnetic field distribution, a larger current is required for driving, which will also bring about the thermal effect of the excitation coil and materials. At the same time, the non-linear change of the winding resistance caused by the thermal effect will have a complex impact on the magnetic field modeling and the subsequent motion control of the magnetic control micro-robot, and temperature control needs to be introduced, which even affects the continuous working time and applicable scenarios of the system. Permanent magnet driving usually consists of a mechanical structure capable of spatial motion such as a three-axis moving platform and a robotic arm, and one or more guiding permanent magnets installed on the end effector thereof. The advantage of permanent magnet driving is that it has strong magnetic field intensity and gradient parameters, can effectively improve the driving ability and driving load, and does not require external power supply, with better energy and cost efficiency.

[0005] The external magnetic field distribution of permanent magnet driving realizes the spatial time-varying characteristics through the spatial sequential motion of the mechanical structure. Its working space expands because it can change with the motion space of the mechanical structure. Permanent magnet driving changes the magnetic field of the controlled magnet by changing the spatial position of the guiding magnet, so as to change the magnetic force applied to the controlled magnet to achieve its motion control, but at the same time increases the overall complexity of the system. Some people have used two mutually perpendicular lead screw guides to drive the guiding permanent magnet and built a two-dimensional permanent magnet driving system to achieve open-loop control of magnetic particles and clusters in the X-Y plane. However, the open-loop system cannot guarantee the motion control accuracy of the controlled magnet. Others have built a two-dimensional magnetic control closed-loop system, which uses two microscopes to feedback the microscopic environment of the micro-robot and couples with an optical camera to collect the macroscopic environment, realizing the closed-loop control of magnetic micro-particles in the two-dimensional plane.

[0006] However, it is still challenging to implement a closed-loop control system for the three degrees of freedom of magnetic microparticles. During the magnetic drive motion of a micro-robot in a liquid environment, the driving factors of the guiding permanent magnet have a great impact on the stability, real-time performance, and accuracy of the three-dimensional motion control of the driven micro-robot, including the accurate model of the magnetic field distribution of the guiding permanent magnet (within the tolerance range), the three-dimensional time-varying relative relationship between the guiding permanent magnet and the driven micro-robot (including the Euclidean distance and Euler angles), the distribution model of the magnetic driving force, and the motion control algorithm based on this model. When discussing the magnetic field problem of a cylindrical magnet, some people have respectively carried out finite element method analysis and dipole modeling analysis on the excited magnetic field. The results show that compared with the dipole model, since the finite element method takes into account the size and shape of the magnet, the results of the finite element method are in good agreement with the actual measurement results. However, the complex finite element method makes it inapplicable to the real-time control of the magnetic field excited by the permanent magnet. Some people have proposed a method for calculating the error of the point dipole model by performing multi-level expansion on the dipole model of the magnet, and have proved the influence of geometric parameters on the model accuracy by comparing with the finite element method, which provides strong help for studying the error of the dipole model and improving the accuracy of the dipole model.

[0007] In a liquid environment, when the robot moves in the Z direction, it is simultaneously affected by buoyancy, magnetic force, viscous resistance, and gravity, and cannot achieve stable equilibrium. In addition, due to the uneven distribution of the magnetic field excited by the permanent magnet and the rapid attenuation of the magnetic field intensity in space with distance, in the permanent magnet control system, the relationship between the magnetic force received by the controlled object and the relative position between the controlled object and the guiding magnet is non-linear. This non-linear relationship needs to be considered and processed during the control process, which poses a challenge to accurately controlling the magnetic force of the robot in the Z direction. Secondly, in order to achieve motion in any direction in a three-dimensional space, it is necessary to establish a three-dimensional dynamic model of the robot to describe its motion characteristics in three directions. The introduction of more parameters increases the complexity of the system kinematic model. In addition, compared with one-dimensional control and two-dimensional control, three-dimensional control involves the simultaneous control of multiple dimensions. The controller needs to update and adjust the control signal at a high frequency to maintain the stability and accuracy of the robot, which puts higher requirements on the computational efficiency and real-time performance of the control algorithm. Some people have designed and built a suspension system composed of a permanent magnet and a linear servo motor, and designed a closed-loop control system through feedback linearization and linear quadratic regulator. However, limited by the degrees of freedom of the servo motor, the system can only achieve high-precision control in the Z direction. Some people have designed a simple PID controller to control the robotic arm through machine vision feedback technology, enabling the end permanent magnet to achieve attitude or position control of the capsule magnet in five degrees of freedom, but the control error caused by the non-linear characteristics of the model is not considered in the controller. Summary of the Invention

[0008] The object of the present invention is achieved by the following technical solutions.

[0009] Specifically, the present invention provides a three-dimensional permanent magnet closed-loop control system for XY plane - Z direction decoupled single magnetic pole and single magnetic bead, including:

[0010] A guiding permanent magnet driving module, an image acquisition and processing module, a motion control module, and a controller;

[0011] The controller, the motion control module, and the guiding permanent magnet driving module are connected in sequence, and the image acquisition and processing module is respectively connected to the output end of the guiding permanent magnet driving module and the input end of the controller;

[0012] The controller controls the motion control module to calculate and the guiding permanent magnet driving module to output a new position point of the magnetic bead according to the received actual position of the magnetic bead and the desired path point, so as to drive the magnetic bead to move.

[0013] Further, the guiding permanent magnet driving module includes two mutually perpendicular lead screw guides, a servo rack device, and an end magnet holder.

[0014] Further, the image acquisition and processing module includes a camera, a fill light, and a receiver.

[0015] Further, the motion control module includes a PID control system, adopting discrete PID control in the XY plane and feedback linearization discrete PID control in the Z direction.

[0016] Further, the motion control module realizes the motion control of the magnetic bead in three-dimensional space by controlling the combination of the relative position parameters w and h of the magnetic bead - magnetic rod, where w is the relative horizontal distance between the magnetic bead and the magnetic rod, and h is the relative vertical distance between the magnetic bead and the magnetic rod.

[0017] Further, in the PID control system, let K p be the proportional time coefficient; K i be the integral time coefficient; K d be the differential time coefficient, then there is the following PID control law:

[0018]

[0019] where e(t) is the PID control error, u(t) is the PID signal output, and the error e(t) is expressed as:

[0020]

[0021] where is the position of the magnetic bead target point, and P B (t) is the reading position of the magnetic bead by the image acquisition and processing module.

[0022] Further, during the control process, the motion control module uses the spatial position coordinates of the magnetic bead and the magnetic bead target coordinates as the inputs of a PID control system. The PID control system outputs a control quantity, which is input into the guiding permanent magnet drive module.

[0023] Further, when the system is used to control the movement of the magnetic bead in a maze, it includes:

[0024] Using an image acquisition and processing module to acquire a maze image and extract the image of the region of interest;

[0025] Performing binarization processing on the extracted image to obtain a bitmap of the maze;

[0026] Taking the bitmap together with the starting and ending coordinates as inputs and passing them to a path planning algorithm, which outputs a complete set of path points;

[0027] Extracting the set of path points and controlling the magnetic bead to move along the set of path points.

[0028] Further, in the PID control system, by establishing a kinematic model and a dynamic model of the magnetic bead - magnetic rod, and linearly transforming the non - linear terms in the kinematic model, a model - based feedback linearization control strategy is carried out.

[0029] Further, the linear transformation includes: by inversely solving the magnetic force model, a relational expression of the output magnetic force and the relative position relationship between the input magnetic bead and magnetic rod is completed, thereby completing the linear transformation of the kinematic model.

[0030] The advantages of the present invention are as follows: Experiments prove that the feedback linearization control of the present invention avoids the control error caused by non - linear terms in traditional PID control, and improves the system's ability to control the movement of the magnetic bead. And finally, through different experiments, the system's path tracking ability for the magnetic bead in one - dimensional, two - dimensional, and three - dimensional spaces is demonstrated, proving that the system can control the magnetic bead to perform cable - free and contact - free high - precision control in a complex three - dimensional narrow space. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Moreover, throughout the drawings, the same reference numerals are used to represent the same components. In the drawings:

[0032] Figure 1 Shows the schematic diagram of a three - dimensional permanent magnet closed - loop control system according to an embodiment of the present invention.

[0033] Figure 2 Shows the actual effect diagram of a three - dimensional permanent magnet closed - loop control system according to an embodiment of the present invention.

[0034] Figure 3 Shows a schematic diagram of the force analysis of the magnetic bead and magnetic rod system according to an embodiment of the present invention.

[0035] Figure 4 Shows a schematic diagram of the approximate fitting of h with respect to w according to an embodiment of the present invention.

[0036] Figure 5 Shows a schematic diagram of the parametric simulation results of the system controlling the movement of the magnetic bead in the X - Y direction and the Z direction.

[0037] Figure 6 Shows a schematic diagram of the motion state (A) when the magnetic bead moves in the X - Y plane while maintaining an arbitrary height Z and (B) when the magnetic bead moves only in the Z direction.

[0038] Figure 7 Displays the PID logic block diagram.

[0039] Figure 8 Is a schematic diagram of the simulation and experimental results for horizontal and vertical control respectively.

[0040] Figure 9 Is a schematic diagram of the parametric numerical solution results of the displacement projection magnitude of the magnetic bead on the X - Y plane for different w values and the parametric numerical solution results of the displacement of the magnetic bead on the Z - direction plane for different h values.

[0041] Figure 10 Is the system control logic block diagram of the present invention.

[0042] Figure 11 Is a schematic diagram of the experimental results of the feedback linearization control of the present invention.

[0043] Figure 12 Is for the magnetic bead at PB =(17, 10, 5) position to maintain stability of the experimental result schematic diagram.

[0044] Figure 13 Is a schematic diagram of the experimental results of controlling the z - direction and x - direction movement of the magnetic bead.

[0045] Figure 14 Is a schematic diagram of the experimental results of motion control in a two - dimensional environment.

[0046] Figure 15 Is a schematic diagram of the experimental results of controlling the magnetic bead in a maze environment.

[0047] Figure 16 Is a schematic diagram of the results of tracking and controlling the magnetic bead in a three - dimensional space.

[0048] Figure 17 Is a schematic diagram of the results of tracking and controlling the magnetic bead in a transparent pipeline.

[0049] Figure 18 Schematic diagram of the experimental process for separation and coupling control during the movement of magnetic beads.

[0050] Figure 19 Schematic diagram of the experimental results for separation and coupling control during the movement of magnetic beads. Specific implementation manners

[0051] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art.

[0052] The present invention uses a single guiding permanent magnet and a three-dimensional motion platform to enable a magnetic microsphere with a diameter of 1 mm to achieve three-dimensional path walking with high real-time performance, stability, and accuracy in a liquid environment. A mechanical model between the guiding magnet and the controlled magnet with an approximation error of less than 8% for a first-order dipole model is established, and then a dynamic model of the controlled magnetic bead is established. Based on the dynamic model, a hybrid control method that uses discrete PID control in the XY plane and feedback linearization discrete PID control in the Z direction is proposed to achieve effective three-dimensional path walking of the magnetic bead. Experiments in a 3D liquid environment, a maze, and a 3D tubular liquid environment have demonstrated the effectiveness of the control system and strategy. For the control performance of the system, when normalized according to the body length of the magnetic bead, in the Z direction, the transition time for the magnetic bead to travel 7 body lengths is 6 s, and the maximum steady-state error is 0.2 body lengths; in the X(Y) direction, the transition time for the magnetic bead to travel 4 body lengths is 26 s, and the maximum steady-state error is 0.05 body lengths.

[0053] The organization of the present invention is as follows: In the first part, a three-dimensional permanent magnet closed-loop control system is introduced. In the second part, the dipole model is derived, and the advantages and limitations of the dipole model are explained. A magnetic field model of the guiding magnet in space and a kinematic model of the "magnetic bead - guiding magnet" are established, and the controlled motion principle of the controlled magnetic bead is explained. In the third part, a system kinematic model is first established and parametric solutions are achieved. The shortest control period and the shortest driving period of the control system are analyzed. The displacement of the magnetic microsphere is discretized on the time scale, and it is shown that the driving period is small enough to enable the system to control the relative position of the magnetic bead - guiding magnet to remain unchanged within one control period. Based on this, a kinematic model of the magnetic bead and the magnetic rod is established. Based on the kinematic model, a PID controller is designed, and a feedback linearization controller is established by performing a linear transformation on the output quantity. Experiments prove that the feedback linearization controller can improve the performance of the motion control of the magnetic microsphere. In the fourth part, one-dimensional, two-dimensional, and three-dimensional path following motion control experiments are carried out, and experiments on the motion control of the magnetic bead in a three-dimensional liquid environment of a transparent infusion tube placed arbitrarily are carried out, realizing the stable motion control of the magnetic bead along the center line in a closed cavity environment along an arbitrary three-dimensional path.

[0054] I. Control System

[0055] The control system consists of a controlled magnetic bead (Magnetic Bead), a guided permanent magnet driving module (Guided Magnet Driving Module), an image acquisition and processing module (Image Acquisition and Processing Module), a motion control module (Motion Control Module), and a manipulation environment (Environment), and their relationship is as Figure 1 shown.

[0056] Specifically, as Figure 2As shown in the figure, the three-dimensional guiding permanent magnet drive module includes two mutually perpendicular lead screw guides, a servo rack device, and an end magnet gripper. The maximum stroke of the lead screw is 10 mm, the lead is 1 mm, the repeat positioning accuracy is 0.1 mm, and the transmission device uses a 28*30 mm two-phase four-wire stepper motor to drive the lead screw, with a step angle of 1.8°; in the rack mechanism, the pitch circle radius of the gear is 10 mm, and the rack mechanism is driven by a high-precision servo motor with a servo rotation angle of 180° and a maximum stroke of the mechanism of 20 mm. The end magnet gripper uses a hand-tightening screw to fix the guiding magnet, and the clamping range is 1 - 4 mm. The image acquisition and processing module consists of a camera, a fill light, and a receiver. The camera uses an industrial camera with a resolution of 2448 px * 2048 px and an image acquisition rate of 23 fps (the camera frame rate can be increased by reducing the camera ROI). The control module includes a lower computer control system and a computer. The lower computer uses a main board to control the operation of the servo motor and connects two stepper motor controllers to drive the two stepper motors respectively. Both stepper motor controllers use a 1 / 8 step control method; the upper computer control software of the computer can use LabVIEW or other control software. During the experiment, the experimental environment is divided into three types, including a 3D liquid environment, a maze, and a 3D tubular liquid environment.

[0057] II. Dynamic Analysis and Driving Strategy

[0058] 2.1 Magnetic Field

[0059] In this system, let the vector position of the geometric center of the controlled magnetic bead in space be The geometric center position of the guiding magnet is with a length of l. Let the controlled magnetic bead be in a static liquid environment, then it is subject to buoyancy the gravity the magnetic force F M and the viscous resistance F adh ; ρ is the liquid density, and the superscript "^" represents the unit vector of the corresponding vector.

[0060] For a permanent magnet without an externally applied magnetic field, the magnetic field H excited by the guiding magnetic rod in space G can be described as the gradient of the magnetic scalar potential which can be defined by the magnetization intensity M of the guiding magnetic rod G as follows:

[0061]

[0062] The above formula can be expressed in integral form through the Green's function in free space:

[0063]

[0064] where S is the surface integral range of the guiding magnetic rod, and V is the volume integral range; is the unit normal vector pointing to the surface of the guiding magnet; P relative = P B - P G is the vector from the center of the guiding magnet to the position of the magnetic bead, and P i is the vector from the center of the guiding magnetic rod to its integration point. and correspond to their respective unit vectors. For a permanent magnet with low magnetic susceptibility and uniform remanence, its internal magnetic field can be described by the quasi-static theory. Therefore, there is Then Equation (2) can be expressed as:

[0065]

[0066] Introduce Legendre polynomials and express Equation (3) using the Taylor series:

[0067]

[0068] where is the Legendre polynomial, and P relative = |P relative |; P i = |P i |. Since the guiding magnet is in free space, the magnetic field represented by the magnetic scalar potential outside the magnet has:

[0069]

[0070] where μ 0 = 4π×10 -7 N·A -2 is the magnetic permeability in free space. Since Therefore, there are no even terms in Equation (5). The first non-zero term after expanding Equation (5) is called the dipole term:

[0071]

[0072] where I is a 3*3 identity matrix, and m G is the magnetic dipole moment of the guiding magnet, which is determined by the geometric parameters and magnetization parameters of the magnet. This makes the multi-level terms expanded from Equation (5) all functions of the magnet geometry on the premise of knowing the magnet magnetization parameters. Let the geometric parameter δ be the ratio of the diameter to the length of the cylindrical magnet. Therefore, the error of the first term of the dipole model is:

[0073]

[0074] Without loss of generality, assume i is an odd number and require the even terms and to be zero, simplifying the error to:

[0075]

[0076] By substituting the geometric parameters of the magnet and constructing an approximate field composed of the first few terms of the multipole expansion, the relative error of the magnet dipole model at any given point is calculated. The results show that for an axially magnetized cylindrical magnet, when the diameter-to-length ratio is 1 / 3 and the distance of the point of interest from the geometric center of the magnet is greater than twice the radius of its minimum circumscribed circle, the approximation error of the first-order dipole model is less than 8%.

[0077] The volume of the controlled magnetic bead is V B ; the magnetization intensity is M B . During the process of the guiding magnet guiding the movement of the controlled magnetic bead, it can be assumed that the direction of the external magnetic field generated by the guiding magnet at the position of the magnetic bead is the same as the magnetization direction of the magnetic bead, that is At this time, the magnetic force received in the space of the controlled magnetic bead is:

[0078]

[0079] 2.2 Dynamic model

[0080] It can be seen from Equation (8) that the magnitude of the magnetic force in each direction is directly related to the gradient of the external magnetic field in that direction. Therefore, increasing the gradient of the magnetic field will lead to an increase in the magnetic force, which is one of the key factors in designing the drive system. Let the relative position of the magnetic bead and the magnetic rod Then the kinematic equation of the magnetic bead when it is controlled by the guiding magnet in the liquid environment is:

[0081]

[0082] Since B G has cylindrical symmetry, the magnetic drive motion control in the X and Y directions can be achieved in the same way. For simplicity of analysis, only the motion in the X-Z plane is analyzed in the present invention, and the implementation method of the motion control in the Y direction refers to that in the X direction. As Figure 3 shown, w is the distance from the center of the magnetic bead to the central axis of the magnetic rod (i.e., the relative horizontal distance between the magnetic bead and the magnetic rod), and h is the distance from the center of the magnetic bead to the end face of the magnetic rod closest to the magnetic bead (i.e., the relative vertical distance between the magnetic bead and the magnetic rod). The viscous resistance received by the controlled magnetic bead in the static liquid environment is:

[0083]

[0084] The magnetic force F received by the magnetic bead M can be expressed as:

[0085]

[0086] From equations (6, 9, 10, 11, 12), the motion states of the magnetic bead when being magnetically towed in space are as follows:

[0087]

[0088] 2.3 Motion control strategy

[0089] The ultimate goal of the system control of the present invention is to achieve precise path tracking ability in three-dimensional space. However, in practice, the object that the system can directly control is the guiding magnet. Therefore, the design of the controller in the Z direction is more challenging than that in the X and Y directions. Considering comprehensively, the motion control of the system in the Z direction and the motion control in the X and Y directions should be considered separately. When establishing the dynamic model, the motion of the magnetic bead is decoupled in the Z direction and the X-Y direction. The motion of the magnetic bead when it only moves in the X-Y direction (only the X direction is described in the exploration process, and the Y direction refers to the motion in the X direction) and the Z direction is in force balance, as well as the motion of the magnetic bead when it only moves in the Z direction and is in force balance in the X direction (including the state when the magnetic bead reaches force balance in both the X direction and the Z direction) are explored:

[0090] 1. When the magnetic bead only moves in the X or Y direction and the Z direction is in force balance, the acceleration of the magnetic bead in the Z direction At this time, it can be obtained that:

[0091]

[0092] And from equation (14), it can be known that at this time when There is a relationship between w and h, such that when the magnetic bead moves in the X direction, it is in force balance in the Z direction:

[0093]

[0094] Substituting into equation (14), the dynamic model in the X direction at this time can be obtained:

[0095]

[0096] 2. When the magnetic bead only moves in the Z direction and is in force balance in the X direction, where w = 0, The velocity of the magnetic bead in the X direction Acceleration At this time, it can be obtained that:

[0097]

[0098] Among them, when the magnetic bead reaches force balance in both the X direction and the Z direction, w = 0, The velocity of the magnetic bead Acceleration At this time, it can be obtained that:

[0099]

[0100] According to the above model, the present invention can be easily obtained. For any w, there exists a corresponding h = such that the magnetic bead maintains a force balance state in the Z direction. At this time, the magnetic bead is subjected to the component force of the magnetic force in the X direction and performs a variable-speed motion on the X-axis. At the same time, when w = 0, there exists a corresponding such that the magnetic bead performs a variable-speed motion in the direction of the Z-axis. Therefore, the motion control of the magnetic bead in three-dimensional space can be achieved by controlling the combination of the relative position parameters w and h of the magnetic bead and the magnetic rod.

[0101] Table 1. Properties of Magnets and Silicone Oil

[0102]

[0103]

[0104] For the dynamic model of the system, solving the analytical solution determines the corresponding relationship between the relative position of the magnetic bead and the magnetic rod and the motion state (displacement, velocity, acceleration) of the magnetic bead during the motion control of the magnetic bead. Due to the inherent non-linear characteristics of the magnetic force model in the system dynamic model, it is difficult to obtain an analytical solution. However, on the premise of knowing the environmental parameters and the performance parameters of the magnetic bead and the magnetic rod, through MATLAB, the accurate numerical solution of Equation (14) is obtained, and the polynomial fitting of its numerical solution is carried out by the least square method (the parameters are shown in Table 1), so as to approximately solve the balance polynomial analytical solution of h with respect to w. Let the velocity of the magnetic bead in the Z direction be zero, and Equation (14) is reconstructed as:

[0105]

[0106] Thereby, it is transformed into a problem of solving the root of a non-linear function for a given w, solving . Take values of w starting from zero (unit: mm) every 0.1 mm n and substitute them into Equation (16) (n = 1, 2, 3... 100). Use the fzero solver in MATLAB to solve and a series of numerical solutions h n can be obtained. The numerical solutions are fitted by a quartic polynomial by the least square method:

[0107]

[0108] where a 1 = -0.001640; a 2 = -0.0171; a 3= -0.0442; a 4 = 19.68. It is easy to obtain from the above formula that when the given environmental parameters, the performance parameters of the magnetic beads and the magnetic rod, and w = 0 The fitting result is as Figure 4 shown.

[0109] III. Control System Design

[0110] 3.1 Driving and Control Period

[0111] The lower computer can use Arduino. As the lower computer in the drive system, its control frequency is 112500Hz, which is much higher than the maximum operating frequency of the servo motor. Therefore, for the drive system, its shortest working cycle depends on the maximum operating frequency of the actuator. Compared with the stepper motor, the servo motor has a lower working frequency. By calculating the linear speed of the servo-driven rack, it is known that the maximum operating speed of the magnetic rod in the Z direction is 80mm / s.

[0112] Let h = h balance - Δh, where Δh is the increment of h based on h = h balance , and the positive or negative sign of Δh represents increase or decrease. By parametrically simulating the motion models of the system controlling the magnetic beads in the X-Y direction and the Z direction in the second part respectively, the Figure 5 results are obtained, where (a) - (c) show the simulation results of the displacement speed, speed, acceleration and w of the magnetic beads within 15ms when moving in the X-Y plane ; (d) - (f) show the simulation results of the displacement speed, speed, acceleration and height increment Δh of the magnetic beads within 15ms when moving in the Z direction . During the simulation process, the initial speed of the magnetic beads is defaulted to zero.

[0113] Let the control period of the motion control module in the control system be T Control ; the driving periods of the image acquisition and processing module and the driving module for controlling the stepper motor and the servo motor are T Drive . From the simulation results, it can be obtained that the time t taken for the magnetic beads to accelerate from the initial state to the maximum speed is less than 10ms. Therefore, in order to minimize the error generated by the second-order term in the dynamic model of the magnetic beads during the motion control process, the system control period is set to T Control = 10ms.

[0114] Secondly, the simulation results show that when the magnetic beads are motion-controlled in the Z direction and Δh ≥ 5(mm), the maximum speed of the magnetic beads is slightly less than the maximum operating speed of the magnetic rod in the Z direction. This enables the magnetic rod to be at the relative height of the magnetic bead - magnetic rod Arrive and maintain the relative height with the magnetic bead within 0.5 ms, so the driving period T is set Drive = 0.5 ms. At the same time, the relative height h between the magnetic bead and the magnetic rod is limited and cannot be greater than

[0115] 3.2 Kinematic model

[0116] The displacement ΔP of the magnetic bead in space within a period of time t B (t) is the integral of its velocity v B within this period of time, that is:

[0117]

[0118] Let k be the moment. In the discrete space, the above formula can be expressed as:

[0119]

[0120] where t = t 1 + t 2 + t 3 … + t k . In actual control, the relative horizontal distance w(t) and the relative vertical distance h(t) between the magnetic bead and the magnetic rod are both control variables related to time in the control process. Let the control displacement be the displacement generated by the magnetic bead within a control period, and the driving displacement be the displacement of the magnetic bead within a driving period. The relationship between the two is that the displacement within a control period is the cumulative sum of the displacement increments of each driving period within this period:

[0121]

[0122] where Since the velocity is defined as the displacement per unit time, in the discrete space, the velocity of the magnetic bead can be regarded as the displacement of the magnetic bead within a driving period. Further discretizing Equation (23) for Equation (22) gives the accumulation of the control displacement with respect to the driving displacement:

[0123]

[0124] It can be seen from Equation (13) that when the relative position between the magnetic bead and the magnetic rod does not change within a control period, the movement direction of the magnetic bead in the three-dimensional space is the same as and remains unchanged in the direction of the magnetic force it receives. At this time, w(t 1 ) = w(t 2 ) = … = w(t ε ), h(t 1 ) = h(t 2 ) = … = h(t ε ). Then, according to Equations (15) and (26), the magnetic bead motion model at this time is:

[0125]

[0126] Since T Drive <<T Control , it is possible to achieve that the relative positions of the magnetic bead and the magnetic rod hardly change within a control period. Let the relative positions of the magnetic bead and the magnetic rod remain unchanged within a control period, and t = kT Control = ε·kT Drive , then during the process of the magnetic bead moving from the initial position P B (k) to the next initial position P B (k + 1), there is:

[0127] P B (k + 1)= P B (k)+ΔP B (26)

[0128] When the magnetic bead maintains an arbitrary height Z and moves in the X - Y plane simultaneously, its motion state is as shown in (A) of Figure 6 , the displacement of the magnetic bead in the X - Y plane within a control period the magnetic force received then there is a corresponding unit vector where the subscript xy represents the projection of the vector in the X - Y plane. The length of the displacement increment of the magnetic bead and the relationship between w and k can be obtained from Equation (20), then the displacement of the magnetic bead at each moment is:

[0129]

[0130] where β(k) is the angle between the moving direction of the magnetic bead in the X - Y plane and the X - axis:

[0131]

[0132] The relationship between the positions of the magnetic rod and the magnetic bead at the k - th moment is:

[0133] P G (k)= P relative + P B (k) (29)

[0134] Then from Equations (20) and (22), it can be obtained that during the process of guiding the magnetic rod from the initial position P G (k) to the next initial position P G (k + 1), there is:

[0135] P G (k + 1)= P relative + P B (k)+ΔPB (30)

[0136] At this time:

[0137]

[0138] If the magnetic bead only moves in the Z direction (as shown in (B) in Figure 6 ), then w = 0, |ΔP B | The relationship with h and k can be solved from Equation (15), and then there is:

[0139]

[0140] Then the process of guiding the magnetic rod from the initial position P G (k) to the initial position P G (k + 1) at the next moment is the same as Equation (25). At this time

[0141] When At this time the magnetic bead will remain stationary at a certain height. However, in actual motion, the magnetic bead is inevitably disturbed by factors outside the magnetic bead - magnetic rod system and is always perturbed in the Z direction. Therefore, the force on the magnetic bead can never be balanced, which also makes it impossible for it to enter an absolutely static state. But the position of the magnetic bead can be made to approach the equilibrium position infinitely by adjusting Δh so that it can reach dynamic stability within an acceptable range.

[0142] 3.3 PID Control Design

[0143] Let be the expected position of the controlled magnetic bead within the control range; K p be the proportional time coefficient; K i be the integral time coefficient; K d be the derivative time coefficient, then there is the following PID control law:

[0144]

[0145] where e(t) is the PID control error and u(t) is the PID signal output. In the permanent magnet control system, the error e(t) can be expressed as:

[0146]

[0147] where is the position of the target point of the magnetic bead, and P B (t) is the position of the magnetic bead read by the vision system.

[0148] Actual programming needs to consider that the system operation is not continuous in time, so discrete PID is used for control. Then we have:

[0149]

[0150] Let ΔP G be the increment of the displacement of the magnetic rod, and we can set:

[0151]

[0152] Then, according to equations (22), (25), and (26), a simple linear decoupling algorithm is designed for the actuator of the control system. Then we have the relationship between the position of the magnetic rod guiding the magnetic bead and the PID output control quantity when the magnetic bead moves in different directions:

[0153] 1. When controlling the magnetic bead to move in the X-Y plane, we have:

[0154]

[0155] Since the servo of the control system is an integral component and the stepper motor is not an integral component, when driving the controlled magnetic bead, the movement in the X-Y plane is controlled in an incremental form. Then we have:

[0156]

[0157] 2. When controlling the magnetic bead to move in the Z direction, we have:

[0158]

[0159] Figure 7 Figure shows the PID logic block diagram. During the control process, the spatial position coordinates P B (k) of the magnetic bead and the target coordinates of the magnetic bead are used as the inputs of the PID system. After passing through the PID controller, the control quantity is input into the drive system. Through equations (29), (31), and (32), and are calculated respectively for horizontal and vertical control. The simulation and experimental results are as shown in Figure 8 Figure.

[0160] In the simulation and experiment of the magnetic bead in the Z direction, a step signal with an amplitude of 3 mm is input to the PID simulation controller and the PID controller at t = 50 s, and then a step signal with an amplitude of -3 mm is input at t = 139 s. In the simulation and experiment of the magnetic bead in the X-Y direction, a step signal with an amplitude of 3 mm is input to the X direction and a step signal with an amplitude of 3 mm is input to the Y direction at t = 30 s for the PID simulation controller and the PID controller respectively.

[0161] The simulation and experimental results show that the transition time \(t\) of the PID simulation in the Z direction at the first input of the step signal s1 = 10 s, and the overshoot is 12% mm. The transition time \(t\) at the second step signal s2 = 10 s, and the overshoot is 12% mm. There is no oscillation after reaching the steady state twice. However, the PID control experiment with the same PID simulation parameters did not reach the steady state after the input of the step signal, but there is a tendency to reach the steady state, and the oscillation is obvious. The maximum oscillation amplitude before the input of the step signal reaches 1.29 mm.

[0162] From the results, it can be obtained that under the same PID parameters, the response time of the PID experiment is much longer than that of the simulation and the oscillation amplitude is larger. After adjusting the proportional coefficient to tune the PID parameters, the PID control experiment in the Z direction of the magnetic bead is carried out again, and the amplitude of the input step signal is 3 mm. The experimental results are as Figure 8 shown in a. The transition time \(t\) of the re-adjusted PID experiment at the first input of the step signal s1 = 16.8 s, its overshoot is 6.8%, and there is oscillation after reaching the steady state, with the maximum amplitude of 0.23 mm; the transition time \(t\) at the second step signal s2 = 28.9 s, the overshoot is 12.3%, and there is oscillation after reaching the steady state, with the maximum amplitude of 0.37 mm. Compared with the PID experiment without adjusted parameters, the transition time is greatly reduced and the oscillation is significantly reduced. Since the first PID control experiment did not reach the steady state, the transition time and overshoot cannot be quantified. However, it can be obtained from the comparison results with the second experiment that the adjusted transition time is significantly less than that of the unadjusted PID control, and the oscillation amplitude after reaching the steady state is significantly reduced. However, even after adjusting the control parameters, there is still a large transition time and a large steady-state error compared with the PID simulation. Compared with the Z-direction control, in the PID simulation experiment in the X-Y direction, the transition time \(t\) in the X direction after the input of the step signal in the PID simulation sx = 7 s, and the overshoot is 0.0031 mm; the transition time \(t\) in the Y direction sy = 7 s, and the overshoot is 0.0049 mm. The transition time \(t\) in the X direction of the PID control experiment after the input of the step signal sx = 30 s, and the overshoot is 0.0878 mm; the transition time \(t\) in the Y direction sy = 27 s, and the overshoot is 0.0899 mm. Compared with the PID control in the Z direction, although the transition time of the PID control in the X-Y direction is significantly longer than that of the PID simulation, both have a lower overshoot than the simulation, and there is no obvious oscillation at the steady state.

[0163] The reason for the difference between PID control and simulation is that PID is a linear control strategy, while the nonlinear nature in the system dynamics model makes it impossible for PID to fully compensate for errors, which also causes the magnetic bead to fail to meet the requirement that the actual displacement in each period is equal to the PID output. Therefore, linear conversion can be performed on the nonlinear term to compensate for the output signal of PID.

[0164] 3.4 Feedback Linear Controller Design

[0165] Since T drive <<T control , when controlling the magnetic bead in the X-Y direction, the relative position of the magnetic bead-magnetic rod can be regarded as remaining unchanged within a control period. Let t = 10 ms, starting from w = 0 mm and h = 15 mm respectively, take values for w and h at intervals of 0.1 mm as w n and h n and substitute them into equations (16) and (17) (n = 1, 2, 3…80), and the corresponding exact solutions and (For the displacement in the Y direction, refer to the X direction) are calibrated successively in the Cartesian coordinate system and From the results, it can be obtained that the corresponding relationship between w and the projection size of the displacement of the magnetic bead in the X direction within 10 ms can be approximately fitted by a straight line passing through the origin (as shown in a of Figure 9 ), so the relationship between w and the displacement of the magnetic bead within one period can be approximately regarded as a linear relationship, which enables the compensation of PID control errors by resetting the linear controllers for the X direction and Y direction in the actuator.

[0166] However, when controlling the magnetic bead in the Z direction, the corresponding relationship between the relative vertical distance h of the magnetic bead-magnetic rod and the displacement of the magnetic bead within one period is nonlinear (as shown in b of Figure 9 ). Therefore, in order to ensure the control performance of the control system simultaneously, the kinematic model of the magnetic bead-magnetic rod is introduced into the PID control system for controlling the Z direction next, and a feedback linearization control system is established.

[0167] In the kinematic model of the magnetic bead-magnetic rod, the main source of the nonlinear nature is the magnetic force model. Therefore, the relationship between the output magnetic force and the relative position of the input magnetic bead-magnetic rod can be obtained by inverse solving the magnetic force model, so as to complete the linear conversion of the kinematic model. However, for the convenience of solving the dynamic model, the linear conversion of the magnetic bead-magnetic rod dynamic model is directly performed here. By taking the inverse analytical solution of h with respect to the displacement Δz control in the Z direction when t = T B for equation (17), the relationship between the displacement increment of the magnetic bead within one control period and the relative height h of the magnetic bead-magnetic rod can be obtained Let the new output be:

[0168]

[0169] Thus, the linearization of the relationship between the Z - direction control signal and the input error is achieved. The magnetic force term in the kinematic model makes the kinematic model too complex to obtain an analytical solution. Therefore, the least - squares method is used to fit the parametric solution results. Because for the result, h n There is a unique corresponding result Therefore, for the inverse solution of Equation (17) for h with respect to Δz B A simple way to obtain the numerical solution is to reverse the coordinate system of the solution of Δz with respect to h, and re - calibrate the result of b in B in turn in the Cartesian coordinates. Perform a least - squares fit on the reversed data points, and find the inverse expression of h with respect to Z Figure 9 by the rational approximation method B where p

[0170]

[0171] where p 1 = 17.51; p 2 = 2.966; q 1 = 1.324; q 2 = 0.1516. After connecting Equation (26) as a calculation link in series with the Z - direction PID control, perform a non - linear transformation on the Z - direction PID output at each moment to obtain a new output Input it into the drive system to drive the magnetic rod, thereby achieving the control of the Z - direction position of the magnetic bead. Its control block diagram is as shown in Figure 10 Figure...

[0172] Finally, conduct a Z - direction control experiment on the magnetic bead with the feedback linearization controller. During the experiment, the target position and the PID parameters are the same as those in the PID simulation. Finally, compare the experimental results of the feedback linearization control with the PID simulation and the experimental results of the adjusted - parameter PID control (as shown in Figure 11 Figure...). The experimental results show that for the feedback linearization control, during the first input step signal, the transition time its overshoot is 1.7%, and there is oscillation after reaching the steady state, with the maximum amplitude being 0.14 mm; during the second step signal, the transition time the overshoot is 0.2%, and there is oscillation after reaching the steady state, with the maximum amplitude being 0.16 mm. Compared with the experiment of the adjusted - parameter PID, the transition time is reduced and the oscillation is significantly reduced.

[0173] IV. Experimental Verification and Analysis

[0174] To evaluate the positioning and tracking capabilities of the system, the present invention conducted the following experiments. First, the present invention experimented with the control capabilities of the system in a single dimension for controlling a magnetic bead. Second, the present invention verified the system's ability to control the magnetic bead in a two-dimensional plane. Then, the present invention tested the system's ability to track an arbitrarily given path and move the magnetic bead along a complex path in three-dimensional space. Finally, the present invention evaluated the system's motion capabilities in a narrow pipe channel. In all experiments, the coordinate unit was measured in millimeters (mm), and the PID parameters are shown in Table 2.

[0175] Table 2

[0176]

[0177] 4.1 Motion Control Experiment in a Single Dimension

[0178] In the first experiment, a coordinate point was set within the workplace by the control system to maintain the stability of the magnetic bead. Then, experiments were conducted to test the motion control capabilities of the system in the Z-direction and the X-direction, respectively. For the control in the Z-direction and the X-direction, the present invention set two coordinate points within the controllable range such that the control system could only cause displacement in the X or Z direction. The coordinates of these points are shown in Table 3 for the first set of experimental paths.

[0179] Table 3

[0180]

[0181] Based on the experimental results of the stability of the magnetic bead at the specified position in space, it can be concluded that the magnetic bead cannot maintain complete static stability in space (as Figure 12 shown). However, dynamic stability of the magnetic bead at the desired height can be achieved through the control system, which is consistent with the conclusion in the second part. During the stabilization process, the magnetic bead oscillates in all three directions. The maximum amplitudes in the X and Y directions are 0.025 mm and 0.005 mm, respectively, which are much smaller than the motion amplitude of 0.143 mm in the Z direction. One of the reasons is that the image acquisition and processing module is limited by the camera frame rate and takes a relatively long time to capture the position information of the magnetic bead within a control cycle, while the time required for the Z direction to reach the target position is the shortest. This results in a deviation between the actual position of the magnetic bead and the position observed by the system, generating errors when controlling the position of the magnetic bead during the actual motion process and leading to displacement errors. In addition, system modeling errors and external disturbances experienced by the magnetic bead (such as temperature changes, vibrations, interfering magnetic fields) also interfere with the control of the magnetic bead's position.

[0182] Based on the experimental results of controlling the motion of the magnetic bead in the Z-direction and the X-direction ( Figure 13) It can be observed that the transition time for controlling the Z-direction movement of the magnetic bead is 6 s, and the average velocity in the Z-direction reaching the target point is 1.17 mm / s. The transition time in the X-direction is 21 s, and the average velocity reaching the target point is 0.19 mm / s.

[0183] It can be seen that the movement velocity of the magnetic bead in the Z-direction is much higher than that in the X or Y direction. This phenomenon can be explained by referring to Figure 9 For comparison with Figure 9 it is found that when w = Δh = h - h balance , within one control period, the displacement in the Z-direction is greater than that in the X or Y direction. This means that there is a problem of inconsistent control velocities between the Z-direction and the X or Y direction, resulting in a shorter transition time for Z-direction control compared to X or Y direction control.

[0184] 4.2 Motion Control Experiments in a Two-Dimensional Environment

[0185] In the second experiment, the waypoints are set in the X-Y plane or the X-Z plane. Then the system is used to test its motion control ability in the X-Y or X-Z plane. The coordinates of these points are shown in Table 4.

[0186] Table 4

[0187]

[0188] The experimental results are as shown in Figure 14 . Figure 14 Among them, a to c show the motion control of the magnetic bead in the X-Y plane, and c illustrates the difference between the desired position and the actual position of the driven magnetic bead in the Z-direction when it moves in the X-Y plane, with a maximum amplitude of 0.21 mm. b to f present the experimental results of controlling the motion of the magnetic bead in the X-Z plane. f shows the difference between the desired position and the actual position of the driven magnetic bead in the Y-direction when it moves in this plane, with a maximum amplitude of 0.09 mm. The desired trajectory of each magnetic bead is indicated by an arrow, and their initial positions are marked by a rectangle. In the experiment, when the magnetic bead moves in the X-Y plane, there will be a certain degree of oscillation in the Z-direction, with a maximum amplitude of 0.21 mm. Similarly, when the magnetic bead moves in the X-Z plane, there will also be a certain degree of oscillation in the Y-direction, with a maximum amplitude of 0.09 mm. Next, a maze is designed within the working range of the system, and the channel width is only 2 mm. Then the starting point and the ending point are set to control the motion trajectory of the magnetic bead. The computer is used to plan the path from the starting point to the ending point and drive the magnetic bead to follow this path. This will verify the effectiveness of the system's ability to track complex paths in the X-Y plane.

[0189] In this experiment, the present invention developed a path planning strategy based on the A* algorithm for controlling the system. First, the present invention used a vision system to acquire a maze image and extract the region of interest (ROI) image. Then, the present invention performed binarization on the extracted image to obtain a bitmap representation of the maze. This bitmap, together with the start and end coordinates, was passed as input to the A* path planning algorithm. The A* algorithm output a complete set of path points. After extracting these waypoints, the system of the present invention controlled the magnetic bead to move along this path. However, in actual operation, since the A* algorithm did not consider the limitation of the collision volume when calculating the optimal path, the magnetic bead sometimes contacted the wall because its predetermined trajectory was closer to the wall than allowed by its radius. To solve this problem, it is proposed to add cost evaluation around the wall area in the future version of the A* path planning algorithm to limit the planned trajectory within a certain range.

[0190] The experimental results of controlling the magnetic bead in the maze environment are also shown in Figure 15 which show that the control system of the present invention can successfully drive and track narrow and complex channels in the X-Y plane, using trajectory tracking technology, and demonstrates the autonomous path planning ability when encountering obstacles in a complex environment.

[0191] 4.3 Motion Control Experiment in 3D Environment

[0192] In the third experiment, a series of waypoints were set in the three-dimensional space to form a target motion path (as shown by the lines in Figure 16 ), and the ability of the system to track this path was tested. Figure 16 In, a shows the results of tracking and controlling the helical path of the magnetic bead in the three-dimensional space, and the trajectory of the magnetic bead movement is shown by taking images every 10 seconds. The solid line represents the planned motion path and the actual trajectory of the magnetic bead; b shows the results of trajectory tracking of the magnetic bead moving in the three-dimensional space. The experimental results show that the control system has the ability to track complex three-dimensional paths.

[0193] In addition, the present invention placed a transparent pipe with an inner diameter of 3 mm in the operating space. This pipe can be freely bent to form an irregular path in the space. By setting waypoints along the empty part of the pipe, the present invention controlled the movement of the magnetic bead. Figure 17 In, a shows the results of tracking and controlling the path of the magnetic bead in the three-dimensional space in the transparent pipe, and images are captured every 10 seconds to show the trajectory of the magnetic bead movement. The solid line represents the planned motion path; b shows the results of trajectory tracking of the magnetic bead moving in the three-dimensional space.

[0194] Figure 17The experimental results shown in indicate that within a pipeline channel with a diameter more than three times its own diameter, magnetic beads can perform contactless and high-precision path tracking motion control. The target trajectory and the maximum straight-line distance are also less than one-fifth of the bead diameter.

[0195] Conclusions and Summaries

[0196] This invention mainly designed and built a three-dimensional permanent magnet closed-loop drive platform, established the kinematic model and dynamic model of the magnetic bead - magnetic rod, and through linear transformation of the non-linear terms in the kinematic model, proposed a model-based feedback linearization control strategy. Experiments have proved that this feedback linearization control avoids the control errors caused by non-linear terms in traditional PID control and improves the system's ability to control the motion of magnetic beads. And finally, through different experiments, the system's path tracking ability for magnetic beads in one-dimensional, two-dimensional, and three-dimensional spaces was demonstrated, proving that the system can control magnetic beads to perform cable-free and contactless high-precision control in complex three-dimensional narrow spaces.

[0197] The movement speed of the magnetic bead in the Z direction is significantly higher than its displacement in the X - Y plane. This phenomenon can be explained by referring to Figure 9 : Comparing with Figure 9 , it is found that when w = Δh = h - h balance , within one control period, the displacement of the magnetic bead in the Z direction is greater than that in the X or Y direction. This means that there is an inconsistency in the control speeds of the magnetic bead's movement in the Z direction and within the X - Y plane, resulting in a shorter transition time for motion control along the Z axis compared to that along the X - Y directions. To further study this characteristic, separation and coupling control experiments were conducted during the movement of the magnetic bead, and path points were set according to their respective movement directions, as shown in Figure 18 . The solid line represents the expected trajectory of the magnetic bead. The results of the separation experiment are shown in Figure 19 . The results show that when controlling the magnetic bead under an oblique path, errors will occur during the movement process for both separation control and coupling control. However, in terms of the results, both control modes can track the path points with approximately the same transition time.

[0198] Secondly, through experiments, it can be known that the acquisition frequency of the image acquisition system will also affect the control accuracy of the system for the movement of magnetic beads. Therefore, for the subsequent system construction, a camera with a higher frequency can be considered as the actuator of the image acquisition system.

[0199] As described above, only the preferred specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A three-dimensional permanent magnet closed-loop control system for XY plane-Z direction decoupled single-pole single magnetic bead, characterized in that: include: Guiding permanent magnet drive module, image acquisition and processing module, motion control module and controller; The controller, the motion control module, and the guide permanent magnet drive module are connected in sequence, and the image acquisition and processing module is respectively connected to the output end of the guide permanent magnet drive module and the input end of the controller; The controller controls the motion control module to calculate and guide the permanent magnet drive module to output the new position point of the magnetic bead according to the received actual position of the magnetic bead and the expected path point, so as to drive the magnetic bead to move.

2. A three-dimensional permanent magnet closed-loop control system according to claim 1, characterized in that: The guide permanent magnet drive module comprises two mutually perpendicular screw guide rails, a steering gear rack device and an end magnet clamp.

3. A three-dimensional permanent magnet closed-loop control system according to claim 1, characterized in that: The image acquisition and processing module includes a camera, a fill light and a receiver.

4. A three-dimensional permanent magnet closed-loop control system according to claim 1, characterized in that: The motion control module includes a PID control system, which adopts discrete PID control in the XY plane and feedback linear discrete PID control in the Z direction.

5. A three-dimensional permanent magnet closed-loop control system according to claim 1, characterized in that: The motion control module realizes the motion control of the magnetic beads in three-dimensional space by controlling the combination of the relative position parameters w and h of the magnetic beads and the magnetic rod, wherein w is the relative horizontal distance between the magnetic beads and the magnetic rod, and h is the relative vertical distance between the magnetic beads and the magnetic rod.

6. A three-dimensional permanent magnet closed-loop control system according to claim 4, characterized in that: In the PID control system, let K p is the proportional time coefficient; K i is the integral time coefficient; K d is the differential time coefficient, then the following PID control rules are obtained: Where e(t) is the PID control error, u(t) is the PID signal output, and the error e(t) is expressed as: in is the magnetic bead target point position, P B (t) is the reading position of the magnetic beads by the image acquisition and processing module.

7. A three-dimensional permanent magnet closed-loop control system according to claim 6, characterized in that: During the control process, the motion control module uses the spatial position coordinates of the magnetic beads and the target coordinates of the magnetic beads as inputs of the PID control system. The PID control system outputs a control quantity, which is then input into the guide permanent magnet drive module.

8. A three-dimensional permanent magnet closed-loop control system according to claim 1, characterized in that: The system is used to control the movement of magnetic beads in a maze, and comprises: Use the image acquisition and processing module to acquire the maze image and extract the region of interest image; Binarize the extracted image to obtain a bitmap of the maze; Passing the bitmap along with the start and end coordinates as input to a path planning algorithm, outputting a complete set of path points; The path point set is extracted, and the magnetic beads are controlled to move along the path point set.

9. A three-dimensional permanent magnet closed-loop control system according to claim 4, characterized in that: In the PID control system, a feedback linearization control strategy based on a model is implemented by establishing a kinematic model and a dynamic model of a magnetic bead-magnetic rod and performing a linear transformation on the nonlinear terms in the kinematic model.

10. A three-dimensional permanent magnet closed-loop control system according to claim 9, characterized in that: The linear transformation includes: completing the relationship between the output magnetic force and the relative position of the input magnetic beads-magnetic rods by inversely solving the magnetic model, thereby completing the linear transformation of the kinematic model.

Images