A Piezoelectric Actuator Impedance Control Method Based on Rate-Dependent Hysteresis Model

Abstract

The present invention belongs to the field of precision motion control, and discloses a piezoelectric driver impedance control method based on a rate-dependent hysteresis model. The method is based on a piezoelectric driver force-position monitoring system to obtain driving voltage, strain and driving force data of a piezoelectric actuator; a dynamically extended asymmetric play operator and its corresponding DE-ASPI algorithm are proposed to describe the composite characteristics of the driver rate-dependent piezoelectric hysteresis and mechanical hysteresis elasticity; based on the proposed DE-ASPI algorithm and the measured strain signal and driving voltage signal, a driving force state observer of the driver is constructed to enable the piezoelectric actuator to obtain driving force state feedback without a force sensor; based on the driving force state feedback, displacement signal and target displacement, an impedance control law of the piezoelectric driver is designed to calculate the expected control force; a PID controller is designed to perform parameter setting, and the compliant control of the system is achieved by adjusting the driving voltage.

Description

Technical Field

[0001] The invention belongs to the field of precision motion control. Aiming at the problem of compliant control of piezoelectric microactuators, the invention designs a piezoelectric driver impedance control method based on a rate-dependent hysteresis model. Background Art

[0002] Piezoelectric microactuators are the core components of micro-electromechanical systems. They can convert electrical input signals into mechanical motion, thereby achieving multi-directional and multi-posture motion. They are widely used in optics, medical, aerospace, robotics and other fields. However, with the gradual miniaturization and precision of application scenarios, higher requirements are placed on the functional integration of sensing, execution and control of microactuators and their environmental interaction.

[0003] Taking piezoelectric-driven micro-grippers in micro-assembly as an example, their micro-actuators are often used to handle small components, such as optical components, microelectronic devices, micromechanical parts, etc. These components are usually very fragile and require extremely high operating precision. The traditional displacement control method is based on the precise control of the position of the object. Due to the high stiffness of the micromanipulator, the system may apply excessive force and damage the target object during the clamping operation, while the single force feedback control cannot guarantee the precise control of the clamping position. The combination of the two requires a more complex sensor layout, which is more difficult to integrate for small micro-actuators. Therefore, there is an urgent need for a piezoelectric drive control method with simple sensor elements and consideration of environmental compliant interaction.

[0004] In 2017, Huaduo Shi's team from Peking University published a paper titled "A micromachined piezoelectric microgripper for manipulation of micro / nanomaterials". The piezoelectric microgripper was designed for micron-sized fibers and can clamp 2μm fibers. However, the control adopts the traditional open-loop control method, which cannot guarantee the system's adaptability to the environment, and its positioning accuracy and clamping force are difficult to guarantee. In 2024, Chen Liguo's team from Soochow University published a paper titled "Research and Application of Microgrippers with Force-Position Hybrid Control Function". Aiming at the needs of high-precision and adaptive target positioning, a dual-input and dual-output position PID control-PI impedance force / position hybrid control method was proposed, which can ensure appropriate displacement and clamping force output for different clamping targets. However, the clamping system uses laser displacement sensors and strain sensors, and the sensing layout is large in size, making it difficult to adapt to narrow and complex clamping environments.

[0005] In the above-mentioned micro-gripping control method, in order to adapt to the clamping of tiny components in a narrow space, open-loop control is adopted based on theoretical simulation values. If different sensor layouts and feedback loops are required for displacement and force to ensure environmental adaptability, the size and complexity of the clamp will inevitably increase. Therefore, a piezoelectric actuator control method with simple sensor elements and consideration of environmental compliance interaction is urgently needed. Summary of the invention

[0006] In order to solve the problem of compliant control of piezoelectric micro-displacement actuators, the present invention proposes a piezoelectric actuator impedance control method based on a rate-dependent hysteresis model. The method is based on the piezoelectric actuator force-position monitoring system to obtain the driving voltage, strain and driving force data of the piezoelectric actuator; a dynamically extended asymmetric play operator (DE-ASplay) and its corresponding DE-ASPI algorithm are proposed to describe the composite characteristics of the driver rate-dependent piezoelectric hysteresis and mechanical hysteresis elasticity; based on the proposed DE-ASPI algorithm and the measured strain signal and driving voltage signal, the driving force state observer of the driver is constructed to enable the piezoelectric ceramic to obtain driving force state feedback under the premise of no force sensor; based on the driving force state feedback, displacement signal and target displacement, the impedance control law of the piezoelectric driver is designed to calculate the expected control force; a PID controller is designed to perform parameter setting, and the compliant control of the system is achieved by adjusting the driving voltage. The invention can realize real-time feedback of the driver displacement and driving force state only through the embedded strain gauge sensor, can control the compliance of the driver movement, and show the expected impedance behavior.

[0007] The technical solution of the present invention:

[0008] A piezoelectric driver impedance control method based on rate-dependent hysteresis model, firstly, build a force-position monitoring system of the piezoelectric driver to collect the driving force and strain signals during the actuation process; build a voltage rate-dependent hysteresis model of the piezoelectric driver based on the proposed DE-ASPI algorithm; build a driving force state observer based on the hysteresis model and the measured strain signal, and train the observer offline through the measured driving force signal; build an impedance control law based on real-time strain information and expected displacement value, and calculate the expected control force in real time; design a PID controller, set parameters, and control the driving voltage to achieve the compliant servo control of the driver. In this way, the impedance control that takes into account the displacement control and driving compliance can be realized when the piezoelectric driver only has strain monitoring.

[0009] The specific steps are as follows:

[0010] (1) Building a piezoelectric actuator force and position monitoring system

[0011] The piezoelectric driver force position monitoring system includes a pre-tightening bolt 1, a piezoelectric driver 2, a measuring base 3, a spherical force transmission seat 4, a pressure sensor 5, a power amplifier 6, a host computer 7, a real-time controller 8 and a force position data acquisition module 9; the spherical force transmission seat 4 is installed on the pressure sensor 5 through the measuring base 3, and the measuring base 3 and the pressure sensor 5 are fixed by bolts; the piezoelectric driver 2 is placed on the spherical force transmission seat 4, and is pressed by the pre-tightening bolt 1 through the measuring base 3; the strain gauge and force sensor output embedded in the piezoelectric driver 2 are connected to the force position data acquisition module 9, and the force The position data acquisition module 9 is connected to the real-time controller 8, and the real-time controller 8 is connected to the host computer 7 through a network cable interface; the power amplifier 6 is connected to the real-time controller 8 and the piezoelectric driver 2, and the construction of the piezoelectric driver force position monitoring system is completed; the control signal transmitted by the real-time controller 8 is amplified 100 times, acting on the piezoelectric driver 2, outputting displacement and force, and monitoring the force position signal through the external pressure sensor 5 and the strain gauge embedded in the piezoelectric driver 2, and the acquisition and storage are realized based on the force position data acquisition module 9, and the data display and instruction interaction are carried out through the host computer 7;

[0012] (2) Based on the piezoelectric actuator force-position monitoring system, an actuation test is designed. The actuator movement is controlled by designing an actuation signal, and the strain and driving force signals during the actuation process are collected. A data training set containing driving voltage, strain and driving force signals is formed through a no-load actuation test and a load-resistance actuation test respectively. The actuator actuation signal selects an increasing triangular wave function and a constant-amplitude swept-frequency triangular wave function, and its function form is as follows:

[0013]

[0014]

[0015] Where k is 1, 2, ..., means k is a positive integer, is the preset minimum amplitude, t is the time variable, is the initial frequency of the frequency sweep, and m is the slope of the linear frequency change; the two obtained piezoelectric hysteresis loops are shown in Figure (3) and Figure (4) respectively.

[0016] (3) Construct a rate-dependent hysteresis model of the piezoelectric actuator. Based on the Play operator of the classic PI algorithm, an asymmetric slope Play operator (ASplay) and a dynamically enhanced asymmetric slope Play operator (DE-ASplay) are proposed. The function form of the ASplay operator is as follows:

[0017] G [ U ] ( t ) = max { a 1 U ( t ) − r ,min { a 2 U ( t ) , G [ U ] ( t − T 0 ) } }

[0018] in, G [ U ] ( t ) is the output of the DE-ASplay operator, , is a constant slope, is the sampling interval, r is the operator threshold, and U(t) is the driving voltage signal.

[0019] The DE-ASplay function is as follows:

[0020] { H [ U ] ( t ) = max { a 1 U ( t ) − r + vD ,min { a 2 U ( t ) + vD , H [ U ] ( t − T 0 ) } } D = Play { d u } = max { 0 , d u − r } + min { 0 , d u + r } d u = w 1 U ˙ + w 2 U ¨ + … w n U n

[0021] Where D is the dynamic compensation term, v is its weight, is the weighted sum of different order derivatives of the driving voltage, to is the weight of the 1st to nth order derivatives, , to They represent the driving voltage and the first to nth order derivatives of the driving voltage respectively.

[0022] ASplay operator introduces slope , , which can better adapt to the asymmetry of the piezoelectric hysteresis loop, and the DE-ASplay operator introduces a dynamic compensation term again, that is, the derivatives of the driving voltage u are input into the Play operator to calculate the contribution of different derivatives to the rate-related hysteresis, and the weighted superposition is performed. The DE-ASplay operator is in the form of Figure 5 As shown. The weighted sum of multiple DE-asplay operators is the DE-ASPI algorithm. Its function form is as follows:

[0023] H DE − ASPI ( U , U ˙ , … U n ) = ∑ i = 1 l λ i H i [ U ] ( t )

[0024] in is the output of DE-ASPI algorithm, l is the number of DE-ASPI operators, represents the weight of the ith operator, H i [ U ] ( t ) Denotes the i-th operator. Based on the driving voltage and strain data obtained from the no-load actuation test, the parameters in the DE-ASPI algorithm are optimized and trained to obtain the rate-dependent hysteresis model of the piezoelectric actuator.

[0025] (4) Construct a driving force state observer. The driving voltage signal based on the piezoelectric actuator can be used to obtain the actuation displacement under no-load condition through the rate-dependent hysteresis model. Because the displacement output of the piezoelectric actuator is equal to the sum of the piezoelectric driving amount and the elastic compression, the elastic compression of the actuator can be calculated through the measured strain signal, and then the driving force can be solved to achieve the observation of the driving force. The flow chart of the driving force state observer is shown in the figure. Figure 6 As shown. The function expression of the driving force state observer is as follows:

[0026]

[0027] in is the actuation displacement value calculated by the strain signal, is the actuator length, is the measured strain value, To obtain the elastic compression, Substitute into the weighted sum of l ASplay operators to get the driving force observation value , represents the weight of the jth ASplay operator, The parameters in the driving force state observer are trained by using a data training set containing driving voltage, strain and driving force signals formed through load resistance test.

[0028] (5) Based on the measured strain signal and the expected driving displacement, the impedance control law is constructed, and its function form is as follows:

[0029]

[0030] in, To achieve desired control, , , are the desired system mass, damping and stiffness, respectively, , , are the displacement, velocity and acceleration values ​​expected by the driver respectively. , , They are the displacement, velocity, and acceleration values ​​measured by the driver. , , Specify the compliance of the system and obtain the desired control force through the impedance control law .

[0031] (6) The driving force observation value obtained by the driving force state observer is used as feedback, the expected control force obtained by the impedance control law is used as the target value, and the PID link is designed as the controller of the system impedance control. Its control block diagram is shown in Figure (7). Its function form is as follows:

[0032]

[0033] Where e represents the deviation between the observed driving force and the expected control force, is the first-order derivative of the deviation between the observed driving force and the expected control force, U is the driving voltage, , , are the control parameters of PID respectively.

[0034] By experimentally adjusting the control parameters of PID, the driving voltage is controlled in real time so that the observed driving force approaches the expected control force, thereby achieving smooth control of the drive. The control result is shown in Figure (8).

[0035] Beneficial effects of the invention: The invention proposes a piezoelectric driver impedance control method based on a rate-dependent hysteresis model. Compared with the traditional method, this method only relies on the embedded strain gauge sensor, can feedback the driver displacement and driving force state in parallel, can effectively ensure the driver positioning accuracy and motion compliance, and can take into account the adaptability of environmental interaction under the premise of simple sensing elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The present invention is a flow chart of a piezoelectric driver impedance control method based on a rate-dependent hysteresis model.

[0037] Figure 2 It is a connection diagram of the piezoelectric driver force position monitoring system of the present invention.

[0038] Figure 3 It is the piezoelectric hysteresis loop of the piezoelectric driver under the increasing triangle wave signal.

[0039] Figure 4 This is the piezoelectric hysteresis loop of the piezoelectric driver under the swept triangle wave signal.

[0040] Figure 5 Schematic diagram of the dynamically enhanced asymmetric slope play operator of the present invention.

[0041] Figure 6 It is a schematic diagram of the driving force state observer of the present invention.

[0042] Figure 7 This is the impedance control block diagram of the present invention.

[0043] Figure 8 This is the system impedance control result of the present invention. DETAILED DESCRIPTION

[0044] The specific implementation of the present invention is described in detail below in combination with the technical scheme and the accompanying drawings.

[0045] Select a cylindrical stacked driver with a specification of φ16×56mm.

[0046] (1) Build a piezoelectric actuator force and position monitoring system. First, pass the spherical force transmission seat 4 through the measuring base 3, fix it on the pressure sensor 5, and connect the measuring base to the pressure sensor through bolts. Then, place the piezoelectric actuator 2 on the spherical force transmission seat 4 and tighten it through the pre-tightening bolt 1. The output signals of the strain gauge and force sensor embedded in the actuator are connected to the force and position data acquisition module 9 and connected to the real-time controller 8. The real-time controller 8 is connected to the host computer through the network cable interface, and the power amplifier 6 is connected to the real-time controller 8 and the piezoelectric actuator 2 to complete the construction of the piezoelectric actuator force and position monitoring system. The control signal transmitted by the controller 8 is amplified by 100 times, so that it acts on the piezoelectric actuator 2 system and outputs displacement and force. The external pressure sensor 5 and the strain gauge embedded in the actuator jointly monitor the force and position signal. The force and position data acquisition module 9 realizes the acquisition and storage of the signal, and the host computer is used for data display and command interaction.

[0047] (2) Based on the piezoelectric actuator force-position monitoring system, an actuation test is designed to collect strain and driving force signals during the actuation process. Through no-load actuation tests and load-resistance actuation tests, a data training set of driving voltage, strain and driving force signals is formed. The actuation signal uses an increasing triangular wave function and a constant amplitude sweep triangular wave function. The function form is as shown in equations (1) and (2), where the parameters , ,

[0048] (3) A rate-dependent hysteresis model of the piezoelectric actuator was constructed. Based on the Play operator of the classic PI algorithm, an asymmetric slope Play operator (ASplay) and a dynamically enhanced asymmetric slope Play operator (DE-ASplay) were proposed, and their functional forms are shown in equations (3) and (4) respectively. The ASplay operator introduces the slope parameter and , in order to better adapt to the asymmetry of the piezoelectric hysteresis loop; and the DE-ASplay operator introduces a dynamic compensation term on this basis, inputs the derivatives of the driving voltage into the Play operator to calculate the contribution of different derivatives to the rate-dependent hysteresis, and performs weighted superposition. The specific form of the DE-ASplay operator is shown in Figure (5). Through the weighted summation of multiple DE-ASplay operators, the DE-ASPI algorithm is finally formed.

[0049] (4) Construct a driving force state observer. The actuating displacement under no-load condition is obtained based on the driving voltage signal of the piezoelectric actuator through the rate-dependent hysteresis model. Since the displacement output of the piezoelectric actuator consists of the superposition of the piezoelectric driving amount and the elastic compression amount, the elastic compression amount of the piezoelectric actuator can be calculated through the measured strain signal. By subtracting the elastic compression amount from the displacement output, the magnitude of the driving force is solved, thereby realizing real-time observation of the driving force state. The observer structure is shown in Figure (6). Its function expression is as shown in Formula (6).

[0050] (5) Based on the measured strain signal and the expected driving displacement, an impedance control law is constructed to adjust the compliance of the system. , damping coefficient , stiffness coefficient To define the dynamic behavior of the system, and thus control the compliance of the system, the impedance control law is shown in Equation (7).

[0051] (6) The driving force observation value calculated by the driving force state observer is used as the feedback signal, and the desired control force obtained by the impedance control law is used as the target value. The PID controller is designed to realize the impedance control of the system. The controller adjusts the driving voltage through the PID link so that the driving force observation value gradually approaches the desired control force, thereby realizing the smooth control of the drive. Its control block diagram is shown in Figure 7 In this process, the parameters of the PID controller are adjusted experimentally to ensure that the system can adjust the drive voltage in real time to optimize the gap between the drive force feedback and the desired control force, and ultimately achieve the expected smooth control effect. Figure 7 For the control block diagram, Figure 8 The control results of the system are shown.

[0052] Compared with traditional methods, this control method has simple sensing elements and can provide parallel feedback of the driver displacement and driving force status through embedded strain gauges, which can effectively ensure the driver positioning accuracy and movement compliance, allowing the driver to flexibly respond to various interactive requirements in a changing working environment, ensuring the stability and reliability of its performance.

Claims

1. A piezoelectric driver impedance control method based on a rate-dependent hysteresis model, characterized in that: Here are the steps: (1) Building a piezoelectric actuator force and position monitoring system The piezoelectric actuator force and position monitoring system comprises a pre-tightening bolt (1), a piezoelectric actuator (2), a measuring base (3), a spherical force transmission seat (4), a pressure sensor (5), a power amplifier (6), a host computer (7), a real-time controller (8) and a force and position data acquisition module (9); the spherical force transmission seat (4) is installed on the pressure sensor (5) through the measuring base (3), and the measuring base (3) and the pressure sensor (5) are fixed by bolts; the piezoelectric actuator (2) is placed on the spherical force transmission seat (4) and is pressed through the measuring base (3) by the pre-tightening bolt (1); the strain gauge embedded in the piezoelectric actuator (2) and the output of the force sensor are connected to the force and position data acquisition module (9); In the block (9), the force position data acquisition module (9) is connected to the real-time controller (8), and the real-time controller (8) is connected to the host computer (7) through a network cable interface; the power amplifier (6) is connected to the real-time controller (8) and the piezoelectric driver (2), thereby completing the construction of the piezoelectric driver force position monitoring system; the control signal transmitted by the real-time controller (8) is amplified by 100 times, and acts on the piezoelectric driver (2), outputting displacement and force, monitoring the force position signal through the external pressure sensor (5) and the strain gauge embedded in the piezoelectric driver (2), and realizing acquisition and storage based on the force position data acquisition module (9), and performing data display and command interaction through the host computer (7); (2) Based on the piezoelectric actuator force-position monitoring system, an actuation test is designed. The actuator movement is controlled by designing an actuation signal, and the strain and driving force signals during the actuation process are collected. A data training set containing driving voltage, strain and driving force signals is formed through a no-load actuation test and a load-resistance actuation test respectively. The actuator actuation signal selects an increasing triangular wave function and a constant-amplitude swept-frequency triangular wave function, and its function form is as follows: Where k is 1, 2, ..., means k is a positive integer, is the preset minimum amplitude, t is the time variable, is the initial frequency of the frequency sweep, and m is the slope of the linear frequency change; (3) Construct a rate-dependent hysteresis model for piezoelectric actuators; Based on the Play operator of the PI algorithm, an asymmetric slope Play operator ASplay and a dynamically enhanced asymmetric slope Play operator DE-Asplay are proposed. The function form of the ASplay operator is as follows: in, is the output of the DE-ASplay operator, , is a constant slope, is the sampling interval, r is the operator threshold, and U(t) is the driving voltage signal; The DE-ASplay function is as follows: Where D is the dynamic compensation term, v is its weight, is the weighted sum of different order derivatives of the driving voltage, to is the weight of the 1st to nth order derivatives, , to represent the driving voltage and the first to nth order derivatives of the driving voltage respectively; The weighted sum of multiple DE-asplay operators is the DE-ASPI algorithm, and its function form is as follows: in, is the output of DE-ASPI algorithm, l is the number of DE-ASPI operators, represents the weight of the ith operator, represents the i-th operator; based on the driving voltage and strain data obtained from the no-load actuation test, the parameters in the DE-ASPI algorithm are optimized and trained to obtain the rate-dependent hysteresis model of the piezoelectric actuator; (4) Construct a driving force state observer; Based on the driving voltage signal of the piezoelectric driver (2), the actuating displacement under the no-load state is obtained by using a hysteresis model related to the passing rate. Since the displacement output of the piezoelectric driver (2) is equal to the sum of the piezoelectric driving amount and the elastic compression amount, the elastic compression amount of the piezoelectric driver (2) is calculated by measuring the strain signal, and then the driving force is solved, thereby realizing the observation of the driving force. The function expression of the driving force state observer is as follows: in, is the actuation displacement value calculated by the strain signal, is the actuator length, is the measured strain value, To obtain the elastic compression, Substitute into the weighted sum of l ASplay operators to get the driving force observation value , represents the weight of the jth ASplay operator, is the displacement target; a data training set including driving voltage, strain and driving force signals formed by load-resistance actuation test is used to train the parameters in the driving force state observer; (5) Based on the measured strain signal and the expected driving displacement, the impedance control law is constructed, and its function form is as follows: in, To achieve desired control, , , are the desired system mass, damping and stiffness, respectively, , , are the displacement, velocity and acceleration values ​​expected by the driver respectively. , , They are the displacement, velocity, and acceleration values ​​measured by the driver respectively; by setting , , Specify the compliance of the system and obtain the desired control force through the impedance control law ; (6) The driving force observation value obtained by the driving force state observer is used as feedback, the expected control force obtained by the impedance control law is used as the target value, and the PID link is designed as the controller of the system impedance control. Its function form is as follows: Where e represents the deviation between the observed driving force and the expected control force, is the first-order derivative of the deviation between the observed driving force and the expected control force, U is the driving voltage, , , They are the control parameters of PID respectively; By experimentally adjusting the control parameters of PID, the driving voltage is controlled in real time so that the observed driving force value approaches the expected control force, thereby achieving smooth control of the drive.

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