Force-displacement synchronous introspection sensing method for tail end of electrothermal micro-actuator

Abstract

The invention discloses a force-displacement synchronous introspection sensing method for the tail end of an electrothermal micro-actuator, and the method comprises the steps: defining a physical input variable and an output variable of a state space model of the electrothermal micro-actuator, and selecting an intermediate variable which can be directly or indirectly measured as a state variable; constructing a nonlinear state equation and a nonlinear output equation, and selectively adding nonlinear terms; reasonable driving voltage excitation signals and tail end load force excitation signals are selected, and data of input variables, output variables and state variables responded in the whole process are synchronously collected; performing parameter identification on the nonlinear state space model by adopting a nonlinear dynamic sparse identification algorithm to obtain a continuous time state equation and an output equation of the system; and converting the continuous time state equation and the output equation into a discrete time state equation and a discrete time output equation, and synchronously estimating the loading force and the output displacement of the tail end of the micro-actuator on line by using state variable data and driving voltage data which are acquired in real time.

Description

Technical Field

[0001] This invention relates to a method for synchronous introspection sensing of force-displacement at the end of an electrothermal micro-actuator. Background Technology

[0002] Microactuators are an indispensable component in micro- and nano-scale mechanisms for performing physical motion. They are commonly used in micro- and nano-manipulation fields requiring precise positioning, such as micro- and nano-manipulation robots, micro-servo valves, and micro-mirrors. When micro- and nano-manipulation robots are applied in biomedical and ultra-precision manufacturing applications, where precise positioning and strict control of interaction with the environment are required, the simultaneous measurement of the end effector displacement and load force, along with force-displacement coordinated control, is crucial for micro-manipulation or micro-assembly.

[0003] Electrothermal microactuators are simple to fabricate, employing various processes such as ultra-precision machining, additive manufacturing, or MEMS fabrication. Furthermore, their structural layer materials are less complex to fabricate than piezoelectric or electromagnetic thin-film materials. Electrothermal microactuators also require low driving voltages, unlike electrostatic or piezoelectric actuators which necessitate boost converters. They offer large output displacement and force density, while maintaining a compact structure and small footprint. Based on these advantages, electrothermal microactuators are particularly suitable for micro-manipulation applications requiring limited operating space and significant driving force.

[0004] However, there are two core bottlenecks: 1) The electrothermal-mechanical multi-field coupling of electrothermal microactuators involves various nonlinear factors such as anisotropy and temperature dependence of material properties, and large deformation geometric nonlinearity. Uncertainties such as actual temperature boundary conditions and the thermodynamic characteristics of the manipulated object in contact with the actuator end not only result in poor thermal stability and poor reliability of driving capability, but also make dynamic modeling extremely difficult, posing a huge challenge to the control of the output displacement and contact force at the actuator end. 2) When electrothermal microactuators are used in the field of interactive micromanipulation, force-displacement coordinated control requires simultaneous online measurement of output displacement and load force. However, existing detection methods usually occupy a large amount of space or increase costs, making it difficult to give full play to the unique advantages of electrothermal microactuators. Seeking soft measurement technology is one solution. Summary of the Invention

[0005] The technical problem to be solved by this invention is that when electrothermal micro-actuators are used in the field of interactive micro-operation, force-displacement coordinated control requires simultaneous online measurement of output displacement and load force. However, existing detection methods usually occupy a large space or increase costs, making it difficult to give full play to the unique advantages of electrothermal micro-actuators. In order to solve the above problems, a method for synchronous introspective sensing of force-displacement at the end of an electrothermal micro-actuator is provided.

[0006] The object of this invention is achieved in the following manner: A method for synchronous introspection sensing of force-displacement at the end of an electrothermal microactuator. The method includes: Step 1: Define the physical input and output variables of the state space model of the electrothermal micro-actuator, and select intermediate variables that can be directly or indirectly measured as state variables. Step 2: Construct nonlinear state equations and nonlinear output equations, and selectively add nonlinear terms to the linear state equations and linear output equations respectively; Step 3: Select appropriate driving voltage excitation signal and end load force excitation signal, and synchronously collect data on input, output variables and state variables of the entire process response; Step 4: Based on Step 2 and Step 3, the nonlinear dynamics sparse identification algorithm is used to identify the parameters of the nonlinear state-space model and obtain the continuous-time state equation and output equation of the system. Step 5: Based on Step 4, the continuous-time state equation and output equation are converted into discrete-time state equation and discrete-time output equation. Using the real-time acquired state variable data and drive voltage data, the load force and output displacement at the end of the micro actuator are estimated online synchronously.

[0007] The definition of the state-space model of the electrothermal micro-actuator in step 1 specifically includes: The input variable is u=[V in F L ] T The number of input variables is r=2; where V in It is the drive voltage control quantity; F L It is the end load force; The output variable is y, and the number of output variables is m=1; where y is the end displacement of the actuator. State vector X=[ Tw-T0 T b -T0 T e -T0 i i'] T Where i' is the first derivative of the driving current i with respect to time, T w It is the temperature of the electrically heated working area, T b It is the base temperature of the electrothermal micro-actuator, T e T0 is the temperature at the execution end, and T0 is the ambient temperature. The number of variables n in the above state vector is equal to the total order n of the dynamic model of the electrothermal micro-actuator. The continuous-time state equation is X'=f(X, u), where X' is the first-order derivative vector of the state vector with respect to time. The continuous-time output equation is y=g(X,u).

[0008] The state variables are not limited to the variables included in the state vectors listed above. As the number of modes of the electrothermal micro-actuator under consideration increases, state variables can be added to the state vectors. Alternatively, the driving current variable i and its derivative in the state vectors listed above can be replaced with the input power variable and its derivative or the impedance variable and its derivative.

[0009] Step 2 specifically includes: The state equation is expressed as X'=f(X, u)=AX+B[V in F L ] T +EV in 2 +F(T w -T b ) 2 +G(T w -T e ) 2 ; Where the coefficients of the linear terms A are 5*5 matrices and the coefficients of the linear terms B are 5*2 matrices, and the nonlinear terms V... in 2 The coefficient E is a 5*1 matrix, and the nonlinear terms (T) w -T b ) 2 The coefficient F is a 5*1 matrix, and the nonlinear terms (T) w -T e ) 2 The coefficient G is a 5*1 matrix. The number of linear terms in the state equation is n+r, the number of nonlinear terms is s, n is the number of variables in the state vector, and r is the number of input variables. The output equation is expressed as y=g(X,u)= CX+D[V in F L ] T +OV in 2 + PF L 0.5 + Q (T w -T b ) 2 +R (T w -T e ) 2 ; Where the coefficients of the linear terms C are 1*5 matrices and the coefficients of the linear terms D are 1*2 matrices, and the nonlinear terms V... in 2 The coefficients O and the nonlinear term F L 0.5 The coefficient P, the nonlinear term (T) w -T b ) 2 The coefficient Q, the nonlinear term (T)w -T e ) 2 The R coefficients are all scalars; the number of linear terms in the output equation is n+r, and the number of nonlinear terms is w.

[0010] Step 3 specifically includes: Drive voltage V in It is an independent active input variable, and a discrete multi-tone excitation method is adopted based on the determination of the amplitude range and frequency range of the driving voltage; End load force F L It is an independent passive input variable or disturbance variable, whose excitation signal adopts constant value excitation or wandering excitation; Under the action of the excitation signal, the driving voltage V is synchronously acquired. in End load force F L The temperature T of the electrically driven working area w The base temperature T of the electrothermal micro-actuator b Temperature T at the end of the execution process e Ambient temperature T0, and drive current i The sampling frequency is greater than twice the maximum frequency of the excitation signal, and the number of sampling time series is Z.

[0011] Step 4 specifically includes: Based on the linear and nonlinear terms in step 2 and the original data of state variables, input variables, and output variables collected in step 3, Constructing the state equations required for sparse identification of nonlinear dynamics. The state variable data matrix has Z rows and n columns, with the column data corresponding to [T], ... w ’ -T0 ’ T b ’ -T0 ’ T e ’ -T0 ’ i’ i’’ The rows of data are arranged according to the sampling time sequence; the input data matrix has Z rows and n+r+s columns, and the column data correspond to [T], ... w -T0T b -T0 T e -T0 i i’ V in F L V in 2 (T w -T b ) 2 Tw -T e ) 2 The rows of data are arranged according to the sampling time sequence; Constructing the output equation required for sparse identification of nonlinear dynamics. The output variable matrix y is Z rows and m columns, and the input data matrix is ​​Z rows and n+r+w columns, with the column data corresponding to [T]... w -T0 T b -T0 T e -T0 i i’ V in F L V in 2 F L 0.5 (T w -T b ) 2 T w -T e ) 2 ], The sparse matrix in the state equation and output equation is solved by either the Sequential Threshold Least Squares (STLS) regression algorithm or the Sequential Threshold Ridge (STRidge) regression algorithm to obtain the continuous-time state equation and output equation of the electrothermal micro-actuator.

[0012] Step 5 specifically includes: The backward difference method is used to transform the continuous-time state equation into a discrete-time state equation, which is expressed as: where T Sampling period, subscript k The sampling time number is used; the discrete-time state equation is about the current time. k and the previous moment k -1 state variable data, current time k Drive voltage data, end load force data, and usage cycle T The function; utilizing the measured state variable data of the current and previous moments, the driving voltage data of the current moment, and the periodicity. T It can solve for the load force value at the current moment, and realize online estimation of the end load force F. L ; The continuous-time output equation is transformed into a discrete-time output equation using the zero-order hold method. The discrete-time output equation is expressed as follows, with its subscripts... k The sampling time number is used; the discrete-time output equation utilizes the state variable data, driving voltage data, and the online estimated end load force F collected at the current time. L This allows us to calculate the output displacement at the current moment.

[0013] When transforming continuous-time state equations into discrete-time state equations, considering the numerical stability, accuracy, and timeliness of the discrete-time model, forward difference method, central difference method, Runge-Kutta method, or bilinear transform method can also be used. When transforming continuous-time output equations into discrete-time output equations, considering the accuracy, timeliness, and smoothness of the discrete-time model, mean approximation method and interpolation method can also be used.

[0014] The method further includes: normalization and denoising of offline data in nonlinear dynamic sparse identification modeling in steps 4 and 5 above, normalization and denoising of online data in synchronous estimation of micro-actuator end load force and output displacement, and optimization of sampling time in the modeling and estimation process.

[0015] The nonlinear terms in the state equation and output equation can be added according to the working mechanism of the micro-actuator, for example, by increasing the driving voltage V. in The coupling term V with current i in ﹒ i, the number s of nonlinear terms in the state equation can be increased or decreased, and the number w of nonlinear terms in the output equation can be increased or decreased.

[0016] The beneficial effects of this invention are as follows: The synchronous introspective sensing method for the load force and output displacement at the end of an electrothermal micro-actuator provided by this invention acquires key temperature variable data and current variable data during voltage excitation at several key locations on the actuator itself and its boundaries in real time. A nonlinear state-space model is constructed, and data-driven sparse identification is used to obtain a mathematical model for synchronous sensing of load force and output displacement. The effective effects are reflected in two aspects: This method avoids the need to arrange displacement and force sensing structures or devices at the actuator end, maintaining the compactness of the actuator end space and controlling costs; the measurement of key temperature variables at several key locations on the actuator itself and its boundaries transforms the uncertainty of the actuator's thermodynamic characteristics into determinism, improving the thermal stability and reliability of the actuator's driving capability, increasing the accuracy of the actuator's dynamic model, and reducing the difficulty of force-displacement coordinated control at the actuator end. Attached Figure Description

[0017] Figure 1 This is a simplified diagram of an electrothermal micro-actuator and a schematic diagram of multiple physical variables involved in the force-displacement synchronous introspective sensing method.

[0018] Figure 2 This is a schematic diagram illustrating the parameter identification of a nonlinear state-space model using a nonlinear dynamics sparse identification algorithm, as described in this invention.

[0019] Figure 3 This is a flowchart of the method of the present invention. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0021] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same technical meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0022] like Figure 1 The diagram shows a simplified representation of an electrothermal microactuator and several physical variables involved in the force-displacement synchronous introspective sensing method. Under the active control of the driving voltage Vin, the main structure of the electrothermal microactuator generates Joule heating due to its conductivity. Joule heating acts as an internal heat source for the actuator, causing its temperature to rise. Under the effect of material thermal expansion, thermal strain is generated, resulting in output displacement at the actuator's end.

[0023] In addition to heat transfer within its own body, electrothermal microactuators also exchange heat with the external environment, including heat transfer with the surroundings and heat conduction with the base. Furthermore, if the actuator's end effector pushes the driven object to move, a contact force exists between the end effector and the driven object, referred to here as the load force. Heat from the actuator may be transferred to the driven object through the end effector. The output displacement of the electrothermal microactuator is affected not only by the temperature field but also by the load force acting as a motion-resisting force. The operating state of the electrothermal microactuator is the result of the coupling of electric, thermal, and mechanical fields.

[0024] The physical characteristics of the electrothermal micro-actuator in this invention include: The physical input variables of the electrothermal microactuator include the drive voltage control quantity V. in End load force F L , Physical output variables, including actuator end displacement y, Artificially introduced measurable intermediate variables, including the temperature T of the electrothermal driven working area. w The base temperature T of the electrothermal micro actuator b Temperature T at the end of the execution process e The ambient temperature T0 and the drive current i, as artificially introduced measurable intermediate variables, are more advantageous in terms of measurement cost and space occupation compared to the end load force variable and output displacement variable to be estimated. The physical quantities to be estimated online include the actuator end load force F. L and actuator end displacement y, like Figure 2 and Figure 3 As shown, this invention discloses a method for synchronous introspection sensing of force-displacement at the end of an electrothermal micro-actuator. The method includes: Step 1: Define the physical input and output variables of the state space model of the electrothermal micro-actuator, and select intermediate variables that can be directly or indirectly measured as state variables. Step 2: Construct nonlinear state equations and nonlinear output equations, and selectively add nonlinear terms to the linear state equations and linear output equations respectively; Step 3: Select appropriate driving voltage excitation signal and end load force excitation signal, and synchronously collect data on input, output variables and state variables of the entire process response; Step 4: Based on Step 2 and Step 3, the nonlinear dynamics sparse identification algorithm is used to identify the parameters of the nonlinear state-space model and obtain the continuous-time state equation and output equation of the system. Step 5: Based on Step 4, the continuous-time state equation and output equation are converted into discrete-time state equation and discrete-time output equation. Using the real-time acquired state variable data and drive voltage data, the load force and output displacement at the end of the micro actuator are estimated online synchronously.

[0025] The definition of the state-space model of the electrothermal micro-actuator in step 1 specifically includes: The input variable is u=[V in F L ] T The number of input variables is r=2; where V in It is the drive voltage control quantity; F L It is the end load force; The output variable is y, and the number of output variables is m=1; where y is the end displacement of the actuator. State vector X=[ T w -T0 T b -T0 T e -T0 i i'] T Where i' is the first derivative of the driving current i with respect to time, T w It is the temperature of the electrically heated working area, T b It is the base temperature of the electrothermal micro-actuator, T e T0 is the temperature at the execution end, and T0 is the ambient temperature; the number of variables n in the above state vector is equal to the total order n of the dynamic model of the electrothermal micro-actuator; The continuous-time state equation is X'=f(X, u), where X' is the first-order derivative vector of the state vector with respect to time; The continuous-time output equation is y=g(X,u).

[0026] The state variables are not limited to the variables included in the state vectors listed above. As the number of modes of the electrothermal micro-actuator under consideration increases, state variables can be added to the state vectors. Alternatively, the driving current variable i and its derivative in the state vectors listed above can be replaced with the input power variable and its derivative or the impedance variable and its derivative.

[0027] Step 2 specifically includes: The state equation is expressed as X'=f(X, u)=AX+B[V in F L ] T +EV in 2 +F(T w -T b ) 2 +G(T w -T e ) 2 ; Where the coefficients of the linear terms A are 5*5 matrices and the coefficients of the linear terms B are 5*2 matrices, and the nonlinear terms V... in 2 The coefficient E is a 5*1 matrix, and the nonlinear terms (T) w -T b ) 2 The coefficient F is a 5*1 matrix, and the nonlinear terms (T) w -T e ) 2 The coefficient G is a 5*1 matrix. The number of linear terms in the state equation is n+r, the number of nonlinear terms is s, n is the number of variables in the state vector, and r is the number of input variables. The output equation is expressed as y=g(X,u)= CX+D[V in F L ] T +OV in 2 + PF L 0.5 + Q (T w -T b ) 2 +R (T w -T e ) 2 ; Where the coefficients of the linear terms C are 1*5 matrices and the coefficients of the linear terms D are 1*2 matrices, and the nonlinear terms V... in 2 The coefficients O and the nonlinear term F L 0.5 The coefficient P, the nonlinear term (T) w -T b ) 2 The coefficient Q, the nonlinear term (T)w -T e ) 2 The R coefficients are all scalars; the number of linear terms in the output equation is n+r, and the number of nonlinear terms is w.

[0028] Step 3 specifically includes: Drive voltage V in It is an independent active input variable, and a discrete multi-tone excitation method is adopted based on the determination of the amplitude range and frequency range of the driving voltage; End load force F L It is an independent passive input variable or disturbance variable, whose excitation signal adopts constant value excitation or wandering excitation; Under the action of the excitation signal, the driving voltage V is synchronously acquired. in End load force F L The temperature T of the electrically driven working area w The base temperature T of the electrothermal micro-actuator b Temperature T at the end of the execution process e Ambient temperature T0, and drive current i The sampling frequency is greater than twice the maximum frequency of the excitation signal, and the number of sampling time series is Z.

[0029] Step 4 specifically includes: Based on the linear and nonlinear terms in step 2 and the original data of state variables, input variables, and output variables collected in step (3), Constructing the state equations required for sparse identification of nonlinear dynamics. The state variable data matrix has Z rows and n columns, with the column data corresponding to [T], ... w ’ -T0 ’ T b ’ -T0 ’ T e ’ -T0 ’ i’ i’’ The rows of data are arranged according to the sampling time sequence; the input data matrix has Z rows and n+r+s columns, and the column data correspond to [T], ... w -T0T b -T0 T e -T0 i i’ V in F L V in 2 (T w -T b ) 2T w -T e ) 2 The rows of data are arranged according to the sampling time sequence; Constructing the output equation required for sparse identification of nonlinear dynamics. The output variable matrix y is Z rows and m columns, and the input data matrix is ​​Z rows and n+r+w columns, with the column data corresponding to [T]... w -T0 T b -T0 T e -T0 i i’ V in F L V in 2 F L 0.5 (T w -T b ) 2 T w -T e ) 2 ], The sparse matrices in the state equation and output equation are solved by the Sequential Threshold Least Squares (STLS) or Sequential Threshold Ridge (STRidge) algorithm to obtain the continuous-time state equation and output equation of the electrothermal micro-actuator.

[0030] Step 5 specifically includes: The backward difference method is used to transform the continuous-time state equation into a discrete-time state equation, which is expressed as: where T Sampling period, subscript k The sampling time number is used; the discrete-time state equation is about the current time. k and the previous moment k -1 state variable data, current time k Drive voltage data, end load force data, and usage cycle T The function; utilizing the measured state variable data of the current and previous moments, the driving voltage data of the current moment, and the periodicity. T It can solve for the load force value at the current moment, and realize online estimation of the end load force F. L ; The continuous-time output equation is transformed into a discrete-time output equation using the zero-order hold method. The discrete-time output equation is expressed as follows, with its subscripts... k The sampling time number is used; the discrete-time output equation utilizes the state variable data, driving voltage data, and the online estimated end load force F collected at the current time. LThis allows us to calculate the output displacement at the current moment.

[0031] When transforming continuous-time state equations into discrete-time state equations, considering the numerical stability, accuracy, and timeliness of the discrete-time model, forward difference method, central difference method, Runge-Kutta method, and bilinear transform method can also be used. When transforming continuous-time output equations into discrete-time output equations, considering the accuracy, timeliness, and smoothness of the discrete-time model, mean approximation method and interpolation method can also be used.

[0032] The sensing method further includes: in order to improve the estimation accuracy, real-time performance and robustness of load force and output displacement, normalization and denoising of offline data in nonlinear dynamic sparse identification modeling in steps 4 and 5 above, normalization and denoising of online data in synchronous estimation of load force and output displacement at the end of the micro actuator, and optimization of sampling time in the modeling and estimation process.

[0033] The state variables also include other easily measurable physical quantities such as input power variables or impedance variables.

[0034] The nonlinear terms in the state equation and output equation can be added according to the working mechanism of the micro-actuator, for example, by increasing the driving voltage V. in The coupling term V with current i in ﹒ i (representing the driving voltage multiplied by the current), the number of nonlinear terms s in the state equation can be increased or decreased, and the number of nonlinear terms w in the output equation can be increased or decreased.

[0035] The present invention provides a method for synchronous introspective sensing of load force and output displacement at the end of an electrothermal micro-actuator. This method acquires key temperature variable data at several points on the actuator itself and its boundaries, as well as current variable data during voltage excitation, through real-time measurement. A nonlinear state-space model is constructed, and data-driven sparse discrimination is used to obtain a mathematical model for synchronous sensing of load force and output displacement. The effectiveness is reflected in two aspects: this method avoids the need to place displacement and force sensing structures or devices at the actuator end, maintaining the compactness of the actuator end space and controlling costs; the measurement of key temperature variables at several points on the actuator itself and its boundaries transforms the uncertainty of the actuator's thermodynamic characteristics into determinism, improving the thermal stability and reliability of the actuator's driving capability, increasing the accuracy of the actuator's dynamic model, and reducing the difficulty of force-displacement coordinated control at the actuator end.

[0036] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several changes and improvements without departing from the overall concept of the present invention, and these should also be considered within the scope of protection of the present invention.

Claims

1. A method for synchronous introspective sensing of force-displacement at the end of an electrothermal micro-actuator, characterized in that: The method includes: Step 1: Define the physical input and output variables of the state space model of the electrothermal micro-actuator, and select intermediate variables that can be directly or indirectly measured as state variables. Step 2: Construct nonlinear state equations and nonlinear output equations, and selectively add nonlinear terms to the linear state equations and linear output equations respectively; Step 3: Select appropriate driving voltage excitation signal and end load force excitation signal, and synchronously collect data on input, output variables and state variables of the entire process response; Step 4: Based on Step 2 and Step 3, the nonlinear dynamics sparse identification algorithm is used to identify the parameters of the nonlinear state-space model and obtain the continuous-time state equation and output equation of the system. Step 5: Based on Step 4, the continuous-time state equation and output equation are converted into discrete-time state equation and discrete-time output equation. Using the real-time acquired state variable data and drive voltage data, the load force and output displacement at the end of the micro actuator are estimated online synchronously.

2. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to claim 1, characterized in that: The definition of the state-space model of the electrothermal micro-actuator in step 1 specifically includes: The input variable is u=[V in F L ] T The number of input variables is r=2; where V in It is the drive voltage control quantity; F L It is the end load force; The output variable is y, and the number of output variables is m=1; where y is the end displacement of the actuator. State vector X=[ T w -T0 T b -T0 T e -T0 i i'] T Where i' is the first derivative of the driving current i with respect to time, T w It is the temperature of the electrically heated working area, T b It is the base temperature of the electrothermal micro-actuator, T e T0 is the temperature at the end of the actuator and T0 is the ambient temperature. The number of variables n in the above state vector is equal to the total order n of the dynamic model of the electrothermal micro-actuator. The continuous-time state equation is X'=f(X, u), where X' is the first derivative vector of the state vector with respect to time. The continuous-time output equation is y=g(X,u).

3. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to claim 2, characterized in that: The state variables are not limited to the variables included in the state vectors listed above. As the number of modes of the electrothermal micro-actuator under consideration increases, state variables can be added to the state vectors. Alternatively, the driving current variable i and its derivative in the state vectors listed above can be replaced with the input power variable and its derivative or the impedance variable and its derivative.

4. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to any one of claims 1 or 2, characterized in that: Step 2 specifically includes: The state equation is expressed as X'=f(X, u)=AX+B[V in F L ] T +EV in 2 +F(T w -T b ) 2 +G(T w -T e ) 2 ; Where the coefficients of the linear terms A are 5*5 matrices and the coefficients of the linear terms B are 5*2 matrices, and the nonlinear terms V... in 2 The coefficient E is a 5*1 matrix, and the nonlinear terms (T) w -T b ) 2 The coefficient F is a 5*1 matrix, and the nonlinear terms (T) w -T e ) 2 The coefficient G is a 5*1 matrix. The number of linear terms in the state equation is n+r, the number of nonlinear terms is s, n is the number of variables in the state vector, and r is the number of input variables. The output equation is expressed as y=g(X,u)= CX+D[V in F L ] T +OV in 2 + PF L 0.5 + Q (T w -T b ) 2 +R (T w -T e ) 2 ; Where the coefficients of the linear terms C are 1*5 matrices and the coefficients of the linear terms D are 1*2 matrices, and the nonlinear terms V... in 2 The coefficients O and the nonlinear term F L 0.5 The coefficient P, the nonlinear term (T) w -T b ) 2 The coefficient Q, the nonlinear term (T) w -T e ) 2 The R coefficients are all scalars; the number of linear terms in the output equation is n+r, and the number of nonlinear terms is w.

5. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to claim 1, characterized in that: Step 3 specifically includes: Drive voltage V in It is an independent active input variable, and a discrete multi-tone excitation method is adopted based on the determination of the amplitude range and frequency range of the driving voltage; End load force F L It is an independent passive input variable or disturbance variable, whose excitation signal adopts constant value excitation or wandering excitation; Under the action of the excitation signal, the driving voltage V is synchronously acquired. in End load force F L The temperature T of the electrically driven working area w The base temperature T of the electrothermal micro-actuator b Temperature T at the end of the execution process e Ambient temperature T0, and drive current i The sampling frequency is greater than twice the maximum frequency of the excitation signal, and the number of sampling time series is Z.

6. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to claim 1, characterized in that: Step 4 specifically includes: Based on the linear and nonlinear terms in step 2 and the original data of state variables, input variables, and output variables collected in step 3, Constructing the state equations required for sparse identification of nonlinear dynamics. The state variable data matrix has Z rows and n columns, with the column data corresponding to [T], ... w ’ -T0 ’ T b ’ -T0 ’ T e ’ -T0 ’i’ i’’ The rows of data are arranged according to the sampling time sequence; the input data matrix has Z rows and n+r+s columns, and the column data correspond to [T], ... w -T0T b -T0 T e -T0 ii' V in F L V in 2 (T w -T b ) 2 T w -T e ) 2 The rows of data are arranged according to the sampling time sequence; Constructing the output equation required for sparse identification of nonlinear dynamics. The output variable matrix y is Z rows and m columns, and the input data matrix is ​​Z rows and n+r+w columns, with the column data corresponding to [T]... w -T0T b -T0 T e -T0 ii' V in F L V in 2 F L 0.5 (T w -T b ) 2 T w -T e ) 2 ], The sparse matrix in the state equation and output equation is solved by either the Sequential Threshold Least Squares (STLS) regression algorithm or the Sequential Threshold Ridge (STRidge) regression algorithm to obtain the continuous-time state equation and output equation of the electrothermal micro-actuator.

7. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to claim 1, characterized in that: Step 5 specifically includes: The backward difference method is used to transform the continuous-time state equation into a discrete-time state equation, which is expressed as: where T Sampling period, subscript k The sampling time number is used; the discrete-time state equation is about the current time. k and the previous moment k -1 state variable data, current time k Drive voltage data, end load force data, and usage cycle T The function; utilizing the measured state variable data of the current and previous moments, the driving voltage data of the current moment, and the periodicity. T It can solve for the load force value at the current moment, and realize online estimation of the end load force F. L ; The continuous-time output equation is transformed into a discrete-time output equation using the zero-order hold method. The discrete-time output equation is expressed as follows, where the subscript k is the sampling time number. Using the discrete-time output equation, the state variable data, driving voltage data, and the online estimated end load force F collected at the current time are utilized. L This allows us to calculate the output displacement at the current moment.

8. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to claim 7, characterized in that: When transforming continuous-time state equations into discrete-time state equations, considering the numerical stability, accuracy, and timeliness of the discrete-time model, forward difference method, central difference method, Runge-Kutta method, or bilinear transform method can also be used. When transforming continuous-time output equations into discrete-time output equations, considering the accuracy, timeliness, and smoothness of the discrete-time model, mean approximation method and interpolation method can also be used.

9. The force-displacement synchronous introspection sensing method at the end of an electrothermal micro-actuator according to claim 1, characterized in that: The method further includes: normalization and denoising of offline data in nonlinear dynamic sparse identification modeling in steps 4 and 5 above, normalization and denoising of online data in synchronous estimation of micro-actuator end load force and output displacement, and optimization of sampling time in the modeling and estimation process.

10. The force-displacement synchronous introspection sensing method at the end of an electrothermal microactuator according to any one of claims 1 or 3, characterized in that: The nonlinear terms in the state equation and output equation can be added according to the working mechanism of the micro-actuator, for example, by increasing the driving voltage V. in The coupling term V with current i in ﹒ i, the number s of nonlinear terms in the state equation can be increased or decreased, and the number w of nonlinear terms in the output equation can be increased or decreased.

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