A force balance control method using a six-dimensional active cellular micro-force sensor

Abstract

This invention discloses a force balance control method for a six-dimensional active cellular micro-force sensor. The micro-force sensor includes a probe, a moving platform, a base, and six measurement branches connecting the moving platform and the base. Each measurement branch consists of a flexible beam, a sensing layer, and a driving layer. The method includes: when the probe at the end of the micro-force sensor is subjected to an external measuring force, the flexible beam deforms accordingly; the real-time pose of the moving platform is measured by the sensing layer of each measurement branch; the difference between the real-time pose and the desired zero pose is used to obtain an error signal, which is then fed into a robust sliding mode predictive controller to generate a corresponding control law; the control law then passes through a damping compensator and a decoupler to obtain a control input voltage signal, which is applied to the driving layer. Under the voltage, the driving layer undergoes bending deformation, causing the moving platform pose to return to the desired equilibrium position. This invention effectively solves the problem of complex lumped interference and achieves the goal of fast response, strong robustness, and high stability force balance control.

Description

Technical Field

[0001] This invention relates to the field of micro-force detection in biological cells, and more specifically, to a force balance control method for a six-dimensional active cell micro-force sensor. Background Technology

[0002] As a crucial functional component in cellular micromanipulation robot systems, cellular microforce sensors enable real-time and comprehensive monitoring and analysis of forces during cell interaction, ensuring reliable operational quality and efficiency, minimizing cell damage, and improving cell survival rates. Since the contact forces that cells can withstand are generally in the micronewton to millinenewton range, various microforce sensor technologies have been proposed by researchers both domestically and internationally to achieve microforce measurement. These technologies can be broadly categorized into passive and active types based on their actuation methods. Passive microforce sensors obtain microforce measurement information "passively" by sensing the strain generated by an elastic body under external force through a force-sensitive element. This method offers advantages such as simple structural design and convenient application; however, limitations imposed by the elastic body's inherent stiffness, sensitivity, and the accuracy of the force-sensitive element make it difficult to simultaneously achieve millinenewton ranges with micronewton accuracy, resulting in poor versatility. The principle of active micro-force sensors is to integrate a drive unit into a traditional passive force sensor and use feedback control to generate a balanced force to ensure that the end of the sensor (such as a probe) is in a zero position, thereby realizing the "active" real-time measurement of external force, improving stiffness without reducing sensitivity, significantly expanding the measurement range, and effectively improving the force sensing accuracy.

[0003] Current research on active microforce sensors mainly adopts an integrated drive-sensing structural design, which satisfies functional requirements while enhancing compactness. However, this integrated drive-sensing approach also suffers from strong coupling nonlinearities (such as coupling of nonlinear effects like hysteresis, creep, and vibration), and the presence of time-varying uncertainties in the extracellular environment (such as culture medium viscosity, ambient temperature, and noise) exposes the system to complex lumped interference. Therefore, the ability to achieve fast response, strong robustness, and high stability force balance control in active microforce sensors under complex lumped interference directly impacts the sensor's final overall measurement performance.

[0004] In response to the above problems, scholars at home and abroad have conducted research on relevant control methods. For example, in the 2008 paper "Integrated IPMC / PVDF sensory actuator and its validation in feedback control" published in *Sensors and Actuators A: Physical*, a proportional-integral control method based on inverse model compensation was proposed to solve the force balance control problem of the coupling between the actuation and sensing layers in active micro-force sensors. In the 2019 paper "Modeling and experimental characterization of an active mems based force sensor" published in *Journal of Micro-Bio Robotics*, a weighted function-optimized H∞ force balance control strategy was proposed, avoiding actuator saturation and interference from unmodeled system dynamics. Furthermore, in the 2018 paper "An adjustable-stiffness MEMS force sensor: Design, characterization, and control" published in *Mechatronics*, a dual-loop control strategy was designed, and the sensor stiffness was adjustable for active force measurement by changing the control voltage. The inner loop uses resonant control to suppress system instability caused by the low damping characteristics of the structure, while the outer loop uses internal model control to improve the sensor's zero-position tracking performance, thereby significantly improving the measurement range and accuracy.

[0005] However, most existing force balance control strategies for micro-force sensors only address the nonlinear control problem of the sensor's own structure, lacking research on compensation for external environmental disturbances during actual cell manipulation. This fails to fully meet the high-precision and diverse application requirements of cell micromanipulation. Furthermore, the designed control strategies are all designed for low-dimensional sensor systems. Once extended to six-dimensional applications, the stability and robustness of the controllers are difficult to guarantee. For six-dimensional active micro-force sensor systems, the complex structure, strong coupling, and time-varying uncertainties of disturbances result in a much higher degree of nonlinearity than traditional low-dimensional systems, placing more stringent demands on the design and performance of the controller. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a six-dimensional active cellular micro-force sensor force balance control method to solve the complex lumped interference problem caused by the strong coupling nonlinearity between the extracellular environment and the structure itself, and to achieve online disturbance compensation and robust force balance control performance.

[0007] Technical Solution: A force balance control method for a six-dimensional active cellular microforce sensor, wherein the six-dimensional active cellular microforce sensor includes a probe, a moving platform, a base, and six measurement branches connecting the moving platform and the base. The probe is fixed to the moving platform, and each measurement branch consists of a flexible beam, a sensing layer, and a driving layer. The sensing layer and the driving layer are symmetrically bonded to both sides of the flexible beam. The method includes:

[0008] When the probe at the end of the micro-force sensor is subjected to an external measuring force, the flexible parallel elastomer undergoes corresponding deformation. The real-time pose q of the moving platform is obtained through the sensing layers of each measuring branch. The real-time pose q is then compared with the desired zero pose q. r The difference is used to obtain the error signal e, which enters the robust sliding mode predictive controller to generate the corresponding control law u. The control law u then passes through the damping compensator N(s) and the decoupler D(s) to obtain the control input voltage signal, which is then applied to the driving layer of each measurement branch. Under the action of the control input voltage, the driving layer undergoes bending deformation, so that the dynamic platform posture is restored to the desired equilibrium position.

[0009] Among them, the robust sliding mode predictive controller is designed for a single subsystem among the six subsystems decoupled from the micro-force sensor system, the i-th subsystem Σ i The output signal of the N-step sliding mode prediction model is:

[0010] S i (k)=Λ i s i (k)+Φ 2i e 2i (k)+Φ 1i e 1i (k)+Θ i E i (k)+Γ i U i (k)+Ξ i F i (k)+Ξ i R i (k)

[0011] The vector expressions are as follows:

[0012] S i (k)=[s i (k+1),s i (k+2),…,s i (k+N)] T ,

[0013]

[0014] U i (k)=[u i(k),u i (k+1),…,u i (k+N-1)] T ,

[0015] F i (k)=[f di (k),f di (k+1),…,f di (k+N-1)] T ,

[0016] R i (k)=[r i (k),r i (k+1),…,r i (k+N-1)] T

[0017] S i (k), E i (k), U i (k), F i (k), R i (k) are vectors composed of values ​​from the next N time steps, where S i (k) is a vector containing N future sliding mode variable values, where the element s i (k+1) represents the sliding mode variable value at the (k+1)th time step, s i (k+N) represents the sliding mode variable value at the (k+N)th time step; E i (k) is a vector containing N future error values, where the element sig(e 1i (k)) γi sig(e) represents the error value at the k-th time step. 1i (k+N-1)) γi U represents the error value at the (k+N-1)th time step; i (k) is a vector containing N future control input values, where the element u i (k) represents the control input value at the k-th time step, u i (k+N-1) represents the control input value at the (k+N-1)th time step; F i (k) is a vector containing N future perturbation values, where element f di (k) represents the perturbation value at the k-th time step, f di (k+N-1) represents the perturbation value at the (k+N-1)th time step; R i (k) is a vector containing N future reference signal values, where the element r i (k) represents the reference signal value at the k-th time step, r i(k+N-1) represents the reference signal value at the (k+N-1)th time step; h is the sampling interval. Let k be the k-th sampling point; For subsystem Σ i A continuously differentiable reference trajectory, and These are the tracking error and its velocity signal, y i (k) represents the subsystem Σ i The output vector; Λ i Φ 2i Φ 1i Θ i ,Γ i Ξ i These are the coefficient matrices for each corresponding vector.

[0018] Furthermore, the sliding mode variable value s i (k) is obtained through the discrete-time proportional-integral-differential type terminal sliding mode function, which is expressed as:

[0019] s i (k)=e 2i (k)+c 1i e 1i (k)+c 2i σ i (k-1),

[0020] The integral error term is:

[0021]

[0022] In the formula, c 1i ,c 2i >0, 0<γ i <1,

[0023] Furthermore, the discretized subsystem Σ i The state space is in the form of:

[0024]

[0025] In the formula, A ci Let B be the system matrix of the i-th subsystem. ci Let B be the control matrix of the input term of the i-th subsystem. c f i Let C be the control matrix for the disturbance term of the i-th subsystem. ci Let f be the output matrix of the i-th subsystem. pi Let be the interference vector of the i-th subsystem.

[0026] Furthermore, the decoupler D(s) is obtained through the following method:

[0027] The sensor dynamics model is rewritten in the following continuous-time state-space form:

[0028]

[0029] In the formula, t is the time quantity. y = [y i ] i＝1,…,6 =q represent the state vector and output vector, respectively; A c B c , These are the system matrix, input control matrix, and disturbance control matrix, respectively; C c =[I 6×6 ,0 6×6 ] represents the system output matrix; I 6×6 It is the identity matrix; The external lumped disturbance vector is bounded; the corresponding input-output transfer function model is:

[0030]

[0031] In the formula, s is the Laplace variable, and G ii (s) is the direct transfer function from the i-th input to the i-th output, G ij Let G(s) be the cross-coupling transfer function from the i-th input to the j-th output. Since the transfer function matrix G(s) is always invertible in actual operation, there exists a decoupling matrix D(s) such that the following equation holds:

[0032] G(s)D(s)=diag{G 11 (s),G 22 (s),…,G 66 (s)}

[0033] In the formula,

[0034]

[0035] Among them, D ij (s)=G ij (s) / G ii (s), i, j = 1, 2, ..., 6 and j ≠ i.

[0036] Furthermore, the damping compensator N(s) is based on the notch filter principle, and its specific form is as follows:

[0037] N(s)=diag{N1(s),N2(s),…,N6(s)}

[0038] The i-th term is:

[0039]

[0040] In the formula, j = 1, 2, ..., M represents the j-th principal resonance mode of the i-th subsystem, M is the number of resonance modes; s is the Laplace variable; k j z represents the notch filter gain relative to the j-th principal resonant mode. 1j z 2j Let p represent the two zeros of the notch filter relative to the j-th principal resonant mode. 1j p 2j These represent the two poles of the notch filter relative to the j-th main resonant mode.

[0041] Furthermore, the dissipation function of the sliding mode prediction model is:

[0042]

[0043] Where X = Λ i s i (k)+Φ 2i e 2i (k)+Φ 1i e 1i (k)+Θ i E i (k)+Ξ i F i (k)+Ξ i R i (k), The weight matrix is ​​used to adjust the magnitude of the control effect.

[0044] Furthermore, the input control voltage of the sliding mode prediction model follows the following constraints:

[0045] u min ≤u i (k+j-1)≤u max (i = 1, ..., 6; j = 1, ..., N)

[0046] In the formula, u min ,u max Let u and y represent the upper and lower bounds of the control action, respectively, and satisfy u. min ≤0≤u max .

[0047] Furthermore, the optimal control sequence of the robust sliding mode predictive controller is obtained by solving the following quadratic programming problem:

[0048]

[0049] stLU i (k)≤Ω

[0050] In the formula, P = Γ i T Γ i +W i ,

[0051]

[0052] In obtaining the optimal control sequence U i After (k), its first element u i (k) is the subsystem Σ i Robust sliding mode predictive control input law.

[0053] Beneficial Effects: This invention combines a designed decoupler, a damping compensator, and a robust sliding mode predictive controller to achieve a force balance control method that effectively solves the complex lumped interference problem faced by six-dimensional active micro-force sensors, realizing the goal of fast response, strong robustness, and high stability force balance control. The designed decoupler achieves decoupling characteristics, decoupling the coupled multi-input multi-output system into six independent single-input single-output subsystems, effectively suppressing cross-coupling nonlinear effects. The designed damping compensator attenuates vibration nonlinear effects caused by the system's high-frequency dynamics. Benefiting from the finite-time convergence of terminal sliding mode control and the fault-tolerant characteristics of model predictive control constraint handling, the robust sliding mode predictive controller designed in this invention complements the advantages of both, effectively suppressing nonlinear effects such as creep, hysteresis, and actuator saturation. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the six-dimensional active cell microforce sensor structure in this invention;

[0055] Figure 2 This is a block diagram of the force balance control structure of the active micro-force sensor based on robust sliding mode predictive control according to the present invention.

[0056] Figure 3 This is the frequency response characteristic curve of the micro-force sensor in this invention under the action of the decoupler;

[0057] Figure 4 This is the frequency response characteristic curve of the micro-force sensor in this invention under the action of the damping compensator;

[0058] Figure 5 This is a curve showing the position of the micro-force sensor probe under external force and the time response of the measured force in this invention. Detailed Implementation

[0059] The technical solutions in the embodiments of the present invention will now be clearly and completely described in conjunction with the accompanying drawings.

[0060] Figure 1 This is a schematic diagram of the six-dimensional active cellular microforce sensor structure of the present invention. Its structure mainly includes a probe, a moving platform, a base, and six measurement branches connecting the moving platform and the base. The probe is fixed to the moving platform, and the measurement branches are composed of a flexible beam, a PVDF (polyvinylidene fluoride) film, and an MFC (piezoelectric fiber composite) film. The PVDF film serves as the sensing layer, and the MFC film serves as the driving layer, symmetrically bonded to both sides of the flexible beam. Each measurement branch is arranged in a rotationally symmetrical pairwise around the sensor's centerline.

[0061] Figure 2 This is a block diagram of an active micro-force sensor force balance control structure based on robust sliding mode predictive control. When the probe at the end of the micro-force sensor is subjected to an external measured force, i.e., f... p During operation, the flexible parallel elastic body (i.e., the six flexible beams of the micro-force sensor) will undergo corresponding deformation. The real-time pose q of the moving platform can be obtained by measuring and calculating the PVDF sensing layer of each measurement branch. After obtaining the pose of the moving platform, it is compared with the desired zero pose q. r The difference is used to obtain the error signal e. The error signal e will enter the robust sliding mode predictive controller to generate the corresponding control law u. The control law u will then pass through the damping compensator N(s) and the decoupler D(s) to obtain the control input voltage signal, which will be applied to the MFC driving layer of each measurement branch of the sensor. Under the action of the control input voltage, the MFC driving layer will undergo bending deformation, so that the moving platform pose will be restored to the desired equilibrium position. Finally, by measuring the driving voltage of the six branches and combining it with the force mapping relationship of the flexible parallel mechanism, the six-dimensional force signal to be measured can be calculated.

[0062] According to an embodiment of the present invention, a decoupler is first designed for the six-dimensional micro-force sensor system to decouple the coupled multi-input multi-output system into six independent single-input single-output subsystems. Then, a damping compensator is designed for each subsystem to suppress high-frequency resonance. Based on this, a robust sliding mode predictive control method is used to perform zero-pose control on each subsystem, and an actual input control law that satisfies the constraints is designed. The specific implementation steps are as follows:

[0063] Step 1: Establish a dynamic model of a six-dimensional micro-force sensor.

[0064] Considering nonlinear lumped disturbances such as hysteresis, vibration, cross-coupling effects, and extracellular environmental disturbances, the dynamic model of the six-dimensional micro-force sensor can be expressed as follows:

[0065]

[0066] In the formula, t is the time quantity. These are the pose, velocity, and acceleration vectors of the moving platform, respectively. These are the nominal mass and the damping matrix, respectively; The nominal stiffness matrix; This is the Jacobian matrix that correlates the speed of the moving platform with the extension speed of each branch; T is the input voltage vector of the driving layer; em The electromechanical conversion ratio; It is a bounded external lumped disturbance vector, including model parameter uncertainties and unmodeled nonlinearities.

[0067] Step 2: Based on the dynamic model in Step 1, design a decoupler to suppress the cross-coupling effect in the multi-input multi-output sensor system.

[0068] Therefore, the sensor dynamics model is rewritten in the following continuous-time state-space form:

[0069]

[0070] In the formula, y = [y i ] i＝1,...,6 =q represents the state vector and the output vector, respectively; It refers to the differential of the state vector x, which is specifically composed of the velocity and acceleration of the moving platform; For the system matrix, These are the control matrices for the input term and the control matrix for the disturbance term, respectively; C c =[I 6×6 ,0 6×6 ] represents the output matrix; I 6×6 Let be the identity matrix. The corresponding input-output transfer function model is:

[0071]

[0072] In the formula, s is the Laplace variable, and G ii (s) is the direct transfer function from the i-th input to the i-th output, G ij Let G(s) be the cross-coupling transfer function from the i-th input to the j-th output. Since the transfer function matrix G(s) is always invertible in practice, there exists a decoupling matrix D(s) such that the following equation holds:

[0073]

[0074] In the formula,

[0075]

[0076] Among them, D ij (s)=G ij (s) / G ii(s), i,j=1,2,…,6 and j≠i. Therefore, the coupled multi-input multi-output sensor system is transformed into six independent single-input single-output subsystems G through the designed decoupler D(s). ii (s) i＝1,…,6 .

[0077] To verify the performance of the designed decoupler, Figure 3 Frequency response curves of a six-dimensional micro-force sensor system before and after decoupling (transfer function matrix G(s)) are presented. Figure 3 It can be seen that the direct transfer function of the main channel (diagonal downwards) remains the same before and after decoupling, while the transfer function of the cross-coupled channel is greatly attenuated in magnitude. Therefore, the coupled multi-input multi-output system is decoupled into six independent single-input single-output subsystems. Figure 3 In dB, decibels are represented, with specific units of μm / V or urad / V. Physically, it represents the ratio of output displacement to input voltage. Since the output displacement of the six-dimensional platform consists of three translations and three rotations, the first three units are μm / V, and the last three units are urad / V.

[0078] Step 3: Under the action of the decoupler in Step 2, design damping compensators for each subsystem to suppress high-frequency resonance of each subsystem.

[0079] The designed damping compensator is based on the notch filter principle, and its specific form is as follows:

[0080]

[0081] The i-th term is:

[0082]

[0083] In the formula, j = 1, 2, ..., M represents the j-th principal resonance mode of the i-th subsystem, and M is the number of resonance modes; k j z represents the notch filter gain relative to the j-th principal resonant mode. 1j z 2j Let p represent the two zeros of the notch filter relative to the j-th principal resonant mode. 1j p 2j These represent the two poles of the notch filter relative to the j-th principal resonant mode. By choosing an appropriate k... j z 1j z 2j and p 1j p 2j The value allows each damping compensator N to... iThe angular frequency of (s) is equal to or close to the main resonant frequency of each subsystem, thereby attenuating the corresponding resonant peak to a satisfactory level.

[0084] To demonstrate the performance of the designed damping compensator, Figure 4 The damping compensator (N) is given. i (s)), six-dimensional micro-force sensor (G ii (s) and the compensated system (G) ii (s)N i The frequency response characteristic curve (s) shows that, under the action of the damping compensator, the resonance peak of each channel subsystem is significantly suppressed. Note that the channels here refer to the control loops of the six decoupled subsystems.

[0085] Step 4: Based on the decouplers and damping compensators designed in Steps 2 and 3, the cross-coupling and vibration nonlinear effects in the sensor system are effectively suppressed. Feedback controllers can be designed separately for each subsystem.

[0086] This invention designs a robust sliding mode predictive controller that combines the finite-time convergence of terminal sliding mode control with the fault-tolerant characteristics of model predictive control constraint processing, effectively suppressing nonlinear effects such as creep, hysteresis, and actuator saturation.

[0087] Specifically, the design of the controller includes the following steps:

[0088] Step (1): Establish a discretized subsystem model.

[0089] To facilitate controller design, firstly, each subsystem G... ii (s) is extended to six generalized single-input single-output subsystems Σ1,…,Σ6, and for the i-th subsystem Σ i Its state-space form can be represented as:

[0090]

[0091] In the formula, Let u be the state vector. i To control the input, y i For subsystem output, f pi For unknown disturbances, A ci B ci , C ci This is the subsystem structure matrix.

[0092] Considering that the force balance control algorithm of the micro-force sensor is implemented through a discrete data sampling system, a zero-order hold is used to discretize the above subsystem model, i.e.:

[0093]

[0094] In the formula, And h is the sampling interval. This is the kth sampling point.

[0095] make For subsystem Σ i A continuously differentiable reference trajectory, and define e 1i (k)=yi(k)-yri(k), These are the tracking error and its velocity signal, y i (k) represents the subsystem Σ i The output vector. Using forward difference operations, and combining equation (9) and e 1i (k), e 2i By defining (k), we can obtain the following discrete-time error dynamics equation:

[0096]

[0097] In the formula, And due to the auxiliary vector r i The reference trajectory in (k) is predetermined and therefore a known quantity; while A di1 A di2 For A di The column vector, namely A di =[A di1 A di2 ].

[0098] Step (2): Establish a sliding mode prediction model.

[0099] Considering the robust anti-interference performance of the sliding mode variable structure, the following discrete-time proportional-integral-differential terminal sliding mode function is designed based on the error dynamics equation of formula (10):

[0100]

[0101] The integral error term is:

[0102]

[0103] In the formula,

[0104] Based on the sliding mode function of formula (11), the single-step forward sliding mode function s can be derived. i (k+1) is:

[0105]

[0106] Subtracting the sliding mode function from formula (11) and combining it with the error dynamics equation of formula (10), we can obtain:

[0107]

[0108] Formula (14) is the dynamic equation of the sliding mode in this invention, and also represents its single-step forward prediction model.

[0109] Based on the single-step forward prediction model of sliding mode state according to formula (14), if the recursion continues until the prediction time domain N is reached, and these N forward recursion equations are fused, the output signal of the N-step sliding mode prediction model can be obtained as follows:

[0110] S i (k)=Λ i s i (k)+Φ 2i e 2i (k)+Φ 1i e 1i (k)+Θ i E i (k)+Γ i U i (k)+Ξ i F i (k)+Ξ i R i (k)(15)

[0111] The vector expressions are as follows:

[0112]

[0113] Predictive control works by using information from the current k-th time step to predict information from the next N time steps. Therefore, S... i (k), E i (k), U i (k), F i (k), R i (k) consists of vectors composed of values ​​from the next N time steps, where...

[0114] S i (k) is a vector containing N future sliding mode variable values, where the element s i (k+1) represents the sliding mode variable value at the (k+1)th time step, s i (k+N) represents the sliding mode variable value at the (k+N)th time step;

[0115] E i (k) is a vector containing N future error values, where the element sig(e 1i (k)) γisig(e) represents the error value at the k-th time step. 1i (k+N-1)) γi This represents the error value at the (k+N-1)th time step;

[0116] U i (k) is a vector containing N future control input values, where the element u i (k) represents the control input value at the k-th time step, u i (k+N-1) represents the control input value at the (k+N-1)th time step;

[0117] F i (k) is a vector containing N future perturbation values, where element f di (k) represents the perturbation value at the k-th time step, f di (k+N-1) represents the perturbation value at the (k+N-1)th time step;

[0118] R i (k) is a vector containing N future reference signal values, where the element r i (k) represents the reference signal value at the k-th time step, r i (k+N-1) represents the reference signal value at the k+N-1th time step.

[0119] And the expressions for each coefficient matrix are as follows:

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] In the formula, A2 = ΨA di2 +hc 1i -1, A 11 =ΨA di1 A 12 =ΨA di2 B u =ΨB di , Γ 31 =B u +A2(1+A 12 B u +hA 11 B u Ξ31 =Ψ+A2(1+A 12 )Ψ+hA 11 Ψ.

[0127] Step (3): Establish a dissipation model.

[0128] According to the principle of model predictive control, in order to obtain the optimal control sequence in the finite time domain, it is necessary to define a suitable dissipation function and minimize it. Therefore, based on the sliding mode predictive model derived in step 4, the following dissipation function is defined:

[0129]

[0130] In the formula, The weight matrix is ​​used to adjust the magnitude of the control action. Since the sliding mode function defined in formula (11) is related to the tracking error, the dissipation function already includes the feedback correction process.

[0131] Substituting the sliding mode prediction model in formula (15) into the dissipation function in formula (23), we get:

[0132]

[0133] Where X = Λ i s i (k)+Φ 2i e 2i (k)+Φ 1i e 1i (k)+Θ i E i (k)+Ξ i F i (k)+Ξ i R i (k). Given the error-related term E i (k) and disturbance-related term F i (k) is unknown and the signal cannot be obtained, so a single-step time delay method is used for estimation, i.e.:

[0134]

[0135] Where f di (k-1) is obtained from the error dynamics equation in formula (10) as follows:

[0136] f di (k-1)=Ψ + e 2i (k)-A di1 e 1i (k-1)-A di2 e 2i (k-1)-B di ui (k-1)-r i (k-1) (26)

[0137] In the formula Ψ + Let be the generalized inverse of matrix Ψ.

[0138] Since the dissipation function equation in formula (23) does not contain the control sequence, it can be ignored during the optimization process. Therefore, the dissipation function can be further simplified to:

[0139]

[0140] Step (4): Add constraints.

[0141] In practical operation, the input control voltage usually needs to be limited to protect the driver from damage. Consider the following constraints:

[0142]

[0143] In the formula, u min ,u max Let u and y represent the upper and lower bounds of the control action, respectively, and satisfy u. min ≤0≤u max .

[0144] Step (5): By combining the dissipation function in formula (27) and the constraints in formula (28), the optimal control sequence can be obtained by solving the following quadratic programming problem:

[0145]

[0146] In the formula, In obtaining the optimal control sequence U i After (k), its first element u i (k) is the subsystem Σ i Robust sliding mode predictive control input law.

[0147] The method provided in this embodiment was used to perform zero-position tracking and force measurement simulation experiments for verification. The results are as follows: Figure 5 As shown, when a specified external force is applied in the Z direction, the six-dimensional active micro-force sensor also undergoes a corresponding displacement in the Z direction. However, under the adjustment of the robust force balance control method proposed in this invention, it can quickly return to the equilibrium position. Correspondingly, by calculating the driving voltage of each measurement branch, the final measured external force change curve is obtained, which shows that it is consistent with the actual applied external force, exhibiting good fast response capability and stable force measurement performance.

Claims

1. A force balance control method for a six-dimensional active cellular micro-force sensor, characterized in that, The six-dimensional active cellular microforce sensor includes a probe, a moving platform, a base, and six measurement branches connecting the moving platform and the base. The probe is fixed to the moving platform, and each measurement branch consists of a flexible beam, a sensing layer, and a driving layer. The sensing layer and the driving layer are symmetrically bonded to both sides of the flexible beam. The method includes: When the probe at the end of the micro-force sensor is subjected to an external measuring force, the flexible beam deforms accordingly. The real-time pose q of the moving platform is obtained through the sensing layer of each measuring branch. The real-time pose q is then compared with the desired zero pose q. r The difference is used to obtain the error signal e, which enters the robust sliding mode predictive controller to generate the corresponding control law u. The control law u then passes through the damping compensator N(s) and the decoupler D(s) to obtain the control input voltage signal, which is then applied to the driving layer of each measurement branch. Under the action of the control input voltage, the driving layer undergoes bending deformation, so that the dynamic platform posture is restored to the desired equilibrium position. Among them, the robust sliding mode predictive controller is designed for a single subsystem among the six subsystems decoupled from the micro-force sensor system, where the i-th subsystem ∑ i The output signal of the N-step sliding mode prediction model is: S i (k)=Λ i s i (k)+Φ 2i e 2i (k)+Φ 1i e 1i (k)+Θ i E i (k)+C i U i (k)+Ξ i F i (k)+Ξ i R i (k) The vector expressions are as follows: S i (k)=[s i (k+1),s i (k+2),…,s i (k+N)] T , YOU i (k)=[u i (k),u i (k+1),…,u i (k+N-1)] T , F i (k)=[f di (k),f di (k+1),…,f di (k+N-1)] T , R i (k)=[r i (k),r i (k+1),…,r i (k+N-1)] T S i (k), E i (k), U i (k), F i (k), R i (k) are vectors composed of values ​​from the next N time steps, where S i (k) is a vector containing N future sliding mode variable values, where the element s i (k+1) represents the sliding mode variable value at the (k+1)th time step, s i (k+N) represents the sliding mode variable value at the (k+N)th time step; E i (k) is a vector containing N future error values, where the elements are... This represents the error value at the k-th time step. This represents the error value at the (k+N-1)th time step, where 0 < γ. i <1; U i (k) is a vector containing N future control input values, where the element u i (k) represents the control input value at the k-th time step, u i (k+N-1) represents the control input value at the (k+N-1)th time step; F i (k) is a vector containing N future perturbation values, where element f di (k) represents the perturbation value at the k-th time step, f di (k+N-1) represents the perturbation value at the (k+N-1)th time step; R i (k) is a vector containing N future reference signal values, where the element r i (k) represents the reference signal value at the k-th time step, r i (k+N-1) represents the reference signal value at the (k+N-1)th time step; Let k be the k-th sampling point; For subsystem ∑ i The continuously differentiable reference trajectory, e 1i (k)=y i (k)-y ri (k) and These are the tracking error and its velocity signal, y i (k) represents the subsystem ∑ i The output vector; Λ i Φ 2i Φ 1i Θ i ,Γ i Ξ i These are the coefficient matrices for each corresponding vector, s i (k) represents the sliding mode variable value.

2. The method according to claim 1, characterized in that, The expressions for each coefficient matrix are as follows: In the formula, A2 = ΨA di2 +hc 1i -1, A 11 =ΨA di1 A 12 =ΨA di2 A di1 A di2 For A di The column vector, namely A di =[A di1 A di2 A di For the discretized subsystem ∑ i The system matrix; h is the sampling interval, B u =ΨB di B di For the discretized subsystem ∑ i Input control matrix; Γ 31 =B u +A2(1+A 12 B u +hA 11 B u Ξ 31 =Ψ+A2(1+A 12 )Ψ+hA 11 Ψ, c 1i ,c 2i >0; Ψ = [0,1].

3. The method according to claim 1, characterized in that, sliding mode variable value s i (k) is obtained through the discrete-time proportional-integral-differential type terminal sliding mode function, which is expressed as: s i (k)=e 2i (k)+c 1i e 1i (k)+c 2i σ i (k-1) The integral error term is: In the formula, c 1i ,c 2i >0, 4. The method according to claim 2, characterized in that, Discretized subsystem ∑ i The state space is in the form of: ∑ i : In the formula, C di =C ci A ci Let B be the system matrix of the i-th subsystem. ci Let be the control matrix of the input term of the i-th subsystem. Let C be the control matrix for the disturbance term of the i-th subsystem. ci Let f be the output matrix of the i-th subsystem. pi Let be the interference vector of the i-th subsystem.

5. The method according to claim 1, characterized in that, The decoupler D(s) is obtained by the following method: The sensor dynamics model is rewritten in the following continuous-time state-space form: In the formula, t is the time quantity. y = [y i ] i＝1,…,6 These are the state vector and the output vector, respectively; A c B c , These are the system matrix, input control matrix, and disturbance control matrix, respectively; C c =[I 6×6 ,0 6×6 ] represents the system output matrix; I 6×6 It is the identity matrix; The external lumped disturbance vector is bounded; the corresponding input-output transfer function model is: In the formula, s is the Laplace variable, and G ii (s) is the direct transfer function from the i-th input to the i-th output, G ij Let G(s) be the cross-coupling transfer function from the i-th input to the j-th output. Since the transfer function matrix G(s) is always invertible in actual operation, there exists a decoupling matrix D(s) such that the following equation holds: G(s)D(s)=diag{G 11 (s),G 22 (s),…,G 66 (s)} In the formula, Among them, D ij (s)=G ij (s) / G ii (s), i, j = 1, 2, ..., 6 and j ≠ i.

6. The method according to claim 5, characterized in that, The sensor dynamics model is expressed as follows: In the formula, These are the real-time pose, velocity, and acceleration vectors of the moving platform, respectively. These are the nominal mass and the damping matrix, respectively; The nominal stiffness matrix; This is the Jacobian matrix that correlates the speed of the moving platform with the extension speed of each branch; T is the input voltage vector of the driving layer; em This is the electromechanical conversion ratio.

7. The method according to claim 1, characterized in that, The damping compensator N(s) is based on the notch filter principle, and its specific form is as follows: N(s)=diag{N1(s),N2(s),…,N6(s)} The i-th term is: In the formula, j = 1, 2, ..., M represents the j-th principal resonance mode of the i-th subsystem, M is the number of resonance modes; s is the Laplace variable; k j z represents the notch filter gain relative to the j-th principal resonant mode. 1j z 2j Let p represent the two zeros of the notch filter relative to the j-th principal resonant mode. 1j p 2j These represent the two poles of the notch filter relative to the j-th main resonant mode.

8. The method according to claim 1, characterized in that, The dissipation function of the sliding mode prediction model is: Where X = Λ i s i (k)+Φ 2i e 2i (k)+Φ 1i e 1i (k)+Θ i E i (k)+Ξ i F i (k)+Ξ i R i (k), The weight matrix is ​​used to adjust the magnitude of the control effect.

9. The method according to claim 8, characterized in that, The input control voltage of the sliding mode prediction model follows these constraints: u min ≤u i (k+j-1)≤u max ,i=1,…,6;j=1,…,N In the formula, u min ,u max Let u and y represent the upper and lower bounds of the control action, respectively, and satisfy u. min ≤0≤u max .

10. The method according to claim 9, characterized in that, The optimal control sequence of the robust sliding mode predictive controller is obtained by solving the following quadratic programming problem: s.t.LU i (k)≤Ω In the formula, In obtaining the optimal control sequence U i After (k), its first element u i (k) is the subsystem ∑ i Robust sliding mode predictive control input law.

Images