CN106357794A - Distributed-network-based mechanical arm system failure detection method - Google Patents

Abstract

The invention discloses a distributed-network-based mechanical arm system failure detection method. The method comprises the following steps: (1) a Takagi-Sugeno model of a mechanical arm system is established; (2) a plurality of sensor nodes with communication and computing capabilities are configured, and each node measures the output data of a mechanical arm and performs data interaction with adjacent nodes to further generate a failure estimation signal; (3) parameters of the failure detection nodes are solved according to an inequation. According to the method, a failure signal can be rapidly and accurately tracked to realize effective detection of a failure, and the method has the advantages of high reliability, high computing capability, layout and wiring flexibility and the like.

Description

Distributed network-based mechanical arm system fault detection method

Technical Field

The invention relates to the field of mechanical arm control, in particular to a mechanical arm system fault detection method based on a distributed network.

Background

The mechanical arm is a mechanical device capable of automatically completing operation according to set setting and requirements, and can partially simulate and replace manual labor to complete complex operation. The arm system is widely used in the fields of industrial manufacturing, medical treatment, military, space exploration and the like.

However, in the use process of the existing mechanical arm system, power supply is abnormal, and the damage of the sensor, the driver or the connecting line and other parts can cause the system to be in fault, while the existing centralized fault detection technology can not find the fault in time, so that the possibility of damage and misoperation of the mechanical arm system can be caused, and meanwhile, the existing fault detection technology has low reliability and poor calculation capability, so that the application of the existing fault detection technology in the mechanical arm system can not be met.

Disclosure of Invention

The invention provides a distributed network-based mechanical arm system fault detection method which can avoid the problems of system modeling error, environmental interference, device aging and the like and effectively realize delay control, aiming at solving the technical problem of the prior art.

The technical problem to be solved by the invention is realized by the following technical scheme, and the mechanical arm system fault detection method based on the distributed network is characterized by comprising the following steps: (1) establishing a Takagi-Sugeno model of the mechanical arm system, and setting the following fuzzy rules:

if phi is₁Is psi_i1And phi is₂Is psi_i2And … and phi_tIs psi_itThen, then

x(k+1)＝A_ix(k)+B_iu(k)+D_iw(k)+E_if(k)

y_p(k)＝C_pix(k)+D_piw(k),i＝1,2,...,r. ①

Phi (k) in formula ① is [ phi ]₁(k),φ₂(k),...,φ_t(k)]Is the decision vector of the model, the symbol psi_ijRepresenting the corresponding fuzzy sets, the coefficient r representing the number of fuzzy rules; vector x (k) is the state variable of the model, vector u (k) is the input signal, vector w (k) is the unknown perturbation signal, vector f (k) is the failure signal, vector y_p(k) Is the p th causeThe system output signal measured by the barrier detection unit, matrix A_i，B_i，D_i，E_i，C_pi，D_piAll are known model parameter matrixes, and based on a fuzzy rule (1), a fuzzy model of the mechanical arm system is established:

$x(k+1)=\underset{i=1}{\overset{r}{\Σ}}{h}_i\left(\mathrm{\φ}\right(k\left)\right)\[A_{i}x\left(k\right)+B_{i}u\left(k\right)+D_{i}w\left(k\right)+E_{i}f\left(k\right)\],$

(2) configuring a plurality of sensor nodes with communication and calculation capabilities, wherein the number of the nodes is n, each node measures output data of the mechanical arm and performs data interaction with a neighboring node, and further generates a fault evaluation signal, and the specific operation process of each node can be described by the following model:

if phi is₁Is psi_i1And phi is₂Is psi_i2And … and phi_tIs psi_itThen, then

${\hat{x}}_p(k+1)=A_i{\hat{x}}_p\left(k\right)+B_{i}u\left(k\right)+E_i{\hat{f}}_p\left(k\right)-\underset{q=1}{\overset{n}{\Σ}}{a}_{pq}{H}_{pq}^i\left({\hat{y}}_q\right(k)-y_q(k\left)\right)$

${\hat{y}}_p\left(k\right)=C_{pi}{\hat{x}}_p\left(k\right),$

In the formula ③, in the formula,is the state vector of the fault detection node p,is an input to the corresponding fault detection node,then the fault estimation signal is generated for the corresponding fault detection node, with the coefficient p being 1,2Andis a programmable parameter matrix of the detection node,

(3) configuring fault detection node parameters, parameter matrixAndsolved by inequality ④, where scalar γ > 0 is the noise suppression indicator of the detector, matrix T and positive definite matrix P > 0 are matrix variables of appropriate dimension, L ═ 0I]， e_nIs an n-dimensional column vector, symbol, with all elements 1Representing the operation of the kronecker product,

determination of matrix variables by means of inequality ④Then, parameter matrixAndthe solution can be obtained as follows:

matrix variables in equation ⑤ And parameter matrixAndhas the following relationship:

element a in formula ⑥_ijFor fault detection of adjacency coefficient between nodes, if a_ij1 means that node i can receive data from node j, whereas a_ijIf 0, node i cannot receive data from node j.

Compared with the prior art, the method comprises the steps of 1) establishing a Takagi-Sugeno model of the mechanical arm system; 2) configuring a plurality of sensor nodes with communication and calculation capabilities, wherein each node respectively measures output data of the mechanical arm and performs data interaction with a neighbor node so as to generate a fault evaluation signal; 3) and solving the fault detection node parameters according to the inequality. The invention can quickly and accurately track the fault signal, realizes effective detection of the fault and has the advantages of high reliability, strong computing capability, flexible layout and wiring and the like.

Drawings

FIG. 1 is a schematic view of the flow structure of the present invention;

FIG. 2 is a schematic diagram of the fault diagnosis of the present invention;

FIG. 3 is an estimated signal generated by node one;

fig. 4 shows an estimated signal generated by node two.

Detailed Description

A fault detection method for a mechanical arm system based on a distributed network comprises the following steps: (1) establishing a Takagi-Sugeno model of the mechanical arm system, and setting the following fuzzy rules:

if phi is₁Is psi_i1And phi is₂Is psi_i2And … and phi_tIs psi_itThen, then

x(k+1)＝A_ix(k)+B_iu(k)+D_iw(k)+E_if(k)

y_p(k)＝C_pix(k)+D_piw(k),i＝1,2,...,r. ①

Phi (k) in formula ① is [ phi ]₁(k),φ₂(k),...,φ_t(k)]Is the decision vector of the model, the symbol psi_ijRepresenting the corresponding fuzzy sets, the coefficient r representing the number of fuzzy rules; vector x (k) is the state variable of the model, vector u (k) is the input signal, vector w (k) is the unknown perturbation signal, vector f (k) is the failure signal, vector y_p(k) Is the system output signal measured by the p-th fault detection unit, matrix A_i，B_i，D_i，E_i，C_pi，D_piAll are known model parameter matrixes, and based on a fuzzy rule (1), a fuzzy model of the mechanical arm system is established:

$x(k+1)=\underset{i=1}{\overset{r}{\Σ}}{h}_i\left(\mathrm{\φ}\right(k\left)\right)\[A_{i}x\left(k\right)+B_{i}u\left(k\right)+D_{i}w\left(k\right)+E_{i}f\left(k\right)\],$

(2) configuring a plurality of sensor nodes with communication and calculation capabilities, wherein the number of the nodes is n, each node measures output data of the mechanical arm and performs data interaction with a neighboring node, and further generates a fault evaluation signal, and the specific operation process of each node can be described by the following model:

if phi is₁Is psi_i1And phi is₂Is psi_i2And … and phi_tIs psi_itThen, then

${\hat{x}}_p(k+1)=A_i{\hat{x}}_p\left(k\right)+B_{i}u\left(k\right)+E_i{\hat{f}}_p\left(k\right)-\underset{q=1}{\overset{n}{\Σ}}{a}_{pq}{H}_{pq}^i\left({\hat{y}}_q\right(k)-y_q(k\left)\right)$

${\hat{y}}_p\left(k\right)=C_{pi}{\hat{x}}_p\left(k\right),$

In the formula ③, in the formula,is the state vector of the fault detection node p,is an input to the corresponding fault detection node,then the fault estimation signal is generated for the corresponding fault detection node, with the coefficient p being 1,2Andis a parameter matrix of a programmable detection node.

(3) The fault detection node parameters and parameter matrix in the step (2)Andsolved by inequality ④, where scalar γ > 0 is the noise suppression indicator of the detector, matrix T and positive definite matrix P > 0 are matrix variables of appropriate dimension, L ═ 0I]， e_nIs an n-dimensional column vector, symbol, with all elements 1Representing a kronecker product operation.

Determination of matrix variables by means of inequality ④Then, parameter matrixAndthe solution can be obtained as follows:

matrix variables in equation ⑤ And parameter matrixAndhas the following relationship:

element a in formula ⑥_ijFor fault detection of adjacency coefficient between nodes, if a_ij1 means that node i can receive data from node j, whereas a_ijIf 0, node i cannot receive data from node j.

Consider a single link rigid mechanical arm connected to a base by a revolute joint and with the plane of motion vertical, whose equation of motion is as follows:

θ represents the radian of the joint angle, M is 1.5kg of the weight of the load, M is 3kg of the weight of the rigid link, and g is 9.8M/s²Is a gravitational acceleration constant, l is the length of the mechanical arm connecting rod, J is 0.875kg m²The moment of inertia is defined as u, and the lowest vertical equilibrium position when the control torque applied to the joint is zero, is defined as θ.

Aiming at a system (VI), establishing the following T-S fuzzy model:

rule one is as follows: if x₁Close to 0, then

$\stackrel{\·}{x}=A_{1c}x+B_{1}u+w$

Rule two: if x₁Close to pi, then

In the formula ⑦, in the formula,

the fuzzy membership function of system ⑧ is h₁(x₁)＝(0.5π-|x₁|)/0.5π，h₂(x₁)＝1-h₁(x₁) Setting a controller K₁＝[10.5000 -5.1057]，K₂＝[3.8800 -5.0628]Sampling period T_s0.5s, the system ⑧ may be discretized as:

rule one is as follows: if x₁Close to 0, then

x(k+1)＝A₁x(k)+B₁w(k)

Rule two: if x₁Close to pi, then

x(k+1)＝A₂x(k)+B₂w(k) ⑨

Wherein,

this example considers the problem of drive failure, i.e., the actual torque applied to the drive deviates from the setpoint, setting parameter E in equations ② and ③_i＝B_i，C_pi＝[1 0]，D₁₁＝D₁₂＝0.1，D₂₁＝D₂₂＝0.3，

The failure detector parameters were found to be:

in the simulation, set noise w (k) to randomly generate between [ -0.5,0.5], generate f (k) as follows:

$f\left(k\right)=\left\{\begin{array}{cc}0& 0\&le;k<100;200\&le;k<300,\\ 5& 100\&le;k<200;300\&le;k<400.\end{array}\right.$

the simulation result is shown in the attached figure, and the fault estimation signal generated by the distributed fault detector can quickly and accurately track the fault signal, so that the fault can be effectively detected.

Claims (1)

1. A mechanical arm system fault detection method based on a distributed network is characterized by comprising the following steps:

(1) establishing a Takagi-Sugeno model of the mechanical arm system, and setting the following fuzzy rules:

if phi is₁Is psi_i1And phi is₂Is psi_i2And … and phi_tIs psi_itThen, then

x(k+1)＝A_ix(k)+B_iu(k)+D_iw(k)+E_if(k)

y_p(k)＝C_pix(k)+D_piw(k),i＝1,2,...,r. ①

Phi (k) in formula ① is [ phi ]₁(k)，φ₂(k)，…，φ_t(k)]Is the decision vector of the model, the symbol psi_ijRepresenting the corresponding fuzzy sets, the coefficient r representing the number of fuzzy rules; vector x (k) is the state variable of the model, vector u (k) is the input signal, vector w (k) is the unknown perturbation signal, vector f (k) is the failure signal, vector y_p(k) Is the system output signal measured by the p-th fault detection unit, matrix A_i，B_i，D_i，E_i，C_pi，D_piAll are known model parameter matrixes, and based on a fuzzy rule (1), a fuzzy model of the mechanical arm system is established:

$x(k+1)=\underset{i=1}{\overset{r}{\mathrm{\&Sigma;}}}{h}_i\left(\mathrm{\&phi;}\left(k\right)\right)[A_{i}x\left(k\right)+B_{i}u\left(k\right)+D_{i}w\left(k\right)+E_{i}f\left(k\right)],$

(2) configuring a plurality of sensor nodes with communication and calculation capabilities, wherein the number of the nodes is n, each node measures output data of the mechanical arm and performs data interaction with a neighboring node, and further generates a fault evaluation signal, and the specific operation process of each node can be described by the following model:

if phi is₁Is psi_i1And phi is₂Is psi_i2And … and phi_tIs psi_itThen, then

${\hat{x}}_p(k+1)=A_i{\hat{x}}_p\left(k\right)+B_{i}u\left(k\right)+E_i{\hat{f}}_p\left(k\right)-\underset{q=1}{\overset{n}{\&Sigma;}}{a}_{pq}{H}_{pq}^i\left({\hat{y}}_q\right(k)-y_q(k\left)\right)$

${\hat{y}}_p\left(k\right)=C_{pi}{\hat{x}}_p\left(k\right),$

In the formula ③, in the formula,is the state vector of the fault detection node p,is an input to the corresponding fault detection node,then the fault estimation signal is generated for the corresponding fault detection node, with the coefficient p being 1,2Andis a programmable testA matrix of parameters of the nodes is formed,

(3) configuring fault detection node parameters, parameter matrixAndby inequality ④

Solving, where the scalar gamma > 0 is the noise suppression index of the detector, the matrix T and the positive definite matrix P > 0 are matrix variables with appropriate dimensionality, and L ═ 0I]， e_nIs an n-dimensional column vector, symbol, with all elements 1Representing the operation of the kronecker product,

determination of matrix variables by means of inequality ④Then, parameter matrixAndthe solution can be obtained as follows:

matrix variables in equation ⑤And parameter matrixAndhas the following relationship:

element a in formula ⑥_ijFor fault detection of adjacency coefficient between nodes, if a_ij1 means that node i can receive data from node j, whereas a_ijIf 0, node i cannot receive data from node j.