A TLOE diagnosis and processing method for manipulator based on square sum evaluation function

Abstract

A method for diagnosing and processing TLOE of a robotic arm based on a sum-of-squares evaluation function relates to the technical field of robotic arm fault diagnosis. The Lagrangian dynamics model of the robotic arm is used to consider the trajectory tracking control problem of the robotic arm with external environmental interference and partial and total efficiency loss of the actuator. The preset performance passive fault-tolerant control law for efficiency loss is constructed through backstepping and adaptive law, and the interference is estimated by using an interference observer. Control laws are designed for the PLOE problem and the TLOE problem respectively, and a state observer is constructed to observe the system state. An active fault diagnosis scheme is designed, and a redundant control idea is used to construct a method for diagnosing and processing robotic arm faults based on the sum-of-squares evaluation function. The method realizes higher-precision, faster, and more adaptable fault diagnosis and processing of the robotic arm, and improves the tolerance of the robotic arm in complex environments.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical arm fault diagnosis, and in particular to a mechanical arm TLOE diagnosis and processing method based on a square sum evaluation function. Background Art

[0002] Trajectory tracking is an important technical means in the production process of robotic arms. It aims to ensure that the robotic arms maintain a stable state and accurate tracking effect during operation. Various control methods under this goal rely on the normal operation of the actuator. However, due to the complexity and variability of actual conditions, robotic arms are prone to failures due to problems such as motor jamming and component aging. These failures are very likely to damage the robotic arm system and even cause safety problems. Traditional simple passive fault-tolerant control is difficult to cope with complex actual conditions. Therefore, in addition to designing corresponding control laws for faults, active diagnosis of faults is also very important.

[0003] In the robot system, the actuator, as the main control component, is one of the components most prone to failure. From the perspective of the effectiveness of executing control commands, actuator failures can generally be divided into two typical types: partial loss of efficiency (PLOE) and total loss of efficiency (TLOE). PLOE type failure means that the performance degradation affects the actuator of one or more robot joints, while TLOE type failure means that the actuator of one or more robot joints is completely out of control, which usually causes more serious consequences than PLOE type failure. At present, scholars in this field have proposed many diagnostic schemes and corresponding control strategies for PLOE type failures encountered by robot arms, but there is a lack of effective diagnostic methods when facing TLOE type failures. Summary of the invention

[0004] In order to address the shortcomings of the background technology, the present invention provides a TLOE diagnosis and processing method for a robotic arm based on a square sum evaluation function, which adopts an interference observer and an adaptive law to estimate external disturbances and fault matrix parameters, and combines passive fault-tolerant control means with an active diagnosis method for TLOE, thereby achieving higher-precision, faster and more adaptable fault diagnosis and processing for the robotic arm, and improving the tolerance of the robotic arm in complex environments.

[0005] To achieve the above object, the present invention adopts the following technical solution: a mechanical arm TLOE diagnosis and processing method based on square sum evaluation function, comprising the following steps:

[0006] Step 1: Model the dynamic model of the robot arm, use the idea of ​​backstepping method and the means of adaptive estimation to construct a preset performance passive fault-tolerant control law to deal with efficiency loss, including the control law for PLOE problem and the control law for TLOE problem, specifically including:

[0007] Considering the robot arm trajectory tracking control problem with external environmental interference and partial efficiency loss of the actuator, the actuator fault is expressed as follows:

[0008] τ(t)=ρτ c (t)+h

[0009] Where τ(t) is the actual control torque output by the actuator affected by efficiency loss, τ c (t) is the control torque to be designed output by the controller, ρ=diag(ρ1,ρ2,...,ρ n ) is the efficiency diagonal matrix and satisfies 0≤ρ i ≤1i=1,2,...,n, n is the number of degrees of freedom of the robot arm, when the i-th joint actuator encounters TLOE, ρ i Take 0, h is the offset, which only exists when the manipulator system encounters TLOE;

[0010] The Lagrangian dynamic equation of the robotic arm is:

[0011]

[0012] Where M(q) is the inertia matrix of the robot arm, is the Coriolis force matrix of the robot, G(q) is the gravity of the robot, q is the joint position, and d(t) is the external disturbance;

[0013] The preset performance convergence is used as the performance target, and the positive definite performance function ρ(t) is selected as follows:

[0014] ρ(t)=(ρ0-ρ ∞ ) -βt +ρ ∞

[0015] Where ρ0,ρ ∞ are all positive real numbers, e -βt is the minimum allowed convergence rate of the error curve;

[0016] Error curve e(t) = qq d ,q d is the trajectory to be tracked, e(t)=[e1(t),e2(t),...,e n (t)] T When the initial error e(0) is positive and negative, the overshoot of e(t) is constrained by -σρ(t) and σρ(t), respectively, 0<σ<1 and is a positive real number, and the steady-state error boundary is given by ρ ∞ ,σρ ∞ Determine, σρ0 reflects the error overshoot value;

[0017] The asymmetric time-varying barrier Lyapunov function direct method is used to deal with the preset performance problem. The time-varying function is shown as follows:

[0018]

[0019] In the formula, and k (t) = [ k 1(t), k 2(t),..., k n (t)] T represent the upper and lower boundaries of the steady-state error, respectively.

[0020] Introducing sliding mode variables for dimension reduction error variables S=[S1,S2,...,S n ] T , where Λ is a positive definite diagonal matrix, let P(e)=[P(e1),...,P(e n )] T ;

[0021] In order to apply the characteristics of the robotic arm, a new Lyapunov function is introduced as follows:

[0022]

[0023]

[0024] Utilizing the characteristics of the robotic arm Eliminate the relevant terms in the above formula to simplify the subsequent derivation;

[0025] Introduce a virtual control law α, α=[α1,α2,...,α n ] T ,as follows:

[0026]

[0027] Where K2 is a positive definite diagonal matrix, is the interference estimate obtained by the interference observer;

[0028] Definition B = ρ -1 =diag(b1,b2,...,b n ),Pick For b i The estimated value of make Further construct the following Lyapunov function:

[0029]

[0030] The design adaptation rate is as follows:

[0031]

[0032] In the formula, γ i represents the adaptive parameter, which is a positive real number;

[0033] Finally, the control law for the PLOE problem is constructed as follows:

[0034]

[0035] Considering the robot trajectory tracking control problem with external environmental interference and actuator total efficiency loss, it is necessary to apply the actual control torques τ1(t) and τ2(t) output by two actuators at the same joint to deal with the complete loss of control of one actuator. Therefore, τ(t) = τ1(t) + τ2(t) = -α. The control torque to be designed output by the adaptive estimation controller is definition: as well as Represents k ji The estimate, j=3,4,5,6, then:

[0036]

[0037] Where ρ1, ρ2 are the efficiency diagonal matrices of the two actuators, ρ1 = diag(ρ 11 ,ρ 12 ,...,ρ 1n ), ρ2=diag(ρ 21 ,ρ 22 ,...,ρ 2n ), h1, h2 are the offsets of the two actuators;

[0038] The design adaptation rate is as follows:

[0039]

[0040] In the formula, γ 3i ,γ 4i ,γ 5i ,γ 6i Represents the adaptive parameter, which is a positive real number, and the Lyapunov function is as follows:

[0041]

[0042] Finally, the control law for the TLOE problem is constructed as follows:

[0043]

[0044] Step 2: Construct a diagnostic processing method for the robot arm TLOE fault based on the square sum evaluation function, which specifically includes:

[0045] Diagnose TLOE faults and decide whether to use redundant actuators based on the diagnosis results;

[0046] Pick The Lagrangian dynamics equation of the robotic arm is transformed into the following form:

[0047]

[0048] in, Design a state observer to observe the system state as follows:

[0049]

[0050] Among them, l1, l2 are the diagonal matrices of unknown constants, λ1, λ2 are the observations of states x1, x2;

[0051] Define the residual:

[0052]

[0053] Among them, r1, r2 represent the observation error of the state;

[0054] The Lyapunov function is selected as follows:

[0055] V r =r T Pr r=[r1,r2] T

[0056] Among them, P is a positive definite matrix, and the derivative of the above formula is:

[0057]

[0058] Where H = [0, M -1 (q)(ρ-I)] T , D=[0,M -1 (q)] T , Q is a symmetric positive definite matrix, and there exists a positive real number ε that satisfies This proves that the residual sum of squares is bounded, and based on it, a fault diagnosis method is constructed;

[0059] Select the sum of squares evaluation function and determine the diagnostic processing method. The sum of squares evaluation function is as follows:

[0060]

[0061] Use the residual change as a diagnostic:

[0062] R=|Δr1|+|Δr2|

[0063] Among them, Δr1 and Δr2 represent the changes of residuals r1 and r2 respectively;

[0064] The processing method is as follows:

[0065] 1) Introduce the instant signal. Once the residual change R exceeds the preset threshold and causes a sudden TLOE fault, the instant signal value is 1;

[0066] 2) Using signal latching means, latch the value at the rising edge of the instant signal to retain the fault characteristics and obtain the signal Instant;

[0067] 3) Select two sets of thresholds, Baverage_th and Saverage_th, one large and one small, for the mean image of the sum of squares evaluation function. For a sudden TLOE fault, if the Instant signal is 1, the threshold is Saverage_th; for a gradual TLOE fault, if the Instant signal is 0, the threshold is Baverage_th; if the actuator is connected to the robotic arm system, the threshold is Saverage_th;

[0068] 4) Introduce the TLOE signal, and perform a smoothing process on the average of the sum of squares evaluation function curve. On this basis, select the average threshold value average_th according to the expected cutoff efficiency. If the average value of the sum of squares evaluation function of any joint is greater than average_th, or Instant is 1, the TLOE signal is set to 1;

[0069] 5) Introduce the fault signal, select the fault threshold fault_th, and when the mean of the sum of squares evaluation function is less than fault_th, set the TLOE signal to 0.

[0070] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention utilizes the Lagrangian dynamic model of the robotic arm, takes into account external environmental interference, adopts interference observers and adaptive laws to estimate external disturbances and fault matrix parameters, and combines passive fault-tolerant control means with active diagnosis methods for TLOE, thereby achieving higher-precision, faster, and more adaptable fault diagnosis and processing for the robotic arm. It is particularly suitable for robotic arm systems that need to be used for a long time and cannot be easily powered off for maintenance. Through the coordinated use of multiple detection means, it can detect multiple fault forms, improve the tolerance of the robotic arm in the face of complex environments, and provide a comprehensive solution for robotic arm trajectory tracking control under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a system block diagram of the method of the present invention;

[0072] Figure 2 is the performance boundary curve when the initial error is positive;

[0073] Figure 3 It is the performance boundary curve when the initial error is negative;

[0074] Figure 4 It is the joint 1 square sum evaluation function value under the gradual TLOE with redundant actuators throughout the process;

[0075] Figure 5 It is the mean of the joint 1 square sum evaluation function under the gradual TLOE with redundant actuators throughout the process;

[0076] Figure 6 It is the mean curve of the sum of squares evaluation function under the gradual TLOE

[0077] Figure 7 It is the instant signal curve under mutant TLOE;

[0078] Figure 8 It is the Instant signal curve under mutant TLOE;

[0079] Fig. 9 It is the fault signal curve under mutant TLOE;

[0080] Fig.10 is the TLOE signal curve under mutant TLOE;

[0081] Fig.11 It is a fault detection signal flow chart;

[0082] Fig.12 is the mutant TLOE variable R curve in the embodiment;

[0083] Fig.13 : is the fault judgment signal image of the mutant TLOE in the embodiment;

[0084] Fig.14 is the position error curve of the mutant TLOE joint 1 in the embodiment;

[0085] Fig.15 is the position error curve of the mutant TLOE joint 2 in the embodiment;

[0086] Fig.16 is the control torque curve of each actuator of the mutant TLOE in the embodiment;

[0087] Fig.17is the mean value curve of the gradual TLOE joint performance function in the embodiment;

[0088] Fig.18 : is the image of each fault judgment signal of the gradual change type TLOE in the embodiment;

[0089] Fig.19 is the position error curve of the gradual TLOE joint 1 in the embodiment;

[0090] Fig. 20 is the position error curve of the gradual TLOE joint 2 in the embodiment;

[0091] Fig.21 : is the control torque curve of each actuator of the gradual TLOE in the embodiment. DETAILED DESCRIPTION

[0092] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0093] like Figures 1 to 11 As shown, a robot arm TLOE diagnosis and processing method based on a square sum evaluation function includes the following steps:

[0094] Step 1: Model the dynamic model of the robot arm, use the idea of ​​backstepping method and the means of adaptive estimation to construct a preset performance passive fault-tolerant control law to deal with efficiency loss, including the control law for PLOE problem and the control law for TLOE problem, as follows:

[0095] Considering the robot arm trajectory tracking control problem with external environmental interference and partial efficiency loss of the actuator, the actuator fault is expressed as follows:

[0096] τ(t)=ρτ c (t)+h

[0097] Where τ(t) is the actual control torque output by the actuator affected by efficiency loss, τ c (t) is the control torque to be designed output by the controller, ρ=diag(ρ1,ρ2,...,ρ n ) is the efficiency diagonal matrix and satisfies 0≤ρ i ≤1i=1,2,...,n, n is the number of degrees of freedom of the robot arm, when the i-th joint actuator encounters TLOE, ρ i Take 0, h is the offset, and exists only when the robot system encounters TLOE.

[0098] The Lagrangian dynamic equation of the robotic arm is:

[0099]

[0100] Where M(q) is the inertia matrix of the robot arm, is the Coriolis force matrix of the robot, G(q) is the gravity of the robot, q is the joint position, and d(t) is the external disturbance.

[0101] Since we want to ensure both the transient and steady-state performance of the robotic arm system, we use the preset performance convergence as the performance target and select the positive definite performance function ρ(t) as follows:

[0102] ρ(t)=(ρ0-ρ ∞ ) -βt +ρ ∞

[0103] Where ρ0,ρ ∞ are all positive real numbers, e -βt is the minimum allowed convergence rate of the error curve.

[0104] Combination Figure 2-3 As shown, the error curve e(t) = qq d ,q d is the trajectory to be tracked, e(t)=[e1(t),e2(t),...,e n (t)] T , i = 1, 2, ..., n, when the initial error e(0) is positive and negative (within the initial value of the performance boundary), the overshoot of e(t) is constrained by -σρ(t) and σρ(t), respectively, 0 < σ < 1 and is a positive real number, and the steady-state error boundary is given by ρ ∞ ,σρ ∞ Determine that σρ0 reflects the error overshoot value.

[0105] The asymmetric time-varying barrier Lyapunov function direct method is used to deal with the preset performance problem. The time-varying function is shown as follows:

[0106]

[0107] In the formula, and k (t) = [ k 1(t), k 2(t),..., k n (t)] T Represent the upper and lower boundaries of the steady-state error, i=1,2,...,n,

[0108] Introduce sliding mode variables S = e(t) + Λe(t) for dimension reduction error variables, S = [S1, S2, ..., S n ] T , i = 1, 2, ..., n, where Λ is a positive definite diagonal matrix, let P(e)=[P(e1),...,P(e n )] T .

[0109] In order to apply the characteristics of the robotic arm, a new Lyapunov function is introduced as follows:

[0110]

[0111]

[0112] Can take advantage of the robot arm characteristics Eliminate the relevant terms in the above formula to simplify the subsequent derivation.

[0113] Introduce a virtual control law α, α=[α1,α2,...,α n ] T , i=1,2,...,n, as follows:

[0114]

[0115] Where K2 is a positive definite diagonal matrix, is the disturbance estimate obtained by the disturbance observer.

[0116] So we have:

[0117]

[0118] Adaptive estimation is used to estimate the elements of the efficiency diagonal matrix ρ to achieve the control compensation effect. It is hoped that the control torque τ c The selection of (t) can offset the virtual control law α, and define B = ρ -1 =diag(b1,b2,...,b n ),Pick For b i The estimated value of i=1,2,...,n, let Further construct the following Lyapunov function:

[0119]

[0120] The design adaptation rate is as follows:

[0121]

[0122] In the formula, γ i Represents the adaptive parameter, which is a positive real number. After substituting it into the Lyapunov function and scaling it, we get:

[0123]

[0124] In the formula, V3(t) represents the value of V3 at time t, V3(0) represents the initial value of V3, λ min ,λ max Respectively represent the minimum and maximum values ​​of the matrix eigenvalues, K1 is a positive definite matrix, is the minimum allowed convergence rate of the Lyapunov function V3.

[0125] Finally, the control law for the PLOE problem is constructed as follows:

[0126]

[0127] Considering the robot trajectory tracking control problem with external environmental interference and actuator total efficiency loss, it is necessary to apply the actual control torques τ1(t) and τ2(t) output by two actuators at the same joint to deal with the complete loss of control of one actuator. Therefore, τ(t) = τ1(t) + τ2(t) = -α. The control torque to be designed output by the adaptive estimation controller is definition: as well as Represents k ji The estimate, i=1,2,...,n,j=3,4,5,6,then:

[0128]

[0129] Where ρ1, ρ2 are the efficiency diagonal matrices of the two actuators, ρ1 = diag(ρ 11 ,ρ 12 ,...,ρ 1n ), ρ2=diag(ρ 21 ,ρ 22 ,...,ρ 2n ), i = 1, 2, ..., n, h1, h2 are the offsets of the two actuators.

[0130] The design adaptation rate is as follows:

[0131]

[0132] In the formula, γ 3i ,γ 4i ,γ 5i ,γ6i Represents the adaptive parameter, which is a positive real number, and the Lyapunov function is as follows:

[0133]

[0134] Substituting the adaptive law into the Lyapunov function, we get:

[0135]

[0136] In the formula,

[0137]

[0138] Finally, the control law for the TLOE problem is constructed as follows:

[0139]

[0140] Step 2: Construct a diagnostic processing method for the robot arm TLOE fault based on the square sum evaluation function, as follows:

[0141] 2.1. The control law designed in step 1 is relatively passive. In order to avoid the damage to the system caused by TLOE failures that may occur at any time, two actuators need to be applied to the same control joint to work together. This will cause a waste of resources when actual failures occur less frequently. Therefore, it is necessary to diagnose the TLOE failure and decide whether to use redundant actuators based on the diagnosis results.

[0142] Pick The Lagrangian dynamics equation of the robotic arm is transformed into the following form:

[0143]

[0144] in, Design a state observer to observe the system state as follows:

[0145]

[0146] Among them, l1, l2 are diagonal matrices of unknown constants, and λ1, λ2 are the observations of states x1, x2.

[0147] Define the residual:

[0148]

[0149] Among them, r1, r2 represent the observation error of the state, and the derivative can be obtained:

[0150]

[0151]

[0152] Where I is the identity matrix of the same dimension as ρ, The Lyapunov function is selected as follows:

[0153] V r =r T Pr r=[r1,r2] T

[0154] Among them, P is a positive definite matrix, and the derivative of the above formula is:

[0155]

[0156] Where H = [0, M -1 (q)(ρ-I)] T , D=[0,M -1 (q)] T , Q is a symmetric positive definite matrix, and there exists a positive real number ε that satisfies It can be proved that the residual sum of squares is bounded, and a fault diagnosis method can be constructed based on it;

[0157] 2.2. Select the sum of squares evaluation function and determine the diagnostic processing method, as follows:

[0158] Common evaluation functions are square and integral functions, with a constant as the threshold:

[0159]

[0160] It will increase slowly when there is no fault. Once a fault occurs, the function curve will increase sharply and exceed the threshold. However, this method will make the function value eventually exceed the set threshold even if there is no fault throughout the process. In addition, the detection speed is not fast enough when a fault occurs. If a TLOE fault occurs, the system will be damaged due to untimely switching of the control method.

[0161] Therefore, the sum of square functions is selected as the evaluation function:

[0162]

[0163] The diagnostic method is determined according to the evaluation function. Prior to this, the detection target needs to be clarified. Since PLOE faults with low efficiency loss can be handled by the adaptive control law of a single actuator, the focus of fault diagnosis will be on TLOE faults and PLOE faults with high efficiency loss (also identified as TLOE) to determine when redundant actuators need to be introduced. In addition, from the perspective of the time when the fault occurs, there are two types of TLOE faults: sudden and gradual. A sudden TLOE fault refers to an actuator whose efficiency becomes 0 at a certain moment or in a very short time; a gradual TLOE fault refers to an actuator whose output efficiency gradually decreases until it approaches TLOE. To detect the two TLOE fault conditions, it is necessary to maintain an extremely fast detection speed for the sudden TLOE fault, and at the same time have a high tolerance for the gradual TLOE fault (the efficiency is low enough to trigger the judgment).

[0164] Since the fault-tolerant control itself will control and compensate for the fault when it occurs, the characteristics of the fault will be concealed. In the early stage of the sudden TLOE fault, the fault cannot be quickly diagnosed by the given threshold. Therefore, the residual change with a faster and stronger reaction is used as a diagnostic method:

[0165] R=|Δr1|+|Δr2|

[0166] Where Δr1 and Δr2 represent the changes of residuals r1 and r2 respectively.

[0167] When appropriate parameter thresholds are selected, this diagnostic method can detect sudden TLOE faults at a very fast speed and apply redundant actuators to avoid system crashes when encountering serious faults. The selection of the threshold R_th should ensure that R is reached in a very short time in the case of sudden TLOE faults and will not or is difficult to reach in the case of gradual TLOE faults. This detection method is used to detect sudden TLOE faults.

[0168] Taking the joint 1 square sum evaluation function value and mean image under the condition of full access to redundant actuators as an example, the square sum evaluation function curve may fluctuate up and down due to the characteristics of tracking signals and interference signals. Figure 4 As shown, it is not conducive to the conventional constant threshold for detection at this time, so the square sum evaluation function curve is smoothed by taking the mean value, combined with Figure 5 As shown, on this basis, the average threshold value average_th is selected according to the expected cutoff efficiency. Once the mean value of the sum of square evaluation function reaches average_th, it can be determined that the actuator efficiency is lower than a certain level, that is, a TLOE fault is considered to have occurred. This detection method is used to detect gradual TLOE faults.

[0169] After the fault is detected and relevant control measures are applied, it is necessary to consider the actuator return after the fault is eliminated. A value slightly higher than the fault-free case is selected as the fault threshold fault_th. If the mean of the sum of squares evaluation function is less than fault_th, it can be determined that the fault has disappeared and the actuator can be retracted from the redundant actuator to the single actuator.

[0170] In actual simulation and experiment, when considering the case of progressive TLOE failure, the introduction of redundant actuators due to the detection of failure in the middle will cause the relevant parameters to mutate at this moment, resulting in a sudden decrease in the mean of the sum of squares evaluation function. Figure 6 As shown, this affects the fault detection judgment. In order to maintain the original judgment result unchanged, a new judgment condition needs to be added here: introduce two groups of thresholds, one large and one small. The larger group of thresholds is Baverage_th, and the smaller group of thresholds is Saverage_th. When the slave actuator is connected to the robotic arm system, the average threshold average_th is lowered to Saverage_th. Baverage_th can ensure that the TLOE fault is detected only when the actuator efficiency is low enough, avoiding the detection method from being overly sensitive. After the slave actuator is introduced, lowering the threshold will not affect the detection result and can avoid the above practical problems.

[0171] The specific implementation method is as follows:

[0172] 1) Introduce instant signal. Once the residual change R exceeds the preset threshold, resulting in a sudden TLOE fault, the instant signal value is 1. Figure 7 As shown;

[0173] 2) Using signal latching means, latch the value at the rising edge of the instant signal to retain the fault characteristics, obtain the signal Instant, and combine Figure 8 As shown;

[0174] 3) Select two sets of thresholds, Baverage_th and Saverage_th, for the mean image of the sum of squares evaluation function. For a sudden TLOE fault, if the Instant signal is 1, the threshold is Saverage_th; for a gradual TLOE fault, if the Instant signal is 0, the threshold is Baverage_th; if the actuator is connected to the robotic arm system, the threshold is Saverage_th;

[0175] 4) Introduce TLOE signal, any joint square sum evaluation function mean is greater than average_th, indicating that a gradual TLOE fault with sufficiently low efficiency is detected, or Instant is 1, indicating that a sudden TLOE fault is detected, and the TLOE signal is set to 1;

[0176] 5) Introduce the fault signal, select the fault threshold fault_th, and when the mean of the square sum evaluation function is less than fault_th, set the TLOE signal to 0.

[0177] Fault signal and TLOE signal combination Fig. 9 , 10 As shown, the overall signal flow combines Fig.11 shown.

[0178] Example

[0179] For a two-degree-of-freedom robotic arm system with external environmental interference, a dynamic model is established, and the robotic arm parameters and initial values ​​of joint position angles and velocities are selected as follows:

[0180]

[0181] q=[q1,q2] T , k1=k2=0.01625,I z1 =I z2 =0.027,

[0182]

[0183]

[0184]

[0185] g=9.81,G(q)=[g1,g2] T

[0186]

[0187] Signal to be tracked Interference signal σ=0.9,positive definite performance function ρ(t)=(1.5-0.02)e -t +0.02, K1=diag(5,5), K2=diag(20,20), Λ=diag(7,7), adaptive constant is γ 3i =γ 4i =0.01,γ 5i =γ 5i =0.02.

[0188] The simulation uses Simulink, and the running time is set to 0 to 100 seconds. The threshold values ​​are selected as follows:

[0189]

[0190] The sudden TLOE fault and the gradual TLOE fault are selected as follows:

[0191] Mutant

[0192]

[0193] Gradient

[0194]

[0195] According to the proposed control law and state observer, the simulation results of the sudden TLOE fault are combined with Figures 12 to 16 As shown in the figure, the simulation results considering the gradual TLOE fault are combined with Figures 17 to 21 As shown. Fig.14 , 15 , 19, and 20, it can be clearly seen that the tracking position error of the robot arm meets the preset performance bounds and converges quickly after adopting the control method, which illustrates the effectiveness of the control law proposed in the present invention. Fig.16 , 21 The control torque of each actuator under two fault conditions is given. The startup time of the actuator meets the goal of fast detection speed in the case of sudden TLOE faults and sufficiently low efficiency in the case of gradual TLOE faults. This shows the effectiveness of the fault detection scheme. Fig.14 , 15 It can also be seen that even in the face of harsh mutation TLOE faults, the error can be guaranteed not to fluctuate significantly and stay close to the performance boundary.

[0196] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0197] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A robot arm TLOE diagnosis and processing method based on square sum evaluation function, characterized by: The following steps are involved: Step 1: Model the dynamic model of the robot arm, use the idea of ​​backstepping method and the means of adaptive estimation to construct a preset performance passive fault-tolerant control law to deal with efficiency loss, including the control law for PLOE problem and the control law for TLOE problem, specifically including: Considering the robot arm trajectory tracking control problem with external environmental interference and partial efficiency loss of the actuator, the actuator fault is expressed as follows: τ(t)=ρτ c (t)+h Where τ(t) is the actual control torque output by the actuator affected by efficiency loss, τ c (t) is the control torque to be designed output by the controller, ρ=diag(ρ1,ρ2,...,ρ n ) is the efficiency diagonal matrix and satisfies 0≤ρ i ≤1i=1,2,...,n, n is the number of degrees of freedom of the robot arm, when the i-th joint actuator encounters TLOE, ρ i Take 0, h is the offset, which only exists when the manipulator system encounters TLOE; The Lagrangian dynamic equation of the robotic arm is: Where M(q) is the inertia matrix of the robot arm, is the Coriolis force matrix of the robot, G(q) is the gravity of the robot, q is the joint position, and d(t) is the external disturbance; The preset performance convergence is used as the performance target, and the positive definite performance function ρ(t) is selected as follows: ρ(t)=(ρ0-ρ ∞ )e -βt +r ∞ Where ρ0,ρ ∞ are all positive real numbers, e -βt is the minimum allowed convergence rate of the error curve; Error curve e(t) = qq d ,q d is the trajectory to be tracked, e(t)=[e1(t),e2(t),...,e n (t)] T When the initial error e(0) is positive and negative, the overshoot of e(t) is constrained by -σρ(t) and σρ(t), respectively, 0<σ<1 and is a positive real number, and the steady-state error boundary is given by ρ ∞ ,σρ ∞ Determine, σρ0 reflects the error overshoot value; The asymmetric time-varying barrier Lyapunov function direct method is used to deal with the preset performance problem. The time-varying function is shown as follows: In the formula, and k (t) = [ k 1(t), k 2(t),..., k n (t)] T represent the upper and lower boundaries of the steady-state error, respectively. Introducing sliding mode variables for dimension reduction error variables S=[S1,S2,...,S n ] T , where Λ is a positive definite diagonal matrix, let P(e)=[P(e1),...,P(e n )] T ; In order to apply the characteristics of the robotic arm, a new Lyapunov function is introduced as follows: Utilizing the characteristics of the robotic arm Eliminate the relevant terms in the above formula to simplify the subsequent derivation; Introduce a virtual control law α, α=[α1,α2,...,α n ] T ,as follows: Where K2 is a positive definite diagonal matrix, is the interference estimate obtained by the interference observer; Definition B = ρ -1 =diag(b1,b2,...,b n ),Pick For b i The estimated value of make Further construct the following Lyapunov function: The design adaptation rate is as follows: In the formula, γ i represents the adaptive parameter, which is a positive real number; Finally, the control law for the PLOE problem is constructed as follows: Considering the robot trajectory tracking control problem with external environmental interference and actuator total efficiency loss, it is necessary to apply the actual control torques τ1(t) and τ2(t) output by two actuators at the same joint to deal with the complete loss of control of one actuator. Therefore, τ(t) = τ1(t) + τ2(t) = -α. The control torque to be designed output by the adaptive estimation controller is definition: as well as Represents k ji The estimate, Then we have: Where ρ1, ρ2 are the efficiency diagonal matrices of the two actuators, ρ1 = diag(ρ 11 ,ρ 12 ,...,ρ 1n ), ρ2=diag(ρ 21 ,ρ 22 ,...,ρ 2n ), h1, h2 are the offsets of the two actuators; The design adaptation rate is as follows: In the formula, γ 3i ,γ 4i ,γ 5i ,γ 6i Represents the adaptive parameter, which is a positive real number, and the Lyapunov function is as follows: Finally, the control law for the TLOE problem is constructed as follows: Step 2: Construct a diagnostic processing method for the robot arm TLOE fault based on the square sum evaluation function, which specifically includes: Diagnose TLOE faults and decide whether to use redundant actuators based on the diagnosis results; Pick The Lagrangian dynamics equation of the robotic arm is transformed into the following form: in, Design a state observer to observe the system state as follows: Among them, l1, l2 are the diagonal matrices of unknown constants, λ1, λ2 are the observations of states x1, x2; Define the residual: Among them, r1, r2 represent the observation error of the state; The Lyapunov function is selected as follows: V r =r T Pr r=[r1,r2] T Among them, P is a positive definite matrix, and the derivative of the above formula is: Where H = [0, M -1 (q)(ρ-I)] T , D=[0,M -1 (q)] T , Q is a symmetric positive definite matrix, and there exists a positive real number ε that satisfies This proves that the residual sum of squares is bounded, and based on it, a fault diagnosis method is constructed; Select the sum of squares evaluation function and determine the diagnostic processing method. The sum of squares evaluation function is as follows: Use the residual change as a diagnostic: R=|Δr1|+|Δr2| Among them, Δr1 and Δr2 represent the changes of residuals r1 and r2 respectively; The processing method is as follows: 1) Introduce the instant signal. Once the residual change R exceeds the preset threshold and causes a sudden TLOE fault, the instant signal value is 1; 2) Using signal latching means, latch the value at the rising edge of the instant signal to retain the fault characteristics and obtain the signal Instant; 3) Select two sets of thresholds, Baverage_th and Saverage_th, one large and one small, for the mean image of the sum of squares evaluation function. For a sudden TLOE fault, if the Instant signal is 1, the threshold is Saverage_th; for a gradual TLOE fault, if the Instant signal is 0, the threshold is Baverage_th; if the actuator is connected to the robotic arm system, the threshold is Saverage_th; 4) Introduce the TLOE signal, and perform a smoothing process on the average of the sum of squares evaluation function curve. On this basis, select the average threshold value average_th according to the expected cutoff efficiency. If the average value of the sum of squares evaluation function of any joint is greater than average_th, or Instant is 1, the TLOE signal is set to 1; 5) Introduce the fault signal, select the fault threshold fault_th, and when the mean of the square sum evaluation function is less than fault_th, set the TLOE signal to 0.

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