CN114035550B - Autonomous underwater robot actuating mechanism fault diagnosis method based on ESO - Google Patents
Autonomous underwater robot actuating mechanism fault diagnosis method based on ESO Download PDFInfo
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Abstract
The invention discloses an ESO-based autonomous underwater robot actuator fault diagnosis method, which comprises the following steps: calculating residual errors of the actual value and the estimated value by using an extended state observer ESO, and performing fault detection according to a judgment threshold value; the disturbance information and the fault information of the actuating mechanism are utilized to design a self-adaptive threshold value to adapt to the change of residual errors, so that misdiagnosis and missed diagnosis are avoided; and constructing an error equation by adopting an extended state observer, and designing a fault reconstructor to reconstruct faults by using a linear transformation matrix and an equivalent control output error injection principle. The method can effectively realize the fault detection and reconstruction of the execution mechanism of the autonomous underwater robot, and effectively solve the problems of the fault diagnosis of the execution mechanism and the engineering application thereof, thereby ensuring the safe operation of the autonomous underwater robot.
Description
Technical Field
The invention belongs to the technical field of fault diagnosis of an underwater robot power system, and relates to an autonomous underwater robot actuator fault diagnosis method based on ESO (Extended State Observer ).
Background
The ocean area is about 70% of the total earth area, and china is not only huge in land area, but also contains a small ocean area. In recent years, the discovery and exploration of marine resources has been continuously developed and has become the mainstream. Autonomous underwater robots (AUVs) play an important role in the marine field as tools for human exploration and development of marine resources. Since the AUV needs to operate in the ocean for a long period of time, conditions in the ocean are extremely severe, the surrounding environment is complex and variable, and various faults may occur in an actuator in a motion control system thereof. If the fault is not detected in time, the AUV works in an unpredictable way, so that the service life of the AUV is shortened, the work task under water is influenced, the safety of personnel and equipment is threatened, and finally disastrous results are brought. The research on the fault diagnosis technology of the underwater robot actuating mechanism improves the safety and reliability of the underwater robot, and is a problem which needs to be solved currently.
Conventional fault diagnosis methods are generally classified into three types: data-driven based methods, analytical model-based methods, and knowledge-based methods. The AUV fault diagnosis method based on the analytical model has good diagnosis effect in a still water environment, is easy to realize real-time diagnosis, and provides useful information for the next fault-tolerant control or fault recovery. Unlike other methods, the method relies on an accurate mathematical model of the subject being diagnosed, with the relevant parameters in the model being used for the method study. ESO belongs to a state estimation method in an analytical model, the state estimation method firstly reconstructs the state of a controlled process, a residual sequence is generated by comparing the state with a variable, an appropriate model is reconstructed, a statistical detection method is used for detecting faults from the residual sequence, and further separation, estimation and decision are performed.
The state-of-the-art estimation method has several drawbacks: 1) The state estimation method needs to partially linearize a nonlinear model, and decoupling cannot be realized for an actual system with unstructured uncertainty; 2) The state estimation method needs a more accurate model, so that the calculated amount is larger and the stability is poorer; 3) The state estimation method has more parameter calculation, and the more parameters can influence the accuracy of fault diagnosis; 4) The stationarity of the fault detection threshold may cause misdiagnosis and missed diagnosis in the diagnosis of the fault.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an ESO-based autonomous underwater robot actuator fault diagnosis method. The method adopts an improved extended state observer, reduces the calculated amount of parameters and avoids the problem of system decoupling; meanwhile, by utilizing the design of the self-adaptive threshold, misdiagnosis and missed diagnosis can be effectively avoided, and the fault detection precision is improved; the improved linear transformation matrix design fault reconstructor is introduced to estimate faults well, and the robustness is high.
In order to solve the technical problems, the invention adopts the following technical scheme.
The invention discloses an ESO-based autonomous underwater robot actuator fault diagnosis method, which comprises the following steps:
step 1, establishing a six-degree-of-freedom model based on an autonomous underwater robot according to coordinate transformation of a static coordinate system and a dynamic coordinate system and basic knowledge of dynamics of underwater motion, and designing a form of the six-degree-of-freedom model under an extended state observer;
step 2, designing an extended state observer by utilizing the form of the six-degree-of-freedom model obtained in the step one under the extended state observer; calculating a residual error between an actual value and an estimated value aiming at an execution mechanism of the underwater robot;
step 3, designing an adaptive threshold based on disturbance and fault information of an executing mechanism so as to avoid misdiagnosis and missed diagnosis, judging whether an actual fault value exceeds the adaptive threshold, and indicating that a fault occurs when the actual fault value exceeds the threshold;
step 4, solving an LMI constraint optimization problem based on an error equation of the extended state observer, and introducing a linear transformation matrix; and obtaining fault information by utilizing an equivalent control output error injection principle, and designing a fault reconstructor to reconstruct faults.
Further, the specific process of the step 1 includes:
step 1.1, establishing a six-degree-of-freedom model based on an autonomous underwater robot according to coordinate transformation of a static coordinate system and a dynamic coordinate system and basic knowledge of dynamics of underwater motion;
step 1.2, simplifying a six-degree-of-freedom model of the underwater robot into a general formula of a state equation of a nonlinear system as follows:
in the formula, b is a parameter input by a system, u and y are input and output by the system respectively, x is a state variable, t is time, w (t) is unknown disturbance of the system, and C is a coefficient matrix with proper dimension; all other parts except the input bu in the system are expanded into a new variable x 2 Equation (1) is thus in the form of under the extended state observer:
where f and eta () are unknown, eta is the uncertainty and external disturbance of the system, x 1 And x 2 Is a state variable, and x 2 =f is the newly generated state variable after expansion.
Further, the specific process of the step 2 includes:
step 2.1. The extended state observer is designed to:
or is
Wherein A, B is a coefficient matrix, anL＝[l 1 l 2 ] T Is the observer gain vector which can be obtained by using a pole allocation method, z is the estimated value of the state variable, ζ is the residual error between the actual value of the state variable and the estimated value of the state variable, and l 1 And/l 2 Is a gain coefficient; when the selection is correct, ESO may provide a state estimate in equation (4), where z 1 ,z 2 State variables x of the system respectively 1 ,x 2 Is a function of the estimated value of (2); estimate z 2 Tracking f, including both internal dynamic response and external disturbances;
step 2.2. Calculate the gain of the observer, which can be parameterized generally as:
[l 1 l 2 ]＝[β 1 ω 0 β 2 ω 0 2 ] (5)
wherein beta is 1 ,β 2 Is a parameter selected such that the characteristic polynomial beta 2 s+β 1 Is Hurwitz, let
s (n+1) +β 1 s n +…+β n s+β n+1 ＝(s+1) (n+1) (6)
Where s is the pole, it should be guaranteed that the root of the feature polynomial is in the left half of the complex plane; thus, the parameters in equation (5) may be selected as:
[l 1 l 2 ]＝[2ω 0 ω 0 2 ] (7)
wherein omega 0 For the bandwidth of the observer, it is necessary in practical applications to constantly change the bandwidth to ensure that the ESO can properly estimate the state variables.
Further, in step 3, the adaptive threshold is designed based on disturbance and fault information of the actuator, and the specific steps include:
step 3.1, judging occurrence of faults according to the logic relation: the I < xi (t) I < epsilon, and the fault does not occur; the I xi (t) I is not less than epsilon, and the fault occurs; wherein epsilon is a fault detection threshold, namely a fixed threshold; ζ is the residual error between the estimated value and the actual value obtained under the extended state observer; through the above formula, the basic steps of fault detection under the observer can be obtained: when the system is in a normal state, the residual error is smaller than a fixed threshold value; when the system fails, the residual error is larger than a fixed threshold;
step 3.2, when the system has no fault, setting a threshold value at the moment as follows:
when the system fails, the threshold value at the moment is set as follows:
wherein f (t) is a fault vector, w (t) is a disturbance vector, ε 1 And epsilon 2 Partial thresholds set under fault and no fault conditions respectively;
the adaptive threshold set in step 3.3 should satisfy the following conditions: epsilon 1 ＜ε＜ε 2 The method comprises the steps of carrying out a first treatment on the surface of the Let epsilon 1 ＝||ξ ω (t)|| 2 ＝α，ε 2 ＝||ξ f (t)|| 2 =β; the self-adaptive threshold value adopts an organic combination of the two, and can be obtained:
ε＝λ 1 (α+λ 2 β) (10)
wherein lambda is 1 、λ 2 Are all designed threshold parameters, and lambda 1 ∈[0,1]，λ 2 ∈[0,1]The method comprises the steps of carrying out a first treatment on the surface of the According to the self-adaptive threshold designed by the formula, when the autonomous underwater robot with the unknown disturbance of the actuating mechanism breaks down, the threshold epsilon can be self-adaptively adjusted, and fault detection based on the self-adaptive threshold is realized.
Further, in step 4, the LMI constraint optimization problem is solved by using the error equation of the extended state observer, and a linear transformation matrix is introduced; the fault information is obtained by utilizing the equivalent control output error injection principle, and then a fault reconstructor is designed to reconstruct faults, and the specific process comprises the following steps:
step 4.1, expressing a state equation of a nonlinear system of a six-degree-of-freedom model of the underwater robot as:
wherein A, B, F, W, C is a coefficient matrix with proper dimension, g (x) is a Lipschitz nonlinear term, f (t) is a fault vector of the actuator, and w (t) is an uncertain vector such as unknown disturbance; the system first satisfies the matching condition, namely rank (D) =rank ([ W F ])=rank (CD), then there is a symmetric positive definite matrix Q, a gain matrix L, a matrix G, and a symmetric positive definite matrix P, so that the following equation is satisfied:
obtaining an error equation of the extended state observer according to the extended state observer designed in the step 2:
in the method, in the process of the invention,e is the estimation error of the observer, E is the coefficient matrix; let A 1 =a-LC, defining γ, γ as constraint optimization coefficient, γ 2 =ψ, ψ is Lipschitz coefficient, and the value is selected according to the actual engineering application;
step 4.2. The system in step 4.1 is matched and the error equation is correct, the following constraint optimization problem is solved:
step 4.3. Introducing a linear transformation matrix K= [ C ] T PC]And rewrites the error equation in step 4.1, lete g To estimate the error, then we can get:
in the method, in the process of the invention,
combining the error equation, we can obtain:
wherein g 1 、g 2 For the estimation error of the nonlinear part, the fault reconstruction is realized by utilizing the principle of equivalent control output error injection, and an error equation (17) can be rewritten as follows:
(-CP -1 C T G T )f(t)＝A 23 e 1 +g 2 +W 12 w(t) (18)
in combination with the solving of the constraint optimization problem in step 4.2, it is possible to obtain:
||-CFf(t)||≤||A 23 ||e 1 +||C|ψ+||W 12 ||w(t) (19)
according to the equivalent control output error injection principle, the estimated value of the reconstruction fault of the executor is given as follows:
since the state estimation error of the observer is generally small, the fault reconstruction error is closely related to the magnitude of the unknown disturbance uncertainty w (t); normally, the uncertainty of unknown disturbances, etc. is much smaller than the fault value, so equation (20) can be regarded as the fault reconstruction value obtained by the fault reconstructor. Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the invention combines the novel extended state observer with the improved self-adaptive threshold value to form a complete fault detection system. The state value is estimated by the extended state observer, residual errors are generated, and the self-adaptive threshold is used as an evaluation standard, so that misdiagnosis and missed diagnosis can be avoided, and the method has stronger robustness. In practical application, when an AUV (autonomous Underwater robot) fails, the failure detection scheme can timely detect the failure and provide an alarm signal so as to avoid accident occurrence; if the fault evaluation is not performed by the self-adaptive threshold, a fault similar to the disturbance is omitted, or the disturbance is mishandled as a fault, so that an accident occurs, and great economic loss is caused.
2. The invention constructs an error equation through the extended state observer, designs a linear transformation matrix to rewrite the error equation, and obtains a fault estimated value. The method can estimate the faults in the system according to the historical data of the operation in the system, and can detect and estimate the faults in the system on line in real time. In practical application, the system fault size can be estimated in advance, fault prevention and treatment are performed in advance, and the running cost is saved, so that the method has important theoretical value and practical significance.
Drawings
Fig. 1 is a schematic diagram of an ESO-based AUV actuator fault diagnosis method of the present invention.
FIG. 2 is a flow chart of one embodiment of an ESO-based AUV actuator fault diagnosis method of the present invention.
Fig. 3 is a schematic view of an autonomous underwater robot in a coordinate system.
FIG. 4 is a flow chart of an extended state observer design according to one embodiment of the invention.
FIG. 5 is a step-by-step flowchart of one embodiment of the present invention.
FIG. 6 is a fault reconstruction flow chart for one embodiment of the present invention.
FIG. 7 is a graph of fault residuals versus fixed threshold for a propulsion system of one embodiment of the invention; wherein fig. 7a is the transverse velocity U and fig. 7b is the longitudinal velocity V.
FIG. 8 is a graph of fault residuals versus adaptive threshold for a propulsion system of one embodiment of the invention; where fig. 8a is the transverse velocity U and fig. 8b is the longitudinal velocity V.
FIG. 9 is a plot of residual error of a rudder angle versus an adaptive threshold for one embodiment of the invention; wherein fig. 9a is a horizontal rudder angle and fig. 9b is a vertical rudder angle.
FIG. 10 is a fault estimation diagram of an actuator of one embodiment of the present invention; wherein fig. 10a is a propulsion system and fig. 10b is a rudder angle.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
Fig. 1 is a schematic diagram of an ESO-based AUV actuator fault diagnosis method of the present invention. The controller controls the executing mechanism to obtain a state value, the extended state observer obtains an estimated value, finally, residual errors are obtained through comparison, and fault information is processed and decided in a residual error sequence.
FIG. 2 is a flow chart of one embodiment of the autonomous underwater robot actuator fault diagnosis method based on ESO of the present invention, the embodiment method comprising the steps of:
and 1, establishing a six-degree-of-freedom model based on the autonomous underwater robot according to the knowledge such as the coordinate transformation of a static coordinate system and a dynamic coordinate system, the dynamics foundation of the underwater motion and the like, and designing the form of the six-degree-of-freedom model under an extended state observer.
Step 2, designing an extended state observer by using the form of the six-degree-of-freedom model obtained in the step 1 under the extended state observer; calculating a residual error between an actual value and an estimated value aiming at an execution mechanism of the underwater robot;
step 3, designing an adaptive threshold based on disturbance and fault information of an executing mechanism so as to avoid misdiagnosis and missed diagnosis, judging whether an actual fault value exceeds the adaptive threshold, and indicating that a fault occurs when the actual fault value exceeds the threshold;
step 4, solving an LMI (Linear Matrix Inequality ) constraint optimization problem based on an error equation of the extended state observer, and introducing a linear transformation matrix; and obtaining fault information by utilizing an equivalent control output error injection principle, and designing a fault reconstructor to reconstruct faults.
In step 1, the specific contents and design steps of the form of the six-degree-of-freedom model under the extended state observer are as follows:
step 1.1, as shown in fig. 3, establishing a six-degree-of-freedom model based on the autonomous underwater robot according to knowledge such as coordinate transformation of a static coordinate system and a dynamic coordinate system, dynamics foundation of underwater motion and the like;
step 1.2, simplifying a six-degree-of-freedom model of the underwater robot into a general formula of a state equation of a nonlinear system as follows:
wherein, b is a parameter input by the system, u, y are input and output by the system, x is a state variable, t is time, w (t) is unknown disturbance of the system, C is a coefficient matrix with proper dimension, and C= [ 10 ]]. ESO is a dynamic process that uses only the input-output information of the original nonlinear system, and does not use any information of the functions in the system to describe the transfer relationship of the object. All other parts except the input bu in the system are expanded into a new variable x 2 Equation (1) is thus in the form of under the extended state observer:
where f and eta () are unknown, eta is the uncertainty and external disturbance of the system, x 1 And x 2 Is a state variable, and x 2 =f is the newly generated state variable after expansion.
In step 2, the specific content and design steps of designing the extended state observer based on the six-degree-of-freedom model are shown in fig. 4:
step 2.1, designing an extended state observer to be:
or is
Wherein A, B is a coefficient matrix, anL＝[l 1 l 2 ] T Is an observer gain vector that can be obtained using any known method (e.g., pole placement), z is an estimate of the state variable, ζ is the residual between the actual value of the state variable and the state variable estimate, l 1 And/l 2 Is the gain factor. When the selection is correct, ESO may provide a state estimate in equation (4), where z 1 ,z 2 State vector x of the system respectively 1 ,x 2 Is used for the estimation of the estimated value of (a). Estimate z 2 Tracking f, including both internal dynamic response and external disturbances.
Step 2.2. Calculate the gain of the observer, which can be parameterized generally as:
[l 1 l 2 ]＝[β 1 ω 0 β 2 ω 0 2 ] (5)
wherein beta is 1 ,β 2 Is a parameter selected such that the characteristic polynomial beta 2 s+β 1 Is Hurwitz. Order the
s (n+1) +β 1 s n +…+β n s+β n+1 ＝(s+1) (n+1) (6)
Where s is the pole, it should be guaranteed that the root of the feature polynomial is in the left half of the complex plane. Thus, the parameters in equation (5) may be selected as:
[l 1 l 2 ]＝[2ω 0 ω 0 2 ] (7)
wherein omega 0 For the bandwidth of the observer, it is necessary in practical applications to constantly change the bandwidth to ensure that the ESO can properly estimate the state variables.
In step 3, an adaptive threshold is designed based on disturbance and fault information of the actuator, and the specific content and design steps are shown in fig. 5:
step 3.1, judging occurrence of faults according to the logic relation: the I < xi (t) I < epsilon, and the fault does not occur; and the I xi (t) I is not less than epsilon, and the fault occurs. Wherein epsilon is a fault detection threshold, namely a fixed threshold; and xi is the residual error of the estimated value and the actual value obtained under the extended state observer. Through the above formula, the basic steps of fault detection under the observer can be obtained: when the system is in a normal state, the residual error is smaller than a fixed threshold value; when the system fails, the residual is greater than a fixed threshold.
Step 3.2, when the system has no fault, setting a threshold value at the moment as follows:
when the system fails, the threshold value at the moment is set as follows:
wherein f (t) is a fault vector, w (t) is a disturbance vector, ε 1 And epsilon 2 The partial thresholds set for the faulty and non-faulty cases, respectively.
The adaptive threshold set in step 3.3 should satisfy the following conditions: epsilon 1 ＜ε＜ε 2 . Let epsilon 1 ＝||ξ ω (t)|| 2 ＝α，ε 2 ＝||ξ f (t)|| 2 =β; the self-adaptive threshold value adopts an organic combination of the two, and can be obtained:
ε＝λ 1 (α+λ 2 β) (10)
wherein lambda is 1 、λ 2 Are all designed threshold parameters, and lambda 1 ∈[0,1]，λ 2 ∈[0,1]. According to the self-adaptive threshold designed by the formula, when the autonomous underwater robot with the unknown disturbance of the actuating mechanism breaks down, the threshold epsilon can be self-adaptively adjusted, and fault detection based on the self-adaptive threshold is realized.
As shown in fig. 6, in step 4, the LMI constraint optimization problem is solved by using the error equation of the extended state observer, and a linear transformation matrix is introduced; the fault information is obtained by utilizing the equivalent control output error injection principle, and then a fault reconstructor is designed to reconstruct faults, and the specific process comprises the following steps:
step 4.1. Describing the state equation of the nonlinear system in step one as follows: the state equation of the nonlinear system of the six-degree-of-freedom model of the underwater robot is expressed as:
wherein A, B, F, W, C is a coefficient matrix with proper dimension, g (x) is Lipschitz nonlinear term, f (t) is fault vector of the actuator, and w (t) is uncertainty vector such as unknown disturbance. The system first satisfies the matching condition, namely rank (D) =rank ([ W F ])=rank (CD), then there is a symmetric positive definite matrix Q, a gain matrix L, a matrix G, and a symmetric positive definite matrix P, so that the following equation is satisfied:
obtaining an error equation of the extended state observer according to the extended state observer designed in the step two:
in the method, in the process of the invention,e is the estimation error of the observer and E is the coefficient matrix. Let A 1 =a-LC, defining γ, γ as constraint optimization coefficient, γ 2 =ψ, ψ is Lipschitz coefficient, and the values are selected according to the actual engineering application.
Step 4.2. The system in step 4.1 is matched and the error equation is correct, the following constraint optimization problem is solved:
step 4.3.Introducing a linear transformation matrix K= [ C ] T PC]And rewrites the error equation in step 4.1, lete g To estimate the error, then we can get:
in the method, in the process of the invention,
combining the error equation, we can obtain:
wherein g 1 、g 2 For the estimation error of the nonlinear part, the fault reconstruction is realized by utilizing the principle of equivalent control output error injection, and an error equation (17) can be rewritten as follows:
(-CP -1 C T G T )f(t)＝A 23 e 1 +g 2 +W 12 w (t) (18) in combination with the solving of the constraint optimization problem in step 4.2, can be obtained:
||-CFf(t)||≤||A 23 ||e 1 +||C|ψ+||W 12 ||w(t) (19)
according to the equivalent control output error injection principle, the estimated value of the reconstruction fault of the executor is given as follows:
since the state estimation error of an observer is generally small, the fault reconstruction error is closely related to the magnitude of the unknown disturbance uncertainty w (t). Normally, the uncertainty of unknown disturbances, etc. is much smaller than the fault value, so equation (20) can be regarded as the fault reconstruction value obtained by the fault reconstructor.
The method of the invention is verified by simulation:
step A, giving a fault condition of an execution mechanism of the autonomous underwater robot; the actuating mechanism comprises a propulsion system and a rudder angle; designing parameter deviation type faults based on an actuating mechanism: (1) designing fault information of a propulsion system as follows: the thrust T is reduced by half at 100s, while the disturbance of the propulsion system is set to: w (t) =0.5 sintsin (t/2) sin (t/3); (2) the fault information of the design rudder angle is: coefficient M of rudder angle δ Half of the time is reduced in 100s, so that the fault of the rudder angle is realized;
step B, writing a six-degree-of-freedom model of the autonomous underwater robot by using a MATLAB program, and designing an extended state observer to realize fault detection of an executing mechanism;
and C, designing a fault reconstructor by using tools such as an LMI tool kit and the like in MATLAB and combining an error equation, a linear transformation matrix and the like.
The solid line in fig. 7 represents the residual between the estimated and actual values of the longitudinal and lateral speeds of the underwater robot under the extended state observer. The small value of the residual error can prove the effectiveness of the extended state observer design. The dashed line represents a fixed threshold obtained after the observer has been proved to converge, but it can be found that the fixed threshold can detect faults in most cases, but the residual fluctuation with disturbances is large, and the fixed threshold is not completely detected.
The solid line in fig. 8 is the same as that in fig. 7, and the dashed line represents an adaptive threshold designed based on disturbance information and fault information of the propulsion system. It can be seen from the figure that no matter how large the fluctuation of the residual error is, the self-adaptive threshold value always changes along with the change of the residual error, so that whether the fault occurs or not can be accurately detected, misdiagnosis and missed diagnosis can be avoided, and the effectiveness of the fault diagnosis of the execution mechanism of the underwater robot is improved.
Fig. 9 is a fault detection diagram of the rudder angle. At the moment of failure, the adaptive threshold will change as the failure changes. Fig. 9a and 9b further verify the validity of the adaptive threshold design.
Fig. 10 is a fault reconstruction of an autonomous underwater robot actuator, fig. 10a and 10b representing propulsion system and rudder angle, respectively. The solid line in the figure represents an ideal fault curve, i.e. the value of the thrust system in the actuator is reduced by half; the dashed line represents the reconstructed value of the fault reconstructor for the fault, and it can be seen from the figure that the dashed line fluctuates up and down around the solid line and eventually approaches the solid line. The fault reconstructor designed based on the extended state observer has proved to have good effect on reconstructing the fault value of the actuator.
In summary, according to the autonomous underwater robot actuator fault diagnosis method based on ESO, the residual error of the actual value and the estimated value is calculated by using an Extended State Observer (ESO), and fault detection is performed according to the judgment threshold; the disturbance information and the fault information of the actuating mechanism are utilized to design a self-adaptive threshold value to adapt to the change of residual errors, so that misdiagnosis and missed diagnosis are avoided; and constructing an error equation by adopting an extended state observer, and designing a fault reconstructor to reconstruct faults by using a linear transformation matrix and an equivalent control output error injection principle. The method can effectively realize the fault detection and reconstruction of the execution mechanism of the autonomous underwater robot, effectively solve the problems of the fault diagnosis of the execution mechanism and the engineering application thereof, and has important significance for the safe operation of the autonomous underwater robot.
Claims (6)
1. An ESO-based autonomous underwater robot actuator fault diagnosis method is characterized by comprising the following steps:
step 1, establishing a six-degree-of-freedom model based on an autonomous underwater robot according to coordinate transformation of a static coordinate system and a dynamic coordinate system and basic knowledge of dynamics of underwater motion, and designing a form of the six-degree-of-freedom model under an extended state observer;
step 2, designing an extended state observer by utilizing the form of the six-degree-of-freedom model obtained in the step one under the extended state observer; calculating a residual error between an actual value and an estimated value aiming at an execution mechanism of the underwater robot;
step 3, designing an adaptive threshold based on disturbance and fault information of an executing mechanism so as to avoid misdiagnosis and missed diagnosis, judging whether an actual fault value exceeds the adaptive threshold, and indicating that a fault occurs when the actual fault value exceeds the threshold;
step 4, solving an LMI constraint optimization problem based on an error equation of the extended state observer, and introducing a linear transformation matrix; and obtaining fault information by utilizing an equivalent control output error injection principle, and designing a fault reconstructor to reconstruct faults.
2. The ESO-based autonomous underwater robot actuator fault diagnosis method according to claim 1, wherein the specific process of step 1 comprises:
step 1.1, establishing a six-degree-of-freedom model based on an autonomous underwater robot according to coordinate transformation of a static coordinate system and a dynamic coordinate system and basic knowledge of dynamics of underwater motion;
step 1.2, simplifying a six-degree-of-freedom model of the underwater robot into a general formula of a state equation of a nonlinear system as follows:
in the formula, b is a parameter input by a system, u and y are input and output by the system respectively, x is a state variable, t is time, w (t) is unknown disturbance of the system, and C is a coefficient matrix with proper dimension; all other parts except the input bu in the system are expanded into a new variable x 2 Equation (1) is thus in the form of under the extended state observer:
where f and η () are both unknown, η is the uncertainty of the systemExternal disturbance, x 1 And x 2 Is a state variable, and x 2 =f is the newly generated state variable after expansion.
3. The ESO-based autonomous underwater robot actuator fault diagnosis method according to claim 1, wherein the specific process of step 2 comprises:
step 2.1. The extended state observer is designed to:
or is
Wherein A, B is a coefficient matrix, anL＝[l 1 l 2 ] T Is the observer gain vector which can be obtained by using a pole allocation method, z is the estimated value of the state variable, ζ is the residual error between the actual value of the state variable and the estimated value of the state variable, and l 1 And/l 2 Is a gain coefficient; when the selection is correct, ESO may provide a state estimate in equation (4), where z 1 ,z 2 State variables x of the system respectively 1 ,x 2 Is a function of the estimated value of (2); estimate z 2 Tracking f, including both internal dynamic response and external disturbances;
step 2.2. Calculate the gain of the observer, which can be parameterized generally as:
[l 1 l 2 ]＝[β 1 ω 0 β 2 ω 0 2 ] (5)
wherein beta is 1 ,β 2 Is a parameter selected such that the characteristic polynomial beta 2 s+β 1 Is Hurwitz, let
s (n+1) +β 1 s n +...+β n s+β n+1 ＝(s+1) (n+1) (6)
Where s is the pole, it should be guaranteed that the root of the feature polynomial is in the left half of the complex plane; thus, the parameters in equation (5) may be selected as:
[l 1 l 2 ]＝[2ω 0 ω 0 2 ] (7)
wherein omega 0 For the bandwidth of the observer, it is necessary in practical applications to constantly change the bandwidth to ensure that the ESO can properly estimate the state variables.
4. The ESO-based autonomous underwater robot actuator fault diagnosis method according to claim 1, wherein in step 3, the adaptive threshold is designed based on disturbance and fault information of the actuator, and the specific steps include:
step 3.1, judging occurrence of faults according to the logic relation: the I < xi (t) I < epsilon, and the fault does not occur; the I xi (t) I is not less than epsilon, and the fault occurs; wherein epsilon is a fault detection threshold, namely a fixed threshold; ζ is the residual error between the estimated value and the actual value obtained under the extended state observer; through the above formula, the basic steps of fault detection under the observer can be obtained: when the system is in a normal state, the residual error is smaller than a fixed threshold value; when the system fails, the residual error is larger than a fixed threshold;
step 3.2, when the system has no fault, setting a threshold value at the moment as follows:
when the system fails, the threshold value at the moment is set as follows:
wherein f(t) is a fault vector, w (t) is a disturbance vector, ε 1 And epsilon 2 Partial thresholds set under fault and no fault conditions respectively;
the adaptive threshold set in step 3.3 should satisfy the following conditions: epsilon 1 ＜ε＜ε 2 The method comprises the steps of carrying out a first treatment on the surface of the Let epsilon 1 ＝||ξ ω (t)|| 2 ＝α，ε 2 ＝||ξ f (t)|| 2 =β; the self-adaptive threshold value adopts an organic combination of the two, and can be obtained:
ε＝λ 1 (α+λ 2 β) (10)
wherein lambda is 1 、λ 2 Are all designed threshold parameters, and lambda 1 ∈[0,1]，λ 2 ∈[0,1]The method comprises the steps of carrying out a first treatment on the surface of the According to the self-adaptive threshold designed by the formula, when the autonomous underwater robot with the unknown disturbance of the actuating mechanism breaks down, the threshold epsilon can be self-adaptively adjusted, and fault detection based on the self-adaptive threshold is realized.
5. The ESO-based autonomous underwater robot actuator fault diagnosis method according to claim 1, wherein in step 4, the LMI constraint optimization problem is solved by using an error equation of an extended state observer, and a linear transformation matrix is introduced; the specific process comprises the following steps:
step 4.1, expressing a state equation of a nonlinear system of a six-degree-of-freedom model of the underwater robot as:
wherein A, B, F, W, C is a coefficient matrix with proper dimension, g (x) is a Lipschitz nonlinear term, f (t) is a fault vector of the actuator, and w (t) is an uncertain vector such as unknown disturbance; the system first satisfies the matching condition, namely rank (D) =rank ([ W F ])=rank (CD), then there is a symmetric positive definite matrix Q, a gain matrix L, a matrix G, and a symmetric positive definite matrix P, so that the following equation is satisfied:
obtaining an error equation of the extended state observer according to the extended state observer designed in the step 2:
in the method, in the process of the invention,e is the estimation error of the observer, E is the coefficient matrix; let A 1 =a-LC, defining γ, γ as constraint optimization coefficient, γ 2 =ψ, ψ is Lipschitz coefficient, and the value is selected according to the actual engineering application;
step 4.2. The system in step 4.1 is matched and the error equation is correct, the following constraint optimization problem is solved:
step 4.3. Introducing a linear transformation matrix K= [ C ] T PC]And rewrites the error equation in step 4.1, lete g To estimate the error, then we can get:
in the method, in the process of the invention,
combining the error equation, we can obtain:
wherein g 1 、g 2 For the estimation error of the nonlinear part, the fault reconstruction is realized by utilizing the principle of equivalent control output error injection, and an error equation (17) can be rewritten as follows:
(-CP -1 C T G T )f(t)＝A 23 e 1 +g 2 +W 12 w (t) (18) in combination with the solving of the constraint optimization problem in step 4.2, can be obtained:
||-CFf(t)||≤||A 23 ||e 1 +||Cψ+||W 12 ||w(t) (19)。
6. the ESO-based autonomous underwater robot actuator fault diagnosis method according to claim 1, wherein in step 4, the fault information is obtained by using the equivalent control output error injection principle, and the fault reconstructor is further designed to reconstruct the fault, and the specific process includes:
according to the equivalent control output error injection principle, the estimated value of the reconstruction fault of the executor is given as follows:
since the state estimation error of the observer is generally small, the fault reconstruction error is closely related to the magnitude of the unknown disturbance uncertainty w (t); normally, the uncertainty of unknown disturbances, etc. is much smaller than the fault value, so equation (20) can be regarded as the fault reconstruction value obtained by the fault reconstructor.
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