Fault-tolerant and vibration suppression control method for rigid-flexible coupled robot based on synchronous disturbance observation and dynamic event triggering

Abstract

This invention discloses a fault-tolerant and vibration suppression control method for rigid-flexible coupled robots based on synchronous disturbance observation and dynamic event triggering. The method includes: establishing a large-deformation dynamic model of the rigid-flexible coupled robot mechanism and constructing rigid coordinates, flexible modal coordinates, and control targets; establishing an actuator effectiveness decay fault model and transforming the original underactuated system into an equivalent fully actuated model oriented towards trajectory tracking; designing a fixed-time synchronous disturbance observer based on error dynamics to estimate external disturbances and composite uncertainties online; constructing a dynamic event triggering mechanism and a time-synchronous fault-tolerant sliding mode control law to achieve synchronous convergence of the system state to the sliding surface within a fixed time; introducing a hybrid reference trajectory and virtual input to establish an augmented state model and designing a robust linear quadratic state feedback controller. This invention achieves coordinated control of trajectory tracking and flexible vibration suppression under conditions of external disturbances, actuator failures, and limited communication resources.

Description

Technical Field

[0001] This invention relates to a fault-tolerant and vibration-suppressing control method for rigid-flexible coupled robots, and more particularly to a fault-tolerant and vibration-suppressing control method for rigid-flexible coupled robots based on synchronous disturbance observation and dynamic event triggering, belonging to the field of robot control technology. Background Technology

[0002] Compared to traditional rigid robot mechanisms, rigid-flexible coupling robot mechanisms offer a higher load-to-mass ratio, better motion flexibility, and a larger workspace, making them valuable for applications in marine engineering, aerospace, and high-precision industrial automation. However, because these mechanisms typically employ lightweight flexible components, their inherent stiffness is insufficient, leading to significant elastic deformation and residual vibration during high-speed motion. This poses considerable challenges for dynamic modeling, trajectory tracking, and active vibration suppression. From a mathematical modeling perspective, flexible dynamics inherently possess distributed parameter characteristics. Existing discretization modeling methods generally face a trade-off between modeling accuracy and the complexity of real-time control implementation. Especially under large deformation conditions, the traditional small-deflection linear assumption fails to accurately reflect geometric nonlinear characteristics.

[0003] In terms of control, existing methods for trajectory tracking and vibration suppression in rigid-flexible coupled robot mechanisms include boundary control, sliding mode control, and backstepping control. However, most methods can only guarantee asymptotic stability, which is insufficient to meet the convergence speed requirements of high-precision, fast-response scenarios. While finite-time control can achieve convergence within a finite time, its convergence time usually depends on the initial state of the system. Fixed-time synchronous control has the advantage that the upper bound of the convergence time is independent of the initial state, making it more suitable for engineering scenarios with high requirements for response timeliness. However, its application in the synchronous control of rigid-flexible coupled robot mechanisms remains relatively limited. Meanwhile, in networked control environments, large amounts of periodic data transmission can consume communication bandwidth and cause network congestion. Traditional static event triggering mechanisms are also difficult to balance control performance and resource utilization in complex systems.

[0004] Furthermore, in practical engineering, actuators may experience effectiveness decay and other faults during long-term operation, accompanied by parameter uncertainties, external disturbances, and even unknown control directions, making it difficult for traditional control methods relying on precise model parameters to maintain stable control performance. While existing research has made some progress in disturbance observation, fault compensation, and event-triggered control, there are still few integrated control methods for trajectory tracking and flexible vibration suppression in rigid-flexible coupled robot mechanisms under complex conditions such as large deformation, underactuation, external disturbances, partial actuator failure, and limited communication resources. Therefore, how to achieve high-precision trajectory tracking and flexible vibration suppression in rigid-flexible coupled robot mechanisms under these complex constraints remains a pressing technical problem to be solved. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to solve the problems existing in the prior art and to provide a fault-tolerant and vibration suppression control method for rigid-flexible coupled robots based on synchronous disturbance observation and dynamic event triggering. Under the conditions of external disturbance, actuator failure and limited communication resources, it can achieve high-precision trajectory tracking of joint angles and effective suppression of flexible vibration, and has strong robustness, fault tolerance and engineering application value.

[0006] Technical solution: The present invention provides a fault-tolerant and vibration suppression control method for rigid-flexible coupled robots based on synchronous disturbance observation and dynamic event triggering, comprising:

[0007] S1. Establish a large deformation dynamic model of the rigid-flexible coupled robot mechanism, and construct rigid coordinates, flexible modal coordinates and control targets;

[0008] S2. Establish an actuator effectiveness decay fault model and transform the original underactuated system into an equivalent fully actuated model for trajectory tracking.

[0009] S3. Design a fixed-time synchronous disturbance observer based on error dynamics to perform online estimation of external disturbances and composite uncertainties;

[0010] S4. Construct a dynamic event triggering mechanism and a time-synchronized fault-tolerant sliding mode control law to enable the system state to reach the sliding mode surface and converge synchronously within a fixed time.

[0011] S5. By introducing a hybrid reference trajectory and virtual input, an augmented state model is established, and a robust linear quadratic state feedback controller is designed to achieve coordinated control of trajectory tracking and flexible vibration suppression.

[0012] Further, step S1 specifically includes:

[0013] S11: Establish the structural model and coordinate system of the rigid-flexible coupling robot mechanism; the rigid-flexible coupling robot mechanism consists of two interconnected links, the first level being a rigid main link and the second level being a flexible secondary link with a beam structure. Both levels of links are driven by independent motors and move in the horizontal plane; establish an inertial coordinate system. and the moving coordinate system And in the following coordinate system, the displacement variables of the flexible link in the horizontal and vertical directions are introduced. and ;in, This represents the angular displacement of a rigid member. Indicates the deflection angle at the base of the flexible link;

[0014] S12: Establish the large deformation geometric relationship of the flexible link; based on the Euler-Bernoulli beam theory, the rotation angle of the flexible link is:

[0015] ;

[0016] S13: Perform modal expansion on the flexible link and determine the truncation form; use polynomial basis functions. An approximate representation of the distributed rotation angles along the length of the flexible link is given, namely...

[0017] ;

[0018] in, For flexible linkage angle, Indicates the amplitude of flexible vibration modes. This represents the total number of vibration modes. The spatial coordinates are along the length of the flexible link.

[0019] S14: Establish the position vector, system energy expression, and virtual work expression; define the position vector of any point on the flexible secondary link in the inertial coordinate system. for:

[0020] ;

[0021] Based on the translational and rotational relationships between the rigid main link and the flexible secondary link, the total kinetic energy of the system is... Represented as:

[0022] Total potential energy caused by elastic deformation of flexible beam for:

[0023] ;

[0024] input torque and virtual work done by external disturbances for:

[0025] ;

[0026] S15: Establish a compact dynamic model based on Hamilton's principle and define the control objective; based on Hamilton's principle...

[0027] ;

[0028] A large deformation dynamic model of a rigid-flexible coupled robot mechanism is obtained.

[0029] Further, step S2 specifically includes:

[0030] S21: Establish an actuator effectiveness decay fault model, represented as:

[0031]

[0032] in, Indicates the desired control torque. This represents the time-varying efficiency coefficient vector coupled to the actuator input channel, and

[0033]

[0034] S22: Transform the original underactuated system into an equivalent fully actuated system; construct the equivalent fully actuated system for trajectory tracking as follows: ;

[0035] S23: Establish an error dynamics model; define the position and attitude tracking errors as follows:

[0036] ;

[0037] The error system is then written as

[0038]

[0039] in

[0040] .

[0041] Furthermore, step S3 specifically includes the following steps:

[0042] The basic definitions required for fixed-time synchronous observations are given; among them, the normalized symbol mapping is defined as follows:

[0043]

[0044] The continuous power operator is defined as

[0045]

[0046] Nussbaum type functions satisfy

[0047]

[0048] And select

[0049]

[0050] At the same time, for any vector and positive numbers ,have

[0051] ;

[0052] Construct the composite disturbance expression and auxiliary state variables, and reorganize the error dynamics into

[0053]

[0054] The composite disturbance term is defined as follows:

[0055]

[0056] Further introduce auxiliary state variables

[0057]

[0058] Redefining intermediate variables

[0059]

[0060] get

[0061]

[0062] Transform the perturbation estimation problem into an intermediate variable. The fixed-time synchronous convergence problem;

[0063] A fixed-time synchronous perturbation observer is constructed, and the convergence of the estimation error is obtained.

[0064] The fixed-time synchronization disturbance observer is constructed as follows:

[0065]

[0066] in, Further

[0067]

[0068] as well as

[0069]

[0070] Therefore, in the choice After parameterization, the fixed-time synchronous disturbance observer ensures that the estimation errors of each disturbance synchronously enter the origin neighborhood within a fixed time period, and the upper bound of the residuals can be further reduced through design parameters, wherein... For the observer's positive constant gain, Let be the gain function of the fixed-time synchronous observer. For the exponent parameter of the consecutive power term.

[0071] Furthermore, step S4 specifically includes the following steps:

[0072] S41: Construct a dynamic event triggering mechanism; to reduce the communication resource consumption caused by controller updates, an event triggering mechanism based on dynamic thresholds is introduced; let the first... The most recent trigger time for each input channel is The next trigger time is Then in the interval The internal control input uses zero-order hold:

[0073]

[0074] in,

[0075]

[0076] If nonlinear mapping If the Lipschitz continuity condition is satisfied, then we have

[0077]

[0078] Further define event triggering error Construct a dynamic event triggering mechanism

[0079]

[0080] Among them, adaptive variables satisfy

[0081]

[0082] S42: Construct the time-synchronized sliding surface and switching function;

[0083] Constructing a switching sliding surface:

[0084]

[0085] in,

[0086]

[0087] Further define auxiliary variables

[0088]

[0089] Switching function Constructed as

[0090]

[0091] in, Determined by the expression

[0092]

[0093] S43: The time-synchronized fault-tolerant sliding mode control law is designed as follows:

[0094]

[0095]

[0096]

[0097] This control law unifies disturbance estimation compensation, fault tolerance compensation, and fixed-time sliding mode convergence mechanism into the same control framework;

[0098] S44: Fixed-time synchronous convergence and singularity avoidance analysis are given. To prove that the designed control law can achieve fixed-time synchronous convergence, a Lyapunov function is constructed:

[0099]

[0100] Taking the derivative, we can further simplify it as follows:

[0101]

[0102] Under the control law of singularity avoidance FTC-DFTSC, the system state can reach the sliding surface within a fixed time. Then, the Lyapunov function is further constructed as follows:

[0103]

[0104] Its derivative is

[0105]

[0106] From the above equation, we can see that the system state components achieve synchronous convergence, and the upper bound of the total convergence time satisfies the following condition. Furthermore, regarding Analyzing the other switching interval separately, we can obtain...

[0107]

[0108] as well as

[0109] .

[0110] Furthermore, step S5 specifically includes the following steps:

[0111] S51: Constructing the hybrid reference trajectory and its dynamic equations; Introducing the hybrid reference trajectory and virtual control input Define error variables

[0112]

[0113] Hybrid reference trajectory is derived from virtual input Generate, its dynamic satisfaction

[0114]

[0115] in,

[0116]

[0117] By introducing a hybrid reference trajectory, the problem of flexible vibration suppression can be embedded into the trajectory generation process;

[0118] S52: Establish the dynamic relationship under the action of virtual input; obtain the dynamic relationship...

[0119]

[0120]

[0121] Further definition

[0122] Then there is

[0123]

[0124] Meanwhile, flexible modes satisfy

[0125] ;

[0126] S53: Establish an augmented state model and design a robust linear quadratic state feedback controller;

[0127] Define augmented state vector

[0128]

[0129] The closed-loop system is then written as

[0130]

[0131] in,

[0132]

[0133]

[0134] Based on the augmented state model described above, performance indices are constructed.

[0135]

[0136] The optimal state feedback control law is obtained by minimizing the aforementioned performance index.

[0137]

[0138] in, The solution to the corresponding differential Riccati equation is given; after introducing this robust linear quadratic state feedback controller, the closed-loop system becomes...

[0139]

[0140] And in The system remains stable under certain conditions; therefore, it achieves coordinated control of trajectory tracking and flexible vibration suppression by using a hybrid reference trajectory, virtual input, and robust linear quadratic state feedback controller.

[0141] Furthermore, the large deformation dynamics model of the rigid-flexible coupling robot mechanism is expressed as follows:

[0142]

[0143] Further definition

[0144]

[0145] The system can then be written in compact matrix form:

[0146]

[0147] in,

[0148]

[0149] and

[0150] .

[0151] Furthermore, the time-synchronized fault-tolerant sliding mode control law, by differentiating the sliding mode surface formula and combining it with the error system, yields:

[0152]

[0153] in

[0154]

[0155] Substituting the actuator effectiveness decay fault model, we get:

[0156]

[0157] in

[0158]

[0159] Thus, a time-synchronized fault-tolerant sliding mode control law is obtained.

[0160] The present invention provides a computer device comprising one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs, when executed by the processors, implement the steps of the rigid-flexible coupling robot fault-tolerant and vibration suppression control method.

[0161] The present invention discloses a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the rigid-flexible coupling robot fault-tolerant and vibration suppression control method.

[0162] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0163] (1) This invention establishes a dynamic model of a rigid-flexible coupled robot mechanism with large deformation based on the principle of virtual work, and transforms the original underactuated system into a form suitable for trajectory tracking control design through equivalent full-drive transformation, thereby improving the consistency between system modeling and control design under large deformation conditions. (2) This invention introduces a fixed-time synchronous disturbance observer, which can realize online estimation of external disturbances and composite uncertainties, thereby improving the robustness and anti-interference ability of the system under disturbance. (3) This invention introduces a dynamic event triggering mechanism, which makes the control input updated only when the triggering condition is met, thereby reducing the communication burden and computational overhead while ensuring control performance. (4) This invention combines fault-tolerant sliding mode control and robust linear quadratic state feedback controller to realize unified control of joint trajectory tracking and flexible vibration suppression, thereby improving the fault tolerance and comprehensive control performance of the system under actuator effectiveness decay conditions. Attached Figure Description

[0164] Figure 1 This is a flowchart of the rigid-flexible coupling robot fault-tolerant and vibration suppression control method of the present invention.

[0165] Figure 2 This is a schematic diagram of a rigid-flexible coupled robot mechanism that undergoes large deformation.

[0166] Figure 3 For example, the joint angle in Example 2 target trajectory Compare the tracking curves.

[0167] Figure 4 The deflection angle of the flexible connecting rod base in Example 2 target trajectory Compare the tracking curves.

[0168] Figure 5 Joint angle and Tracking error diagram.

[0169] Figure 6 In Example 3 The comparison tracking curve.

[0170] Figure 7 In Example 3 The comparison tracking curve.

[0171] Figure 8 This is a comparison diagram of the first vibration mode.

[0172] Figure 9 This is a comparison diagram of the second vibration mode.

[0173] Figure 10 The vibration response diagram is shown under FTC-DFTSC.

[0174] Figure 11 This is a vibration response diagram under DFTSC.

[0175] Figure 12 Actual external disturbances under FTC-DFTSC The disturbance observation diagram.

[0176] Figure 13 Actual external disturbances under FTC-DFTSC The disturbance observation diagram.

[0177] Figure 14 For FTC-DFTSC control input Event trigger interval graph.

[0178] Figure 15 For FTC-DFTSC control input Event trigger interval graph. Detailed Implementation

[0179] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0180] like Figure 1 As shown, this embodiment provides a fault-tolerant and vibration suppression control method for rigid-flexible coupled robots based on synchronous disturbance observation and dynamic event triggering, including the following steps:

[0181] S1: Establish a large deformation dynamic model of the rigid-flexible coupled robot mechanism, and construct rigid coordinates, flexible modal coordinates, and control targets; S11: Establish the structural model and coordinate system of the rigid-flexible coupled robot mechanism. The rigid-flexible coupled robot mechanism consists of two levels of interconnected links. The first level is a rigid main link, and the second level is a flexible secondary link with a beam structure. Both levels of links are driven by independent motors and move in the horizontal plane; establish an inertial coordinate system. and the moving coordinate system And in the following coordinate system, the displacement variables of the flexible link in the horizontal and vertical directions are introduced. and ;in, This represents the angular displacement of a rigid member. This indicates the deflection angle at the base of the flexible connecting rod.

[0182] S12: Establish the large deformation geometry of the flexible link. Based on the Euler-Bernoulli beam theory, assuming the flexible link is inextensible and neglecting the cross-sectional shear effect, considering only the planar bending behavior, the distributed rotation angle of the flexible link satisfies:

[0183]

[0184] When the beam Axial deflection satisfies When, take an approximation Therefore,

[0185]

[0186] Through the above processing, the geometric relationship of the flexible link under large deformation conditions is transformed into an expression form that can be used for subsequent modal development.

[0187] S13: Perform modal expansion on the flexible link and determine the truncation form. Polynomial basis functions are used. An approximate representation of the distributed rotation angles along the length of the flexible link is given, namely...

[0188]

[0189] in, Indicates the amplitude of flexible vibration modes. Indicates the rotation angle of the flexible link. This represents the total number of vibration modes. Let be the spatial coordinates along the length of the flexible link. Preferably, take . Then the rotation angle variable of the flexible link can be written as:

[0190]

[0191] in, Indicates the angular position of the flexible link. and This represents the amplitude of the flexible vibration mode. This step achieves a reduced-order modeling from a distributed parameter description to a finite-dimensional rigid-flexible coupled state description.

[0192] S14: Establish the position vector, system energy expression, and virtual work expression. Define the position vector of any point on the flexible secondary link in the inertial coordinate system. for:

[0193]

[0194] Based on the translational and rotational relationships between the rigid main link and the flexible secondary link, the total kinetic energy of the system is... Represented as:

[0195] in, Indicates joint mass. Indicates the length of the rigid link. Indicates the length of the flexible beam. Indicates the moment of inertia of the wheel hub. Indicates mass density, This indicates the angular displacement of the rigid main connecting rod. Indicates the rotation angle of the flexible link distribution. This represents the position vector of any point on the flexible secondary link in the inertial coordinate system.

[0196] Total potential energy caused by elastic deformation of flexible beam for:

[0197]

[0198] in, Indicates uniform bending stiffness.

[0199] input torque and virtual work done by external disturbances for

[0200]

[0201] In the formula, and These represent the control input torques acting on the two drive joints, respectively. and These represent the external disturbance torque on the corresponding input channel. This indicates the angular displacement of the rigid main connecting rod. This indicates the deflection angle at the base of the flexible connecting rod.

[0202] This step lays the foundation for the subsequent derivation of a compact dynamic model based on Hamilton's principle.

[0203] S15: Establish a compact dynamic model based on Hamilton's principle and define the control objective. (Based on Hamilton's principle)

[0204]

[0205] Obtain the large deformation dynamics model of the rigid-flexible coupled robot mechanism

[0206]

[0207] Further definition

[0208]

[0209] The system can then be written in compact matrix form.

[0210]

[0211] in,

[0212]

[0213] and

[0214]

[0215] The control objective of this invention is to design a sliding mode trajectory tracking controller that enables joint angle position... Track the desired trajectory within a fixed time period And simultaneously suppress flexible vibrations caused by large deformation. .

[0216] S2. Establish an actuator effectiveness decay fault model and transform the original underactuated system into an equivalent fully actuated model for trajectory tracking.

[0217] S21: Establish an actuator effectiveness decay fault model. Considering the partial effectiveness decay of the actuator during actual operation, the mathematical model is as follows:

[0218]

[0219] in, Indicates the desired control torque. This represents the time-varying efficiency coefficient vector coupled to the actuator input channel, and

[0220]

[0221] This step integrates actuator failures into the controller design framework.

[0222] S22: Transform the original underactuated system into an equivalent fully actuated system. Since the system is an underactuated rigid-flexible coupled system, it cannot directly control the unactuated flexible coordinates. Therefore, it is necessary to first construct an equivalent fully actuated framework for trajectory tracking. According to the main coupling relationship in equation (3), we have

[0223]

[0224] Further definition

[0225]

[0226]

[0227] This yields an equivalent full-drive system for trajectory tracking.

[0228]

[0229] In the formula, Represents the equivalent nonlinear term, Represents a rigid coordinate vector. This represents the external disturbance vector. This represents the control input vector.

[0230] This step provides the foundation for subsequent error dynamics construction and observer design.

[0231] S23: Establish the error dynamics model. To facilitate the subsequent design of the fixed-time synchronization perturbation observer, the position and attitude tracking errors are further defined as follows:

[0232]

[0233] The error system is then written as

[0234]

[0235] in

[0236]

[0237] Through the above transformation, the original dynamic problem is uniformly transformed into a fixed-time synchronous control problem of error dynamics.

[0238] S3. Design a fixed-time synchronous disturbance observer based on error dynamics to perform online estimation of external disturbances and composite uncertainties.

[0239] S31: Provides the fundamental definitions required for fixed-time synchronous observation. To construct a fixed-time synchronous perturbation observer, we first introduce the relevant definitions required for fixed-time synchronous stability analysis. The normalized symbolic mapping is defined as follows:

[0240]

[0241] The continuous power operator is defined as

[0242]

[0243] Nussbaum type functions satisfy:

[0244]

[0245] And select

[0246]

[0247] At the same time, for any vector and positive numbers ,have

[0248]

[0249] The above definition provides a theoretical basis for the design of subsequent fixed-time synchronous observers and fault-tolerant control laws.

[0250] Theorem 1: The designed fixed-time synchronous disturbance observer can accurately estimate the composite disturbance term and external disturbance within a fixed time, and the observation error synchronously enters the origin neighborhood.

[0251] The proof is as follows:

[0252] According to the error dynamics reconstruction results, the composite disturbance term satisfies

[0253]

[0254] And introduce auxiliary state variables

[0255]

[0256] Further define intermediate variables

[0257]

[0258] Based on this, a fixed-time synchronous disturbance observer is constructed.

[0259]

[0260] In the formula, This indicates the error in perturbation estimation. Represents the equivalent inertia matrix. This represents the estimated value of the composite disturbance. Indicate intermediate variables The observed values, Indicate intermediate variables The observation error.

[0261] in, Therefore, the disturbance estimation error satisfies...

[0262]

[0263] And the observation error satisfies

[0264]

[0265] From the formula satisfied by the above observation error, it can be seen that the observation error It satisfies the fixed-time convergence condition; and combining this with the formula satisfied by the above-mentioned disturbance estimation error, it can be seen that the disturbance estimation error... It has a synchronous convergence relationship with the observation error. Therefore, with appropriate selection Subsequently, the fixed-time synchronized disturbance observer can accurately estimate the composite disturbance term and external disturbance within a fixed time period, and the observation error is synchronously incorporated into the origin neighborhood. For the observer's positive constant gain, Let be the gain function of the fixed-time synchronous observer. For the exponent parameter of the consecutive power term.

[0266] S4. Construct a dynamic event triggering mechanism and a time-synchronized fault-tolerant sliding mode control law to enable the system state to reach the sliding surface and converge synchronously within a fixed time.

[0267] S41: Construct a dynamic event triggering mechanism. To reduce the communication resource consumption caused by controller updates, an event triggering mechanism based on dynamic thresholds is introduced. Let the... The most recent trigger time for each input channel is The next trigger time is Then in the interval The internal control input uses zero-order hold:

[0268]

[0269] in,

[0270]

[0271] If nonlinear mapping If the Lipschitz continuity condition is satisfied, then we have

[0272]

[0273] Further define event triggering error Construct a dynamic event triggering mechanism

[0274]

[0275] Among them, adaptive variables satisfy

[0276]

[0277] This step ensures that control inputs are updated only when trigger conditions are met, thereby reducing unnecessary control refreshes.

[0278] S42: Constructing the time-synchronized sliding surface and switching function. Considering the need to achieve synchronous convergence of trajectory errors within a fixed time period and to avoid the singularities that may arise from traditional terminal sliding mode, a switching sliding surface is constructed.

[0279]

[0280] in,

[0281]

[0282] Further define auxiliary variables

[0283]

[0284] Switching function Constructed as

[0285]

[0286] in, Determined by the expression

[0287]

[0288] and It is a relatively small constant. This switching structure can avoid singularities while maintaining fixed-time convergence.

[0289] S43: Design time-synchronized fault-tolerant sliding mode control law. Sliding mode surface formula. By taking the derivative and combining it with the error system formula in step S23, we can obtain:

[0290]

[0291] in

[0292]

[0293] Substituting equation (4) into the equation, we get...

[0294]

[0295] in

[0296]

[0297] Based on this, a time-synchronized fault-tolerant sliding mode control law was designed.

[0298]

[0299]

[0300]

[0301] This control law unifies disturbance estimation compensation, fault tolerance compensation, and fixed-time sliding mode convergence mechanism into the same control framework.

[0302] Theorem 2: Under the singularity avoidance FTC-DFTSC control law, if the control gain satisfies the design conditions, the system state can reach the sliding surface within a fixed time and achieve synchronous convergence on the sliding surface.

[0303] The proof of the above theorem consists of two steps.

[0304] A: Prove that the system state reaches the sliding surface within a fixed time interval;

[0305] Based on the constructed switching sliding surface and fault-tolerant control law, the Lyapunov function is first constructed.

[0306]

[0307] Differentiating the above equation, we get

[0308]

[0309] By further combining the control law and error dynamics, we can obtain

[0310]

[0311] From the above equation, we can see that the Lyapunov function The system satisfies the fixed-time convergence condition, therefore the system state can be determined within a fixed time. It reaches the sliding surface inside.

[0312] B: Prove that the system state achieves fixed-time synchronous convergence on the sliding surface.

[0313] When the system state reaches the sliding surface, that is... Further construct the Lyapunov function.

[0314]

[0315] Its derivative satisfies

[0316]

[0317] As can be seen from the above equation, the system state variables further change over a fixed time on the sliding surface. The system achieves synchronous convergence, therefore the total convergence time satisfies the condition that the system can achieve synchronous convergence. .

[0318] In summary, under the action of singularity-avoidance switching sliding surface and fault-tolerant control law FTC-DFTSC, the system state can reach the sliding surface within a fixed time and achieve synchronous convergence on the sliding surface.

[0319] Theorem 3: The designed switching control structure can avoid singularities and ensure that the closed-loop system has input-to-state stability.

[0320] The proof is as follows:

[0321] The switching control structure is analyzed in two cases.

[0322] when and Sometimes,

[0323]

[0324] When the system is in another switching interval, there is

[0325]

[0326] Furthermore, the control input can be written as

[0327]

[0328] And can be further expanded into

[0329]

[0330] because and Therefore , Therefore, it can be concluded that there are no singular terms in the control law. Further analysis combining the switching structure and the boundedness of the control input reveals that the closed-loop system possesses input-to-state stability. Thus, the designed switching control structure can avoid singularities and ensure input-to-state stability of the closed-loop system.

[0331] S5. By introducing a hybrid reference trajectory and virtual input, an augmented state model is established, and a robust linear quadratic state feedback controller is designed to achieve coordinated control of trajectory tracking and flexible vibration suppression.

[0332] S51: Constructing a hybrid reference trajectory and its dynamic equations. To simultaneously achieve vibration modal stability and trajectory tracking, a hybrid reference trajectory is introduced. and virtual control input The error variables are defined as follows:

[0333]

[0334] The hybrid trajectory is generated by virtual input. Generate, its dynamic satisfaction

[0335]

[0336] in,

[0337]

[0338] By introducing a hybrid reference trajectory, the problem of flexible vibration suppression can be embedded into the trajectory generation process.

[0339] S52: Establish the dynamic relationship under the action of virtual input. From the dynamic relationship, we obtain...

[0340]

[0341]

[0342]

[0343] Further definition

[0344]

[0345] Then there is

[0346]

[0347] Meanwhile, the flexible mode satisfies:

[0348]

[0349] This step links hybrid trajectory generation, joint tracking, and flexible vibration dynamics.

[0350] S53: Establish the augmented state model and design a robust linear quadratic state feedback controller. Define the augmented state vector:

[0351]

[0352] The closed-loop system can then be written as:

[0353]

[0354] in,

[0355]

[0356]

[0357] Based on the above augmented state model, the performance index is constructed as follows:

[0358]

[0359] The optimal state feedback control law is obtained by minimizing the aforementioned performance index.

[0360]

[0361] in, This is the solution to the corresponding differential Riccati equation. After introducing this robust linear quadratic state feedback controller, the closed-loop system becomes...

[0362]

[0363] And in The system remains stable under these conditions. Therefore, by employing a hybrid reference trajectory, virtual input, and robust linear quadratic state feedback controller, coordinated control of trajectory tracking and flexible vibration suppression is achieved.

[0364] Example 2

[0365] This embodiment uses the parameters of the rigid-flexible coupling robot mechanism shown in Table 1 to verify the trajectory tracking performance and fixed-time synchronous convergence performance of the rigid-flexible coupling robot fault-tolerant and vibration suppression control method described in this embodiment under normal working conditions.

[0366] Table 1:

[0367] parameter meaning numerical values Moment of inertia of flexible link Flexible beam length Uniform bending stiffness Hub moment of inertia Joint quality rigid link length rigid link mass mass density

[0368] The controller parameters are shown in Table 2:

[0369] Control methods Parameter configuration Fault-tolerant dynamic event triggering fixed-time synchronization control Fault-tolerant dynamic sliding mode control Fault-tolerant fixed-time synchronization control

[0370] In addition, the parameters for the fixed-time synchronization disturbance observer and the dynamic event triggering mechanism are set as follows: The expected trajectory is taken as External disturbances are taken as The actuator effectiveness matrix is ​​taken as .

[0371] The FTC-DFTSC control method described in this invention is compared with the FTC-DSMC control method. Figure 3 and Figure 4 It can be seen that the FTC-DFTSC control method of the present invention can effectively track the desired trajectories of both joint angles, and the tracking process is more stable; from Figure 5 It can be seen that the control method described in this invention has a faster tracking error convergence speed and a smaller error amplitude. Therefore, under normal operating conditions, the method described in this invention can achieve high-precision joint angle trajectory tracking and enable the system state to converge synchronously within a fixed time, verifying the correctness of Theorem 2 in Example 1.

[0372] Example 3

[0373] This embodiment is used to verify the effectiveness of the present invention in fault-tolerant control performance, flexible vibration suppression performance, disturbance observation performance, and dynamic event triggering mechanism under actuator effectiveness decay fault conditions.

[0374] In this embodiment, the controlled object still uses the parameters shown in Table 1, the controller parameters still use the parameters shown in Table 2, and the fixed-time synchronous disturbance observer parameters, dynamic event triggering mechanism parameters, desired trajectory, external disturbance, and actuator effectiveness matrix are all the same as in Embodiment 2.

[0375] In this embodiment, the FTC-DFTSC control method with an FTC module is compared with the control method without an FTC module. Figure 6 and Figure 7 It can be seen that, under the condition of actuator effectiveness decay failure, when using the control method described in this invention, the system can still maintain good tracking performance for the desired trajectories of the two joint angles. Figures 8 to 11 It can be seen that, in the presence of actuator failure, after adopting the control method described in this invention, both the first and second vibration modes are more effectively suppressed, and the overall vibration response is less than that without the FTC module, indicating that this invention has a superior effect in flexible vibration suppression. Figure 12 and Figure 13 It can be seen that the fixed-time synchronized disturbance observer can accurately estimate the two disturbance components online, indicating that the fixed-time synchronized disturbance observer constructed in this invention has good disturbance reconstruction capability, thus verifying the correctness of Theorem 1 in Example 1. Figure 14 and Figure 15 As can be seen, under the dynamic event triggering mechanism, the control input is not updated continuously, but only when the triggering condition is met, thereby effectively reducing the controller update frequency and saving communication resources.

[0376] Therefore, under the combined conditions of actuator effectiveness decay fault, external disturbance and limited communication resources, the control method of the present invention can still achieve high-precision trajectory tracking, good flexible vibration suppression and online disturbance estimation, and can reduce the number of control input updates through dynamic event triggering mechanism, further verifying the correctness of Theorems 1, 2 and 3 in Example 1.

[0377] Example 4

[0378] This embodiment also provides a computer device, including one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs, when executed by the processors, implement the steps of the described method for fault-tolerant and vibration suppression control of a rigid-flexible coupled robot based on synchronous disturbance observation and dynamic event triggering.

[0379] Example 5

[0380] This embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the described method for fault-tolerant and vibration-suppressing control of a rigid-flexible coupled robot based on synchronous disturbance observation and dynamic event triggering.

Claims

1. A fault-tolerant and vibration-suppressive control method for rigid-flexible coupled robots based on synchronous disturbance observation and dynamic event triggering, characterized in that, include: S1. Establish a large deformation dynamic model of the rigid-flexible coupled robot mechanism, and construct rigid coordinates, flexible modal coordinates and control targets; S2. Establish an actuator effectiveness decay fault model and transform the original underactuated system into an equivalent fully actuated model for trajectory tracking. S3. Design a fixed-time synchronous disturbance observer based on error dynamics to perform online estimation of external disturbances and composite uncertainties; S4. Construct a dynamic event triggering mechanism and a time-synchronized fault-tolerant sliding mode control law to enable the system state to reach the sliding mode surface and converge synchronously within a fixed time. S5. By introducing a hybrid reference trajectory and virtual input, an augmented state model is established, and a robust linear quadratic state feedback controller is designed to achieve coordinated control of trajectory tracking and flexible vibration suppression.

2. The rigid-flexible coupling robot fault-tolerant and vibration suppression control method according to claim 1, characterized in that, Step S1 specifically includes: S11: Establish the structural model and coordinate system of the rigid-flexible coupling robot mechanism; the rigid-flexible coupling robot mechanism consists of two interconnected links, the first level being a rigid main link and the second level being a flexible secondary link with a beam structure. Both levels of links are driven by independent motors and move in the horizontal plane; establish an inertial coordinate system. and the moving coordinate system And in the following coordinate system, the displacement variables of the flexible link in the horizontal and vertical directions are introduced. and ;in, This represents the angular displacement of a rigid member. Indicates the deflection angle at the base of the flexible link; S12: Establish the large deformation geometric relationship of the flexible link; based on the Euler-Bernoulli beam theory, the rotation angle of the flexible link is: ； S13: Perform modal expansion on the flexible link and determine the truncation form; use polynomial basis functions. An approximate representation of the distributed rotation angles along the length of the flexible link is given, namely... ； in, For flexible linkage angle, Indicates the amplitude of flexible vibration modes. This represents the total number of vibration modes. The spatial coordinates are along the length of the flexible link. S14: Establish the position vector, system energy expression, and virtual work expression; define the position vector of any point on the flexible secondary link in the inertial coordinate system. for: ； Based on the translational and rotational relationships between the rigid main link and the flexible secondary link, the total kinetic energy of the system is... Represented as: Total potential energy caused by elastic deformation of flexible beam for: ； input torque and virtual work done by external disturbances for: ； S15: Establish a compact dynamic model based on Hamilton's principle and define the control objective; based on Hamilton's principle... ； A large deformation dynamic model of a rigid-flexible coupled robot mechanism is obtained.

3. The rigid-flexible coupling robot fault-tolerant and vibration suppression control method according to claim 1, characterized in that, Step S2 specifically includes: S21: Establish an actuator effectiveness decay fault model, represented as: in, Indicates the desired control torque. This represents the time-varying efficiency coefficient vector coupled to the actuator input channel, and S22: Transform the original underactuated system into an equivalent fully actuated system; construct the equivalent fully actuated system for trajectory tracking as follows: ; S23: Establish an error dynamics model; define the position and attitude tracking errors as follows: ； The error system is then written as in 。 4. The rigid-flexible coupling robot fault-tolerant and vibration suppression control method according to claim 1, characterized in that, Step S3 specifically includes the following steps: The basic definitions required for fixed-time synchronous observations are given; among them, the normalized symbol mapping is defined as follows: The continuous power operator is defined as Nussbaum type functions satisfy And select At the same time, for any vector and positive numbers ,have ； Construct the composite disturbance expression and auxiliary state variables, and reorganize the error dynamics into The composite disturbance term is defined as follows: Further introduce auxiliary state variables Redefining intermediate variables get Transform the perturbation estimation problem into an intermediate variable. The fixed-time synchronous convergence problem; Construct a fixed-time synchronous perturbation observer and obtain the conclusion that the estimation error converges; The fixed-time synchronization disturbance observer is constructed as follows: in, Further as well as Therefore, in the choice After parameterization, the fixed-time synchronous disturbance observer ensures that the estimation errors of each disturbance synchronously enter the origin neighborhood within a fixed time period, and the upper bound of the residuals can be further reduced through design parameters, wherein... For the observer's positive constant gain, Let be the gain function of the fixed-time synchronous observer. For the exponent parameter of the consecutive power term.

5. The rigid-flexible coupling robot fault-tolerant and vibration suppression control method according to claim 1, characterized in that, Step S4 specifically includes the following steps: S41: Construct a dynamic event triggering mechanism; to reduce the communication resource consumption caused by controller updates, an event triggering mechanism based on dynamic thresholds is introduced; let the first... The most recent trigger time for each input channel is The next trigger time is Then in the interval The internal control input uses zero-order hold: in, If nonlinear mapping If the Lipschitz continuity condition is satisfied, then we have Further define event triggering error Construct a dynamic event triggering mechanism Among them, adaptive variables satisfy S42: Construct the time-synchronized sliding surface and switching function; Constructing a switching sliding surface: in, Further define auxiliary variables Switching function Constructed as in, Determined by the expression S43: The time-synchronized fault-tolerant sliding mode control law is designed as follows: This control law unifies disturbance estimation compensation, fault tolerance compensation, and fixed-time sliding mode convergence mechanism into the same control framework; S44: Fixed-time synchronous convergence and singularity avoidance analysis are given. To prove that the designed control law can achieve fixed-time synchronous convergence, a Lyapunov function is constructed: Taking the derivative, we can further simplify it as follows: Under the control law of singularity avoidance FTC-DFTSC, the system state can reach the sliding surface within a fixed time. Then, the Lyapunov function is further constructed as follows: Its derivative is From the above equation, we can see that the system state components achieve synchronous convergence, and the upper bound of the total convergence time satisfies the following condition. Furthermore, regarding Analyzing the other switching interval separately, we can obtain: as well as 。 6. The rigid-flexible coupling robot fault-tolerant and vibration suppression control method according to claim 1, characterized in that, Step S5 specifically includes the following steps: S51: Constructing the hybrid reference trajectory and its dynamic equations; Introducing the hybrid reference trajectory and virtual control input Define error variables Hybrid reference trajectory is derived from virtual input Generate, its dynamic satisfaction in, By introducing a hybrid reference trajectory, the problem of flexible vibration suppression can be embedded into the trajectory generation process; S52: Establish the dynamic relationship under the action of virtual input; obtain the dynamic relationship... Further definition Then there is Meanwhile, flexible modes satisfy ； S53: Establish an augmented state model and design a robust linear quadratic state feedback controller; Define augmented state vector The closed-loop system is then written as in, Based on the augmented state model described above, the performance index is constructed as follows: By minimizing the aforementioned performance metric, the optimal state feedback control law is obtained: in, The solution to the corresponding differential Riccati equation is given; after introducing this robust linear quadratic state feedback controller, the closed-loop system becomes... And in The system remains stable under certain conditions; therefore, it achieves coordinated control of trajectory tracking and flexible vibration suppression by using a hybrid reference trajectory, virtual input, and robust linear quadratic state feedback controller.

7. The rigid-flexible coupling robot fault-tolerant and vibration suppression control method according to claim 2, characterized in that, The large deformation dynamics model of the rigid-flexible coupling robot mechanism is expressed as follows: Further definition The system can then be written in compact matrix form: in, and 。 8. The rigid-flexible coupling robot fault-tolerant and vibration suppression control method according to claim 5, characterized in that, The time-synchronized fault-tolerant sliding mode control law is obtained by differentiating the sliding mode surface formula and combining it with the error system: in Substituting the actuator effectiveness decay fault model, we get: in Thus, a time-synchronized fault-tolerant sliding mode control law is obtained.

9. A computer device, characterized in that, It includes one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs, when executed by the processors, implement the steps of the rigid-flexible coupling robot fault-tolerant and vibration suppression control method as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the rigid-flexible coupling robot fault-tolerant and vibration suppression control method as described in any one of claims 1-8.

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