Self-adaptive iterative learning fault-tolerant control method suitable for preset performance of mechanical arm system

Abstract

The invention relates to a self-adaptive iterative learning fault-tolerant control method for preset performance of a mechanical arm system. The method comprises the following steps: S1, establishing a mechanical arm dynamic model with an actuator fault; s2, defining a preset performance function and first-order subsystem coordinate transformation; s3, constructing a Lyapunov function and designing a virtual controller; s4, defining second-order subsystem coordinate transformation; and S5, proposing an adaptive iterative learning law, and designing a control input signal. Through reasonable scheme design and verification of the system, a tracking control scheme is designed, so that the specified performance of the high-order nonlinear system influenced by the fault of the actuator is ensured.

Description

Technical Field

[0001] The present invention relates to the field of robotics technology, and in particular to an adaptive iterative learning fault-tolerant control method suitable for preset performance of a robotic arm system. Background Art

[0002] High-order nonlinear systems usually have complex dynamic behaviors and nonlinear characteristics, so the control design of such systems is a challenging problem. In the past, Chen Yong and others have studied the iterative learning control (ILC) method in dealing with high-order nonlinear systems. However, traditional ILC algorithms often have strict assumptions and restrictions on system models, which makes the ILC method face great difficulties when facing nonlinear systems.

[0003] Recently, Bechlioulis et al. proposed a new method called preset performance control (PPC), which can meet the predefined boundaries of transient and steady-state behavior of the output error. The current progress of adaptive learning control methods has been applied to solve the prescribed performance control of high-order nonlinear systems. Shi Xiaoning et al. solved the problem of predetermined performance control of unknown nonlinear systems subject to full state constraints. Sui Shuai et al. studied the design problem of adaptive backstepping control based on neural networks for random nonlinear systems with finite-time prescribed performance, and also conducted research on error-constrained finite-time fuzzy adaptive control for non-strict feedback random high-order nonlinear systems. In recent years, Zhang Jinxi et al. have made many progresses in adaptive preset performance control of nonlinear systems with actuator failures, and have developed a state feedback fault-tolerant control method suitable for introducing uncertain nonlinear systems. This method has the characteristics of unknown control direction and minimal complexity, and can achieve the prescribed tracking performance. Hu Qinglei et al. discussed the solution of attitude tracking control problems under conditions of unknown inertial parameters, unexpected disturbances, actuator failure and input saturation, ensuring the realization of preset performance. Summary of the invention

[0004] The technical problem to be solved by the present invention is: to overcome the deficiencies of the prior art and propose a fault-tolerant control method based on adaptive iterative learning to solve the tracking problem of the robotic arm system under the same initial conditions to ensure the specified performance of the system.

[0005] The technical solution of the present invention is:

[0006] An adaptive iterative learning fault-tolerant control method for preset performance of a robotic arm system comprises the following steps:

[0007] S1. Establish a dynamic model of the robot arm with actuator failure;

[0008] S2, defining a preset performance function and a first-order subsystem coordinate transformation;

[0009] S3, construct Lyapunov function, design virtual controller and adaptive iterative learning law;

[0010] S4, define the second-order subsystem coordinate transformation;

[0011] S5. Construct Lyapunov function, design control input signal and adaptive iterative learning law.

[0012] In step S1, a dynamic model of a robotic arm with actuator failure is established:

[0013]

[0014] Where k represents the number of iterations, Represents the angle of the rigid link of the robotic arm system; represents the angular velocity of the rigid connection of the robot system; represents the angular acceleration of the rigid link of the robotic arm system; u k Represents the input of the rigid link of the robot system; y k Represents the output of the rigid link of the robotic arm system; J is the moment of inertia of the servo motor; D is the unknown damping coefficient; M is the mass of the link; L is the distance from the joint axis to the center of mass; g is the acceleration due to gravity.

[0015] In step S2, a preset performance function and a first-order subsystem coordinate transformation are defined:

[0016] Step S21: According to the preset performance control method, first define the tracking error:

[0017]

[0018] in, is the desired tracking trajectory.

[0019] Then the performance function is used to constrain the error:

[0020]

[0021] in, is the overshoot suppression parameter.

[0022] Define a positive and smoothly decaying performance function:

[0023]

[0024] Among them, l ∞ >l0>0 and l are both positive parameters to be designed.

[0025] Step S22: Since it is difficult to directly design a controller under constraints, the following error conversion method is introduced:

[0026]

[0027] in, is the conversion function.

[0028] Step S23: Considering is strictly monotonically increasing, and its inverse function is:

[0029]

[0030] Where, ρ(t) = e(t) / l(t), is the conversion error.

[0031] For the conversion error, the derivative can be obtained:

[0032]

[0033] in, and are unknown and known nonlinear smooth functions respectively. And Here, γ and Γ are known.

[0034] In step S3, construct the Lyapunov function, design the virtual controller and the adaptive iterative learning law:

[0035] Step S31: Fuzzy logic function Approximate a nonlinear smooth function term involving unknowns:

[0036]

[0037] in, Assume that ε1(X1) satisfies and is any positive constant.

[0038] Step S32: For the defined coordinate transformation, the following Lyapunov function may be selected:

[0039]

[0040] Among them, 0<∈1<1,γ1>0 is the constant to be designed, and yes Estimates.

[0041] For the Lyapunov function, taking the derivative we get:

[0042]

[0043] Step S33: According to the backstepping design process, the following virtual controller and adaptive iterative learning law are designed:

[0044]

[0045] Among them, c1>0 and is a constant to be designed and satisfies

[0046] In step S4, the second-order subsystem state coordinate transformation is designed according to the definition:

[0047] Step S41: For the above-mentioned robot arm system, the following second-order subsystem state coordinate transformation is designed:

[0048]

[0049] in, is the angular velocity of the rigid connection of the robotic arm system; δ 1,k is the first-order virtual controller; is the second-order subsystem error signal.

[0050] For the definition of the second-order subsystem error signal, taking its derivative we can get:

[0051]

[0052] Step S42: Control input vector u when the actuator fails k ,satisfy:

[0053]

[0054] Among them, β(t) is the actuator effectiveness factor, v k (t) = [v 1,k (t),v 2,k (t)…,v m,k (t)] T is the actual control signal received by the receiver, It indicates that the actuator is stuck; when σ=1, it indicates that the actuator has failed.

[0055] Step S43: Under the influence of the actuator failure, the second-order subsystem error signal satisfies:

[0056]

[0057] in, represents the control signal received by the j-th actuator in the k-th iteration; The lower bound of j , the upper bound is u 0,kIt is a fuzzy adaptive controller designed using the backstepping method.

[0058] In step S5, the construction of the Lyapunov function, design of the control input signal and the adaptive iterative learning law specifically include:

[0059] Step S51: Fuzzy logic function For nonlinear smooth functions with unknown Perform a fuzzy approximation:

[0060]

[0061] in, Assume that ε2(X2) satisfies and is any positive constant.

[0062] Step S52: In combination with the coordinate transformation defined above, select the following Lyapunov function:

[0063]

[0064] Among them, 0< ∈2 <1,γ2>0 is a constant to be designed, and yes Estimates.

[0065] For the Lyapunov function, taking the derivative we get:

[0066]

[0067] Step S53: According to the backstepping design process, the following control input signal and adaptive iterative learning law are designed:

[0068]

[0069] Among them, c2>0 and is a constant to be designed and satisfies

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] 1. The present invention discloses an iterative learning method for a robotic arm system with actuator failure. Taking into account the initial state and actuator failure, a class of high-order non-strict feedback nonlinear fault-tolerant control systems is designed, which improves the control accuracy of the robotic arm and is more practical.

[0072] 2. The present invention discloses an iterative learning method for a robotic arm system with actuator failure, which introduces a preset performance adaptive iterative learning control structure into the robotic arm control system for the first time. The conversion of the finite time performance function and the output error ensures the stability of the system after the conversion and the accuracy of transient and steady-state tracking errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0074] Figure 1 It is a schematic diagram of the tracking performance of the robot system at the 100th iteration when the actuator of the present invention fails.

[0075] Figure 2 It is a schematic diagram of the tracking error response of the manipulator system under the preset performance control of the present invention at the 100th iteration.

[0076] Figure 3 It is a schematic diagram of the trajectory of the control input signal and the actuator of the present invention. DETAILED DESCRIPTION

[0077] In order to enable persons skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0078] Example

[0079] This example discloses an adaptive iterative learning fault-tolerant control method for preset performance of a robotic arm system, comprising the following steps:

[0080] S1. Establish a dynamic model of the robot arm with actuator failure;

[0081] S2, defining a preset performance function and a first-order subsystem coordinate transformation;

[0082] S3, construct Lyapunov function, design virtual controller and adaptive iterative learning law;

[0083] S4, define the second-order subsystem coordinate transformation;

[0084] S5. Construct Lyapunov function, design control input signal and adaptive iterative learning law.

[0085] Step S1: Establish a dynamic model of the robot arm with actuator failure.

[0086] The robot arm is a nonlinear system. Considering the influence of initial conditions, the following second-order system is given:

[0087]

[0088] Where k represents the number of iterations, Represents the angle of the rigid link of the robotic arm system; represents the angular velocity of the rigid connection of the robot system; represents the angular acceleration of the rigid link of the robotic arm system; u k Represents the input of the rigid link of the robot system; y k Represents the output of the rigid link of the robotic arm system; J is the moment of inertia of the servo motor; D is the unknown damping coefficient; M is the mass of the link; L is the distance from the joint axis to the center of mass; g is the acceleration due to gravity.

[0089] Step S2: See Figure 1 As shown, the preset performance function and the first-order subsystem coordinate transformation are defined.

[0090] Specifically include:

[0091] Step S21: According to the preset performance control method, define the tracking error:

[0092]

[0093] in, is the desired tracking trajectory.

[0094] Then the performance function is used to constrain the error:

[0095]

[0096] in, is the overshoot suppression constant.

[0097] Define a positive and smoothly decaying performance function:

[0098] l(t)=(l0-l ∞ ) -lt +l ∞ (4)

[0099] Among them, l ∞ >l0>0 and l are both positive constants to be designed.

[0100] Step S22: Since it is difficult to directly design a controller under constraints, the following error conversion method is introduced:

[0101]

[0102]

[0103] in, is the conversion function.

[0104] Step S23: Considering is strictly monotonically increasing, and its inverse function is:

[0105]

[0106] Where, ρ(t) = e(t) / l(t), is the conversion error.

[0107] For the conversion error, the derivative can be obtained:

[0108]

[0109] in, and are unknown and known nonlinear smooth functions respectively. And Here, γ and Γ are known.

[0110] Step S3: Construct the Lyapunov function, design the virtual controller and the adaptive iterative learning law.

[0111] Specifically include:

[0112] Step S31: Fuzzy logic function Approximate a nonlinear smooth function term involving unknowns:

[0113]

[0114] in, Assume that ε1(X1) satisfies and is any positive constant.

[0115] S32: For the defined coordinate transformation, the following Lyapunov functions can be selected:

[0116]

[0117] Among them, 0<ε1<1,γ1>0 are constants to be designed, and yes Estimates.

[0118] For the Lyapunov function, taking the derivative we get:

[0119]

[0120] Step S33: According to the backstepping design process, the following virtual controller and adaptive iterative learning law are designed:

[0121]

[0122] Among them, c1>0 and is a constant to be designed and satisfies

[0123] Step S4: The definition designs the second-order subsystem state transformation.

[0124] Specifically include:

[0125] Step S41: Design the following second-order subsystem state transformation:

[0126]

[0127] in, is the angular velocity of the rigid connection of the robotic arm system; δ 1,k is the first-order virtual controller; is the second-order subsystem error signal.

[0128] For the definition of the second-order subsystem error signal, taking its derivative we can get:

[0129]

[0130] Step S42: Control input vector u when the actuator fails k ,satisfy:

[0131]

[0132] Among them, β(t) is the actuator effectiveness factor, v k (t) = [v 1,k (t),v 2,k (t)…,v m,k (t)] T is the actual control signal received by the receiver, It indicates that the actuator is stuck; when σ=1, it indicates that the actuator has failed.

[0133] Step S43: Under the influence of the actuator failure, the second-order subsystem error signal is:

[0134]

[0135] in, represents the control signal received by the j-th actuator in the k-th iteration; The lower bound of j , the upper bound is u0,k It is a fuzzy adaptive controller designed using the backstepping method.

[0136] Step S5: See Figure 3 As shown, actuator failure is considered, the Lyapunov function is constructed, and the control input signal and adaptive iterative learning law are designed.

[0137] Specifically include:

[0138] Step S51: Fuzzy logic function Fuzzy approximation of nonlinear smooth functions with unknowns:

[0139]

[0140] in, Assume that ε2(X2) satisfies and is any positive constant.

[0141] Step S52: In combination with the coordinate transformation defined above, select the following Lyapunov function:

[0142]

[0143] Among them, 0<ε2<1,γ2>0 are constants to be designed, and yes Estimates.

[0144] For the Lyapunov function, taking the derivative we get:

[0145]

[0146] Step S53: According to the backstepping design process, the following control input signal and adaptive iterative learning law are obtained:

[0147]

[0148] Among them, c2>0 and is a constant to be designed and satisfies

[0149] The parameter values ​​of the robot arm system used in the embodiment are set to the moment of inertia J = 1; D = 2; M = 2; the controller related parameters are set to: ε1 = 0.6, ε2 = 0.6, γ1 = 0.6, γ2 = 0.8, l=1; the initial angle of the rigid link is: The preset performance function related parameters are set to: l0=1,l ∞ =0.01, l=0.8; sampling time is: 0.01s.

[0150] Actuator failure u k =u 1,k +u 2,k , considering the actuator stuck fault and actuator failure fault, the parameters are set as:

[0151] b1=0.3, b2=0.5, β2(t)=0.7+0.01sin(t).

[0152] Depend on Figure 1 It can be seen that: considering the actuator failure, within 5 seconds, as the number of iterations increases, the control strategy can not only gradually compensate for the uncertainty and interference caused by the actuator failure, but also maintain the good tracking performance of the robotic arm system. In addition, this method optimizes the speed and accuracy of error convergence, so that the final tracking error achieves a higher accuracy.

[0153] Depend on Figure 2 It can be seen that by using pre-defined performance indicators, we can significantly reduce the impact of actuator failures on the robot system. Specifically, these performance indicators effectively reduce the tracking error caused by actuator failures by optimizing the response of the control system. This not only improves the robustness of the system to failures, but also maintains the stability of the tracking error convergence rate, thereby avoiding large maximum overshoots when failures occur. In this way, the system is able to maintain a more stable and controllable performance in the face of actuator failures, ensuring the reliability and efficiency of the overall system.

[0154] This embodiment mainly uses the system output angle as a performance parameter. Figure 1 The system tracking effect diagram when the actuator fails at the 100th iteration is given; Figure 2 The tracking error response under the preset performance control at the 100th iteration is given; Figure 3 Given a controller u 0,100 (t),u 1,100 (t),u 2,100 (t) The trajectory of the 100th iteration. From the above pictures, it can be seen that the control method provided by the present invention can make the robot system more stable through the specified performance under the influence of actuator failure.

[0155] Although the present invention has been described in detail by referring to the accompanying drawings and in combination with the preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, a person of ordinary skill in the art may make various equivalent modifications or substitutions to the embodiments of the present invention, and these modifications or substitutions shall be within the scope of the present invention. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, and all of these shall be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. An adaptive iterative learning fault-tolerant control method suitable for preset performance of a robotic arm system, characterized in that: The steps include: S1. Establish a dynamic model of the robot arm with actuator failure; S2, defining a preset performance function and a first-order subsystem coordinate transformation; S3, construct Lyapunov function, design virtual controller and adaptive iterative learning law; S4, define the second-order subsystem coordinate transformation; S5. Construct Lyapunov function, design control input signal and adaptive iterative learning law.

2. The adaptive iterative learning fault-tolerant control method for a preset performance of a robotic arm system according to claim 1, characterized in that: In step S1, the dynamic model of the robot arm with actuator failure is: Where k represents the number of iterations, Represents the angle of the rigid link of the robotic arm system; represents the angular velocity of the rigid connection of the robot system; represents the angular acceleration of the rigid link of the robotic arm system; u k Represents the input of the rigid link of the robot system; y k Represents the output of the rigid link of the robotic arm system; J is the moment of inertia of the servo motor; D is the unknown damping coefficient; M is the mass of the link; L is the distance from the joint axis to the center of mass; g is the acceleration due to gravity.

3. The adaptive iterative learning fault-tolerant control method for a preset performance of a robotic arm system according to claim 1, characterized in that: In step S2, a preset performance function and a first-order subsystem coordinate transformation are defined, specifically including: Step S21: For the preset performance control method, the following tracking error is defined: in, is the desired tracking trajectory; Then the performance function is used to constrain the error: in, is the overshoot suppression constant; Define a positive and smoothly decaying performance function: in, and l are both positive constants to be designed; Step S22: Since it is difficult to directly design a controller under constraints, the following error conversion method is introduced: in, is the conversion function; Step S23: Considering is strictly monotonically increasing, and its inverse function is: in, is the conversion error; For the conversion error, the derivative can be obtained: in, and are unknown and known nonlinear smooth functions respectively; Here, γ and Γ are known.

4. The adaptive iterative learning fault-tolerant control method for preset performance of a robotic arm system according to claim 1, characterized in that: In S3, the Lyapunov function is constructed and the virtual controller is designed, including: Step S31: Fuzzy logic function Approximate a nonlinear smooth function term involving unknowns: in, Assume that ε1(X1) satisfies and is any positive constant; Step S32: For the coordinate transformation defined above, the following Lyapunov function may be selected: Among them, 0<∈1<1,γ1>0 is the designed constant, and yes estimates; By taking the derivative of the above Lyapunov function, we can get: Step S33: According to the backstepping design process, the following virtual controller and adaptive iterative learning law are designed: Among them, c1>0 and is a constant to be designed and satisfies .

5. The adaptive iterative learning fault-tolerant control method for preset performance of a robotic arm system according to claim 1, characterized in that: In S4, the second-order subsystem coordinate transformation is defined, including: Step S41: For the above-mentioned robot arm system, the following second-order subsystem state coordinate transformation is designed: in, is the angular velocity of the rigid connection of the robotic arm system; δ 1,k is the first-order virtual controller; is the second-order subsystem error signal; For the definition of the second-order subsystem error signal, taking its derivative we can get: Step S42: Control input vector u when the actuator fails k ,satisfy: Among them, β(t) is the actuator effectiveness factor, v k (t) = [v 1,k (t),v 2,k (t)…,v m,k (t)] T is the actual control signal received by the receiver, Indicates that the actuator is stuck; when σ=1, it indicates that the actuator fails; Step S43: Under the influence of the actuator failure, the second-order subsystem error signal satisfies: in, represents the control signal received by the j-th actuator in the k-th iteration; The lower bound of j , the upper bound is u 0,k It is a fuzzy adaptive controller designed using the backstepping method.

6. The adaptive iterative learning fault-tolerant control method for preset performance of a robotic arm system according to claim 1, characterized in that: In S5, the Lyapunov function is constructed, and the control input signal and adaptive iterative learning law are designed, including: Step S51: Fuzzy logic function Fuzzy approximation of nonlinear smooth functions with unknowns: in, Assume that ε2(X2) satisfies and is any positive constant; Step S52: In combination with the coordinate transformation defined above, select the following Lyapunov function: Among them, 0<∈2<1,γ2>0 is the constant to be designed, and yes estimates; For the above Lyapunov function, we can get the following derivative: Step S53: According to the backstepping design process, the following control input signal and adaptive iterative learning law are designed: Among them, c2>0 and is a constant to be designed and satisfies

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