An adaptive preset time control method and system for a flexible robot arm

Abstract

The application provides an adaptive preset time control method and system for a flexible mechanical arm, relates to the field of control science and engineering, and comprises the following steps: constructing a dynamic model of the flexible mechanical arm and deducing a nonlinear system state equation; constructing a time transformation function and a coordinate transformation function based on the system state equation; constructing an adaptive preset time controller by using the time transformation function and the coordinate transformation function, connecting a dead zone compensator in series at the output end of the controller, compensating an ideal input control signal, obtaining an actual control input, and applying the actual control input to the flexible mechanical arm; and the application introduces the time transformation function into the control of the flexible mechanical arm, combines a Lyapunov function and an adaptive estimation method, finally outputs asymptotic tracking of a given tracking curve, guarantees global prescribed transient performance, and makes the performance indexes in terms of the stable time and the tracking precision able to be pre-assigned offline according to task requirements, instead of depending on initial states and any design parameters.

Description

Technical Field

[0001] This invention relates to the field of control science and engineering, and specifically to an adaptive preset time control method and system for a flexible robotic arm. Background Technology

[0002] In the field of robotics, the emergence of flexible robotic arms marks a new stage in the development of robotics technology. Compared with traditional rigid robotic arms, flexible robotic arms, with their unique design and superior performance, demonstrate powerful advantages in performing more complex tasks. Flexible robotic arms can adapt to various environments, whether in precision assembly, biomedical engineering, or disaster relief, accomplishing tasks that are almost impossible for traditional robotic arms due to their flexibility and agility. However, flexible robotic arms are affected by various external disturbances during operation, such as wind and vibration. These disturbances alter the dynamic characteristics of the flexible robotic arm, causing its end-effector motion to exhibit nonlinear, strongly coupled, and time-varying features. Therefore, it is difficult to establish an accurate kinematic model of the flexible robotic arm's end-effector to describe these characteristics. To ensure the safe, efficient, and reliable operation of the robotic arm, stable control inevitably becomes a crucial part of the robot design process.

[0003] In robot control systems, stable control techniques are widely used. However, traditional control methods (such as asymptotic stability control) suffer from the problem of infinite convergence time, meaning the system state only converges to an equilibrium point as time approaches infinity. To address this issue, finite-time control was proposed. While its convergence time is finite, it heavily depends on the system's initial state, making it difficult to accurately predict task completion time in practical applications due to the unknown initial state. In recent years, fixed-time control techniques have further developed, employing specific Lyapunov function designs to create an upper bound on the convergence time independent of the initial state. However, this upper bound is typically a complex function related to system parameters and control gain. This means that during controller design, a clear convergence time cannot be directly and independently set according to task requirements; instead, the upper bound can only be indirectly influenced by repeatedly adjusting controller parameters, a cumbersome and imprecise process. Therefore, to overcome the limitation of fixed-time control's inability to directly set the convergence time, preset-time control techniques have gradually developed. These techniques, with convergence times strictly independent of the system's initial state, have become a research hotspot.

[0004] For nonlinear systems with uncertainties, constructing robust pre-set time controllers remains challenging. Current research does not address stable control under pre-set time convergence settings; some results based on fixed-time control only allow the system state or tracking error to converge to a small neighborhood near the origin within a fixed time, rather than precisely to the origin. In flexible robotic arm control systems, there are unknown time-varying disturbances such as elastic vibrations and unknown loads. These performance limitations may lead to residual vibrations not being completely suppressed within the predetermined time, sudden controller failure, system performance degradation, or even catastrophic accidents. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes an adaptive preset time control method and system for flexible robotic arms. By introducing a time transformation function into the control of the flexible robotic arm and combining it with Lyapunov functions and adaptive estimation methods, the system output achieves asymptotic stability with respect to a given tracking curve within a preset time, ensuring globally defined transient performance. This allows performance indicators in terms of stability time and tracking accuracy to be pre-allocated offline according to task requirements, without depending on the initial state of the system or any design parameters.

[0006] According to some embodiments, the present invention adopts the following technical solution:

[0007] An adaptive preset time control method for a flexible robotic arm includes:

[0008] A dynamic model of a flexible robotic arm is constructed, and based on this model, the state equations of a nonlinear system containing mismatched inherent unknown parameters and external unmodeled dynamic disturbances are derived.

[0009] Based on the system state equation, a time transformation function is constructed. By redefining the time scale, the finite time is mapped to the infinite time domain, so that the error dynamics converge within a preset time. At the same time, a coordinate transformation function is constructed to convert the state variables into error coordinates to constrain the tracking error variables that include joint position error and flexible deformation error.

[0010] By using time transformation functions and coordinate transformation functions, virtual control laws, adaptive control laws, and ideal input control laws are constructed to form an adaptive preset time controller. The stability condition of the controller is verified by Lyapunov function. A dead zone compensator is connected in series at the output of the verified controller to compensate for the ideal input control generated by the controller, so as to obtain the actual control input and apply it to the flexible robotic arm to realize adaptive preset time control.

[0011] According to some embodiments, the present invention adopts the following technical solution:

[0012] An adaptive preset time control system for a flexible robotic arm includes:

[0013] The modeling module is configured to: construct a dynamic model of the flexible robotic arm and derive the state equations of the nonlinear system containing mismatched inherent unknown parameters and external unmodeled dynamic disturbances based on the model;

[0014] The construction module is configured to: construct a time transformation function based on the system state equation, and map finite time to infinite time domain by redefining the time scale, so that the error dynamics converge within a preset time. At the same time, it constructs a coordinate transformation function to convert the state variables into error coordinates to constrain the tracking error variables that include joint position error and flexible deformation error.

[0015] The control module is configured to: construct a virtual control law, an adaptive control law, and an ideal input control law using time transformation functions and coordinate transformation functions, forming an adaptive preset time controller; and verify whether the controller meets the stability condition through a Lyapunov function; and connect a dead zone compensator in series at the output of the verified controller to compensate for the ideal input control generated by the controller, thereby obtaining the actual control input and applying it to the flexible robotic arm to achieve adaptive preset time control.

[0016] According to some embodiments, the present invention adopts the following technical solution:

[0017] A computer program product includes a computer program that, when executed by a processor, implements the aforementioned adaptive preset time control method for a flexible robotic arm.

[0018] According to some embodiments, the present invention adopts the following technical solution:

[0019] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned adaptive preset time control method for a flexible robotic arm.

[0020] According to some embodiments, the present invention adopts the following technical solution:

[0021] An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the adaptive preset time control method for a flexible robotic arm.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] This invention introduces a time transformation function into the control system of a flexible robotic arm in a nonlinear system, and combines Lyapunov functions and adaptive estimation methods to ultimately output an asymptotic tracking curve. This enables the handling of nonlinear systems with high relative degrees and time-varying uncertainties. Simultaneously, it ensures system convergence within a specified time and is independent of initial states and any design parameters. Furthermore, it actively suppresses complex disturbances such as elastic vibration of the flexible arm and sudden changes in unknown loads. This allows the flexible robotic arm to avoid the problems of time-consuming and random convergence, and difficulty in coordinating with production cycles, inherent in traditional adaptive control systems, when operating in complex dynamic scenarios. Attached Figure Description

[0024] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0025] Figure 1 This is a flowchart of the method in Example 1.

[0026] Figure 2 This is a model diagram of a single-link flexible robotic arm as shown in Example 1.

[0027] Figure 3 This is a system state and tracking signal trajectory diagram with dead-zone input in Example 1.

[0028] Figure 4 This is a parameter estimation trajectory diagram for the input with dead zone in Example 1.

[0029] Figure 5 This is a trajectory diagram of the actual control input and ideal input control signals, including dead-zone input, for Example 1. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0032] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0033] Example 1

[0034] One embodiment of the present invention provides an adaptive preset time control method for a flexible robotic arm, comprising:

[0035] Step S1: Construct a dynamic model of the flexible robotic arm, and derive the state equation of the nonlinear system containing mismatched inherent unknown parameters and external unmodeled dynamic disturbances based on the model;

[0036] Step S2: Based on the system state equation, construct a time transformation function. By redefining the time scale, the finite time is mapped to the infinite time domain, so that the error dynamics converge within a preset time. At the same time, construct a coordinate transformation function to convert the state variables into error coordinates to constrain the tracking error variables that include joint position error and flexible deformation error.

[0037] Step S3: Using time transformation function and coordinate transformation function, construct virtual control law, adaptive control law and ideal input control law to form an adaptive preset time controller, and verify whether the controller meets the stability condition through Lyapunov function; connect dead zone compensator in series at the output of the verified controller to compensate for the ideal input control generated by the controller, obtain the actual control input and apply it to the flexible robotic arm to realize adaptive preset time control.

[0038] As one embodiment, the present invention provides an adaptive preset time control method for a flexible robotic arm. By introducing a time transformation function into the flexible robotic arm control and combining it with a Lyapunov function and an adaptive estimation method, the system output achieves asymptotic stability of the given tracking curve within a preset time, ensuring globally defined transient performance. This allows performance indicators in terms of stabilization time and tracking accuracy to be pre-allocated offline according to task requirements, without depending on the initial state and any design parameters. A single-link flexible robotic arm is used as an example to illustrate the specific implementation process.

[0039] Reference Figure 1 The motion principle of the joints in a single-link flexible robotic arm is analyzed. Using the Euler-Lagrange modeling method, the dynamic model of the robotic arm is defined as follows:

[0040] (1)

[0041] in, and These represent the link angle and angular velocity of the flexible robotic arm, respectively. It is the rotational inertia of the flexible robotic arm. It is the damping coefficient. This represents the length from the joint axis to the center of mass. It is the mass of the connecting rod. Represents gravitational acceleration. It is an unknown Lipschitz continuous function that satisfies , For actual control input, For ideal input control signals.

[0042] The system parameters in the robotic arm control system are all considered time-varying and are unknown for control design purposes; therefore, the following is chosen: That is, the angle and angular velocity are the state variables of the system. Based on formula (2), formula (1) can be rewritten as the system state equation as shown below:

[0043] (2)

[0044] make , , We can obtain:

[0045] (3)

[0046] To facilitate the design of the control system, it is necessary to first introduce the corresponding assumptions and lemmas:

[0047] Assumption 1: Inverse system It is finite-time input-state stable, meaning it has a positive definite Lyapunov function. , Class function , and known positive real numbers , , Makes all ,have:

[0048] (4)

[0049] Assumption 2: There exists a continuous nonnegative function. and , making

[0050] (5)

[0051] in, It is an unknown non-negative constant (coupled unknown parameter).

[0052] Lemma 1: For system (3), assume there exists a continuously differentiable, positive definite, and radially unbounded function that satisfies:

[0053] (6)

[0054] Where, constant ,and Therefore, this system can achieve generalized fixed-time stability—uniformly bounded stability—and adjust the time function. satisfy:

[0055] (7)

[0056] Furthermore, if constant and Since it can be adjusted arbitrarily, the system can achieve generalized fixed-time stability – any preset stability time.

[0057] Lemma 2: If there exists a continuous, radially unbounded, and positive definite function , making

[0058] (8)

[0059] in, Therefore, the origin of this system (2) is globally time-stable, and the time function is adjusted. It can be estimated as follows:

[0060] (9)

[0061] In order to achieve the desired performance target, this embodiment introduces a time transformation function, specifically:

[0062] First, the time transformation function is defined as follows: for a given precision bound and convergence time A time-varying function , defined in And abbreviated as , where t is time, ranging from [0, T], and T is the set convergence time.

[0063] In this embodiment, the expression for the time transformation function is:

[0064] (10)

[0065] in, , For convergence time.

[0066] Simultaneously, coordinate transformation is performed on the control design. The coordinate transformation function is as follows:

[0067] (11)

[0068] in, It is a virtual control law in controller design, making but .

[0069] Next, the controller design is performed for the system represented by formula (3):

[0070] Introduce the following virtual control law :

[0071] (12)

[0072] Among them, the function .

[0073] Solve according to formulas (3) and (11). Time derivative:

[0074] (13)

[0075] from Subsystem Begin by setting variables Assuming it is a control input, design the time derivative of the following Lyapunov function:

[0076] (14)

[0077] satisfy:

[0078] (15)

[0079] Virtual control law Substituting into the above equation, we can obtain:

[0080] (16)

[0081] make Considering unknown parameters ,Will As The estimated value, As an estimation error, the Lyapunov function is chosen:

[0082] (17)

[0083] in, For positive integers, satisfying:

[0084] (18)

[0085] Using Assumption 2 and Lemma 2, we can obtain:

[0086] (19)

[0087] and

[0088] (20)

[0089] Substituting (20) into equation (18), we get:

[0090] (twenty one)

[0091] Parameter update law:

[0092] (twenty two)

[0093] And the ideal input control law, generating the ideal input control signal. This can be expressed as a formula:

[0094] (twenty three)

[0095] Pick Let it be an intermediate variable.

[0096] (twenty four)

[0097] in, and It is a non-negative function. and It is a known constant.

[0098] To address the steady-state error and performance degradation caused by actuator dead-zone nonlinearity, a dead-zone compensator is connected in series after the adaptive preset time controller. This compensator, based on a mathematical model of the actuator dead zone, compensates for the ideal input control signal output by the controller, thereby effectively offsetting or weakening the actual impact of the dead zone. The dead-zone compensator can work in conjunction with the adaptive preset time controller to jointly ensure the preset time convergence performance of the system.

[0099] Specifically, the compensated actual control input signal This can be expressed as a formula:

[0100] (25)

[0101] in, and It is a non-negative function that satisfies , and These are the positive dead zone parameters and the negative dead zone parameters, which satisfy... and .

[0102] Meanwhile, in the simulation, it is assumed that the length L(t) has a nominal value and that there is a perturbation. To illustrate the performance of the system represented by Equation (3) in the presence of parameters and in the case of unmodeled dynamics, we further assume a disturbance. ,in It is an unknown constant, assumed to be... Control can yield the following state equation:

[0103] (26)

[0104] in, , , , It conforms to the form of equation (2).

[0105] Based on the above design, this embodiment sets the following parameters for the robotic arm's dynamic model: moment of inertia. Damping coefficient robotic arm quality Gravitational acceleration Link length The simulation time range is set to... The initial state of the system is as follows: These correspond to the initial positions of the joints. and initial velocity and auxiliary variables and The initial values. The design parameters for the dead-zone compensator are as follows: , , , ; , , , The backstepping controller design incorporates controller parameters. = 5 and =8, used to adjust the system's response speed and stability to meet the controller design requirements.

[0106] Simulation results are as follows Figure 3-5 As shown, where Figure 3 The system state with dead-time input is shown. , with auxiliary variables The trajectory that changes over time. Figure 4 Describes parameter estimation with dead-zone input. The trajectory that changes over time. Figure 5 The actual control inputs, including dead-time inputs, are displayed. A trajectory that changes over time and occurs at a preset time. Convergence to These results clearly show that all closed-loop signals are bounded, which is consistent with the theoretical results.

[0107] Therefore, based on the above process description, a new preset time control scheme is proposed by introducing a time transformation function and integrating the Lyapunov function and adaptive estimation method. Compared with existing results, this scheme has the following characteristics: (1) The introduced time transformation function breaks through the traditional fixed time scale limitation and can dynamically adjust the time perception dimension according to the system state; (2) After integrating the Lyapunov function, a stability criterion coupled with the time transformation is constructed. When dealing with nonlinear and time-varying systems, it can accurately characterize the stability boundary of the state trajectory as time changes; (3) It does not require precise prior knowledge of the disturbance boundary and parameter true value. By dynamically adjusting the control gain through the adaptive law, the preset time convergence characteristics can still be guaranteed when dealing with time-varying parameters, thus expanding the applicable scenarios of the control scheme.

[0108] Example 2

[0109] One embodiment of the present invention provides an adaptive preset time control method for a flexible robotic arm, using a general nonlinear flexible robotic arm with unmodeled dynamics as the control object. The specific implementation process is as follows:

[0110] Step 1: The expression for a nonlinear system with unmodeled dynamics is:

[0111] (27)

[0112] in, It is an ideal input control signal. and These are the system status and the actual control input, respectively. It is an unmodeled dynamic. It's about unmodeled dynamics. and system status The function. ， It is a known smooth mapping and satisfies . It is an unknown Lipschitz continuous function that satisfies .

[0113] Step Two: The goal of this embodiment is to systematically design an adaptive preset time controller that, given time-varying parameters, ensures the system state converges to the origin and remains zero at any preset time. To facilitate the design of the control system, corresponding assumptions and lemmas need to be introduced first, as shown below:

[0114] Assumption 1: Unmodeled dynamics It is finite-time input-state stable, meaning it has a positive definite Lyapunov function. , Class function , and known positive real numbers , , , Makes all ,

[0115] (28)

[0116] Assumption 2: There exists a continuous nonnegative function. and , making

[0117] (29)

[0118] in It is an unknown non-negative constant (coupled unknown parameter).

[0119] Lemma 1: For system (3), assume there exists a continuously differentiable, positive definite, and radially unbounded function. satisfy:

[0120] (30)

[0121] where constant ,and Therefore, this system can achieve generalized fixed-time stability—uniformly bounded stability—and adjust the time function. satisfy:

[0122] (31)

[0123] Furthermore, if constant and The time can be adjusted arbitrarily, thus enabling the system to achieve generalized fixed-time stability – any preset stability time.

[0124] Lemma 2: If there exists a continuous, radially unbounded, and positive definite function , making

[0125] (32)

[0126] Therefore, the origin of this system (1) is globally fixed-time stable, and the time function is adjusted. It can be estimated as follows:

[0127] (33)

[0128] Step 3: The adaptive control law in this embodiment is designed as follows:

[0129] First, a control law containing adjustment parameters is designed, and then an online adjustment mechanism is designed. A partial state feedback control scheme is developed for system (26). Specifically, express The estimated value, It is the estimation error.

[0130] Step 4: From Subsystem Begin. Set variables Consider it a control input. Let ,in It is virtual control. Let the time derivative of the following Lyapunov function be...

[0131] (34)

[0132] satisfy

[0133] (35)

[0134] Introduce the following virtual control law:

[0135] (36)

[0136] Among them, parameters .

[0137] Step 5: Substituting (36) into (35), we can obtain:

[0138] (37)

[0139] make and take the Lyapunov function.

[0140] (38)

[0141] So For the time derivative satisfies

[0142] (39)

[0143] in, It is a design constant.

[0144] Step Six: Record Choose virtual control law

[0145] (40)

[0146] in, This is a design constant. Through some simple calculations, we can obtain:

[0147] (41)

[0148] Step 7: Assuming a smooth virtual control has been designed This makes for (set up ) The time derivative of the following function

[0149] (42)

[0150] satisfy:

[0151] (43)

[0152] in, ( ).make And select the following Lyapunov functions:

[0153] (44)

[0154] Furthermore, we can obtain:

[0155] (45)

[0156] Choosing a virtual control law:

[0157] (46)

[0158] in It is a positive constant. Substituting it directly, we get:

[0159] (47)

[0160] Step 8: Consider unknown parameters ,Will As its estimated value, As an estimation error, the Lyapunov function is chosen:

[0161] (48)

[0162] in, It is a non-negative constant. It satisfies:

[0163] (49)

[0164] Using Assumption 2 and Lemma 2, we can obtain:

[0165] (50)

[0166] and,

[0167] (51)

[0168] Step 9: Substitute (50) into We can obtain:

[0169] (52)

[0170] Step 10: Select the adaptive control law:

[0171] (53)

[0172] And the ideal input control law, generating the ideal input control signal. This can be expressed as a formula:

[0173] (54)

[0174] Then we can get:

[0175] (55)

[0176] Pick Let it be an intermediate variable.

[0177]

[0178] in, and It is a non-negative function. and It is a known constant.

[0179] Introducing a dead-time compensator can obtain the actual control input. :

[0180] (56)

[0181] in, and It is a non-negative function that satisfies , and These are the positive dead zone parameters and the negative dead zone parameters, which satisfy... and .

[0182] In this example, the design process was completed using a reverse recursive design technique. And if the aforementioned assumptions 1-2 are satisfied, and the function is appropriately chosen... If definition 1 is satisfied, then there exists a continuously time-varying adaptive controller defined by (52) and (53) such that the state of system (26) is such that... Unmodeled dynamics and ideal input control Within the specified time Converging inward to the origin while maintaining and It is bounded. The specific stability analysis process is as follows:

[0183] prove:

[0184] (1) First, in order to handle unmodeled dynamics This embodiment uses a variable supply rate technique and considers the function:

[0185] (57)

[0186] Its time derivative satisfies:

[0187] (58)

[0188] Based on the local small gain condition, a desired function can be found. , making

[0189] (59)

[0190] Then, the Lyapunov function of the entire closed-loop system is chosen as follows:

[0191] (60)

[0192] And satisfy

[0193] (61)

[0194] remember ,and You can get

[0195] (62)

[0196] Considering , can be obtained in Above And thus for all , and Both are bounded.

[0197] consider:

[0198]

[0199] (63)

[0200] remember , ,and , can be obtained in superior It is bounded. There are positive constants. , making

[0201] (64)

[0202] (2) The following conclusion will be obtained in this part of the proof:

[0203] All error functions All within the preset time Before convergence to zero System status At the preset time It converged to the expected value.

[0204] The proof is as follows:

[0205] Application Hypothesis 2:

[0206] (65)

[0207] because and exist The system is bounded on the upper bound, thus the entire closed-loop system is not dynamically modeled. At the preset time The interior remains bounded.

[0208] Considering:

[0209] (66)

[0210] We can obtain:

[0211] (67)

[0212] Combination It can be seen that, Therefore, according to Theorem 1, we can conclude that:

[0213] (68)

[0214] Considering It disappears at zero point and combines By definition, we can further obtain:

[0215] (69)

[0216] In addition, when At that time, according to L'Hôpital's rule, the following derivation holds:

[0217] (70)

[0218] Because superior and It is bounded, therefore it can be obtained. .

[0219] (3) The following conclusions will be drawn in this part of the proof:

[0220] State of the entire closed-loop system and theoretical input control At the preset time It converges inward to the origin, which can be expressed by the following formula:

[0221] ,as well as (71)

[0222] because , ,and We can obtain:

[0223] (72)

[0224] because .according to as well as:

[0225] (73)

[0226] Further, we can obtain .

[0227] Considering ,and , You can get Given You can get Considering as well as and ,have From equation (68), we can see that:

[0228] (74)

[0229] This means:

[0230] (75)

[0231] Given:

[0232] (76)

[0233] We can obtain:

[0234] (77)

[0235] because and You can get Then, by , as well as It can be known that

[0236] (78)

[0237] And from as well as We can conclude that:

[0238] (79)

[0239] Using the same method, we can obtain

[0240] (80)

[0241] Given

[0242] (82)

[0243] And adaptive control laws:

[0244] (83)

[0245] It can be obtained and

[0246] Consider unmodeled dynamics Within the specified time The convergence properties within the region. According to Lemma 1, the parameters can be adjusted. and This makes the unmodeled dynamics In Previously, it converged to the origin. The state of the entire closed-loop system. and unmodeled dynamics and theoretical input control It will converge to the origin within the preset time T, thus achieving the control objective.

[0247] The proof is complete.

[0248] In traditional methods for controlling robotic arms, some systems only consider unknown constant parameters, neglecting nonlinear systems with time-varying uncertain parameters and unknown disturbances. When dealing with tracking control problems, conventional preset time strategies are often used. However, because the elastic modes of the flexible arm are easily affected by the initial state and the deformation of the mechanical arm, the control results are significantly dependent on the initial vibration state. In this embodiment, the time transformation and coordinate transformation method cleverly introduces a time transformation function, solving the performance limitation problem caused by the initial deformation of the flexible arm and vibration errors in preset time control. This embodiment can ultimately achieve accurate convergence of the system state within a preset time, rather than merely maintaining a bounded error, significantly improving the tracking accuracy and transient performance adaptability of the flexible robotic arm.

[0249] Example 3

[0250] One embodiment of the present invention provides an adaptive preset time control system for a flexible robotic arm, comprising:

[0251] The modeling module is configured to: construct a dynamic model of the flexible robotic arm and derive the state equations of the nonlinear system containing mismatched inherent unknown parameters and external unmodeled dynamic disturbances based on the model;

[0252] The construction module is configured to: construct a time transformation function based on the system state equation, and map finite time to infinite time domain by redefining the time scale, so that the error dynamics converge within a preset time. At the same time, it constructs a coordinate transformation function to convert the state variables into error coordinates to constrain the tracking error variables that include joint position error and flexible deformation error.

[0253] The control module is configured to: construct a virtual control law, an adaptive control law, and an ideal input control law using time transformation functions and coordinate transformation functions, forming an adaptive preset time controller; and verify whether the controller meets the stability condition through a Lyapunov function; and connect a dead zone compensator in series at the output of the verified controller to compensate for the ideal input control generated by the controller, thereby obtaining the actual control input and applying it to the flexible robotic arm to achieve adaptive preset time control.

[0254] Example 4

[0255] One embodiment of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned adaptive preset time control method for a flexible robotic arm.

[0256] Example 5

[0257] In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned adaptive preset time control method for a flexible robotic arm.

[0258] Example 6

[0259] One embodiment of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the adaptive preset time control method for a flexible robotic arm.

[0260] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0261] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0262] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An adaptive preset time control method for a flexible robotic arm, characterized in that, include: A dynamic model of a flexible robotic arm is constructed, and based on this model, the state equations of a nonlinear system containing mismatched inherent unknown parameters and external unmodeled dynamic disturbances are derived. Based on the system state equations, a time transformation function is constructed. By redefining the time scale, finite time is mapped to an infinite time domain, enabling the error dynamics to converge within a preset time. Simultaneously, a coordinate transformation function is constructed to convert state variables into error coordinates, thereby constraining the tracking error variables, which include joint position errors and flexible deformation errors. The time transformation function is as follows: Where T is the convergence time, and t is time, ranging from [0, T]. The coordinate transformation function is: in, For the desired output, It is a virtual control law in controller design; Using time transformation functions and coordinate transformation functions, a virtual control law, an adaptive control law, and an ideal input control law are constructed to form an adaptive preset time controller. The stability condition of the controller is verified using a Lyapunov function. The virtual control law is expressed by the following formula: Among them, parameters is a nonnegative constant, and T is the convergence time; The adaptive control law is expressed by the following formula: in, As The estimated value, For positive integers, It is a continuous nonnegative function; The ideal input control law, used to generate the ideal input control signal, is expressed by the formula: Among them, parameters It is a non-negative constant. and Coordinate transformation function For virtual control laws, As The estimated value, It is a non-negative function; A dead-time compensator is connected in series at the output of the verified controller to compensate for the ideal input control generated by the controller, obtaining the actual control input which is then applied to the flexible robotic arm to achieve adaptive preset time control. The dead-time compensator is used to compensate for the ideal input control signal generated by the controller. Let it be an intermediate variable: in, and It is a non-negative function. and It is a known constant; By introducing a dead-time compensator, a compensated input control signal is obtained. : in, and It is a non-negative function that satisfies , and These are the positive dead zone parameters and the negative dead zone parameters, which satisfy... and .

2. The adaptive preset time control method for a flexible robotic arm as described in claim 1, characterized in that, The state equation of the nonlinear system is expressed by the following formula: in, It is an ideal input control signal. and These are the system status and the actual control input, respectively. It is the unmodeled dynamics in the system. It concerns the unmodeled dynamics of the system. and system status The function, function is a known smooth mapping that satisfies , It is an unknown Lipschitz continuous function that satisfies .

3. An adaptive preset time control system for a flexible robotic arm, characterized in that, include: The modeling module is configured to: construct a dynamic model of the flexible robotic arm and derive the state equations of the nonlinear system containing mismatched inherent unknown parameters and external unmodeled dynamic disturbances based on the model; The construction module is configured to: construct a time transformation function based on the system state equation, redefine the time scale to map finite time to an infinite time domain, enabling the error dynamics to converge within a preset time; and simultaneously construct a coordinate transformation function to convert state variables into error coordinates to constrain the tracking error variables, which include joint position errors and flexible deformation errors. The time transformation function is: Where T is the convergence time; The coordinate transformation function is: in, For the desired output, It is a virtual control law in controller design; The control module is configured to: construct a virtual control law, an adaptive control law, and an ideal input control law using a time transformation function and a coordinate transformation function, forming an adaptive preset time controller; and verify whether the controller meets the stability condition using a Lyapunov function; the virtual control law is expressed by the formula: Among them, parameters is a nonnegative constant, and T is the convergence time; The adaptive control law is expressed by the following formula: in, As The estimated value, For positive integers, It is a continuous nonnegative function; The ideal input control law, used to generate the ideal input control signal, is expressed by the formula: Among them, parameters It is a non-negative constant. and Coordinate transformation function For virtual control laws, As The estimated value, It is a non-negative function; A dead-time compensator is connected in series at the output of the verified controller to compensate for the ideal input control generated by the controller, obtaining the actual control input which is then applied to the flexible robotic arm to achieve adaptive preset time control. The dead-time compensator is used to compensate for the ideal input control signal generated by the controller. Let it be an intermediate variable: in, and It is a non-negative function. and It is a known constant; By introducing a dead-time compensator, a compensated input control signal is obtained. : in, and It is a non-negative function that satisfies , and These are the positive dead zone parameters and the negative dead zone parameters, which satisfy... and .

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