Under-actuated crane all-drive system method based on low gain feedback

Abstract

The invention relates to the technical field of robot intelligent control, in particular to an under-actuated crane all-drive system method based on low gain feedback. A to-be-determined coupling signal containing trolley displacement and a load swing angle is constructed, a second derivative of the signal about time is deduced, an all-wheel-drive system model is further obtained through deduction, a nonlinear observer is introduced into the model, unknown disturbance borne by the under-actuated crane in the complex working condition is estimated and compensated, and therefore the under-actuated crane under the complex working condition is determined. And the anti-interference capability of the whole system is ensured. According to the method, a linear closed-loop system is further constructed, an auxiliary function containing load swing angle information is introduced into the linear closed-loop system to improve the suppression capability on load swing, a system state tracking error is introduced, and then a state-space equation is reconstructed. A low-gain feedback control rate is also designed, so that the actuator is prevented from falling into a working condition of input saturation.

Description

Technical Field

[0001] The present invention relates to the technical field of robot intelligent control, and specifically relates to a method for a fully actuated underactuated crane system based on low-gain feedback. Background Art

[0002] The number of control inputs of an underactuated crane is less than the number of degrees of freedom to be controlled. Therefore, compared with a fully actuated system, such a system is more difficult to control due to its inherent strong nonlinear and coupling characteristics. For example, in the operation process of an underactuated crane, there may be actual working conditions such as actuator input saturation. Actuator input saturation means that when the control input value given to the actuator by the crane is too large, it exceeds the range that the actuator can handle, resulting in the actuator entering a saturated state, that is, the actuator cannot achieve the expected execution effect.

[0003] In summary, the actuators of existing underactuated cranes are prone to input saturation faults.

[0004] Therefore, the existing technology still needs to be improved. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a method for a fully actuated underactuated crane system based on low-gain feedback, which solves the problem that the actuators of existing underactuated cranes are prone to input saturation faults.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention provides a method for a fully actuated underactuated crane system based on low-gain feedback, which includes:

[0008] Obtain the system parameter matrix of the crane, and apply the Riccati equation to the system parameter matrix to solve the positive definite solution of the Riccati equation;

[0009] Determine the system state tracking error of the crane, and apply a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane;

[0010] Determine the reference input value of the controller according to the pre-input data;

[0011] Based on the reference input value, obtain the control input value output by the controller through the controller. The control input value is used to be input to the actuator of the crane, so as to drive the crane through the controller.

[0012] In one implementation, the determining the system state tracking error of the crane includes:

[0013] Obtain the parameter values and status values of the crane, where the status values include displacement and the swing angle of the load suspended on the crane, and determine a coupling signal including the parameter values and the status values;

[0014] Obtain the tracking trajectory of the crane, and determine the system state tracking error of the crane based on the tracking trajectory, the swing angle, and the coupling signal.

[0015] In one implementation, the determining the system state tracking error of the crane based on the tracking trajectory, the swing angle, and the coupling signal includes:

[0016] Determine the second derivative of the tracking trajectory, determine the second derivative of the coupling signal, and determine the second derivative of the swing angle;

[0017] Perform a weighted calculation on the second derivative of the coupling signal, the second derivative of the swing angle, and the second derivative of the tracking trajectory to obtain an intermediate value, and construct a system state tracking error in vector form based on the intermediate value and the swing angle.

[0018] In one implementation, the applying a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane includes:

[0019] Obtain a preset positive definite matrix, and determine the input matrix in the system parameter matrix, where the input matrix is used to characterize the influence degree of the input of the controller on the status value of the crane;

[0020] Apply a low-gain feedback control algorithm to the positive definite matrix, the input matrix, the system state tracking error, and the positive definite solution to obtain the pre-input data in matrix form of the controller.

[0021] In one implementation, the determining the reference input value of the controller based on the pre-input data includes:

[0022] Determine the first element value and the second element value in the pre-input data in matrix form;

[0023] Determine the second derivative of the tracking trajectory, and determine a first input value based on the first element value and the second derivative of the tracking trajectory;

[0024] Determine a second input value based on the second element value and a set positive parameter value, where the positive parameter value is used to characterize the influence degree of the swing angle of the load on the system state tracking error, and the load is the load suspended on the crane;

[0025] Determine the reference input value of the controller according to the first input value and the second input value.

[0026] In one implementation, the obtaining, by the controller, of the control input value output by the controller based on the reference input value includes:

[0027] Estimate the disturbance data suffered by the crane at the current moment;

[0028] Based on the reference input value and the disturbance data at the current moment, obtain, by the controller, the control input value at the current moment output by the controller.

[0029] In one implementation, the estimating of the disturbance data suffered by the crane at the current moment includes:

[0030] Obtain the control input value at the previous moment and the coupling signal at the previous moment, where the coupling signal at the previous moment is composed of the parameter value of the crane and the state value of the crane at the previous moment;

[0031] Based on the control input value at the previous moment and the coupling signal at the previous moment, estimate the disturbance data suffered by the crane at the current moment.

[0032] In a second aspect, an underactuated crane full-drive system device based on low-gain feedback is further provided in an embodiment of the present invention, where the device includes the following components:

[0033] An equation solving module, configured to obtain the system parameter matrix of the crane and apply a Riccati equation to the system parameter matrix to solve a positive definite solution of the Riccati equation;

[0034] A pre-input data calculation module, configured to determine the system state tracking error of the crane and apply a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane;

[0035] A reference input value calculation module, configured to determine the reference input value of the controller according to the pre-input data;

[0036] A control input value calculation module, configured to obtain, by the controller, the control input value output by the controller based on the reference input value, where the control input value is used to be input to the actuator of the crane to drive the crane through the controller.

[0037] Third aspect, the embodiments of the present invention further provide a terminal device. The terminal device includes a memory, a processor, and a low-gain feedback-based underactuated crane full-drive system program stored in the memory and executable on the processor. When the processor executes the low-gain feedback-based underactuated crane full-drive system program, the steps of the above-mentioned low-gain feedback-based underactuated crane full-drive system method are implemented.

[0038] Fourth aspect, the embodiments of the present invention further provide a computer-readable storage medium. A low-gain feedback-based underactuated crane full-drive system program is stored on the computer-readable storage medium. When the low-gain feedback-based underactuated crane full-drive system program is executed by a processor, the steps of the above-mentioned low-gain feedback-based underactuated crane full-drive system method are implemented.

[0039] Beneficial effects: The present invention first solves the positive definite solution of the Riccati equation including the system parameters of the crane, and then applies the low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller, and obtains the reference input value of the controller based on the pre-input data. The controller obtains the control input value of the actuator based on its reference input value. Since the present invention calculates the pre-input data of the controller based on the low-gain feedback control algorithm, the pre-input data can constrain the reference input value of the controller, thereby improving the control input value of the actuator, and finally avoiding the unnecessary negative impact caused by the actuator falling into the input saturation condition. Description of the Drawings

[0040] Figure 1 is the overall flowchart of the present invention;

[0041] Figure 2 is the working schematic diagram of the crane in the embodiments of the present invention;

[0042] Figure 3 is the simulation diagram of Experiment 1 in the embodiments of the present invention;

[0043] Figure 4 is the simulation diagram of Experiment 2 in the embodiments of the present invention;

[0044] Figure 5 is the structural diagram of the low-gain feedback-based underactuated crane full-drive system device provided by the present invention;

[0045] Figure 6 is the internal structure principle block diagram of the terminal device provided in the embodiments of the present invention. Detailed Embodiments

[0046] The technical solutions in the present invention will be clearly and completely described below in conjunction with the embodiments and the accompanying drawings of the specification. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0047] It has been found through research that the number of control inputs of an underactuated crane is less than the number of degrees of freedom to be controlled. Therefore, compared with a fully actuated system, such a system is more difficult to control due to its inherent strong nonlinear and coupling characteristics. For example, in the operation process of an underactuated crane, there may be actual working conditions such as actuator input saturation. Actuator input saturation means that when the control input value given to the actuator by the crane is too large, it exceeds the range that the actuator can handle, resulting in the actuator entering the saturation state, that is, the actuator cannot achieve the expected execution effect.

[0048] To solve the above technical problems, the present invention provides a method for a fully actuated system of an underactuated crane based on low-gain feedback, which solves the problem that the actuators of existing underactuated cranes are prone to input saturation faults.

[0049] The method for a fully actuated system of an underactuated crane based on low-gain feedback in this embodiment can be applied to a terminal device. The terminal device can be a terminal product with data processing functions, such as a computer, etc. In this embodiment, as Figure 1 shown, the method for a fully actuated system of an underactuated crane based on low-gain feedback specifically includes the following steps:

[0050] S100, obtain the system parameter matrix of the crane, and apply the Riccati equation to the system parameter matrix to solve the positive definite solution P(ω) of the Riccati equation;

[0051] S200, determine the system state tracking error e of the crane, and apply a low-gain feedback control algorithm to the system state tracking error e and the positive definite solution P(ω) to obtain the pre-input data u of the controller of the crane;

[0052] S300, determine the reference input value of the controller according to the pre-input data;

[0053] S400, through the controller, based on the reference input value, obtain the control input value output by the controller. The control input value is used to be input to the actuator of the crane to drive the crane through the controller.

[0054] In Embodiment 1, in this embodiment, the Riccati equation in S100 is:

[0055] A T P(ω)+P(ω)A - P(ω)BR -1 BT P(ω) = -ηP(ω)

[0056] where A ∈ D 4×4 is the system matrix of the crane, B ∈ D 4×2 is the input matrix of the crane. For the same crane, the values of A and B are fixed. A and B are the system parameter matrices. η is the adjustment coefficient of the above Riccati equation, and P(ω) is the unique positive definite solution of the Riccati equation. The Riccati equation is the Riccati equation, that is, by solving the Riccati equation, P(ω) can be obtained.

[0057] In this embodiment, it can also be set that P(ω) = W -1 (ω), and by solving W(ω), the positive definite solution P(ω) can be obtained. And W(ω) is the unique positive definite solution of the Lyapunov function. The Lyapunov function is as follows:

[0058]

[0059] where I4 represents the fourth-order identity matrix.

[0060] Embodiment 2, based on Embodiment 1, in this embodiment, the specific steps for calculating the system state tracking error e in step S200 are as follows: Obtain the parameter values of the crane (the parameter values include the mass M of the crane and the mass m of the load) and the state values. The state values include the displacement x and the swing angle θ of the load suspended on the crane, and determine the coupling signal x including the parameter values and the state values c ; Obtain the tracking trajectory x of the crane r , and determine the second derivative of the tracking trajectory x r Determine the second derivative of the coupling signal x Determine the second derivative of the coupling signal x c Determine the second derivative of the swing angle θ Determine the second derivative of the swing angle θ Perform weighted calculation on the second derivative of the coupling signal and the second derivative of the swing angle and the second derivative of the tracking trajectory to obtain an intermediate value ( c is a positive parameter), and based on the intermediate value construct the system state tracking error e in vector form for the swing angle θ:

[0061]

[0062] is the first integral of, e p is the second integral of, For the first derivative of the swing angle θ (where θ is a function of time t and this function is a prior art) as shown Figure 2 , and the tracking trajectory x r is also a function of time t, and this function is also a prior art.

[0063] In this embodiment, by setting to constrain e and then constrain the subsequent constrained reference input value v, thereby improving the final control input value F x , and finally the control input value F x can prevent the phenomenon of excessive swing of the load.

[0064] In this embodiment, the coupling signal x c has the following calculation formula:

[0065] x c =(M + m)x + f(θ)

[0066] f(θ) is an auxiliary function to be determined related to the load swing angle θ, that is, f(θ)=ml sinθ, as Figure 2 shown, where l is the length of the suspension rope of the suspended load, and this length is a fixed length.

[0067] Embodiment 3, based on Embodiment 2 or Embodiment 1, applying a low-gain feedback control algorithm to the system state tracking error e and the positive definite solution P(ω) in step S200 to obtain the pre-input data u of the controller of the crane, specifically including: obtaining a preset positive definite matrix R (R ∈ D 2×2 ), and determining the input matrix B in the system parameter matrix, where the input matrix B is used to characterize the influence degree of the input of the controller on the state value of the crane; applying a low-gain feedback control algorithm to the positive definite matrix R, the input matrix B, the system state tracking error e and the positive definite solution P(ω) to obtain the pre-input data u in matrix form of the controller:

[0068] u=-R -1 B T P(ω)e

[0069] The input matrix B in this embodiment, the system matrix A of the crane and the pre-input data u satisfy the following expression:

[0070]

[0071] Among them, the values of A and B are expressed as follows:

[0072]

[0073] In this embodiment, the pre-input data u is designed through a low-gain feedback control strategy, and then the reference input value v is constrained, and the control input value F output by the fully actuated feedback controller is improved. x , while suppressing the load swing and achieving accurate positioning of the crane, it avoids unnecessary negative impacts caused by the actuator falling into the input saturation condition.

[0074] Embodiment 4, based on Embodiment 1 or Embodiment 2 or Embodiment 3, in this embodiment, step S300 includes the following specific steps S301, S302, S303, and S304:

[0075] S301, determine the first element value and the second element value in the pre-input data u that constitutes the matrix form.

[0076]

[0077] S302, determine the second derivative of the tracking trajectory, and determine the first input value based on the first element value and the second derivative of the tracking trajectory.

[0078] Convert the first element value in the pre-input data u into form. Since is known and u is known, the first input value v can be calculated. x .

[0079] S303, determine the second input value based on the second element value and the set positive parameter value. The positive parameter value is used to characterize the influence degree of the swing angle of the load on the system state tracking error, and the load is the load suspended on the crane.

[0080] Similarly, convert the second element value in the pre-input data u into v θ / c form. Since c and u are known, the second input value v can be calculated. θ .

[0081] S304, determine the reference input value v of the controller based on the first input value and the second input value:

[0082] v x +v θ = v

[0083] Embodiment 5, based on any one of Embodiments 1 to 4, in this embodiment, step S400 includes the following specific steps S401, S402, and S403:

[0084] S401, obtain the control input value at the previous moment (represented by F' x representing the control input value at the previous moment) and the coupling signal at the previous moment (represented by x'c (representing the coupling signal at the previous moment), the coupling signal at the previous moment is composed of the parameter values (including M and m) of the crane and the state value of the crane at the previous moment.

[0085] x′ c =(M + m)x′ + f(θ′)

[0086] In the formula, x′ represents the state value of the displacement at the previous moment, and θ′ represents the state value of the swing angle at the previous moment.

[0087] S402. Based on the control input value at the previous moment (represented by F′ x representing the control input value at the previous moment) and the coupling signal x′ at the previous moment c , estimate the disturbance data suffered by the crane at the current moment

[0088]

[0089] where ζ is an auxiliary function related to the system input and state, and ε is a positive gain to be adjusted. is the first derivative of x′ c .

[0090] S403. Through the controller, based on the reference input value v at the current moment and the disturbance data obtain the control input value F at the current moment output by the controller x :

[0091]

[0092] In this embodiment, based on the control input value input to the actuator at the previous moment and the coupling signal at the previous moment, estimate the possible external disturbances (such as collisions and wind loads) of the crane at the current moment, that is, estimate the unknown external disturbances. Based on the estimated external disturbances, calculate the control input value F x , so that the actuator based on this control input value F x can resist external interference, thus ensuring the stable operation of the crane.

[0093] Embodiment 6. Based on the dynamic model of the underactuated crane system with unknown disturbances, calculate the control input value F x input to the actuator, where the dynamic model is:

[0094]

[0095] In the formula, g represents the acceleration due to gravity, and d represents the unknown disturbance.

[0096] Combined with the second derivative of the coupling signal with respect to time, the above dynamic model can be improved to obtain the dynamic model of the improved underactuated crane system.

[0097] Among them, the second derivative of the coupling signal with respect to time is:

[0098]

[0099] The dynamic model of the improved underactuated crane system is:

[0100]

[0101] From f(θ) = mlsinθ, that is:

[0102]

[0103] Embodiment 7, this embodiment provides a low-gain feedback control gain BR as follows -1 B T And the control gain vector A x0～1 And A θ0～1 Relationship:

[0104]

[0105] Among them, A x0～1 And A θ0～1 These two control gain vectors and u also have the following relationship:

[0106]

[0107] Next, two groups of experiments are used to prove the performance of the full-drive system method based on low-gain feedback of the present invention:

[0108] Experiment 1, in this experiment, a friction force model is introduced to simulate the unknown disturbance suffered by the underactuated crane during operation, so as to test the estimation accuracy of the unknown disturbance of the present invention; by changing the adjustment parameter ω, the effectiveness of the low-gain feedback control method is verified, and the simulation results are as Figure 3 shown. It can be seen from Figure 3 that the method proposed by the present invention can ensure that the trolley accurately reaches the target position, and at the same time can effectively suppress and eliminate the load swing; the proposed observer can accurately estimate the unknown friction force and provide timely compensation feedback to the system; in addition, as ω decreases, the input of the actuator also decreases accordingly, which indicates that by adjusting the parameter ω, the actuator can be effectively prevented from falling into the input saturation condition.

[0109] Experiment 2. In this experiment, several interference signals are introduced, namely: a constant interference signal of -5N is introduced from 0 to 3s, a sinusoidal interference signal of 5N is introduced from 3 to 7s, a constant interference signal of 5N is introduced from 7 to 10s, and a step interference signal of 5N is introduced from 10 to 14s. The simulation results are as Figure 4 shown. It can be seen from Figure 4 that the observer of the present invention can accurately estimate these different types of interference signals and provide timely compensation to the controller; it can also quickly suppress the load swing while ensuring the accurate positioning of the trolley. Therefore, the proposed full-drive system method based on low-gain feedback still has good performance in complex working conditions.

[0110] In summary, the present invention fully considers the unknown disturbances suffered by the underactuated crane during operation and multiple complex working conditions such as input saturation of the actuator. This method optimizes the full-drive feedback controller through a low-gain feedback control strategy to avoid the actuator falling into input saturation; it can also accurately estimate unknown disturbances such as collisions and wind loads, effectively suppress and eliminate the load swing while ensuring the accurate positioning of the trolley, and greatly improve the working efficiency of the underactuated crane system.

[0111] This embodiment also provides an underactuated crane full-drive system device based on low-gain feedback, as Figure 5 shown. The device includes the following components:

[0112] Equation solving module 01, which is used to obtain the system parameter matrix of the crane and apply the Riccati equation to the system parameter matrix to solve the positive definite solution of the Riccati equation;

[0113] Pre-input data calculation module 02, which is used to determine the system state tracking error of the crane and apply a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane;

[0114] Reference input value calculation module 03, which is used to determine the reference input value of the controller according to the pre-input data;

[0115] Control input value calculation module 04, which is used to obtain the control input value output by the controller based on the reference input value through the controller. The control input value is used to be input into the actuator of the crane to drive the crane through the controller.

[0116] Based on the above embodiments, the present invention also provides a terminal device, and its principle block diagram can be as Figure 6As shown. The terminal device includes a processor, a memory, a network interface, and a display screen connected via a system bus. Among them, the processor of the terminal device is used to provide computing and control capabilities. The memory of the terminal device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the terminal device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, it implements a method for an underactuated crane full-drive system based on low-gain feedback. The display screen of the terminal device can be a liquid crystal display screen or an electronic ink display screen.

[0117] Those skilled in the art can understand that Figure 6 the principle block diagram shown in is only a block diagram of some structures related to the solution of the present invention, and does not constitute a limitation on the terminal device to which the solution of the present invention is applied. The specific terminal device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0118] In one embodiment, a terminal device is provided. The terminal device includes a memory, a processor, and a program for an underactuated crane full-drive system based on low-gain feedback stored in the memory and executable on the processor. When the processor executes the program for the underactuated crane full-drive system based on low-gain feedback, the following operation instructions are implemented:

[0119] Obtain the system parameter matrix of the crane, and apply the Riccati equation to the system parameter matrix to solve the positive definite solution of the Riccati equation;

[0120] Determine the system state tracking error of the crane, and apply a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane;

[0121] Based on the pre-input data, determine the reference input value of the controller;

[0122] Through the controller, based on the reference input value, obtain the control input value output by the controller. The control input value is used to be input to the actuator of the crane to drive the crane through the controller.

[0123] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include non-volatile and / or volatile memories. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An underactuated crane full-drive system method based on low-gain feedback, characterized in that Including: Obtain the system parameter matrix of the crane, and apply the Riccati equation to the system parameter matrix to solve the positive definite solution of the Riccati equation; Determine the system state tracking error of the crane, apply a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane; Determine the reference input value of the controller according to the pre-input data; Based on the reference input value, obtain the control input value output by the controller through the controller. The control input value is used to be input into the actuator of the crane to drive the crane through the controller.

2. The method for an underactuated crane full-drive system based on low-gain feedback as claimed in claim 1, wherein The determining the system state tracking error of the crane includes: Obtain the parameter value and state value of the crane. The state value includes displacement and the swing angle of the load suspended on the crane, and determine the coupling signal including the parameter value and the state value; Obtain the tracking trajectory of the crane, and determine the system state tracking error of the crane according to the tracking trajectory, the swing angle and the coupling signal.

3. The method for an underactuated crane full-drive system based on low-gain feedback according to claim 2, wherein The determining the system state tracking error of the crane according to the tracking trajectory, the swing angle and the coupling signal includes: Determine the second derivative of the tracking trajectory, determine the second derivative of the coupling signal, and determine the second derivative of the swing angle; Perform weighted calculation on the second derivative of the coupling signal, the second derivative of the swing angle and the second derivative of the tracking trajectory to obtain an intermediate value, and construct the system state tracking error in vector form according to the intermediate value and the swing angle.

4. The method for an underactuated crane full-drive system based on low-gain feedback according to claim 1, wherein The applying a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane includes: Obtain a preset positive definite matrix, and determine the input matrix in the system parameter matrix. The input matrix is used to characterize the influence degree of the input of the controller on the state value of the crane; Apply a low-gain feedback control algorithm to the positive definite matrix, the input matrix, the system state tracking error and the positive definite solution to obtain the pre-input data of the controller in matrix form.

5. The method for an underactuated crane full-drive system based on low-gain feedback according to claim 4, characterized in that, The determining the reference input value of the controller according to the pre-input data includes: Determine the first element value and the second element value in the pre-input data in matrix form; Determine the second derivative of the tracking trajectory, and determine the first input value according to the first element value and the second derivative of the tracking trajectory; Determine the second input value according to the second element value and the set positive parameter value. The positive parameter value is used to characterize the influence degree of the swing angle of the load on the system state tracking error. The load is the load suspended on the crane; Determine the reference input value of the controller according to the first input value and the second input value.

6. The method for an underactuated crane full drive system based on low-gain feedback according to claim 1, characterized in that, The obtaining the control input value output by the controller through the controller based on the reference input value includes: Estimate the disturbance data suffered by the crane at the current moment; Based on the reference input value and the disturbance data at the current moment by the controller, obtain the control input value at the current moment output by the controller.

7. The method for an underactuated crane full-drive system based on low-gain feedback according to claim 6, characterized in that, The estimation of the disturbance data suffered by the crane at the current moment includes: Obtain the control input value at the previous moment and the coupling signal at the previous moment, where the coupling signal at the previous moment is composed of the parameter value of the crane and the state value of the crane at the previous moment; Based on the control input value at the previous moment and the coupling signal at the previous moment, estimate the disturbance data suffered by the crane at the current moment.

8. An underactuated crane full-drive system device based on low-gain feedback, characterized in that, The device includes the following components: An equation solving module, configured to obtain the system parameter matrix of the crane and apply the Riccati equation to the system parameter matrix to solve the positive definite solution of the Riccati equation; A pre-input data calculation module, configured to determine the system state tracking error of the crane and apply a low-gain feedback control algorithm to the system state tracking error and the positive definite solution to obtain the pre-input data of the controller of the crane; A reference input value calculation module, configured to determine the reference input value of the controller based on the pre-input data; A control input value calculation module, configured to obtain the control input value output by the controller based on the reference input value by the controller, and the control input value is used to be input to the actuator of the crane to drive the crane by the controller.

9. A terminal device, characterized in that, The terminal device includes a memory, a processor, and an underactuated crane full-drive system program based on low-gain feedback stored in the memory and executable on the processor. When the processor executes the underactuated crane full-drive system program based on low-gain feedback, the steps of the underactuated crane full-drive system method according to any one of claims 1-7 are implemented.

10. A computer-readable storage medium, characterized in that, An underactuated crane full-drive system program based on low-gain feedback is stored on the computer-readable storage medium. When the underactuated crane full-drive system program based on low-gain feedback is executed by the processor, the steps of the underactuated crane full-drive system method according to any one of claims 1-7 are implemented.

Images