Robust control method, system and product for underactuated crane based on full drive system

Abstract

The present invention belongs to the field of crane control technology, and provides a robust control method, system and product for an underactuated crane based on a full-drive system. The technical solution is as follows: based on the full-drive system method, a robust control method for an uncertain underactuated crane system is constructed. First, an uncertain crane system error model with a general form is designed, in which the system uncertainty factors only need to satisfy the bounded assumption; then, a robust stable control method is constructed to ensure that the positioning error eventually converges globally to an arbitrarily small area. According to the Lyapunov stability theorem, the stability of the closed-loop system is strictly proved. The present invention does not require any linearization processing or ignores some nonlinear terms, and ensures that the error vector converges to an arbitrarily small area.

Description

Technical Field

[0001] The present invention belongs to the technical field of crane control, and in particular relates to a robust control method, system and product for an underactuated crane based on a full-drive system. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] As a typical underactuated electromechanical system, the tower crane system works in a complex environment and is inevitably affected by internal and external disturbances. Therefore, the robustness requirement should be fully considered when designing the controller.

[0004] Existing control methods for improving the robustness of tower crane systems include several robust control methods such as adaptive control methods, model predictive control methods, fuzzy logic-based control methods, passivity / energy-based control methods, and neural network-based control methods.

[0005] The above robust control method has proposed many valuable results for the underactuated tower crane system, but there are the following problems when controlling the tower crane system:

[0006] The controller still needs to meet specific forms or conditions, and there is no rigorous theoretical analysis. Lack of theoretical guarantees, these methods may not be applied in practice; (2) For highly coupled under-actuated tower crane systems, there are few studies that directly construct a full-drive system by constructing auxiliary functions. Specific model transformations usually correspond to specific objects.

[0007] (3) Most of the existing control methods for tower crane systems are designed based on the linearized tower crane system model. When the state variables of the system cannot be close enough to the equilibrium point, the linearized model is very different from the original crane model, which may seriously affect the control performance of the system and even cause system instability. Summary of the invention

[0008] In order to solve at least one technical problem existing in the above-mentioned background technology, the present invention provides a robust control method, system and product of an under-actuated crane based on a full-drive system. The robust control method based on the full-drive system ensures that the error vector converges to an arbitrarily small area without linearizing the nonlinear dynamic model of the tower crane system or ignoring some nonlinear terms, and does not require precise system parameters. Therefore, it has a wide range of applications and great practical value.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

[0010] A first aspect of the present invention provides a robust control method for an underactuated crane based on a full drive system, comprising the following steps:

[0011] Construct a dynamic model of a four-degree-of-freedom tower crane system;

[0012] The dynamic model of the four-degree-of-freedom tower crane system is split into a first subsystem model including a drivable state variable and a non-drivable state variable and a second subsystem model;

[0013] The positioning error vector is introduced, and the first subsystem model and the second subsystem model are combined to obtain the full drive system model;

[0014] For the full drive system model, a robust controller for the full drive system is designed with the goal of stabilizing the closed-loop system and globally converging the positioning error to an arbitrarily small area.

[0015] The crane system is controlled using the designed full drive system robust controller.

[0016] Furthermore, after obtaining the robust controller of the full-drive system, the stability of the closed-loop system is rigorously proved according to the Lyapunov stability theorem.

[0017] Furthermore, the expression of the dynamic model of the four-degree-of-freedom tower crane system is:

[0018] ,

[0019] ,

[0020] , ,

[0021] , ,

[0022] ,

[0023] ,

[0024] ,

[0025] in, represents the state vector, , Represent the state vector The first-order time derivative and the second-order time derivative of is a positive definite symmetric inertia matrix, represents the centripetal-Coriolis force matrix, represents the gravity vector, represents the control input vector, Indicates the uncertainty factor of the system; is the mass of the trolley, is the load mass, is the length of the suspension rope, is the cantilever moment of inertia, To control the torque of the cantilever swing, is the trolley translation control force, is the acceleration due to gravity, is the cantilever rotation angle, is the trolley displacement, is the load swing angle, for , , , Abbreviation of , , , respectively , , , The first time derivative of is the uncertainty factor of the system.

[0026] Furthermore, the expressions of the first subsystem model and the second subsystem model including the drivable state variables and the undrivable state variables are:

[0027] ,

[0028] ,

[0029] , , ,

[0030] , , , ,

[0031] , , ,

[0032] in, , Represent the drivable state variables The first and second time derivatives of , Represent the non-drivable state variables The first and second time derivatives of .

[0033] Furthermore, the expression of the positioning error vector is:

[0034] ,

[0035] ,

[0036] in, represents a drivable state variable, represents the desired cantilever rotation angle, Indicates the desired position of the trolley.

[0037] Furthermore, the expression of the full drive system model is:

[0038] ,

[0039] ,

[0040] ,

[0041] ,

[0042] in, as well as Represent the error vector The first and second time derivatives of is a positive definite diagonal matrix, Represents the total uncertainty factor.

[0043] Furthermore, the expression of the robust controller is:

[0044] ,

[0045] in, represents the control matrix of the two generations of regulation, represents the auxiliary vector, represents the state vector, , ,in is the unit diagonal matrix, is a positive definite symmetric matrix, For any given positive number, represents a known constant vector.

[0046] Furthermore, the region where the state vector finally converges is:

[0047] ,

[0048] in, Representation Matrix The smallest characteristic root of represents any positive real number.

[0049] A second aspect of the present invention provides a robust control system for an underactuated crane based on a full drive system, which adopts the robust control method for an underactuated crane based on a full drive system described in the first aspect, and comprises:

[0050] A dynamic model building module, which is used to build a dynamic model of a four-degree-of-freedom tower crane system;

[0051] A full-drive model building module is used to split the dynamic model of the four-degree-of-freedom tower crane system into a first subsystem model and a second subsystem model including drivable state variables and non-drivable state variables; introduce a positioning error vector, combine the first subsystem model and the second subsystem model, and obtain a full-drive system model;

[0052] Robust controller design module, which is used to design a robust controller for the full drive system model with the goal of eventually global convergence of the positioning error to an arbitrarily small area;

[0053] The control module is used to control the crane system using the designed full drive system robust controller.

[0054] A third aspect of the present invention provides a program product.

[0055] A program product, which is a computer program product, comprises a computer program. When the computer program is executed by a processor, the steps in the robust control method for an underactuated crane based on a full drive system described in the first aspect are implemented.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The present invention is based on a robust control method for a full-drive system. Aiming at the full-drive system model, the present invention aims to stabilize the closed-loop system and globally converge the positioning error to an arbitrarily small area. The robust controller of the full-drive system is designed to ensure that the error vector converges to an arbitrarily small area without linearizing the nonlinear dynamic model of the tower crane system or ignoring some nonlinear terms.

[0058] 2. The control method proposed in the present invention does not require precise system parameters, so it has a wide range of applications and great practical value.

[0059] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0061] Figure 1 is a flow chart of a robust control method for an underactuated crane based on a full-drive system provided by an embodiment of the present invention;

[0062] Figure 2 is a schematic diagram of a four-degree-of-freedom tower crane system provided by an embodiment of the present invention;

[0063] Figure 3 It is a block diagram of a robust control method for an underactuated crane based on a full-drive system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0065] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0066] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0067] In response to the defects in the robust control of under-driven cranes mentioned in the background technology of this application, the robust control method based on the full-drive system designed in this application ensures that the error vector converges to an arbitrarily small area without linearizing the nonlinear dynamic model of the tower crane system or ignoring some nonlinear terms. It does not require precise system parameters and therefore has a wide range of applications and great practical value.

[0068] Embodiment 1

[0069] like Figure 1 As shown, this embodiment provides a robust control method for an underactuated crane based on a full drive system, comprising the following steps:

[0070] Step 1: Construct a dynamic model of a four-degree-of-freedom tower crane system;

[0071] like Figure 1The figure shows a schematic diagram of a four-degree-of-freedom tower crane system. The dynamic model of the four-degree-of-freedom tower crane system is shown in formula (1):

[0072] (1)

[0073] in, represents the state vector, , Represent the state vector The first-order time derivative and the second-order time derivative of is a positive definite symmetric inertia matrix, represents the centripetal-Coriolis force matrix, represents the gravity vector, represents the control input vector, represents the uncertainty factor of the system, The specific expression is as follows:

[0074] ,

[0075] ,

[0076] ,

[0077] ,

[0078] ,

[0079] ,

[0080] ,

[0081] ,

[0082] in, is the mass of the trolley, is the load mass, is the length of the suspension rope, is the cantilever moment of inertia, To control the torque of the cantilever swing, is the trolley translation control force, is the acceleration due to gravity, is the cantilever rotation angle, is the trolley displacement, is the load swing angle, for , , , Abbreviation of , , , respectively , , , The first time derivative of .

[0083] Step 2: split the dynamic model of the four-degree-of-freedom tower crane system into a first subsystem model and a second subsystem model including drivable state variables and non-drivable state variables;

[0084] In order to use the full drive system method later, the system (1) is divided into the following two subsystems:

[0085] (2)

[0086] (3)

[0087] in, as well as represents the drivable state variables and the non-drivable state variables, , Represent the drivable state variables The first and second time derivatives of , Represent the non-drivable state variables The first and second time derivatives of , and:

[0088] ,

[0089] Not difficult to get is a positive definite symmetric matrix, so equation (3) can be calculated as:

[0090] (4)

[0091] in, is the uncertainty factor of the system.

[0092] Substituting formula (4) into formula (2), we can get:

[0093] (5)

[0094] in, , .

[0095] Step 3: Introduce the positioning error vector, combine the first subsystem model and the second subsystem model, and obtain the full drive system model;

[0096] Define the positioning error vector for:

[0097] (6)

[0098] in, The expression is as follows:

[0099] (7)

[0100] in, represents the desired cantilever rotation angle, Indicates the desired position of the trolley.

[0101] Substituting formula (6) into formula (5), we can get:

[0102] (8)

[0103] in, as well as Represent the error vector The first and second time derivatives of .

[0104] Inspired by the static torque method, by introducing a positive definite diagonal matrix We can get:

[0105] (9)

[0106] in, represents the total uncertainty factor. The selection is flexible.

[0107] From formula (9), it is easy to get:

[0108] (10)

[0109] It's obvious , then the error system (10) is called a full-drive system.

[0110] Step 4: For the full drive system model, with the goal of stabilizing the closed-loop system and the positioning error eventually converging to an arbitrarily small area, design a robust controller for the full drive system, including:

[0111] Step 401: Description of the full drive robust control problem for the uncertain tower crane error system:

[0112] Assumption 1. The total system uncertainty factor is bounded, and its mathematical description is:

[0113] (11)

[0114] in, represents a known constant vector.

[0115] This embodiment is to solve the full drive robust control problem of the uncertain tower crane error system. To ensure the stability of the uncertain error system (10), it is equivalent to solving the following robust control problem.

[0116] For the uncertain error model (10), the robust controller can be designed as:

[0117] (12)

[0118] Then the closed-loop system can be stable, and the error vector converges globally to an arbitrarily small area, where represents the control matrix of the two generations of regulation, Represents an auxiliary vector.

[0119] Step 402: Derive the linear system

[0120] From formula (10) and (12), we can get:

[0121] (13)

[0122] Define a new state vector , then equation (13) can be described as a state space equation in the following form:

[0123] (14)

[0124] in, ,in is the unit diagonal matrix.

[0125] To solve the above problem (12), the following three lemmas are introduced.

[0126] Lemma 1: Let the matrix satisfy

[0127] (15)

[0128] in, represents a positive real number, represents the characteristic root, represents the real part, then there exists a positive definite symmetric matrix So that:

[0129] (16)

[0130] Lemma 2: For any positive real number Existence Matrix satisfy:

[0131] (17)

[0132] Then, according to Lemma 1, when equation (17) holds, there exists a positive definite symmetric matrix satisfy:

[0133] (18)

[0134] Lemma 3: Define a and b as two real numbers, and b>0, then the following formula always holds:

[0135] (19)

[0136] Step 403: Controller design and stability analysis

[0137] Theorem 1: Definition For any given positive number, the matrix If the condition of formula (18) is satisfied, then the expression for designing the robust controller of the full drive system is:

[0138] (20)

[0139] Then the state vector can be guaranteed Converges to the following region:

[0140] (twenty one),

[0141] in, Representation Matrix The smallest characteristic root of .

[0142] prove:

[0143] The Lyapunov candidate function is constructed as:

[0144] (twenty two),

[0145] Taking the derivative of both ends of equation (22) with respect to time, we can obtain:

[0146] (twenty three),

[0147] The last term of formula (23) can be calculated as:

[0148] (twenty four),

[0149] From equations (23) and (24), we can get:

[0150] (25),

[0151] It can be seen that the closed-loop system is Lyapunov stable.

[0152] It is not difficult to obtain formula (25):

[0153] (26),

[0154] Then, it is easy to know:

[0155] (27),

[0156] Therefore, the state vector Finally, it converges to the following area:

[0157] (28)

[0158] According to the results of equations (25) and (28), Theorem 1 is proved.

[0159] Through the above scheme, the present invention constructs a robust stable control method to ensure that the positioning error eventually converges globally to an arbitrarily small area; according to the Lyapunov stability theorem, the stability of the closed-loop system is strictly proved.

[0160] Step 5: Use the designed full drive system robust controller to control the crane system.

[0161] Embodiment 2

[0162] This embodiment provides an underactuated crane robust control system based on a full drive system, and adopts the underactuated crane robust control method based on a full drive system of the first embodiment, including:

[0163] A dynamic model building module, which is used to build a dynamic model of a four-degree-of-freedom tower crane system;

[0164] A full-drive model building module is used to split the dynamic model of the four-degree-of-freedom tower crane system into a first subsystem model and a second subsystem model including drivable state variables and non-drivable state variables; introduce a positioning error vector, combine the first subsystem model and the second subsystem model, and obtain a full-drive system model;

[0165] Robust controller design module, which is used to design a robust controller for the full drive system model with the goal of eventually global convergence of the positioning error to an arbitrarily small area;

[0166] The control module is used to control the crane system using the designed full drive system robust controller.

[0167] Embodiment 3

[0168] This embodiment provides a program product, which is a computer program product, including a computer program. When the computer program is executed by a processor, the steps in the robust control method for an under-actuated crane based on a full-drive system described in Embodiment 1 are implemented.

[0169] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A robust control method for an underactuated crane based on a full drive system, characterized in that: The steps include: A dynamic model of a four-degree-of-freedom tower crane system is constructed; the expression of the dynamic model of the four-degree-of-freedom tower crane system is: ， ， ， ， ， ， ， ， ， in, represents the state vector, , Represent the state vector The first-order time derivative and the second-order time derivative of is a positive definite symmetric inertia matrix, represents the centripetal-Coriolis force matrix, represents the gravity vector, represents the control input vector, Indicates the uncertainty factor of the system; is the mass of the trolley, is the load mass, is the length of the suspension rope, is the cantilever moment of inertia, To control the torque of the cantilever swing, is the translation control force of the trolley, is the acceleration due to gravity, is the cantilever rotation angle, is the trolley displacement, is the load swing angle, for , , , Abbreviation of , , , respectively , , , The first time derivative of is the uncertainty factor of the system; The dynamic model of the four-degree-of-freedom tower crane system is split into a first subsystem model and a second subsystem model including drivable state variables and non-drivable state variables; wherein the expressions of the first subsystem model and the second subsystem model including drivable state variables and non-drivable state variables are: ， ， ， ， ， ， ， ， ， ， ， ， in, , Represent the drivable state variables The first and second time derivatives of , Represent the non-drivable state variables The first and second time derivatives of ; The positioning error vector is introduced, and the first subsystem model and the second subsystem model are combined to obtain the full drive system model; the expression of the positioning error vector is: ， ， in, represents a drivable state variable, represents the desired cantilever rotation angle, Indicates the desired position of the trolley; The expression of the full drive system model is: ， ， ， ， ， in, as well as Represent the error vector The first and second time derivatives of is a positive definite diagonal matrix, represents the total uncertainty factor; For the full-drive system model, the full-drive system robust controller is designed with the goal of stabilizing the closed-loop system and the positioning error finally converging to an arbitrarily small area globally. After obtaining the full-drive system robust controller, the stability of the closed-loop system is strictly proved according to the Lyapunov stability theorem. The expression of the robust controller is: ， in, represents the control matrix of the two generations of regulation, represents the auxiliary vector, represents the state vector, , ,in is the unit diagonal matrix, is a positive definite symmetric matrix, For any given positive number, represents a known constant vector; the region where the state vector finally converges is: ， in, Representation Matrix The smallest characteristic root of represents any positive real number; The crane system is controlled using the designed full drive system robust controller.

2. The robust control system of an underactuated crane based on a full drive system adopts the robust control method of an underactuated crane based on a full drive system as claimed in claim 1, characterized in that: include: A dynamic model building module, which is used to build a dynamic model of a four-degree-of-freedom tower crane system; A full-drive model building module is used to split the dynamic model of the four-degree-of-freedom tower crane system into a first subsystem model and a second subsystem model including drivable state variables and non-drivable state variables; introduce a positioning error vector, combine the first subsystem model and the second subsystem model, and obtain a full-drive system model; Robust controller design module, which is used to design a robust controller for the full drive system model with the goal of eventually global convergence of the positioning error to an arbitrarily small area; The control module is used to control the crane system using the designed full drive system robust controller.

3. A program product, the program product being a computer program product, comprising a computer program, characterized in that: When the computer program is executed by a processor, the steps of the robust control method for an underactuated crane based on a full drive system as claimed in claim 1 are implemented.

Images