Bridge crane control method based on adaptive integral ida-pbc

Abstract

The application provides a bridge crane control method based on adaptive integral IDA-PBC, and belongs to the technical field of crane control. The application comprises the following steps: a dynamic model of the bridge crane is established, an inertia matrix and a potential energy function are determined; the dynamic model is converted into an open-loop port controlled Hamilton form, the general form of an energy shaping controller and a damping injection controller is determined; the specific form of the expected potential energy function, the energy shaping controller and the damping injection controller is obtained; the adaptive integral controller is obtained by matching the open-loop port controlled Hamilton form and the state of the extended closed-loop Hamilton form; the adaptive law of unknown parameters is obtained by using the system stability condition; the system matrix and the actual characteristic polynomial are obtained by using the state equation of the closed-loop system, the expected characteristic polynomial is established by configuring to the ideal pole, and the control parameters are solved. The application can not only improve the trolley positioning accuracy and effectively reduce the load swing, but also can estimate the unknown parameters in the system in real time.

Description

Technical Field

[0001] This invention relates to the technical field of crane control, and in particular to a control method for bridge cranes based on adaptive integral IDA-PBC. Background Technology

[0002] Bridge cranes, also known as overhead cranes or gantry cranes, are... Figure 2 As shown, bridge cranes are core heavy-duty lifting equipment that spans the work area and achieves material handling through the coordinated action of trolley lateral movement and vertical lifting mechanism. As an indispensable key equipment in industrial production and logistics transportation, their operational efficiency, control precision, and operational safety directly determine the production cycle, operating costs, and personnel and equipment safety of related industries, occupying an important strategic position in national economic development. With its advantages of simple structure, strong load-carrying capacity, and high space utilization, bridge cranes have developed into a standardized and serialized product system over many years, becoming the most widely used and numerous type of lifting machinery, supporting the stable operation and high-quality development of many key industries. In terms of application scenarios, bridge cranes are found in all core areas of industrial production and infrastructure construction, covering indoor and outdoor mining enterprises, steel metallurgy, railway transportation, ports and docks, logistics turnover, construction, power plant operation and maintenance, heavy machinery manufacturing, and nuclear power plants, among other departments and locations. With the advancement of "dual-carbon" goals and the implementation of intelligent manufacturing, bridge cranes are gradually evolving from traditional execution units into data nodes in intelligent factories, with their application scenarios continuously expanding and the requirements for control performance constantly increasing.

[0003] Despite the increasingly widespread application and continuous technological advancements of bridge cranes, their control systems still face numerous significant challenges and technical bottlenecks during actual operation, hindering further improvements in operational accuracy, efficiency, and safety. Firstly, bridge cranes are essentially highly coupled, nonlinear, underactuated systems. The number of control inputs is less than the system's degrees of freedom, and there is a strong coupling relationship between trolley movement, load swaying, and hoisting actions, making controller design difficult. Traditional control methods struggle to achieve precise and coordinated control of multiple actions. Secondly, various uncertainties and disturbances exist during operation, including track errors, wind load disturbances, changes in mechanical friction, unmodeled dynamics, and external environmental interference. These factors severely impact control performance, leading to poor load sway suppression and decreased positioning accuracy. Furthermore, traditional control methods struggle to balance positioning speed and sway suppression, resulting in either low positioning efficiency or residual sway, failing to meet the stringent requirements of precision handling in high-end manufacturing.

[0004] With the full implementation of the new special equipment safety regulations and the accelerated advancement of intelligent manufacturing, the industrial sector has placed higher demands on the control precision, response speed, safety, and intelligence level of bridge cranes. There is an urgent need to develop a control method that can effectively solve the above-mentioned control difficulties, adapt to complex working conditions, and possess high robustness and adaptability, so as to improve the operating performance, safety reliability, and intelligence level of bridge cranes and meet the needs of high-quality development in various industries. This is also a technical bottleneck that urgently needs to be overcome in the field of bridge crane control. Summary of the Invention

[0005] To address the technical problems of low control accuracy, inability to effectively suppress load sway, and insufficient consideration of the influence of unknowns in the system in traditional bridge cranes, this invention proposes a bridge crane control method based on adaptive integral IDA-PBC. The IDA-PBC (Interconnection and Damping Assignment - Passivity-Based Control) algorithm is used to transform the system model, solving for the energy shaping controller and damping injection controller. This reconstructs the desired equilibrium point of the system and enhances its dissipation characteristics, rapidly suppressing oscillations, accelerating convergence, and improving the system's anti-interference capability. Then, through state transformation, the closed-loop extended port controlled Hamiltonian form is obtained, leading to the calculation of the adaptive integral controller and the adaptive law for the unknown parameters. This effectively reduces steady-state error and achieves accurate estimation of the system's unknown parameters.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: a bridge crane control method based on adaptive integral IDA-PBC, comprising the following steps:

[0007] Step 1: Establish the dynamic model of the bridge crane and determine the system's inertia matrix and potential energy function;

[0008] Step 2: Based on the inertia matrix and potential energy function, the dynamic model is transformed into an open-loop port controlled Hamiltonian form. Using the design concept of standard IDA-PBC, the general forms of the energy shaping controller and damping injection controller are determined.

[0009] Step 3: Solve the two partial differential equations that couple kinetic and potential energy to obtain the desired potential energy function, and obtain the specific forms of the energy shaping controller and the damping injection controller;

[0010] Step 4: Using state transformation technology, the open-loop port-controlled Hamiltonian form is transformed into the extended closed-loop Hamiltonian form; the states of the open-loop port-controlled Hamiltonian form and the extended closed-loop Hamiltonian form are matched to obtain the adaptive integral controller; the derivative of the Hamiltonian function of the closed-loop system is calculated, and the adaptive law of the unknown parameters is obtained using the system stability condition.

[0011] Step 5: Use the state equations of the closed-loop system to obtain the system matrix and the actual characteristic polynomial of the system. Configure the system to the ideal poles to establish the fifth-order desired characteristic polynomial. Solve for the control parameters of the system by combining the actual characteristic polynomial and the desired characteristic polynomial.

[0012] Preferably, the method for establishing the dynamic model of the bridge crane is as follows: selecting the horizontal displacement of the trolley. With load swing angle For generalized coordinates, the Lagrangian function is obtained from the difference between the total kinetic energy and the gravitational potential energy of the load. Based on the Lagrangian function, the generalized coordinates are... and generalized coordinates Differentiating and rearranging, we obtain the dynamic model of the bridge crane as follows:

[0013] ;

[0014] ;

[0015] in, and These are the acceleration of the trolley and the angular acceleration of the load, respectively. For the mass of the car, For the mass of the load, Let g be the unknown coefficient of friction, g be the acceleration due to gravity, and L be the length of the rope. Indicates the speed of the car. The angular velocity of the load; the main controller ; For energy shaping controller, For damping injection controller, It is an adaptive integral controller;

[0016] The method for determining the system's inertia matrix and potential energy function is as follows:

[0017] The dynamic model of the bridge crane at the load swing angle Linearization at point:

[0018] ;

[0019] ;

[0020] The inertia matrix is ​​then: The potential energy function is .

[0021] Preferably, the method for determining the general form of the energy shaping controller and the damping injection controller is as follows;

[0022] The dynamic model can be expressed in open-loop port-controlled Hamiltonian form as follows:

[0023] ;

[0024] in, for An identity matrix of order 1 For the input matrix, Represents momentum. Represents friction. The coefficient of friction is unknown. For bridge crane systems with respect to generalized coordinates and momentum Hamiltonian energy function, and Representing the Hamiltonian energy function respectively Seeking information about generalized coordinates and momentum The partial derivatives; The derivative of the generalized coordinates, Let T be the derivative of momentum, and T represent the transpose of the matrix.

[0025] The general forms of the energy shaping controller and the damping injection controller are expressed as follows:

[0026] ;

[0027] ;

[0028] in, To inject controller gain into the damping, For the desired inertia matrix, Let be the desired potential energy function. These are free parameters; Let be the desired Hamiltonian energy function. and These are the desired Hamiltonian energy functions. Regarding generalized coordinates and momentum The partial derivatives;

[0029] Integrating energy shaping controller and damping injection controller Then, the open-loop port controlled Hamiltonian form is transformed into the desired Hamiltonian form:

[0030] ;

[0031] in, Here is the damping matrix.

[0032] Preferably, the desired inertia matrix Expected potential energy function and free parameters The partial differential equation must be satisfied:

[0033] ;

[0034] ;

[0035] in, Represents the input matrix The orthogonal complement matrix satisfies ;

[0036] Hamiltonian energy function ;

[0037] And the desired Hamiltonian energy function is: ;

[0038] The desired inertia matrix is ​​designed. for: Among them, the intermediate coefficient , Intermediate coefficient ;

[0039] The desired potential energy function is expressed as: ;in, All parameters are freely adjustable;

[0040] Solving the partial differential equation and simplifying it yields the generalized coordinates. The simplified form of the expected potential energy function is:

[0041] ;

[0042] Among them, intermediate variables .

[0043] Preferably, the input matrix Expected inertia matrix Inertia matrix Hamiltonian energy function and the expected Hamiltonian energy function Integrating energy shaping controller and damping injection controller The general form of the energy shaping controller and damping injection controller The specific form is expressed as follows:

[0044] ;

[0045] ;

[0046] Among them, intermediate variables .

[0047] Preferably, the implementation steps for obtaining the adaptive integral controller are as follows:

[0048] Step 1: Define state transitions Transform the open-loop port-controlled Hamiltonian form into the extended closed-loop Hamiltonian form:

[0049] ;

[0050] ;

[0051] Among them, intermediate variables , For gain coefficient, This represents an estimated value of friction. The Hamiltonian energy function is in closed-loop Hamiltonian form. In the integration state, This represents the deviation between the actual value and the estimated value. Integral state The derivative, and Let these represent the new generalized velocity and momentum derivatives after coordinate transformation, respectively. For the new generalized coordinates The expected potential energy function, To control the gain, , and Representing the Hamiltonian energy function respectively Seeking information about , and The partial derivatives; For the true value of the unknown parameter, These are estimated values ​​for unknown parameters;

[0052] Step 2: Simultaneous state transformation and the momentum derivative in closed-loop Hamiltonian form The state solution yields the adaptive integral controller as follows:

[0053]

[0054] Among them, intermediate variables .

[0055] Preferably, the derivative of the Hamiltonian energy function in the closed-loop Hamiltonian form is:

[0056] ;

[0057] in, Term representing and related to generalized speed, For Hamiltonian energy function Seeking information about Partial derivatives, It is a state transition Part of;

[0058] To ensure system stability, the adaptive law for the unknown friction coefficient is: ;

[0059] Adaptive law for unknown friction coefficient Substituting the derivative of the Hamiltonian energy function ,available The system is stable.

[0060] Preferably, in the main controller Under the influence of the open-loop port controlled Hamiltonian form and the linearized dynamic model, the state equation of the system is expressed as:

[0061] ;

[0062] in, and Let these be the momentum of the trolley and the load, respectively. and These are the rates of change of the angular momentum of the trolley and the load, respectively. Represents unknown friction parameters And adaptive law The error;

[0063] The system matrix is:

[0064] ;

[0065] Among them, intermediate variables .

[0066] Preferably, the actual characteristic polynomial of the system matrix A is solved based on the determinant expansion method:

[0067] ;

[0068] Where s is the variable of the characteristic polynomial; coefficients

[0069] ;

[0070] The ideal poles are set to five negative real numbers, including one dominant pole. and four non-dominant poles The ideal characteristic polynomial is expressed as:

[0071] ;

[0072] Among them, coefficient

[0073] ;

[0074] After simultaneously solving the actual and ideal characteristic polynomials, the control parameters are obtained by solving algebraic equations. We obtain, where the intermediate matrix intermediate matrix .

[0075] Preferably, the total kinetic energy is: ;

[0076] With the origin of the inertial coordinate system as the zero point of potential energy, the gravitational potential energy of the load is: ;

[0077] For generalized coordinates The generalized force of the car is For generalized coordinates The generalized force of the load is .

[0078] Compared with existing technologies, the beneficial effects of this invention include: establishing a dynamic model of the bridge crane, determining the inertia matrix and potential energy function; designing a standard port-controlled Hamiltonian system structure based on the dynamic model of the bridge crane; solving the partial differential equations composed of the potential energy function, and calculating the energy shaping controller and damping injection controller using the steps of the standard IDA-PBC algorithm; constructing an extended closed-loop port-controlled Hamiltonian system using state transformation technology; calculating the adaptive integral controller and the adaptive law of the unknown parameters to achieve real-time estimation of the unknown parameters; and using pole placement to configure the poles of the closed-loop system to ideal poles to achieve dynamic adjustment of control parameters. This invention not only enables precise positioning of the trolley but also effectively suppresses load swaying during transportation, significantly improving lifting accuracy and operational efficiency.

[0079] This invention employs the IDA-PBC algorithm to analyze the system of a bridge crane from an energy perspective, providing a more intuitive understanding of system energy changes. This facilitates the design of control laws to rapidly dissipate oscillation energy, efficiently suppressing load sway and positioning the trolley. Simultaneously, it ensures stable operation of the closed-loop system from a physical perspective. The energy shaping controller and damping injection controller are solved strictly according to the standard IDA-PBC algorithm, accurately matching the system's passive characteristics and dynamic structure, ensuring the rigor of the theoretical derivation. To solve the partial differential equations, the form of the inertia matrix and the structure of the desired potential energy function are carefully designed, greatly simplifying the equation solution. State transformation technology is introduced, adding an adaptive integral controller to the system's main controller. Adaptive laws for unknown parameters are designed while ensuring system stability. For the system's control parameters, pole placement is used to configure the system to ideal poles. This invention not only improves trolley positioning accuracy and effectively reduces load sway but also enables real-time estimation of unknown parameters in the system. Experimental verification on a test platform shows that this invention can achieve precise trolley tracking and effective load sway suppression, meeting the needs of complex bridge crane application scenarios. Attached Figure Description

[0080] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0081] Figure 1 This is a flowchart of the present invention.

[0082] Figure 2 This is a schematic diagram of a bridge crane.

[0083] Figure 3 This is a diagram showing the tracking and positioning error of the trolley during the operation of a bridge crane.

[0084] Figure 4 This is a diagram showing the load swing angle of a bridge crane during operation.

[0085] Figure 5 This is a diagram showing the changes in control inputs during the operation of a bridge crane.

[0086] Figure 6 This is a graph showing the real-time estimation results of unknown parameters of a bridge crane during operation. Detailed Implementation

[0087] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0088] like Figure 1 As shown, a control method for a bridge crane based on adaptive integral IDA-PBC is proposed. The concept is as follows: First, based on the physical structure of the bridge crane, a dynamic model, inertia matrix, and potential energy function are established, and the model is transformed into a port-controlled Hamiltonian system. Then, for the partial differential equations composed of the potential energy function, the energy shaping controller and damping injection controller are obtained based on the standard IDA-PBC algorithm. Finally, using state transformation technology, an extended closed-loop port-controlled Hamiltonian system is established. An adaptive integral controller is obtained through state matching, and the adaptive law for the unknown parameters is determined by differentiating the Hamiltonian function, achieving real-time estimation of the unknown parameters. Pole placement is used to determine the system's control parameters, enabling the system to achieve ideal control effects. This invention first determines the dynamic model, inertia matrix, and potential energy function, solves the partial differential equations, and calculates the energy shaping controller and damping injection controller. Then, state transformation technology is used to obtain the adaptive integral controller and the adaptive law for the unknown parameters. Finally, pole placement is used to solve for the system's control parameters. The specific steps are as follows:

[0089] Step 1: Establish the dynamic model of the bridge crane and determine the system's inertia matrix and potential energy function.

[0090] The method for constructing the dynamic model, inertia matrix, and potential energy function is as follows:

[0091] Step 1: Model Assumptions and Parameter Definitions. For example... Figure 2 The bridge crane shown is assumed to have a mass of [missing information]. A rigid body, the load is considered as mass. The mass of the point mass is ignored; the mass and length of the rope are fixed at L. Consider the horizontal motion and pendulum oscillation within the amplitude-varying plane; select the horizontal displacement of the trolley. With load swing angle For generalized coordinates; the coefficient of friction is The acceleration due to gravity is g; the system's main controller is defined as...

[0092] ;

[0093] in, For energy shaping controller, For damping injection controller, An adaptive integral controller is used, and the three components work together to control the bridge crane to complete its operations.

[0094] Step 2: Coordinate System Construction and Position Coordinate Derivation. Establish an inertial coordinate system with the ground projection of the crane's rotation center as the origin, and obtain the trolley coordinates as follows: The coordinates of the loaded mass point are ( , ), and the x-coordinate y-axis .

[0095] Step 3: Calculate the system's kinetic energy. The kinetic energy of the car... and the kinetic energy of the load They can be represented as:

[0096] ;

[0097] ;

[0098] in, Indicates the speed of the car. ω represents the angular velocity of the load.

[0099] The total kinetic energy of the system obtained by merging is:

[0100] .

[0101] Step 4: Calculation of system potential energy. Taking the origin of the inertial coordinate system as the zero point of potential energy, the gravitational potential energy of the load can be expressed as:

[0102] .

[0103] Step 5: Lagrange function and definition of generalized force. The Lagrange function is obtained from the difference between total kinetic energy and gravitational potential energy. For generalized coordinates The generalized force of the car is For generalized coordinates The generalized force of the load is Generalized coordinates are independent variables describing the motion of a system, while generalized forces are the equivalent driving forces acting on these variables. The two are related through the Lagrange equation, and the generalized forces directly determine the dynamic evolution of the corresponding generalized coordinates.

[0104] Step 6: Generalized coordinates based on the Lagrange function (Lag) and generalized coordinates After differentiation and simplification, the dynamic model of the bridge crane is obtained as follows:

[0105] ;

[0106] ;

[0107] in, and These are the acceleration of the trolley and the angular acceleration of the load, respectively.

[0108] Step 7: To facilitate controller design, the above system is configured with a load swing angle... Linearization at point:

[0109] ;

[0110] ;

[0111] Linearization is based on the load swing angle The Taylor expansion formula at point is: and However, in the first formula, the sin expression becomes a third-order minor quantity and can be discarded; in the second formula... become .

[0112] Step 8: Based on the dynamic model of the bridge crane, the inertia matrix and potential energy function can be expressed as follows:

[0113] ;

[0114] ;

[0115] The inertia matrix is ​​determined by the coefficient matrix of the acceleration term (i.e., the coefficients of the second derivative of the linearized equation), and the potential energy function is obtained by integrating over the gravity term (i.e., over the integral of the equation with respect to the acceleration term). (Obtained through integration). This step establishes a dynamic model based on the physical structural characteristics of the bridge crane, facilitating controller design. Simultaneously, the establishment of the inertia matrix and potential energy function lays the groundwork for the application of the IDA-PBC algorithm.

[0116] Step 2: Based on the inertia matrix and potential energy function, the dynamic model is transformed into an open-loop port-controlled Hamiltonian form. Using the design concept of standard IDA-PBC, the general forms of the energy shaping controller and damping injection controller are determined.

[0117] The construction methods for port-controlled Hamiltonian form and controller general form are as follows:

[0118] Step 1: Represent the dynamic model in open-loop port-controlled Hamiltonian form as follows:

[0119] ;

[0120] ;

[0121] ;

[0122] in, for An identity matrix of order 1 For the input matrix, Represents momentum. Represents friction. The coefficient of friction is unknown. For the system output, For bridge crane systems with respect to generalized coordinates and momentum Hamiltonian energy function, and Representing the Hamiltonian energy function respectively Seeking information about generalized coordinates and momentum The partial derivatives of . The derivative of the generalized coordinates, i.e., the generalized velocity. is the derivative of momentum, i.e., the rate of change of momentum, and T represents the transpose of the matrix.

[0123] Step 2: Following the design principles of the standard IDA-PBC (by reshaping the system's Hamiltonian energy function, interconnection structure, and damping characteristics, the original system is configured as a port-controlled dissipative Hamiltonian, thereby achieving stable control under passive guarantee), the general forms of the energy shaping controller and damping injection controller can be expressed as follows:

[0124] ;

[0125] ;

[0126] in, To inject controller gain into the damping, For the desired inertia matrix, Let be the desired potential energy function. These are free parameters. Let be the desired Hamiltonian energy function. and These are the desired Hamiltonian energy functions. Regarding generalized coordinates and momentum The partial derivatives of , and the expected Hamiltonian energy function is defined as:

[0127] ;

[0128] Furthermore, the desired inertia matrix Expected potential energy function and free parameters The following partial differential equations must be satisfied:

[0129] ;

[0130] ;

[0131] in, Represents the input matrix The orthogonal complement matrix satisfies .

[0132] Step 3: Introduce the energy shaping controller and damping injection controller Then, the above open-loop port-controlled Hamiltonian form can be transformed into the desired Hamiltonian form:

[0133] ;

[0134] in, This is the damping matrix. The system's overall controller in the open-loop port controlled Hamiltonian form of step 1 in step two. The energy shaping controller has been obtained above. and damping injection controller After being integrated into the system, only the adaptive integral controller remains. Thus, the above formula is obtained. Furthermore, by incorporating the energy shaping controller... and damping injection controller Combining the system from step 1 of step two with the system described above, the simplified results in the first row are equal, and the simplified results in the second row are also equal, meaning that in the energy shaping controller... and damping injection controller Under the influence of , some terms are canceled out, and a new Hamiltonian form is obtained.

[0135] This step, by transforming the crane's dynamic model into a port-controlled Hamiltonian form, allows for a more intuitive analysis of the system's energy changes. Utilizing the design principles of the standard IDA-PBC, the general forms of the energy shaping controller and damping injection controller can be obtained.

[0136] Step 3: Solve the two partial differential equations of kinetic and potential energy coupling to obtain the desired potential energy function, and further obtain the specific forms of the energy shaping controller and the damping injection controller.

[0137] The steps for solving the partial differential equations and calculating the specific forms of the energy shaping controller and damping injection controller are as follows:

[0138] Step 1: Design the desired inertia matrix The form is:

[0139] ;

[0140] Among them, the intermediate coefficient , Intermediate coefficient Inertia matrix Positive definiteness must be satisfied, therefore the intermediate coefficients must satisfy... , Intermediate coefficient The design facilitates the solution of partial differential equations.

[0141] Step 2: Express the desired potential energy function as:

[0142] ;

[0143] in, All parameters are freely adjustable. Adding adjustable parameters to the controller allows for flexible adjustment of the system's dynamic response.

[0144] Step 3: Solve the partial differential equation to obtain the desired inertia matrix. Inertia matrix and the expected potential function Substituting into the partial differential equation and simplifying, we obtain the generalized coordinates. The simplified form of the expected potential energy function is:

[0145] ;

[0146] Among them, intermediate variables .

[0147] Step 4: Input matrix Expected inertia matrix Inertia matrix Hamiltonian energy function and the expected Hamiltonian energy function Integrating energy shaping controller and damping injection controller The general form of the energy shaping controller can be obtained. and damping injection controller The specific form can be expressed as:

[0148] ;

[0149] ;

[0150] Among them, intermediate variables .

[0151] This step addresses the biggest obstacle in the application of the IDA-PBC algorithm: solving the partial differential equations. Through a special design of the inertia matrix and desired potential function structure, the solution to the partial differential equations is greatly simplified. Then, by substituting the solution to the partial differential equations into the general form of the controller, the specific forms of the energy shaping controller and the damping injection controller can be obtained.

[0152] Step 4: Using state transformation technology, the open-loop port-controlled Hamiltonian form in Step 2 is transformed into an extended closed-loop Hamiltonian form; the states of the open-loop port-controlled Hamiltonian form and the extended closed-loop Hamiltonian form are matched to obtain the adaptive integral controller; the derivative of the Hamiltonian function of the closed-loop system is calculated, and the adaptive law of the unknown parameters is obtained using the system stability condition.

[0153] The calculation steps for the extended closed-loop Hamiltonian form and the adaptive integral controller are as follows:

[0154] Step 1: Define state transitions The open-loop expected Hamiltonian form in step two can be transformed into the extended closed-loop Hamiltonian form:

[0155]

[0156]

[0157] Among them, intermediate variables , For gain coefficient, This represents an estimated value of friction. The Hamiltonian energy function is in closed-loop Hamiltonian form. In the integration state, This represents the deviation between the actual value and the estimated value. Integral state The derivative, and Let these represent the new generalized velocity and momentum derivatives after coordinate transformation, respectively. For the new generalized coordinates The expected potential energy function, To control the gain, , and Representing the Hamiltonian energy function respectively Seeking information about , and The partial derivatives; For the true value of the unknown parameter, These are estimated values ​​for unknown parameters.

[0158] Step 2: Simultaneous state transformation The momentum derivative of the second line of the closed-loop Hamiltonian form The state can be solved to obtain the adaptive integral controller as follows:

[0159]

[0160] Among them, intermediate variables .

[0161] Step 3: Differentiating the Hamiltonian energy function in the closed-loop Hamiltonian form, we have:

[0162] ;

[0163] in, Term representing and related to generalized speed, For Hamiltonian energy function Seeking information about Partial derivatives, It is a state transition Part of it.

[0164] To ensure system stability, the adaptive law for the unknown parameters must satisfy:

[0165] ;

[0166] An adaptive law with unknown parameters is used to dynamically update the adaptive integral controller. The estimated values ​​of the unknown parameters involved.

[0167] This step transforms the closed-loop Hamiltonian form into an adaptive integral form through state changes (the closed-loop system introduces an integral state term and an error term for the unknown parameter), and the introduction of the unknown parameter does not disrupt the structure and stability of the Hamiltonian form. From the perspective of system stability, the necessary conditions that the adaptive law for the unknown parameter must satisfy are analyzed, achieving accurate estimation of the unknown parameter while ensuring system stability. The adaptive law for the unknown parameter... Substitute the derivative of the Hamiltonian energy function in step 3 The result is that This means the system is stable. The estimation of unknown parameters is achieved through an adaptive law. ensure.

[0168] Step 5: Obtain the system matrix using the state equations of the closed-loop system (Hamiltonian form), further obtain the actual characteristic polynomial of the system, and establish the desired characteristic polynomial of the fifth order; solve the control parameters of the system by simultaneously solving the two polynomials, and configure the system to the ideal poles.

[0169] Step 1: Solve the state equations of the closed-loop system. (In the main controller...) Under the influence of the combined effects of the Hamiltonian structural form in step 1 of step 2 and the linearized crane model in step 7 of step 1, the state equation of the system can be expressed as:

[0170] ;

[0171] in, and Let these be the momentum of the trolley and the load, respectively. and These are the rates of change of the angular momentum of the trolley and the load, respectively. Represents the true value of the unknown parameter and estimated value The error.

[0172] The core of all the previous results is to solve for the overall controller. The above formula represents the closed-loop system obtained by incorporating the main controller into the open-loop system. This closed-loop system no longer contains any controller.

[0173] Its system matrix can be expressed as:

[0174] ;

[0175] Among them, intermediate variables .

[0176] Step 2: Solve for the actual characteristic polynomial of the system matrix A using the determinant expansion method:

[0177] ;

[0178] Where s is the variable of the characteristic polynomial.

[0179] .

[0180] Step 3: The system matrix A is of order 5, so it needs a total of five poles. Setting them to negative real numbers ensures that the system response decays exponentially, guaranteeing monotonically convergent convergence without oscillations or overshoot. Ideally, the five poles should be negative real numbers, including one dominant pole. and four non-dominant poles Its ideal characteristic polynomial can be expressed as:

[0181]

[0182] Among them, intermediate variables

[0183] .

[0184] Step 4: After simultaneously solving the actual characteristic polynomial and the ideal characteristic polynomial, the relevant control parameters can be obtained by solving the algebraic equations. We obtain, by combining these two equations, we have Then, the control parameters are solved using MATLAB tools. The intermediate matrix is ​​one such example. intermediate matrix .

[0185] The advantage of this step is that it eliminates the need to adjust control parameters through traditional trial and error. Pole configuration can set the system poles to ideal poles, greatly reducing the time spent on parameter tuning.

[0186] According to the method of the present invention, in Figure 2 Control experiments were conducted on the bridge crane platform shown. To fully examine the control capabilities of the present invention, an external disturbance was applied to the load 50 to 60 seconds after the program started running, in order to simulate uncertain disturbances in actual application scenarios.

[0187] Figure 3 The results of the real-time tracking and positioning error of the crane trolley in this invention show that the overall error is controlled within -0.05m to 0.04m, and external disturbances do not increase the positioning error of the trolley.

[0188] Figure 4 The diagram shows the effect of this invention on the load sway reduction in a crane. It can be observed that the load sway does not exceed 1 degree throughout the entire test range. When disturbances are present, the sway angle only fluctuates slightly and then returns to the steady-state value, indicating that this invention can effectively suppress the load sway.

[0189] Figure 5 The diagram shows the magnitude of the control input force for the crane according to the present invention. It can be seen that the magnitude of the control input remains within a reasonable range and there are no abnormal sudden changes.

[0190] Figure 6 The graph shows the real-time estimation results of unknown parameters in the system according to the present invention, demonstrating that the present invention can effectively estimate the potential uncertainties in the system.

[0191] This invention first establishes a dynamic model of the bridge crane based on its physical structure, determining the inertia matrix and potential energy function. The model is then transformed into a standard port-controlled Hamiltonian system to intuitively describe the energy changes within the system. Next, by solving the partial differential equations, an energy shaping controller and a damping injection controller based on the IDA-PBC algorithm are obtained. Finally, using state transformation technology, an extended closed-loop port-controlled Hamiltonian system structure is established. From the perspective of system state and stability, an adaptive integral controller and an adaptive law for unknown parameters are determined. Furthermore, pole placement is introduced to dynamically adjust the control parameters in the system, enabling the system to reach ideal poles. This invention achieves precise trolley positioning and effective load mitigation, and can estimate uncertainties in the system in real time, making it applicable to complex bridge crane applications.

[0192] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A control method for a bridge crane based on adaptive integral IDA-PBC, characterized in that, Includes the following steps: Step 1: Establish the dynamic model of the bridge crane and determine the system's inertia matrix and potential energy function; Step 2: Based on the inertia matrix and potential energy function, the dynamic model is transformed into an open-loop port controlled Hamiltonian form. Using the design concept of standard IDA-PBC, the general forms of the energy shaping controller and damping injection controller are determined. Step 3: Solve the two partial differential equations that couple kinetic and potential energy to obtain the desired potential energy function, and obtain the specific forms of the energy shaping controller and the damping injection controller; Step 4: Using state transformation technology, the open-loop port-controlled Hamiltonian form is transformed into the extended closed-loop Hamiltonian form; the states of the open-loop port-controlled Hamiltonian form and the extended closed-loop Hamiltonian form are matched to obtain the adaptive integral controller; the derivative of the Hamiltonian function of the closed-loop system is calculated, and the adaptive law of the unknown parameters is obtained using the system stability condition. Step 5: Use the state equations of the closed-loop system to obtain the system matrix and the actual characteristic polynomial of the system. Configure the system to the ideal poles to establish the fifth-order desired characteristic polynomial. Solve for the control parameters of the system by combining the actual characteristic polynomial and the desired characteristic polynomial.

2. The bridge crane control method based on adaptive integral IDA-PBC according to claim 1, characterized in that, The method for establishing the dynamic model of the bridge crane is as follows: selecting the horizontal displacement of the trolley. With load swing angle For generalized coordinates, the Lagrangian function is obtained from the difference between the total kinetic energy and the gravitational potential energy of the load. Based on the Lagrangian function, the generalized coordinates are... and generalized coordinates Differentiating and rearranging, we obtain the dynamic model of the bridge crane as follows: ； ； in, and These are the acceleration of the trolley and the angular acceleration of the load, respectively. For the mass of the car, For the quality of the load, Let g be the unknown coefficient of friction, g be the acceleration due to gravity, and L be the length of the rope. Indicates the speed of the car. The angular velocity of the load; the main controller ; For energy shaping controller, For damping injection controller, It is an adaptive integral controller; The method for determining the system's inertia matrix and potential energy function is as follows: The dynamic model of the bridge crane at the load swing angle Linearization at point: ； ； The inertia matrix is ​​then: The potential energy function is .

3. The bridge crane control method based on adaptive integral IDA-PBC according to claim 2, characterized in that, The method for determining the general form of the energy shaping controller and the damping injection controller is as follows: The dynamic model can be expressed in open-loop port-controlled Hamiltonian form as follows: ； in, for An identity matrix of order 1 For the input matrix, Represents momentum. Represents friction. The coefficient of friction is unknown. For bridge crane systems with respect to generalized coordinates and momentum Hamiltonian energy function, and Representing the Hamiltonian energy function respectively Seeking information about generalized coordinates and momentum The partial derivatives; The derivative of the generalized coordinates, Let T be the derivative of momentum, and T represent the transpose of the matrix. The general forms of the energy shaping controller and the damping injection controller are expressed as follows: ； ； in, To inject controller gain into the damping, Let be the desired inertia matrix. Let be the desired potential energy function. These are free parameters; Let Hamiltonian energy function be the desired function. and These are the desired Hamiltonian energy functions. Regarding generalized coordinates and momentum The partial derivatives; Integrating energy shaping controller and damping injection controller Then, the open-loop port controlled Hamiltonian form is transformed into the desired Hamiltonian form: ； in, Here is the damping matrix.

4. The bridge crane control method based on adaptive integral IDA-PBC according to claim 3, characterized in that, Desired inertia matrix Expected potential energy function and free parameters The partial differential equation must be satisfied: ； ； in, Represents the input matrix The orthogonal complement matrix satisfies ; Hamiltonian energy function ; And the desired Hamiltonian energy function is: ; The desired inertia matrix is ​​designed. for: Among them, the intermediate coefficient , Intermediate coefficient ; The desired potential energy function is expressed as: ;in, All parameters are freely adjustable; Solving the partial differential equation and simplifying it yields the generalized coordinates. The simplified form of the expected potential energy function is: ； Among them, intermediate variables .

5. The bridge crane control method based on adaptive integral IDA-PBC according to claim 4, characterized in that, Input matrix Expected inertia matrix Inertia matrix Hamiltonian energy function and the expected Hamiltonian energy function Integrating energy shaping controller and damping injection controller The general form of the energy shaping controller and damping injection controller The specific form is expressed as follows: ； ； Among them, intermediate variables .

6. The bridge crane control method based on adaptive integral IDA-PBC according to any one of claims 3-5, characterized in that, The steps to obtain the adaptive integral controller are as follows: Step 1: Define state transitions Transform the open-loop port-controlled Hamiltonian form into an extended closed-loop Hamiltonian form: ； ； Among them, intermediate variables , This is the gain coefficient. This represents an estimated value of friction. The Hamiltonian energy function is in closed-loop Hamiltonian form. In the integration state, This represents the deviation between the actual value and the estimated value. Integral state The derivative of and Let these represent the new generalized velocity and momentum derivatives after coordinate transformation, respectively. For the new generalized coordinates The expected potential energy function, To control the gain, , and Representing the Hamiltonian energy function respectively Seeking information about , and The partial derivatives; For the true value of the unknown parameter, These are estimated values ​​for unknown parameters; Step 2: Simultaneous state transformation and the momentum derivative in closed-loop Hamiltonian form The state solution yields the adaptive integral controller as follows: Among them, intermediate variables .

7. The bridge crane control method based on adaptive integral IDA-PBC according to claim 6, characterized in that, Differentiating the Hamiltonian energy function in the closed-loop Hamiltonian form, we have: ； in, Term representing and related to generalized speed, For Hamiltonian energy function Seeking information about Partial derivatives, It is a state transition Part of; To ensure system stability, the adaptive law for the unknown friction coefficient is: ; Adaptive law for unknown friction coefficient Substituting the derivative of the Hamiltonian energy function ,available The system is stable.

8. The bridge crane control method based on adaptive integral IDA-PBC according to any one of claims 3-5 and 7, characterized in that, In the main controller Under the influence of the open-loop port controlled Hamiltonian form and the linearized dynamic model, the state equation of the system is expressed as: ； in, and Let these be the momentum of the trolley and the load, respectively. and These are the rates of change of the angular momentum of the trolley and the load, respectively. Represents unknown friction parameters And adaptive law The error; The system matrix is: ； Among them, intermediate variables .

9. The bridge crane control method based on adaptive integral IDA-PBC according to claim 8, characterized in that, Solving for the actual characteristic polynomial of the system matrix A using the determinant expansion method: ； Where s is the variable of the characteristic polynomial; coefficients ； The ideal poles are set to five negative real numbers, including one dominant pole. and four non-dominant poles The ideal characteristic polynomial is expressed as: ； Among them, coefficient ； After simultaneously solving the actual and ideal characteristic polynomials, the control parameters are obtained by solving algebraic equations. We obtain, where the intermediate matrix intermediate matrix .

10. The bridge crane control method based on adaptive integral IDA-PBC according to claim 9, characterized in that, The total kinetic energy is: ; With the origin of the inertial coordinate system as the zero point of potential energy, the gravitational potential energy of the load is: ; For generalized coordinates The generalized force of the car is For generalized coordinates The generalized force of the load is .

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