MHC rotary crane motion control method and system based on MPC

Abstract

The invention discloses an MHC rotating crane motion control method and system based on MPC. The method comprises the steps that S101, all to-be-controlled parameter values are calculated according to given positions; s102, solving an optimal control sequence at the moment according to a predictive control algorithm; s103, designing a state observer according to the output, the input and the state of the moment, observing the state of the next moment, designing by adopting a full-dimensional linear state observer method, and adjusting parameters by adopting a DLQR method to obtain state information of the next moment to be used in the step S102 of the next moment; and S104, measuring the output of a real system, and sending the output to the step S103 at the next moment. According to the MPC-based MHC rotary crane motion control method and system provided by the invention, the position of the crane is controlled, so that the crane can reach a specified position, and the swing angle of a suspended load can be limited within a certain range.

Description

Technical Field

[0001] This application relates to the field of hoisting system transportation, and in particular to a motion control method and system for an MHC rotary crane based on MPC. Background Technology

[0002] As a core piece of equipment in port logistics, bulk cargo handling, and heavy equipment transfer, the MHC (Mobile Harbor Crane) rotary crane primarily functions to achieve precise displacement of heavy objects in three-dimensional space through the coordinated actions of its rotation, luffing, and hoisting mechanisms. With the continuous growth of global port throughput, the expansion of cargo types to include high-value, precision equipment, and the increasing demand for port automation and intelligent transformation, higher requirements are being placed on the motion control performance of MHC rotary cranes. These cranes must not only ensure high-precision positioning during heavy object transfer but also suppress swaying vibrations of the load, while simultaneously considering the dynamic response speed and energy efficiency of the equipment to adapt to stable operation under complex conditions such as gusts of wind, sudden load changes, and uneven tracks.

[0003] Therefore, it is necessary to provide a motion control method and system for MHC rotary cranes based on MPC to solve the above problems. Summary of the Invention

[0004] This application provides a motion control method and system for an MHC rotary crane based on MPC. By controlling the position of the crane, it ensures that the crane can reach the designated position and that the swing angle of the load can be limited within a certain range.

[0005] In a first aspect, this application provides a motion control method for an MHC rotary crane based on MPC, the method comprising the following steps: Step S101: Calculate the values ​​of each parameter to be controlled based on the given position; Step S102: Solve for the optimal control sequence at this moment using the predictive control algorithm. ; Step S103: Design a state observer based on the output, input and state at this moment, observe the state at the next moment, use the full-dimensional linear state observer method for design, adjust the parameters using the DLQR method to obtain the state information at the next moment, and use it in step S102 at the next moment. Step S104: Measure the output of the real system and send it to step S103 at the next moment.

[0006] Preferably, the calculation of the values ​​of each parameter to be controlled based on the given position is specifically performed using the following formula:

[0007] in, This indicates the location of the port crane. This refers to the rotation angle of the crane. This is the length of the crane's rope. The rotation angle of the load.

[0008] Preferably, the optimal control sequence for the current moment is obtained by solving the predictive control algorithm. The specific calculation is performed using the following formula:

[0009] in, These are the prediction time domain and control time domain of the system, respectively. For system reference input, These represent the system's weight matrices, Indicates the current moment. Show the output.

[0010] Preferably, The relationship between them is:

[0011] in, These represent the output and control sequences, respectively. .

[0012] Preferably, By differentiating the vectors, we can obtain the optimal sequence. The expression is: .

[0013] Preferably, the optimal sequence Substitute the values ​​into the constraints and determine whether the constraints are satisfied. If all constraints are satisfied, then the optimal sequence is... This is the optimal solution. If there are unmet constraints, then proceed with the following steps: According to the formula Solve for the optimal sequence; Formula Substitute the value into the following formula to solve for the optimal value. : ; according to Repeat the previous step until all values ​​are found. Compared with the previous iteration If the sum of the squares of the differences is less than or equal to the first threshold, then... The sequence is the optimal solution.

[0014] Preferably, the design using the full-dimensional linear state observer method is as follows:

[0015] in, Representative at the The state observation values ​​of each sampling point For output, For input, This is the observer state feedback matrix.

[0016] Preferably, the parameter is adjusted using the DLQR method, specifically calculated using the following formula:

[0017] in, It is the error weight matrix. It is the input weight matrix. This is the feedback matrix.

[0018] Preferably, the feedback matrix The specific calculation is performed using the following formula: .

[0019] Secondly, this application also provides an MHC rotary crane motion control system based on MPC, comprising: a server, the server including a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described method.

[0020] This application offers the following advantages over existing technologies: It provides a motion control method and system for an MHC rotating crane based on MPC. The method includes: Step S101: Calculating the values ​​of various parameters to be controlled based on a given position; Step S102: Solving for the optimal control sequence u at the current moment using a predictive control algorithm; Step S103: Designing a state observer based on the output, input, and state at the current moment, observing the state at the next moment, using a full-dimensional linear state observer method for design, and adjusting the parameters using the DLQR method to obtain the state information for the next moment, which is then used in Step S102 at the next moment; Step S104: Measuring the output of the actual system and sending it to Step S103 at the next moment. By controlling the position of the crane, it ensures that the crane can reach the specified position and that the swing angle of the load can be limited within a certain range. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0022] Figure 1 This is a flowchart of a motion control method for an MHC rotary crane based on MPC, as described in an embodiment of this application. Figure 2 This is a basic control block diagram of an MHC rotary crane motion control method based on MPC in an embodiment of this application; Figure 3 This is a basic schematic diagram of a crane according to an MHC rotary crane motion control method based on MPC in an embodiment of this application; Figure 4 The figure shows the unconstrained MPC simulation results of an MHC rotary crane motion control method based on MPC in an embodiment of this application. Figure 5 This is a constrained MPC simulation result diagram of a motion control method for an MHC rotary crane based on MPC in an embodiment of this application.

[0023] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0025] To address the aforementioned issues, this application provides an embodiment of an MHC rotary crane motion control method and system based on MPC. By controlling the position of the crane, it ensures that the crane can reach the designated position and that the swing angle of the load can be limited within a certain range.

[0026] Figure 1 This is a flowchart of a motion control method for an MHC rotary crane based on MPC, as described in an embodiment of this application. Figure 2 This is a basic control block diagram of an MHC rotary crane motion control method based on MPC in an embodiment of this application; Figure 3 This is a basic schematic diagram of a crane according to an MHC rotary crane motion control method based on MPC in an embodiment of this application; Figure 4 The figure shows the unconstrained MPC simulation results of an MHC rotary crane motion control method based on MPC in an embodiment of this application. Figure 5 This is a constrained MPC simulation result diagram of a motion control method for an MHC rotary crane based on MPC in an embodiment of this application.

[0027] Now see Figures 1 to 5 ,like Figure 1 As shown, this invention provides a motion control method for an MHC rotating crane based on MPC, the method comprising the following steps: Step S101: Calculate the values ​​of each parameter to be controlled based on the given position; Step S102: Solve for the optimal control sequence at this moment using the predictive control algorithm. ; Step S103: Design a state observer based on the output, input and state at this moment, observe the state at the next moment, use the full-dimensional linear state observer method for design, adjust the parameters using the DLQR method to obtain the state information at the next moment, and use it in step S102 at the next moment. Step S104: Measure the output of the real system and send it to step S103 at the next moment.

[0028] Specifically, such as Figure 2 As shown, module one is the attitude calculation module, which calculates the values ​​of various parameters to be controlled based on the given position. Module two is the MPC controller, which is the main control algorithm part and is used to input control signals. Module three is the crane model part, which can obtain the final output signal through the input signal. Module four is the state observer part, which observes the state of various parts of the system through the output signal.

[0029] I. System Model Section A schematic diagram of a rotating crane is shown below. Figure 3 As shown, based on the dynamic characteristics of the rotating crane, the kinematic equations of the variable rope length rotating crane can be obtained using the Euler-Lagrange equations, as shown in equation (1):

[0030] in, This refers to the rotation angle of the crane. This is the length of the crane's rope. For the rotation angle of the load, Approximately 0, at the equilibrium point Linear expansion of the position yields the linear state-space equation of equation (1):

[0031] in:

[0032] To perform predictive control, the rope length and rotation angle of the mobile port crane need to be obtained from the position information of the port crane. The following approximation is made, as shown in equation (3):

[0033] In specific implementation, according to Figure 3 The positional relationship shown can be used to determine the location of the port crane. As shown in equation (4):

[0034] in, This indicates the location of the port crane. This refers to the rotation angle of the crane. This is the length of the crane's rope. The rotation angle of the load.

[0035] Therefore, according to equation (4), given the load position of the mobile port crane Considering the load swing angle under steady state Since the value is 0, the rotation angle of the MHC and the rope length can be calculated as follows:

[0036] II. Design of Control Algorithm The primary control method chosen for the controller section is constrained model predictive control (MPC). MPC allows for the inclusion of constraints during the controller's design and optimization.

[0037] Generally, the discretized linear system satisfies the form of equation (6). In the linearized MHC crane system, Since it is a zero vector, its influence will not be considered in the following explanation of the principle.

[0038]

[0039] in, These are the parameter values ​​obtained after discretizing the system using a zero-order hold.

[0040] In practical implementation, the optimal control sequence at the current moment is obtained by solving the predictive control algorithm. Specifically, the objective function for optimizing the MPC algorithm is designed in the form of equation (7) using the following formula:

[0041] in, These are the prediction time domain and control time domain of the system, respectively. For system reference input, These represent the system's weight matrices, Indicates the current moment. Show the output.

[0042] In equation (7), These represent the prediction and control time domains of the system, respectively, and are important parameters in this MPC method. Representing the prediction time domain, at the current control moment, MPC predicts the time length of future outputs using the system model. For example, at the current moment... ,predict The purpose of the system output at any given time is to enable the controller to determine the optimization direction based on the output deviation over a period of time in the future, so as to avoid focusing only on the present and causing subsequent overshoot or lag. Representing the control time domain, it refers to the time length during which the optimal control quantity is calculated using optimization algorithms, i.e., only for the future. Generate a control input sequence at each time point, for example However, it ultimately only executes the control variables at the current moment. The control parameters will be re-optimized in the next cycle.

[0043] For the system based on the first Step output The predicted first Step output, For the system in the first Step input, For system reference input, These represent the system's weight matrix, respectively. To simplify the parameter tuning process, Generally, a diagonal matrix is ​​chosen, where each element in the diagonal matrix represents the importance of the input or output at the corresponding position.

[0044] In practical implementation, each output is obtained according to equation (6). With input arrive The relationship between them is:

[0045] in, These represent the output and control sequences, respectively.

[0046]

[0047] In practical implementation, substitute equation (8) into equation (7), and... By differentiating the vectors, we can obtain the optimal sequence. The expression is:

[0048] The above algorithm is an unconstrained predictive control optimization algorithm. When constraints are added, namely the constraints shown in equation (10), the constrained optimization problem is transformed into an unconstrained problem as shown in equation (11):

[0049] in, It is the constraint matrix, calculated using equation (8). Since we only consider the case where the output constraint is within a certain interval, The i-th row and j-th column represent the j-th control variable in the i-th constraint. coefficient, These are constraint values, denoted as the left interval vector and right interval vector of all output constraint ranges. Calculated using equation (8) The i-th term represents a constant term in the i-th constraint that is independent of the decision variable.

[0050]

[0051] in, The definition is shown in equation (7). These are Lagrange multipliers. If equation (11) has a solution, then for the solution... The following Kuhn-Tucker conditions must be met:

[0052] Therefore, if equation (11) has a solution, it must satisfy the following condition: , It must be less than or equal to ,at this time It must be less than or equal to 0, at which point the minimum value is obtained exactly at the constraint boundary. Since the quadratic optimization shown in equation (7) is a convex optimization, it can be solved by performing a calculation. Therefore, the solution is divided into two cases for discussion: the first case: This means that the optimal solution must be within the constraints, which is equivalent to solving the optimization problem of equation (7) under unconstrained conditions. In the second case, there are several constraints that make the equation less than 0, that is, equal to 0. For ease of solution, equation (9) is solved by a two-step optimization algorithm to solve equations (13) and (14):

[0053] make The symbols are defined in equations (7) and (11).

[0054] The solution to equation (13) is shown in equation (15):

[0055] Substituting equation (15) into equation (14), the optimization problem can be transformed into:

[0056]

[0057] in, Equation (16) is solved using Hildersee programming, an iterative optimization algorithm. The parameters obtained in the previous iteration are treated as constants and substituted into the optimization problem for solution. The updated formula is:

[0058] Represents the Lagrange multiplier of the i-th constraint obtained in the m-th iteration. This represents the i-th element in the K vector. The control quantity obtained by representing the element in the i-th row and j-th column of the H matrix is:

[0059] In the formula, The definition is shown in equation (14). The definition is shown in equation (11).

[0060] In practical implementation, to ensure the optimality of the solution, the following optimization algorithm is designed: Step 1: Calculate the optimal control sequence using equation (9), substitute it into the constraint conditions, and determine whether the constraint conditions are met.

[0061] Step 2: If all constraints are satisfied, the control sequence obtained in Step 1 is the optimal solution. If there are unsatisfied constraints, proceed to Step 3.

[0062] Step 3: Solve for the optimal sequence according to equation (15), substitute the value of equation (13) into equation (12) to solve for equation (12), and solve for the optimal sequence according to equation (14). .

[0063] Step 4: Repeat Step 3 based on the values ​​obtained in the previous step until the sum of the squares of all the differences between the obtained values ​​and the values ​​obtained in the previous iteration is less than or equal to the first threshold. The resulting sequence is the optimal solution.

[0064] IV. Observer Design In practical implementation, a linear state observer is used to observe state variables that cannot be measured. The expression of the full-dimensional state observer of the discretized system designed based on equation (6) is shown in equation (19) below:

[0065] in Representative at the The state observation values ​​of each sampling point For output, For input, This is the observer state feedback matrix.

[0066] Rewriting equation (19) in the form of an error state equation, we get:

[0067] In practical implementation, the DLQR (Discrete Linear Quadratic Regulator) algorithm is used to design the system of equations (19) and (20), and the optimization objective is shown in equation (20) below:

[0068] Where Q is the error weight matrix and R is the input weight matrix. Feedback matrix The calculation method is shown in the following formula (22):

[0069] The overall control process described above is adopted for design. The basic parameters of the crane, as well as the initial and reference values ​​of the control target, are shown in Table 1 below, where is the inherent parameter of the crane, and is the overall height of the gantry in the yard, which remains unchanged: Table 1. Description of basic experimental parameters

[0070] It can be seen that in the simulation results with and without constraints, All five variables can converge to the reference value, and the state observer's observations can eventually converge to the true value. Figure 4 This is the unconstrained MPC. It can be seen that the system's swing angle can reach a maximum of approximately [value missing]. With constraints added, [condition missing]... back, Figure 5 The control results show that, with other variables remaining unchanged in terms of control performance, the swing angle of the crane load can be limited to a certain range using the algorithm described above.

[0071] This application also provides an MHC rotary crane motion control system based on MPC, comprising: a server, the server including a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described method.

[0072] In summary, the embodiments of this application provide a motion control method and system for an MHC rotating crane based on MPC. The method includes: step S101: calculating the values ​​of various parameters to be controlled based on a given position; step S102: solving for the optimal control sequence u at the current moment using a predictive control algorithm; step S103: based on the output y, input u, and state at that moment... Design a state observer to observe the state at the next moment. The design adopts the full-dimensional linear state observer method, and the parameters are adjusted using the DLQR method to obtain the state information at the next moment, which is used in step S102 of the next moment; Step S104: Measure the output of the real system and send it to step S103 of the next moment. By controlling the position of the crane, ensure that the crane can reach the specified position and that the swing angle of the load can be limited within a certain range.

[0073] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0074] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A motion control method for an MHC rotating crane based on MPC, characterized in that, The method includes the following steps: Step S101: Calculate the values ​​of each parameter to be controlled based on the given position; Step S102: Solve for the optimal control sequence at this moment using the predictive control algorithm; Step S103: Design a state observer based on the output, input and state at this moment, observe the state at the next moment, use the full-dimensional linear state observer method for design, adjust the parameters using the DLQR method to obtain the state information at the next moment, and use it in step S102 at the next moment. Step S104: Measure the output of the real system and send it to step S103 at the next moment.

2. The MHC rotary crane motion control method based on MPC according to claim 1, characterized in that, The calculation of the values ​​of each parameter to be controlled based on the given position is specifically performed using the following formula: in, This indicates the location of the port crane. This refers to the rotation angle of the crane. This is the length of the crane's rope. The rotation angle of the load.

3. The MHC rotary crane motion control method based on MPC according to claim 1, characterized in that, The optimal control sequence for the current moment is obtained using the predictive control algorithm. The specific calculation is performed using the following formula: in, These are the prediction time domain and control time domain of the system, respectively. For system reference input, These represent the system's weight matrices, Indicates the current moment. This indicates the output.

4. The MHC rotary crane motion control method based on MPC according to claim 3, characterized in that, The relationship between them is: in, These represent the output and control sequences, respectively. 。 5. The MHC rotary crane motion control method based on MPC according to claim 4, characterized in that, By differentiating the vectors, we can obtain the optimal sequence. The expression is: 。 6. The MHC rotary crane motion control method based on MPC according to claim 5, characterized in that, Substitute the optimal sequence into the constraint conditions and determine whether the constraint conditions are met. If all constraints are satisfied, then the optimal sequence is... This is the optimal solution. If there are unmet constraints, then proceed with the following steps: According to the formula Solve for the optimal sequence; Formula Substitute the value into the following formula to solve for the optimal value. : ； according to Repeat the previous step until all values ​​are found. Compared with the previous iteration If the sum of the squares of the differences is less than or equal to the first threshold, then... The sequence is the optimal solution.

7. The MHC rotary crane motion control method based on MPC according to claim 1, characterized in that, The design using the full-dimensional linear state observer method is detailed below: in, Representative at the The state observation values ​​of each sampling point For output, For input, This is the observer state feedback matrix.

8. The MHC rotary crane motion control method based on MPC according to claim 7, characterized in that, The parameters are adjusted using the DLQR method, specifically calculated using the following formula: in, It is the error weight matrix. It is the input weight matrix. This is the feedback matrix.

9. The MHC rotary crane motion control method based on MPC according to claim 8, characterized in that, The feedback matrix The specific calculation is performed using the following formula: 。 10. A motion control system for an MHC rotary crane based on MPC, characterized in that, include: The server includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method according to any one of claims 1-9.

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