Container crane optimal control method and system based on multiple targeting methods

Abstract

The invention discloses a container crane optimal control method and system based on a multiple targeting method. The method comprises the steps that an operator appoints the starting and ending positions of a container, performance indexes of the loading and unloading process and control constraints; a self-adaptive multiple targeting method is adopted, and a control strategy enabling the performance index of the loading and unloading process to be optimal is obtained; and converting the control strategy into a control instruction of a motor of the container crane, and executing corresponding actions by an execution motor according to the received control instruction. The system is composed of an execution motor, a position sensor, a field bus network, a DCS, a control room display and a motor controller. A control room engineer appoints starting and ending positions of a container, the DCS obtains a control strategy with optimal loading and unloading process performance indexes through a self-adaptive multiple targeting method, converts the control strategy into a control instruction of a motor, and sends the control instruction to a motor controller, so that an execution motor executes corresponding actions, and a position sensor collects position information of the container in real time and returns the position information to the DCS. A control room engineer can master the loading and unloading process at any time.

Description

Technical Field

[0001] The present invention relates to the field of crane control, and particularly to an optimal control method and system for container cranes based on an adaptive multiple shooting method. It can automatically control the moving speed and position of the container to optimize the performance index of the loading and unloading process and improve the stability and efficiency of the container loading and unloading process. Background Art

[0002] Container cranes are the main equipment for loading and unloading containers between container ships and the quay front. The loading and unloading capacity and speed of quay cranes directly determine the productivity of terminal operations. Container transport ships are developing towards larger and more intelligent directions, and the requirements for the productivity of quay cranes are also getting higher and higher.

[0003] For quay cranes with determined technical parameters, the key factor affecting their productivity is the control strategy of container loading and unloading speed. Since the technical parameters and operation requirements of different quay cranes in different ports are different, it is of great significance to automatically control shore container cranes according to specific parameters and operation requirements.

[0004] Currently, in the control methods of domestic quay cranes, the optimal control theory and corresponding methods are rarely adopted, and the parameters in the controller are often set based on existing experience. The productivity and safety need to be further improved. The safety of quay cranes can be guaranteed and the productivity can be further improved after adopting the optimal control method. Summary of the Invention

[0005] The present invention discloses an optimal control method and system for container cranes based on an adaptive multiple shooting method. The system consists of an execution motor, a position sensor, a fieldbus network, a DCS, a control room display, and a motor controller. The engineer in the control room designates the starting and ending positions of the container. The DCS obtains the control strategy that optimizes the performance index of the loading and unloading process through the adaptive multiple shooting method, converts it into a control instruction for the motor, and sends it to the motor controller through the fieldbus network, so that the execution motor performs corresponding actions. The position sensor real-time collects the position information of the container and sends it back to the DCS, enabling the engineer in the control room to master the loading and unloading process at any time. The present invention can optimize the performance index of the loading and unloading process and improve the stability and efficiency of the container loading and unloading process.

[0006] Specifically:

[0007] An optimal control method for container cranes based on the multiple shooting method, the steps including:

[0008] (1) Operators designate the starting and ending positions of the container, the performance index of the loading and unloading process, and the control constraints;

[0009] (2) By adopting the adaptive multiple shooting method, a control strategy that optimizes the performance index of the loading and unloading process is obtained (optimizing the performance index means the stability of the container loading and unloading process, such as the minimum swing).

[0010] (3) Convert the control strategy into the control instruction of the motor of the container crane, and the motor executes the corresponding actions according to the received control instruction.

[0011] The derivation process of the mathematical model of the control strategy is as follows:

[0012] Describe the loading and unloading process of the quay crane container as:

[0013]

[0014] Where:

[0015] t represents time,

[0016] u(t) represents the control vector of the loading and unloading process (the control vector generally includes: the torque of the executing motor);

[0017] x(t) represents the state information of the loading and unloading process (the state information generally includes: the horizontal and vertical positions of the lifted container in the air, the horizontal and vertical speeds, the swing speed and the swing position);

[0018] f is a system of differential equations established according to the physical principles of the crane (the system of differential equations represents the movement process of the container in the air and is a function of the state vector, the control vector, and time);

[0019] The problem Q of optimizing the performance index of the container loading and unloading process is expressed as:

[0020]

[0021] x(t 0 ) = x 0

[0022] x(t f ) = x f

[0023]

[0024] C(x(t), u(t), t) ≤ 0

[0025] Where:

[0026] t 0 represents the start time of the loading and unloading process, t f represents the end time of the loading and unloading process,

[0027] J represents the objective function to be minimized,

[0028] Let \(L\) denote a function related to the state vector, control vector, and time,

[0029] and \(u\) and denote the lower and upper bounds of the control vector \(u(t)\) respectively,

[0030] where \(C\) is the inequality constraint,

[0031] and \(x\) 0 is the initial state, and \(x\) f is the state at time \(t\) f ;

[0032] The problem \(Q\) is essentially an optimal control problem;

[0033] In step (ii), the multiple shooting method is adopted to solve the problem \(Q\). The loading and unloading process is divided into multiple sub - time intervals according to the time interval. Within each sub - interval, polynomial functions are used to approximate the state variables and control variables. The specific steps are as follows:

[0034] 2.1) Collect the following three types of information in step (i): the starting and ending positions of the container, the performance indicators of the loading and unloading process, and the control constraints;

[0035] 2.2) Make the following settings:

[0036] Adopt piece - wise constant parameterization for the control vector;

[0037] Parameterize the initial state of each segment;

[0038] Set the number of segments \(N\) of the loading and unloading process. The control grid corresponding to any segment is the initial guess value of the parameterization vector of the control strategy the initial guess value of the state at the beginning of each segment of the loading and unloading process Let \(k\) 1 denote the iteration number, and \(k\) 2 denote the approximation number;

[0039] Set the computational accuracy \(tol\) of the non - linear programming NLP problem 1 and the convergence accuracy \(tol\) of the adaptive approximation 2 ;

[0040] Set the iteration number \(k\) 1 and the approximation number \(k\) 2 to zero;

[0041] 2.3) When \(k\) 2 = 0, execute step 2.4); otherwise,

[0042] Through the adaptive approximation method, perform adaptive approximation processing on the control grid to obtain the grid nodes to be optimized New control grid and its corresponding parameterized vector Then execute step 2.4);

[0043] 2.4) Obtain the state information of this iteration through the problem discretization method and the objective function value

[0044] 2.5) Obtain the gradient information of this iteration through gradient calculation

[0045] When k 1 = 0, skip step 2.6) and directly execute step 2.7); otherwise, execute step 2.6);

[0046] 2.6) NLP convergence judgment:

[0047] If the absolute value of the difference from the objective function value of the previous iteration is less than the precision tol 1 , then the convergence condition is satisfied, and execute step 2.9);

[0048] If the convergence is not satisfied, continue to execute step 2.7);

[0049] 2.7) Use the value of to overwrite the value of and increase the iteration count by 1;

[0050] 2.8) Utilize the objective function value and gradient information obtained in steps 2.4) and 2.5, and obtain a new control strategy that is better than by calculating the optimization direction and optimization step size After this step is completed, jump back to step 2.4) again;

[0051] 2.9) Approximation convergence judgment:

[0052] Denote When k 2 = 0, execute step 2.1); otherwise,

[0053] Judge whether the absolute value of the difference from the objective function value of the previous adaptive approximation is less than the precision tol 2 ,

[0054] If so, the convergence condition is satisfied, and convert the control strategy of this iteration into the motor control instruction output; otherwise,

[0055] the convergence is not satisfied, set the approximation count k 2 := k2 +1, continue to execute step 2.3) until the approximation convergence judgment is satisfied.

[0056] The adaptive approximation method in step 2.3) includes the following steps:

[0057] 2.3.1) Calculate the left slope at the grid node by the following formula and the right slope

[0058]

[0059] where u k represents the parameter of the control strategy on the k-th segment, and τ k represents the grid node between u k and u k+1 ;

[0060] 2.3.2) When the right slope k at the grid node τ and the left slope k+1 at the grid node τ satisfy

[0061]

[0062] where ε s is a positive real number. If

[0063]

[0064] then select the grid node τ k as the node to be optimized; if

[0065]

[0066] then select the grid node τ k+1 as the node to be optimized;

[0067] 2.3.3) If the left and right slopes at the grid node τ k meet the following requirements, then remove this node from the grid:

[0068]

[0069] where ε e is a relatively small positive real number; after removing the grid node τ k , the grids corresponding to u k and u k+1 are merged into a new grid, and the parameter on it is updated to (u k +u k+1 ) / 2;

[0070] 2.3.4) If the left slope at the grid node τ k satisfies:

[0071]

[0072] where ε i is a positive real number greater than ε e , then insert a grid node in [τ k-1 , τ k ; if the right slope at the grid node τ k satisfies:

[0073]

[0074] then insert a grid node in [τ k-1 , τ k ;

[0075] 2.3.5) Generate a new control grid and the corresponding parameterized vector according to the nodes removed and inserted in steps 2.3.3) and 2.3.4).

[0076] In step 2.4), the control quantity u(t) is represented as a linear combination of piecewise constant functions and the state trajectory x(t) is represented by M-order Lagrange interpolation basis functions, i.e.:

[0077] u(t) ≈ u i i = 1, 2,..., N (9)

[0078]

[0079] where: t represents time, N is the number of segments for discretizing the time interval [t 0 , t f , is the Lagrange interpolation basis function, u i is the discrete parameter of the control vector u(t) in the i-th segment, and the linear combination coefficient s i,j is the value of x(t) at the Gaussian collocation point t i,j ;

[0080] In the multiple shooting method, the initial state of each segment is also discretized:

[0081] x(t i ) = z i , i = 1,…, N - 1 (11)

[0082] where t i is the termination time node of the i-th segment, and z i is the parameterized state at time t i ;

[0083] Since the derivative function expressions of all basis functions are known, the formula (10) is differentiated:

[0084]

[0085] where f is the system of differential equations describing the motion process;

[0086] The system of differential equations of the state trajectory is discretized into an algebraic equation form:

[0087]

[0088] The objective function and constraints are discretely expressed using u i , z i and s i,j to obtain the NLP problem to be solved:

[0089]

[0090] where J is the objective function, X represents the parameters of the discrete state vector at the collocation points, Z 0 is the parameter composed of all z i , U represents the parameter composed of all u i , and C E and C I represent the equality constraint and inequality constraint respectively.

[0091] In step 2.5), the steps for gradient calculation are as follows:

[0092] Write equation (13) in the following form:

[0093] F(X,U,Z 0 ) = 0 (15)

[0094] where F is the set of all equalities; perform a first-order Taylor expansion on equation (15):

[0095]

[0096] Calculate the first-order sensitivity information through equation (16)

[0097]

[0098] Obtain the first-order gradient information from the first-order sensitivity information:

[0099]

[0100] First-order sensitivity information and with respect to Z 0The gradient information is also obtained by the same method.

[0101] In step 2.6), it is implemented by the following steps:

[0102] 2.6.1) If the absolute value difference between the objective function value of the current iteration and 1 that of the previous iteration is less than the precision tol,

[0103] then the convergence condition is satisfied, and the control strategy of this iteration is converted into the control instruction output of the motor; if the convergence condition is not satisfied, then step 2.6.2) is continued; the value of is overwritten with the value of 1 and the iteration number k

[0104] 2.6.2) is increased by 1; 1 Regarding the control strategy 1 as a certain point in the vector space, denoted as P

[0105] 2.6.3) Starting from point P 1 and according to the selected NLP algorithm and the gradient information 1 at point P construct an optimization direction and an optimization step size

[0106] 2.6.4) Through formula construct another point P in the vector space corresponding to 2 such that the objective function value 2 corresponding to P is better than where I is a vector with the same dimension as

[0107] An optimal control system for a container crane based on the multiple shooting method, comprising: an execution motor, a position sensor, a fieldbus network, a DCS, a container position information display device in the main control room, and a motor controller; the optimal control method for the container crane based on the multiple shooting method is integrated in the DCS;

[0108] The operation process of the optimal control system includes:

[0109] Step A1: An engineer in the control room designates the starting and ending positions of the container, the performance indicators and control constraints of the loading and unloading process;

[0110] ​Step A2: The DCS executes the internal multiple shooting method to obtain a control strategy that optimizes the performance indicators of the container handling process;

[0111] Step A3: The DCS converts the control strategy into control instructions for the execution motors and sends them to the corresponding motor controllers through the fieldbus network, enabling the execution motors to perform corresponding actions according to the received control instructions;

[0112] Step A4: The position sensor collects the real-time position information of the container, sends it back to the DCS through the fieldbus network, and displays it on the container position information display device, enabling the control room engineer to keep track of the handling process at any time.

[0113] The beneficial effects of the present invention are mainly manifested in that: the optimal control system of the container crane based on the adaptive multiple shooting method precisely controls the container handling process, can improve the operation and production efficiency of the crane, and optimize the performance indicators of the handling process. The calculation of sensitivity information speeds up the convergence rate of the method and improves the calculation efficiency of the method. This method can obtain the control strategy for the optimal control of the container crane under the condition of meeting the constraints.

[0114] The present invention can optimize the performance indicators of the handling process, improve the performance indicators (such as stability) of the container handling process, and has a high-efficiency control method. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Figure 1 is a schematic structural diagram of the optimal control system of the container crane based on the adaptive multiple shooting method;

[0116] Figure 2 is a structural diagram of the internal modules of the DCS of the optimal control system of the container crane based on the adaptive multiple shooting method. DETAILED DESCRIPTION OF THE INVENTION

[0117] In order to improve the productivity of the quay crane, the present invention provides an optimal control system for a container crane based on an adaptive multiple shooting method with fast calculation speed and high calculation accuracy.

[0118] The container handling process can be described as:

[0119]

[0120] where t represents time, u(t) represents the control vector of the handling process; x(t) represents the state information of the handling process; f is a system of differential equations established based on the physical principles of the crane. It can be seen from this description that the container handling process can be represented by a system of differential equations.

[0121] Optimize the performance indicators of the container loading and unloading process (specifically, for example, minimize the swing of the container during loading and unloading), then the final expression of this problem is:

[0122]

[0123] Where t 0 represents the start time of the loading and unloading process, t f represents the end time of the loading and unloading process, J represents the objective function to be minimized, L represents a function related to the state vector, control vector, and time, u and represent the lower and upper bounds of the control vector u(t) respectively, C is the inequality constraint condition, x 0 is the initial state, x f is the state at time t f . This problem is essentially an optimal control problem. Traditional methods for solving such problems have the defects of low efficiency and poor accuracy, and it is difficult to meet the requirements of high approximation efficiency in actual operations.

[0124] The present invention uses the multiple shooting method to solve this problem. The multiple shooting method is a numerical method for solving optimal control problems. Its core idea is to parameterize the continuous control vector on a discrete time grid and use the initial value of the state vector on each time sub-interval as a new degree of freedom, that is, the parameter to be optimized. By independently solving the state differential equations of each sub-interval and introducing matching conditions as equality constraints to ensure the continuity of the state trajectory. In this way, the original problem is transformed into a nonlinear programming NLP problem for solution.

[0125] In the multiple shooting method, first divide the time interval into multiple sub-time intervals, and approximate the state variables and control variables using polynomial functions within each sub-interval. The multiple shooting method takes the initial value of the state variable within each sub-time interval as the parameter to be optimized, solves the state differential equation in segments, and sets the continuity condition constraints for each time interval. By iteratively optimizing these parameters, the objective function reaches the optimal value.

[0126] The technical solution of the present invention is: an optimization method of the adaptive multiple shooting method is integrated in the distributed control system DCS, and based on this, a set of optimal control systems for container cranes is constructed. Its complete structure is as Figure 1 shown, including an execution motor 11, a position sensor 12, a fieldbus network 13, a DCS 14, a container position information display device 15 in the main control room, and a motor controller 16.

[0127] The operation process of the optimal control system includes:

[0128] Step A1: The control room engineer specifies the start and end positions of the container, the performance indicators of the loading and unloading process, and the control constraints;

[0129] Step A2: The DCS executes the internal adaptive multiple shooting method to obtain a control strategy that optimizes the performance index of the loading and unloading process;

[0130] Step A3: The DCS converts the calculated control strategy into a control instruction for the motor and sends it to the motor controller through the fieldbus network, so that the executing motor performs corresponding actions according to the received control instruction;

[0131] Step A4: The position sensor real-time collects the position information of the container, sends it back to the DCS through the fieldbus network, and displays it in the main control room, so that the control room engineer can always master the loading and unloading process.

[0132] The object of the present invention is achieved by the following technical solutions:

[0133] The DCS of the optimal control system for container cranes integrating the adaptive multiple shooting method is the core of the present invention, including an information acquisition module 21, an initialization module 22, an adaptive approximation module 23, a problem discretization module 24, a gradient calculation module 25, a non-linear programming (NLP) problem solving module 26, an approximation convergence judgment module 27, and a control instruction output module 28, where

[0134] 1. Information acquisition module: It includes three sub-modules: container start and end position acquisition, performance index acquisition, and control constraint acquisition.

[0135] 2. Adaptive multiple shooting method (MSM), the operation steps are as follows:

[0136] Step B1: The information acquisition module 21 obtains the start and end positions of the specified container, the performance index of the loading and unloading process, and the control constraints;

[0137] Step B2: The initialization module 22 starts to run, parameterizes the control vector with piecewise constant parameters, parameterizes the initial state of each segment, sets the number of segments N of the loading and unloading process, and the corresponding control grid is The initial guess value of the parameterized vector of the control strategy The initial guess value of the initial state of each segment Set the calculation accuracy tol of the NLP problem 1 And the convergence accuracy tol of the adaptive approximation 2 , and set the iteration number k 1 And the approximation number k 2 To zero;

[0138] Step B3: When k 2When it is equal to 0, step B4 is executed; otherwise, the control grid is adaptively approximated by the adaptive approximation module 23 to perform adaptive approximation processing to obtain the grid nodes to be optimized The new control grid and its corresponding parameterization vector Execute step B4;

[0139] Step B4: Obtain the state information of this iteration through the problem discretization module 24 and the objective function value

[0140] Step B5: Obtain the gradient information of this iteration through the gradient calculation module 25 When k 1 is equal to 0, step B6 is skipped and step B7 is directly executed;

[0141] Step B6: The NLP problem solving module 26 runs, and the convergence is judged through the NLP convergence judgment module. If the absolute value of the difference from the objective function value of the previous iteration is less than the precision tol 1 , the convergence condition is satisfied, and step B9 is executed; if the convergence is not satisfied, step B7 is continued to be executed;

[0142] Step B7: Use the value to overwrite the value, and increase the iteration number k 1 by 1;

[0143] Step B8: The NLP problem solving module 26 uses the objective function value and gradient information obtained in steps B4 and B5 to calculate the optimization direction and optimization step size to obtain a new control strategy that is better than After this step is executed, it jumps back to step B4 again;

[0144] Step B9: The approximation convergence judgment module 27 runs, and record When k 2 is equal to 0, step B1 is executed; otherwise, judge whether the absolute value of the difference from the objective function value of the previous adaptive approximation is less than the precision tol 2 , if so, the convergence condition is satisfied, and the control strategy of this iteration is converted into a motor control instruction output; otherwise, the convergence is not satisfied, and the approximation number k 2 := k 2 + 1, and step B3 is continued to be executed until the approximation convergence judgment module is satisfied.

[0145] ​3. The adaptive approximation module is implemented by the following steps:

[0146] Step C1: Calculate the left slope at the grid node by the following formula and the right slope

[0147]

[0148] where u k represents the parameter of the control strategy on the k-th segment, and τ k represents the grid node between u k and u k+1 .

[0149] Step C2: When the right slope k at the grid node τ and the left slope k+1 at the grid node τ satisfy

[0150]

[0151] where ε s is a positive real number. If

[0152]

[0153] then select the grid node τ k as the node to be optimized; if

[0154]

[0155] then select the grid node τ k+1 as the node to be optimized.

[0156] Step C3: If the left and right slopes at the grid node τ k meet the following requirements, then remove this node from the grid:

[0157]

[0158] where ε e is a relatively small positive real number. After removing the grid node τ k , the grids corresponding to u k and u k+1 are merged into a new grid, and the parameter on it is updated to (u k + u k+1 ) / 2.

[0159] Step C4: If the left slope at the grid node τ k satisfies:

[0160]

[0161] Among them, ε i is a positive real number greater than ε e , then grid nodes are inserted on [τ k-1 , τ k . If the right slope at the grid node τ k satisfies:

[0162]

[0163] then grid nodes are inserted on [τ k-1 , τ k . In practical applications, the number of added nodes can be freely set according to the absolute values of the left and right slopes.

[0164] Step C5: Generate a new control grid and the corresponding parameterized vector according to the nodes removed and inserted in Steps C3 and C4.

[0165] 4. The problem discretization module is implemented by the following steps:

[0166] The control quantity u(t) is represented as a linear combination of piecewise constant functions, and the state trajectory x(t) is represented by the linear combination of M-order Lagrange interpolation basis functions, that is:

[0167] u(t) ≈ u i i = 1, 2,..., N (9)

[0168]

[0169] Among them, t represents time, N is the number of segments for discretizing the time interval [t 0 , t f , is the Lagrange interpolation basis function, u i is the discrete constant of the control vector u(t) in the i-th segment, and the linear combination coefficient s i,j is the value of x(t) at the Gaussian collocation point t i,j .

[0170] In the multiple shooting method, the initial state of each segment is also discretized:

[0171] x(t i ) = z i , i = 1,..., N - 1 (11)

[0172] Among them, t i is the termination time node of the i-th segment, and z i is the state parameterized at time t i .

[0173] Since the derivative function expressions of all basis functions are known, take the derivative of Equation (10):

[0174]

[0175] where f is the differential equation system describing the motion process.

[0176] Discretize the differential equation system of the state trajectory into the form of algebraic equations:

[0177]

[0178] Express other objective functions, constraints, etc. in terms of u i , z i and s i,j to obtain the NLP problem to be solved:

[0179]

[0180] where J is the objective function, X represents the parameters of the discrete state vector at the collocation points, Z 0 is the parameter composed of all z i , U represents the parameters of the discrete control vector, C E and C I represent the equality constraint and the inequality constraint respectively.

[0181] 5. Gradient calculation module, implemented by the following steps

[0182] Write Equation (13) in the following form:

[0183] F(X,U,Z 0 ) = 0 (15)

[0184] where F is the set of all equalities. Perform a first-order Taylor expansion on Equation (15):

[0185]

[0186] Calculate the first-order sensitivity information through Equation (16)

[0187]

[0188] Obtain the first-order gradient information from the first-order sensitivity information:

[0189]

[0190] First-order sensitivity information and the gradient information with respect to Z 0 are also obtained by the same method.

[0191] 6. The NLP problem-solving module is implemented as follows:

[0192] Step E1: If the absolute value difference between the objective function value of the previous iteration 1 is less than the precision tol

[0193] then the convergence condition is satisfied, and the control strategy of this iteration is converted into the control instruction output of the motor; if the convergence condition is not satisfied, then continue to execute Step E2; cover the value of with the value of 1 and increase the iteration count k by 1;

[0194] Step E3: Regard the control strategy as a certain point in the vector space, denoted as P 1 , and the objective function value corresponding to P 1 is

[0195] Step E4: Starting from the point P 1 , construct an optimization direction 1 in the vector space according to the selected NLP algorithm and the gradient information at the point P and a step size and

[0196] Step E5: Construct another point P in the vector space corresponding to through the formula 2 such that the objective function value corresponding to P 2 is better than where I is a vector with the same dimension as

[0197] Finally, the DCS converts the control strategy obtained by the adaptive multiple shooting method into the control instruction of the motor, sends it to the motor controller through the fieldbus network, enables the executing motor to perform corresponding actions, and at the same time uses the position sensor to collect the position information of the container in real time and send it back to the DCS, so that the control room engineer can always master the loading and unloading process.

[0198] The present invention will be further described below in conjunction with specific embodiments.

[0199] ​​The scenario to which the present invention is applied in this example is as follows: After a large cargo ship arrives at the port, container loading and unloading are required, that is, the container is placed from the cargo ship to a designated position. During the loading and unloading process, the movement of the container is divided into horizontal movement and vertical movement. Then, for the process of transferring the container from the cargo ship to the truck by a crane, the optimal control strategy in the method of the present invention is to optimize the performance index of the operation process. The mathematical model of this problem is as follows:

[0200]

[0201] x(0) = [0, 22, 0, 0, -1, 0] T

[0202] x(9) = [10, 14, 0, 2.5, 0, 0] T

[0203] |u 1 | ≤ 2.83374

[0204] -0.80865 ≤ u 2 ≤ 0.71265

[0205] |x 4 | ≤ 2.5

[0206] |x 5 | ≤ 1

[0207] Wherein:

[0208] (17.2656, 27.0756 represent quantities related to the model, 0, 22, 0, 0, -1, 0 represents the initial state of the container, and 10, 14, 0, 2.5, 0, 0 represents the initial state of the container

[0209] J represents minimizing the swing during the loading and unloading process, and is a function of the swing position and swing speed

[0210] x 1 (t) represents the horizontal position of the container, in meters;

[0211] x 2 (t) represents the vertical position of the container, in meters;

[0212] x 4 (t) and x 5 (t) are the corresponding horizontal and vertical speeds, and they are respectively not greater than 2.5 and 1, in m / s;

[0213] x 3 (t) represents the swing position (when moving, the container will deviate from the vertical direction by an angle, which is called the swing position here, in rad (radians); x 6(t) represents the swing speed, in rad / s;

[0214] The starting and ending positions of the container are x(0) (corresponding to 0, 22, 0, 0, -1, 0) and x(9) (corresponding to 10, 14, 0, 2.5, 0, 0). In this example, in the multiple shooting method, the container loading and unloading process is divided into 8 segments, which are regarded as 8 time grids;

[0215] Control variable u 1 (t) and u 2 (t) represents the motor torque (the two motors control the horizontal and vertical movements of the container, respectively, and their ranges are [-2.83374, 2.83374] and [-0.80865, 0.71265] (constraints on the control variables (input)), in N·m;

[0216] In order to obtain the control strategy that minimizes the objective function, the DCS runs the adaptive multi-targeting method. The operation process is as follows: Figure 2 shown.

[0217] 1. Information collection module 21: including three sub-modules: container start and end position collection, performance index collection, and control constraint collection.

[0218] 2. Adaptive multiple targeting method, the operation steps are as follows:

[0219] Step F1: The information collection module 21 obtains the starting and ending positions of the container specified by the engineer x(0)=[0,22,0,0,-1,0] T and x(9) = [10, 14, 0, 2.5, 0, 0] T , Performance indicators of loading and unloading process and control constraints |u 1 |≤2.8337 and -0.80865≤u 2 ≤0.71265;

[0220] Step F2: Initialization module 22 starts running, parameterizes the control vector using piecewise constants, parameterizes the initial state of each segment, sets the number of segments of the loading and unloading process to 8, and the corresponding control grid is the initial guess value of the parameterization vector for the uniform partitioning and control strategy 0.5, The initial guess value of is the initial value of the corresponding state. Set the calculation accuracy of the NLP problem tol 1 And the convergence accuracy of adaptive approximation tol 2 10 respectively -6 and 10 -4 , the number of iterations k 1 and the number of approximations k 2 Set to zero;

[0221] Step F3: When k 2 = 0, execute step F4; otherwise, the control grid is adjusted by the adaptive approximation module 23. Perform adaptive approximation processing to obtain the grid nodes to be optimized New Control Grid and its corresponding parameterized vector Execute step F4;

[0222] Step F4: Obtain the status information of this iteration through the problem discretization module 24 and the objective function value

[0223] Step F5: Obtain the gradient information of this iteration through the gradient calculation module 25 When k 1 =0, skip step F6 and go directly to step F7;

[0224] Step F6: The NLP problem solving module 26 runs, and the NLP convergence judgment module performs convergence judgment. If The objective function value of the previous iteration The absolute value difference is less than the precision tol 1 , then the convergence condition is met, and step F9 is executed; if the convergence is not met, step F7 is continued;

[0225] Step F7: Use The value of The value of and the number of iterations k 1 Increase by 1;

[0226] Step F8: The NLP problem solving module 26 uses the objective function value and gradient information obtained in steps F4 and F5 to calculate the optimization direction and optimization step length to obtain the ratio New and better control strategy After this step is completed, jump to step F4 again;

[0227] Step F9: Approximation convergence judgment module 27 runs, recording When k 2 = 0, execute step F10, otherwise, judge The objective function value of the last adaptive approximation Is the absolute value of the difference less than the precision tol 2 If yes, the convergence condition is met, and the control strategy of this iteration is converted into the motor control command output. Otherwise, the convergence is not satisfied, and the number of approximations k is set. 2 :=k 2+1, continue to execute step F3 until the approximation convergence judgment module is satisfied.

[0228] For each algorithm module in the multiple shooting method, reference can be made to the corresponding part in the foregoing text.

[0229] Finally, DCS converts the control strategy obtained by the adaptive multiple shooting method into control instructions for the motor, and sends them to the motor controller through the fieldbus network, enabling the execution motor to perform corresponding actions. At the same time, the position sensor is used to collect the position information of the container in real time and send it back to DCS, enabling the control room engineer to keep track of the loading and unloading process at any time.

[0230] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the inventive concept, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. An optimal control method for a container crane based on a multiple shooting method, characterized by the following steps: include: (a) The operator specifies the starting and ending positions of the container, the performance indicators and control constraints of the loading and unloading process; (ii) Adopting the adaptive multiple-targeting method to obtain the control strategy that optimizes the performance indicators of the loading and unloading process; (3) converting the control strategy into control instructions for the motor of the container crane, and executing the motor to perform corresponding actions according to the received control instructions; The mathematical model derivation process of the control strategy is: The loading and unloading process of the quay crane container is described as: in: t represents time, u(t) represents the control vector of the loading and unloading process; x(t) represents the status information of the loading and unloading process; f is a set of differential equations based on the physics of the crane; The problem Q of optimizing the performance index of container loading and unloading process is expressed as: x(t0)=x0 x(t f )=x f C(x(t),u(t),t)≤0 in: t0 represents the starting time of the loading and unloading process, t f Indicates the end time of the loading and unloading process. J represents the objective function to be minimized. L represents a function related to the state vector, control vector and time, u and denote the lower and upper bounds of the control vector u(t), respectively. C is the inequality constraint, x0 is the initial state, x f t f The state of the moment; Problem Q is essentially an optimal control problem; In step (ii), the multiple shooting method is used to solve the problem Q. The loading and unloading process is divided into multiple sub-time intervals according to the time interval. In each sub-time interval, a polynomial function is used to approximate the state variables and control variables. The specific steps include: 2.1) Collect the starting and ending positions of the containers in step (i), the performance indicators of the loading and unloading process, and the control constraints; 2.2) Make the following settings: Use piecewise constant parameterization for the control vector; Parameterize the initial state of each segment; Set the number of segments N of the loading and unloading process, and the control grid corresponding to any segment is Initial guess for the parameterization vector of the control strategy The initial state guess value of each loading and unloading process k1 represents the number of iterations, k2 represents the number of approximations; Set the calculation accuracy tol1 of the nonlinear programming NLP problem and the convergence accuracy tol2 of the adaptive approximation; Set the number of iterations k1 and the number of approximations k2 to zero; 2.3) When k2 = 0, execute step 2.4); otherwise, Through the adaptive approximation method, the control grid Perform adaptive approximation processing to obtain the grid nodes to be optimized New Control Grid and its corresponding parameterized vector Then execute step 2.4); 2.4) Obtain the status information of this iteration through the problem discretization method and the objective function value 2.5) Obtain the gradient information of this iteration through gradient calculation When k1=0, skip step 2.6) and directly execute step 2.7); otherwise, execute step 2.6); 2.6) NLP convergence judgment: if The objective function value of the previous iteration If the absolute value of the difference is less than the precision tol1, the convergence condition is met and step 2.9 is executed; If convergence is not satisfied, continue to step 2.7); 2.7) Use The value of The value of and increase the number of iterations by 1; 2.8) Using the objective function value and gradient information obtained in steps 2.4) and 2.5, the optimization direction and optimization step length are calculated to obtain the ratio New and better control strategy After this step is completed, jump to step 2.4 again); 2.9) Approximation convergence judgment: remember When k2=0, execute step 2.1); otherwise, judge The objective function value of the last adaptive approximation Is the absolute value of the difference less than the precision tol2? If yes, the convergence condition is met, and the control strategy of this iteration is converted into the motor control command output; otherwise, If the convergence is not satisfied, set the number of approximations k2:=k2+1 and continue to execute step 2.3) until the approximation convergence is satisfied.

2. The optimal control method for container crane based on multiple targeting method according to claim 1 is characterized in that The adaptive approximation method of step 2.3) comprises the steps of: 2.3.1) Calculate the left slope at the grid node by the following formula: and the right slope Among them, u k represents the parameters of the control strategy on the kth segment, τ k Indicates u k and u k+1 The mesh nodes between; 2.3.2) When the grid node τ k The right slope at and the grid node τ k+1 The left slope at satisfy Among them, ε s is a positive real number, if Then select the grid node τ k As the node to be optimized; if Then select the grid node τ k+1 As the node to be optimized; 2.3.3) If the grid node τ k If the left and right slopes of the node meet the following requirements, the node is removed from the grid: Among them, ε e is a small positive real number; the grid node τ k After elimination, u k and u k+1 The corresponding grids are merged into a new grid, and the parameters on it are updated as (u k +u k+1 ) / 2; 2.3.4) If the grid node τ k The left slope at satisfies: Among them, ε i is a value greater than ε e positive real number, then in [τ k-1 ,τ k ] inserts a grid node; if the grid node τ k The right slope at satisfies: Then in [τ k-1 ,τ k ] to insert a grid node; 2.3.5) Generate a new control mesh and corresponding parameterization vectors based on the nodes removed and inserted in steps 2.3.3) and 2.3.4).

3. The optimal control method for container crane based on multiple targeting method according to claim 1 is characterized in that In step 2.4), the control variable u(t) is expressed by a linear combination of the piecewise constant function and the state trajectory x(t) by the M-order Lagrange interpolation basis function, that is: u(t)≈u i i=1,2,...,N (9) Where: t represents time, N represents the time interval [t0,t f ] to discretize the number of segments, is the Lagrange interpolation basis function, u i is the discrete parameter of the control vector u(t) in the i-th segment, and the linear combination coefficient s i,j is x(t) at the Gaussian collocation point t i,j The value on In the multiple-targeting method, the initial state of each segment is also discretized: x(t i )=z i ,i=1,…,N-1 (11) where t i is the end time node of the i-th segment, z i t i The state of moment parameterization; Since the derivative expressions of all basis functions are known, the derivative of formula (10) is: Where f is a set of differential equations describing the motion process; Discretize the differential equations of the state trajectory into algebraic equations: The objective function and constraints are expressed as u i 、z i and i,j By performing discrete expression, we can obtain the NLP problem to be solved: Where J is the objective function, X represents the parameters of the discrete state vector at the configuration point, and Z0 is the sum of all z i The parameters of the composition, U represents all u i The parameters of the composition, C E and C I represent equality constraints and inequality constraints respectively.

4. The optimal control method for container crane based on multiple targeting method according to claim 1 is characterized in that In step 2.5), the steps of gradient calculation are: Formula (13) can be written as follows: F(X,U,Z0)=0 (15) Where F is the set of all equations; perform first-order Taylor expansion on equation (15): The first-order sensitivity information is calculated by formula (16): The first-order gradient information is obtained through the first-order sensitivity information: First-order sensitivity information The gradient information of Z0 is also obtained using the same method.

5. The optimal control method for container crane based on multiple targeting method according to claim 1 is characterized in that In step 2.6), the following steps are used: 2.6.1) If The objective function value of the previous iteration If the absolute value difference of is less than the precision tol1, the convergence condition is met, and the control strategy of this iteration is converted into the control command output of the motor; if the convergence condition is not met, continue to step 2.6.2); 2.6.2) Use The value of The value of and increase the number of iterations k1 by 1; 2.6.3) Control strategy As a point in the vector space, denoted as P1, the objective function value corresponding to P1 is 2.6.4) Starting from point P1, according to the selected NLP algorithm and the gradient information at point P1 Constructing an optimal direction in vector space And Xun Uber 2.6.5) Pass-through Construct the corresponding vector space Another point P2, so that the objective function value corresponding to P2 Compare Better, where I is Vectors of the same dimension.

6. An optimal control system for container crane based on multiple shooting method, characterized by include: Executing motors, position sensors, fieldbus networks, DCS, container position information display devices in the main control room, and motor controllers; The optimal control method for a container crane based on a multiple targeting method as described in any one of claims 1 to 5 is integrated in the DCS; The operation process of the optimal control system includes: Step A1: Engineers in the control room specify the starting and ending locations of the containers, the performance indicators of the loading and unloading process, and the control constraints; Step A2: DCS executes the internal multiple shooting method to obtain the control strategy that optimizes the performance index of the container loading and unloading process; Step A3: The DCS converts the control strategy into a control instruction for the execution motor, and sends it to the corresponding motor controller through the fieldbus network, so that the execution motor performs the corresponding action according to the received control instruction; Step A4: The position sensor collects the real-time position information of the container, sends it back to the DCS via the field bus network, and displays it on the container position information display device, so that the control room engineer can grasp the loading and unloading process at any time.

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