CN107857196A - A kind of bridge-type container crane swings optimal control system - Google Patents

Abstract

The invention discloses an optimal swing control system for a bridge-type container crane. Motor controller composition. The engineer in the control room specifies the location and loading and unloading time of the container, and the DCS executes the internal optimal control algorithm to output the control strategy that minimizes the swing energy of the container loading and unloading, and converts it into a control command for the traction motor, which is sent to The traction motor controller, the motor controller outputs the control value through the analog-to-digital converter to make the traction motor perform corresponding actions. At the same time, the position sensor collects the position information of the container in real time and sends it back to the control room, so that the engineer can grasp the loading and unloading process at any time. The invention can minimize the swing of the container during loading and unloading, thereby improving the safety and efficiency of container loading and unloading at the port.

Description

An Optimal Swing Control System for Bridge Container Crane

technical field

The invention relates to the field of bridge crane control, and mainly relates to an optimal swing control system of a bridge container crane. It can automatically control the loading and unloading of the bridge container crane to minimize the swing energy of the container during the moving process, so as to improve the safety and efficiency of container loading and unloading in the port.

Background technique

The handling of containers is critical to port operations. However, with the high speed of loading and unloading, when the container arrives at the designated position, the residual swing of the load due to the acceleration and deceleration of the crane, the lifting action of the load, and the disturbance caused by wind and friction also increases, which not only reduces the handling accuracy, It slows down the speed of handling and increases the possibility of accidents. As the main equipment for loading and unloading container ships in the port, the bridge side container crane's control strategy has an important impact on the safe and efficient loading and unloading of containers. Therefore, it is of great significance to automatically optimize the swing control of the bridge container crane according to specific parameters and operating requirements.

At present, the optimal control theory and corresponding methods are rarely used in the control methods of domestic bridge cranes. The parameters in the controller are often set according to the existing experience, and the loading and unloading efficiency and safety need to be further improved. After adopting the optimal control method, the control quality and safety of the bridge crane can be guaranteed, and the loading and unloading efficiency can be further improved.

Contents of the invention

In order to improve the efficiency of port container loading and unloading, the present invention provides an optimal swing control system for bridge container cranes.

The object of the present invention is achieved through the following technical solutions: an optimal control system for the swing of a bridge container crane, which can automatically control the loading and unloading of the bridge container crane, so that the swing energy of the container is minimized during the movement, so as to increase the port height of the container. Safety and efficiency of loading and unloading. It is composed of traction motor, container position sensor, analog-to-digital converter, digital-to-analog converter, field bus network, distributed control system (DCS), control room display, and traction motor controller. The operating process of the control system includes:

Step 1): The engineer in the control room specifies the location coordinates that the container needs to reach, the time limit of the loading and unloading process, and the performance parameter constraints of the traction motor;

Step 2): DCS executes the internal optimal control algorithm to obtain the traction motor speed control strategy that minimizes the swing angle during container loading and unloading;

Step 3): The DCS converts the obtained motor speed control strategy into the control command of the traction motor, and sends it to the digital-to-analog converter in the front section of the traction motor controller through the field bus network, so that the traction motor controller controls the traction motor according to the received control command. The motor performs the corresponding action;

Step 4): The container position sensor collects the position information of the container in real time, and sends it back to DCS through the field bus network after analog-to-digital conversion, and displays it in the main control room, so that engineers can monitor the loading and unloading process at any time.

The DCS includes an information collection module, an initialization module, a fast solution module for differential algebraic equations (Ordinarydifferential equations, ODE for short), a gradient solution module, a nonlinear programming problem solution module, and a control instruction output module. The information acquisition module includes three sub-modules: container position acquisition, traction motor performance constraint acquisition, and loading and unloading time setting acquisition. There are four sub-modules for optimization correction and NLP convergence judgment.

The model of the loading and unloading process of the port container crane can be described as:

Among them, t represents time, u(t) represents the velocity vector composed of velocity components in various directions; x(t) represents the status information of the loading and unloading process; F(x(t),u(t),t) is according to the A system of differential equations established by the principles of physics. It can be seen from the description that the loading and unloading process of the container can be expressed by a set of differential equations in mathematics.

The control objective of this system is to minimize the swing energy of the container during loading and unloading, so the objective function is expressed as:

Among them, t ₀ represents the starting time of the loading and unloading process, t _f represents the final value time of the loading and unloading process specified by the engineer in the control room, J represents the objective function, L ₀ (x(t),u(t),t) represents the container loading and unloading process The swing angle function in the objective function in .

At the same time, the overhead container crane is affected by the performance parameters of the traction motor and the container moves to meet the position requirements, there are constraints, and its function is expressed as:

Among them, E(x(t), u(t), t) represents the container reach position constraint function, and G(x(t), u(t), t) represents the traction motor performance parameter constraint function. Therefore, the minimum swing energy control problem of the bridge container crane can be finally expressed as:

The technical scheme adopted by the present invention to solve the technical problem is: an optimal control algorithm is integrated in a distributed control system (DCS), and an optimal control system is constructed on the basis of this.

The complete structure of the control system includes a container position sensor 21, an analog-to-digital converter 22, a field bus network 23, a DCS 24, a control room display 25, a digital-to-analog converter 26, a traction motor controller 27, and a traction motor 28.

The operating process of the system includes:

Step 1): The engineer in the control room specifies the location coordinates that the container needs to reach, the time limit of the loading and unloading process, and the performance parameter constraints of the traction motor;

Step 2): DCS executes the internal optimal control algorithm to obtain the traction motor speed control strategy that minimizes the swing energy during container loading and unloading;

Step 3): The DCS converts the obtained motor speed control strategy into the control command of the traction motor, and sends it to the digital-to-analog converter in the front section of the traction motor controller through the field bus network, so that the traction motor controller controls the traction motor according to the received control command. The motor performs the corresponding action;

Step 4): The container position sensor collects the position information of the container in real time, and sends it back to DCS through the field bus network after analog-to-digital conversion, and displays it in the main control room, so that engineers can monitor the loading and unloading process at any time.

The DCS includes an information collection module, an initialization module, an ODE solution module, a gradient calculation module, an NLP problem solution module, and a control instruction output module. Among them, the information collection module includes three sub-modules of container starting and ending position collection, performance index collection, and speed control constraint collection. The NLP problem solving module includes three sub-modules: optimization direction calculation, optimization step calculation, and NLP convergence judgment.

The DCS includes an information collection module, an initialization module, an ODE fast solution module, a gradient solution module, a nonlinear programming problem solution module, and a control instruction output module. Among them, the information collection module includes three sub-modules: container position collection, traction motor performance constraint collection, loading and unloading time setting collection, and the NLP problem solving module includes four sub-modules: optimization direction solution, optimization step size solution, optimization correction, and NLP convergence judgment .

The DCS executes an internal optimal control algorithm to obtain a traction motor speed control strategy that minimizes the swing angle of the container loading and unloading process, and the operation steps are as follows:

Step 1): the information collection module 31 acquires the initial position of the container and the arrival position specified by the engineer, the performance constraints of the traction motor and the setting of loading and unloading time;

Step 2): The initialization module 32 starts to run, adopts segment constant parameterization, sets the segment number NE of the loading and unloading process, the initial guess value u ^(k) of the parameterized vector of the traction motor control variable, sets the calculation accuracy tol, and sets The number of iterations k is set to zero;

Step 3): Obtain the state information x ^(k) (t) and the objective function value J ^(k) of this iteration through the ODE fast solution module 33 .

Step 4): obtain this iterative objective function gradient information dJ ^(k) and constraint condition gradient information g ^(k) by gradient solving module 34; Skip step 5) when k=0) and directly execute step 7);

Step 5): The NLP problem solving module 35 runs, and the convergence judgment is performed by the NLP convergence judgment module. If the absolute value of the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration If the value difference is less than the precision tol, it is judged that the convergence is satisfied, and the traction motor speed control strategy of this iteration is converted into the control command output of the motor; if the convergence is not satisfied, then continue to perform step 6);

Step 6): Cover the last iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and add 1 to the number of iterations k;

Step 7): The NLP problem solving module 35 uses the objective function value and gradient information obtained in steps 3) and 4) to solve the optimization direction and the optimization step size, and perform optimization correction to obtain the ratio u ^{(k-1 )} A better new speed control strategy u ^(k) . After this step is executed, jump to step 3) again until the NLP convergence judgment module is satisfied.

The described ODE fast solution module adopts the fourth-level fifth-order Runge-Kutta method, and the solution formula is:

Among them, t represents the time, t _i represents the integration time selected by the Runge-Kutta method, h is the integration step size, F(·) is the function describing the state differential equation, K ₁ , K ₂ , K ₃ , K ₄ represent The function values of the four nodes in the integration process of the Runge-Kutta method, x ^(k) (t _i ) represents the state information of the container at the time t _i in the k iteration,

The gradient solving module adopts the sensitivity trajectory equation method:

Step 1): Define the sensitivity trajectory equation Γ ^(k) (t) of the kth iteration as:

The solution formula of Γ ^(k) (t) is:

where t represents time, Indicates the derivative of the sensitivity trajectory equation with respect to time t in the kth iteration, F(u ^(k) ,x ^(k) (t),t) is a function describing the state differential equation, Γ ^(k) (t ₀ ) represents the sensitivity The initial moment state value of the trajectory equation at the kth iteration, x ₀ represents the initial moment state value of the state differential equation function.

Step 2): Using the fourth-level and fifth-order Runge-Kutta method to solve the value of the sensitivity trajectory equation Γ ^(k) (t) at each integration time, the solution formula is:

Among them, t represents the time, t _i represents a certain time point in the control process selected by the Runge-Kutta method, h is the integral step size, x ^(k) (t _i ) represents the container at the time t _i in the k iteration The state information of , S(·) is the function describing the sensitivity equation, Q ₁ , Q ₂ , Q ₃ , Q ₄ respectively represent the function values of the four nodes in the integration process of the Runge-Kutta method.

Step 3): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information dJ ^(k) of the objective function:

Among them, Φ ₀ (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the objective function, and L ₀ (u ^(k) ,x ^(k) (t),t) represents the objective function integral item.

Step 4): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information g ^(k) of the constraints:

Among them, Φ _j (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the jth constraint function, L _j (u ^(k) ,x ^(k) (t),t ) represents the integral term of the jth constraint function, and m represents the number of constraints.

Described NLP problem solving module adopts the following steps to realize:

Step 1): If the absolute value difference between the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration is less than the accuracy tol, it is judged that the convergence is satisfied, and this iteration The speed control strategy of the traction motor is converted into the control command output of the traction motor; if the convergence is not satisfied, continue to perform step 2);

Step 2): Cover the last iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and increase the number of iterations k by 1;

Step 3): take the motor speed control strategy u ^(k-1) as a certain point in the vector space, denoted as P ₁ , and the corresponding objective function value of P ₁ is J ^(k-1) ;

Step 4): Starting from point P ₁ , according to the selected NLP algorithm and the gradient information dJ ^(k-1) of the objective function at point P ₁ and the gradient information g ^(k-1) of constraints, construct a search vector space Optimal direction d ^(k-1) and step size α ^(k-1) ;

Step 5): Construct another point P ₂ corresponding to u ^(k) in the vector space through the formula u ^(k) =u ^(k-1) +α ^(k-1) d ^(k-1) ;

Step 6): Using optimization correction to obtain another point P ₃ corresponding to u ^(k) in the vector space, so that the objective function value J ^(k) corresponding to P ₃ is better than J ^(k-1) .

The beneficial effects of the present invention are mainly manifested in that the optimal control system for the swing of the bridge container crane based on the control vector parameterization method can calculate the optimal control strategy of the bridge container crane. The fourth-order and fifth-order Runge-Kutta method is used to solve the sensitivity trajectory equations, and more accurate results can be obtained. The solution method of the gradient information of the problem is given, which can speed up the convergence speed of the problem and reduce the calculation time of the optimal strategy for the swing of the bridge container crane. The invention can realize the minimum swing energy in the container loading and unloading process of the bridge type container crane, and improve the safety and efficiency of container loading and unloading at port heights.

Description of drawings

Fig. 1 is a functional schematic diagram of the present invention;

Fig. 2 is a structural representation of the present invention;

Fig. 3 is a DCS internal module structure diagram of the present invention;

Fig. 4 is the traction motor speed control strategy figure obtained to embodiment 1;

Fig. 5 is a diagram of container swing angle changes corresponding to the traction motor speed control strategy in Fig. 4 .

Detailed ways

As shown in Figure 1, the model of the loading and unloading process of the port container set crane can be described as:

Among them, t represents time, u(t) represents the velocity vector composed of velocity components in various directions; x(t) represents the status information of the loading and unloading process; F(x(t),u(t),t) is according to the A system of differential equations established by the principles of physics. It can be seen from the description that the loading and unloading process of the container can be expressed by a set of differential equations in mathematics.

The control objective of this system is to minimize the swing energy of the container during loading and unloading, so the objective function is expressed as:

Among them, t ₀ represents the starting time of the loading and unloading process, t _f represents the final value time of the loading and unloading process specified by the engineer in the control room, J represents the objective function, L ₀ (x(t),u(t),t) represents the container loading and unloading process The swing angle function in the objective function in .

At the same time, the overhead container crane is affected by the performance parameters of the traction motor and the container moves to meet the position requirements, there are constraints, and its function is expressed as:

Among them, E(x(t), u(t), t) represents the container reach position constraint function, and G(x(t), u(t), t) represents the traction motor performance parameter constraint function. Therefore, the minimum swing energy control problem of the bridge container crane can be finally expressed as:

The technical scheme adopted by the present invention to solve the technical problem is: an optimal control algorithm is integrated in a distributed control system (DCS), and an optimal control system is constructed on the basis of this.

The complete structure of the control system is shown in Figure 2, including container position sensor 21, analog-to-digital converter 22, fieldbus network 23, DCS24, control room display 25, digital-to-analog converter 26, traction motor controller 27, Traction motor 28.

The operating process of the system includes:

Step 1): The engineer in the control room specifies the location coordinates that the container needs to reach, the time limit of the loading and unloading process, and the performance parameter constraints of the traction motor;

Step 2): DCS executes the internal optimal control algorithm to obtain the traction motor speed control strategy that minimizes the swing energy during container loading and unloading;

Step 3): The DCS converts the obtained motor speed control strategy into the control command of the traction motor, and sends it to the digital-to-analog converter in the front section of the traction motor controller through the field bus network, so that the traction motor controller controls the traction motor according to the received control command. The motor performs the corresponding action;

Step 4): The container position sensor collects the position information of the container in real time, and sends it back to DCS through the field bus network after analog-to-digital conversion, and displays it in the main control room, so that engineers can monitor the loading and unloading process at any time.

The DCS includes an information collection module, an initialization module, an ODE solution module, a gradient calculation module, an NLP problem solution module, and a control instruction output module. Among them, the information collection module includes three sub-modules of container starting and ending position collection, performance index collection, and speed control constraint collection. The NLP problem solving module includes three sub-modules: optimization direction calculation, optimization step calculation, and NLP convergence judgment.

The DCS includes an information collection module, an initialization module, an ODE fast solution module, a gradient solution module, a nonlinear programming problem solution module, and a control command output module. Among them, the information collection module includes three sub-modules: container position collection, traction motor performance constraint collection, loading and unloading time setting collection, and the NLP problem solving module includes four sub-modules: optimization direction solution, optimization step size solution, optimization correction, and NLP convergence judgment .

The DCS executes an internal optimal control algorithm to obtain a traction motor speed control strategy that minimizes the swing angle of the container loading and unloading process, and the operation steps are as follows:

Step 1): the information collection module 31 acquires the initial position of the container and the arrival position specified by the engineer, the performance constraints of the traction motor and the setting of loading and unloading time;

Step 2): The initialization module 32 starts to run, adopts segment constant parameterization, sets the segment number NE of the loading and unloading process, the initial guess value u ^(k) of the parameterized vector of the traction motor control variable, sets the calculation accuracy tol, and sets The number of iterations k is set to zero;

Step 3): Obtain the state information x ^(k) (t) and the objective function value J ^(k) of this iteration through the ODE fast solution module 33 .

Step 4): obtain this iterative objective function gradient information dJ ^(k) and constraint condition gradient information g ^(k) by gradient solving module 34; Skip step 5) when k=0) and directly execute step 7);

Step 5): The NLP problem solving module 35 runs, and the convergence judgment is performed by the NLP convergence judgment module. If the absolute value of the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration If the value difference is less than the precision tol, it is judged that the convergence is satisfied, and the traction motor speed control strategy of this iteration is converted into the control command output of the motor; if the convergence is not satisfied, then continue to perform step 6);

Step 6): Cover the last iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and add 1 to the number of iterations k;

Step 7): The NLP problem solving module 35 uses the objective function value and gradient information obtained in steps 3) and 4) to solve the optimization direction and the optimization step size, and perform optimization correction to obtain the ratio u ^{(k-1 )} A better new speed control strategy u ^(k) . After this step is executed, jump to step 3) again until the NLP convergence judgment module is satisfied.

The described ODE fast solution module adopts the fourth-level fifth-order Runge-Kutta method, and the solution formula is:

Among them, t represents the time, t _i represents the integration time selected by the Runge-Kutta method, h is the integration step size, F(·) is the function describing the state differential equation, K ₁ , K ₂ , K ₃ , K ₄ represent The function values of the four nodes in the integration process of the Runge-Kutta method, x ^(k) (t _i ) represents the state information of the container at the time t _i in the k iteration,

The gradient solving module adopts the sensitivity trajectory equation method:

Step 1): Define the sensitivity trajectory equation Γ ^(k) (t) of the kth iteration as:

The solution formula of Γ ^(k) (t) is:

where t represents time, Indicates the derivative of the sensitivity trajectory equation with respect to time t in the kth iteration, F(u ^(k) ,x ^(k) (t),t) is a function describing the state differential equation, Γ ^(k) (t ₀ ) represents the sensitivity The initial moment state value of the trajectory equation at the kth iteration, x ₀ represents the initial moment state value of the state differential equation function.

Step 2): Using the fourth-level and fifth-order Runge-Kutta method to solve the value of the sensitivity trajectory equation Γ ^(k) (t) at each integration time, the solution formula is:

Among them, t represents the time, t _i represents a certain time point in the control process selected by the Runge-Kutta method, h is the integral step size, x ^(k) (t _i ) represents the container at the time t _i in the k iteration The state information of , S(·) is the function describing the sensitivity equation, Q ₁ , Q ₂ , Q ₃ , Q ₄ respectively represent the function values of the four nodes in the integration process of the Runge-Kutta method.

Step 3): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information dJ ^(k) of the objective function:

Among them, Φ ₀ (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the objective function, and L ₀ (u ^(k) ,x ^(k) (t),t) represents the objective function integral item.

Step 4): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information g ^(k) of the constraints:

Among them, Φ _j (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the jth constraint function, L _j (u ^(k) ,x ^(k) (t),t ) represents the integral term of the jth constraint function, and m represents the number of constraints.

Described NLP problem solving module adopts the following steps to realize:

Step 1): If the absolute value difference between the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration is less than the accuracy tol, it is judged that the convergence is satisfied, and this iteration The speed control strategy of the traction motor is converted into the control command output of the traction motor; if the convergence is not satisfied, continue to perform step 2);

Step 2): Cover the last iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and increase the number of iterations k by 1;

Step 3): take the motor speed control strategy u ^(k-1) as a certain point in the vector space, denoted as P ₁ , and the corresponding objective function value of P ₁ is J ^(k-1) ;

Step 4): Starting from point P ₁ , according to the selected NLP algorithm and the gradient information dJ ^(k-1) of the objective function at point P ₁ and the gradient information g ^(k-1) of constraints, construct a search vector space Optimal direction d ^(k-1) and step size α ^(k-1) ;

Step 5): Construct another point P ₂ corresponding to u ^(k) in the vector space through the formula u ^(k) =u ^(k-1) +α ^(k-1) d ^(k-1) ;

Step 6): Using optimization correction to obtain another point P ₃ corresponding to u ^(k) in the vector space, so that the objective function value J ^(k) corresponding to P ₃ is better than J ^(k-1) .

Example 1

Using bridge crane to load and unload the container from the freighter to the transfer truck at the terminal within the specified time range, the swing energy of the container is required to be the minimum during the loading and unloading process. Combined with the performance constraints of the crane, the mathematical model of this problem is obtained as follows:

where J represents the swing energy objective function of the container to be minimized, x ₁ (t) represents the horizontal position of the container, x ₂ (t) represents the vertical position of the container, x ₃ (t) represents the swing angle of the container, and x ₄ (t) represents the horizontal speed of the crane, x ₅ (t) is the vertical speed of the crane, x ₆ (t) is the swing angular velocity of the container, u ₁ (t) and u ₂ (t) represent the speed of the crane in the horizontal and vertical directions Control amount. In Example 1, the engineer in the control room requires the container to move from position (0,22) to (10,14) within 10 seconds. In order to obtain the traction motor speed control strategy that minimizes the objective function, the DCS runs the optimal control algorithm, Its operation process is shown in Figure 3, and the execution steps are as follows:

Step 1): The engineer in the control room sets the initial position x(t ₀ )=[0,22,0,0,0,0] of the container, and the designated arrival position x(t _f )=[10,14,0,0, 0,0], loading and unloading time setting t _f =10 and traction motor performance constraints -2.5≤x ₄ (t)≤2.5, -1≤x ₅ (t)≤1, -2.83374≤u ₁ (t)≤2.83374 , -0.80865≤u ₂ (t)≤0.71265 input information collection module 31;

Step 2): The initialization module 32 starts to run, adopts segment constant parameterization, sets the segment number of the loading and unloading process as NE=50, and the initial guess value u ^(k) of the parameterization vector of the traction motor control variable is 0.5, sets The calculation accuracy tol is 10 ^-4 , and the number of iterations k is set to zero;

Step 3): Obtain the state information x ^(k) (t) and the objective function value J ^(k) of this iteration through the ODE fast solution module 33 .

Step 4): obtain this iterative objective function gradient information dJ ^(k) and constraint condition gradient information g ^(k) by gradient solving module 34; Skip step 5) when k=0) and directly execute step 7);

Step 5): The NLP problem solving module 35 runs, and the convergence judgment is performed by the NLP convergence judgment module. If the absolute value of the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration If the value difference is less than the accuracy of 10 ^-4 , it is judged that the convergence is satisfied, and the traction motor speed control strategy of this iteration is converted into the motor control command output; if the convergence is not satisfied, continue to step 6);

Step 6): Cover the last iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and add 1 to the number of iterations k;

Step 7): The NLP problem solving module 35 uses the objective function value and gradient information obtained in steps 3) and 4) to solve the optimization direction and the optimization step size, and perform optimization correction to obtain the ratio u ^{(k-1 )} A better new speed control strategy u ^(k) . After this step is executed, jump to step 3) again until the NLP convergence judgment module is satisfied.

The described ODE fast solution module adopts the fourth-level fifth-order Runge-Kutta method, and the solution formula is:

Among them, t represents time, t _i represents a certain time point in the control process selected by the Runge-Kutta method, x ^(k) (t _i ) represents the state information of the container at the time t _i in the k iteration, F( ) is a function describing the state differential equation, K ₁ , K ₂ , K ₃ , and K ₄ respectively represent the function values of the four nodes in the integration process of the Runge-Kutta method, and the formula for determining the integration step size h is:

t _i+1 represents the next time node of t _i in the selection control process of the Runge-Kutta method.

The gradient solving module adopts the sensitivity trajectory equation method:

Step 1): Define the sensitivity trajectory equation Γ ^(k) (t) of the kth iteration as:

The solution formula of Γ ^(k) (t) is:

where t represents time, Indicates the derivative of the sensitivity trajectory equation with respect to time t in the kth iteration, F(u ^(k) ,x ^(k) (t),t) is a function describing the state differential equation, Γ ^(k) (t ₀ ) represents the sensitivity The initial moment state value of the trajectory equation at the kth iteration, x ₀ represents the initial moment state value of the state differential equation function.

Step 2): Using the fourth-level and fifth-order Runge-Kutta method to solve the value of the sensitivity trajectory equation Γ ^(k) (t) at each integration time, the solution formula is:

Among them, t represents the time, t _i represents a certain time point in the control process selected by the Runge-Kutta method, h is the integral step size, x ^(k) (t _i ) represents the container at the time t _i in the k iteration The state information of , S(·) is the function describing the sensitivity equation, Q ₁ , Q ₂ , Q ₃ , Q ₄ respectively represent the function values of the four nodes in the integration process of the Runge-Kutta method.

Step 3): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information dJ ^(k) of the objective function:

Among them, Φ ₀ (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the objective function, and L ₀ (u ^(k) ,x ^(k) (t),t) represents the objective function integral item.

Step 4): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information g ^(k) of the constraints:

Among them, Φ _j (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the jth constraint function, L _j (u ^(k) ,x ^(k) (t),t ) represents the integral term of the jth constraint function, and m represents the number of constraints.

Described NLP problem solving module adopts the following steps to realize:

Step 1): If the absolute value difference between the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration is less than the accuracy tol, it is judged that the convergence is satisfied, and this iteration The speed control strategy of the traction motor is converted into the control command output of the traction motor; if the convergence is not satisfied, continue to perform step 2);

Step 2): Cover the last iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and increase the number of iterations k by 1;

Step 3): take the motor speed control strategy u ^(k-1) as a certain point in the vector space, denoted as P ₁ , and the corresponding objective function value of P ₁ is J ^(k-1) ;

Step 4): Starting from point P ₁ , according to the selected NLP algorithm and the gradient information dJ ^(k-1) of the objective function at point P ₁ and the gradient information g ^(k-1) of constraints, construct a search vector space Optimal direction d ^(k-1) and step size α ^(k-1) ;

Step 5): Construct another point P ₂ corresponding to u ^(k) in the vector space through the formula u ^(k) =u ^(k-1) +α ^(k-1) d ^(k-1) ;

Step 6): Using optimization correction to obtain another point P ₃ corresponding to u ^(k) in the vector space, so that the objective function value J ^(k) corresponding to P ₃ is better than J ^(k-1) .

Finally, DCS converts the speed control strategy obtained through the continuous rapid response method into motor control instructions, and sends them to the motor controller through the field bus network to make the execution motor perform corresponding actions. To DCS, so that the control room engineer can grasp the loading and unloading process at any time.

The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be assumed that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field of the present invention, without departing from the concept of the invention, some simple deduction or replacement can also be made, which should be regarded as belonging to the protection scope of the present invention.

Claims (1)

1. An optimal control system for the swinging of a bridge-type container crane, which can automatically control the loading and unloading of the bridge-type container crane, so as to minimize the swing energy of the container during the moving process, so as to improve the safety and efficiency of container loading and unloading at the port. It is characterized in that it is composed of a traction motor, a container position sensor, an analog-to-digital converter, a digital-to-analog converter, a field bus network, a distributed control system (DCS), a display in a control room, and a traction motor controller. The operating process of the control system includes: Step 1): The engineer in the control room specifies the location coordinates that the container needs to reach, the time limit of the loading and unloading process, and the performance parameter constraints of the traction motor; Step 2): DCS executes the internal optimal control algorithm to obtain the traction motor speed control strategy that minimizes the swing angle during container loading and unloading; Step 3): The DCS converts the obtained motor speed control strategy into the control command of the traction motor, and sends it to the digital-to-analog converter in the front section of the traction motor controller through the field bus network, so that the traction motor controller controls the traction motor according to the received control command. The motor performs the corresponding action; Step 4): The container position sensor collects the position information of the container in real time, and sends it back to DCS through the field bus network after analog-to-digital conversion, and displays it in the main control room, so that engineers can monitor the loading and unloading process at any time. The DCS includes an information collection module, an initialization module, a fast solution module for differential algebraic equations (Ordinarydifferential equations, ODE for short), a gradient solution module, a nonlinear programming problem solution module, and a control command output module. The information acquisition module includes three sub-modules: container position acquisition, traction motor performance constraint acquisition, and loading and unloading time setting acquisition. There are four sub-modules for optimization correction and NLP convergence judgment. The DCS implements an internal optimal control algorithm to obtain a traction motor speed control strategy that minimizes the swing energy in the container loading and unloading process, and the operation steps are as follows: Step 1): the information collection module 31 acquires the initial position of the container and the arrival position specified by the engineer, the performance constraints of the traction motor and the setting of loading and unloading time; Step 2): The initialization module 32 starts to run, adopts segment constant parameterization, sets the segment number NE of the loading and unloading process, the initial guess value u ^(k) of the parameterization vector of the traction motor control variable, sets the calculation accuracy tol, and sets The number of iterations k is set to zero; Step 3): Obtain the state information x ^(k) (t) and the objective function value J ^(k) of this iteration through the ODE fast solution module 33 . Step 4): obtain this iterative objective function gradient information dJ ^(k) and constraint condition gradient information g ^(k) by gradient solving module 34; Skip step 5) when k=0) and directly execute step 7); Step 5): The NLP problem solving module 35 runs, and the convergence judgment is performed by the NLP convergence judgment module. If the absolute value of the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration If the value difference is less than the precision tol, it is judged that the convergence is satisfied, and the traction motor speed control strategy of this iteration is converted into the control command output of the motor; if the convergence is not satisfied, then continue to perform step 6); Step 6): Overwrite the previous iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and add 1 to the number of iterations k; Step 7): The NLP problem solving module 35 uses the objective function value and gradient information obtained in steps 3) and 4) to solve the optimization direction and the optimization step size, and perform optimization correction to obtain the ratio u ^{(k-1 )} A better new speed control strategy u ^(k) . After this step is executed, jump to step 3) again until the NLP convergence judgment module is satisfied. The described ODE fast solution module adopts the fourth-level fifth-order Runge-Kutta method, and the solution formula is: <mrow><mtable><mtr><mtd><mrow><msub><mi>K</mi><mn>1</mn></msub><mo>=</mo><mi>F</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>K</mi><mn>2</mn></msub><mo>=</mo><mi>F</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><mi>h</mi><mo>/</mo><mn>2</mn><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>/</mo><mn>2</mn><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>K</mi><mn>3</mn></msub><mo>=</mo><mi>F</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><msub><mi>K</mi><mn>2</mn></msub><mi>h</mi><mo>/</mo><mn>2</mn><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>/</mo><mn>2</mn><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>K</mi><mn>4</mn></msub><mo>=</mo><mi>F</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><msub><mi>K</mi><mn>3</mn></msub><mi>h</mi><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><mfrac><mi>h</mi><mn>6</mn></mfrac><mrow><mo>(</mo><msub><mi>K</mi><mn>1</mn></msub><mo>+</mo><mn>2</mn><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><mn>2</mn><msub><mi>K</mi><mn>3</mn></msub><mo>+</mo><msub><mi>K</mi><mn>4</mn></msub><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow> Among them, t represents the time, t _i represents the integration time selected by the Runge-Kutta method, h is the integration step size, x ^(k) (t _i ) represents the state information of the container at the time t _i in the k iteration, F (·) is a function describing the state differential equation, and K ₁ , K ₂ , K ₃ , and K ₄ respectively represent the function values of the four nodes in the integration process of the Runge-Kutta method. The gradient solving module adopts the sensitivity trajectory equation method: Step 1): Define the sensitivity trajectory equation Γ ^(k) (t) of the kth iteration as: <mrow><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&amp;part;</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow> The solution formula of Γ ^(k) (t) is: <mrow><mtable><mtr><mtd><mrow><msup><mover><mi>&amp;Gamma;</mi><mo>&amp;CenterDot;</mo></mover><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>S</mi><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&amp;part;</mo><mi>F</mi><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mfrac><mrow><mo>&amp;part;</mo><mi>F</mi><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>x</mi><mn>0</mn></mrow>msub></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow> where t represents time, Indicates the derivative of the sensitivity trajectory equation with respect to time t in the kth iteration, F(u ^(k) ,x ^(k) (t),t) is a function describing the state differential equation, Γ ^(k) (t ₀ ) represents the sensitivity The initial moment state value of the trajectory equation at the kth iteration, x ₀ represents the initial moment state value of the state differential equation function. Step 2): Using the fourth-level and fifth-order Runge-Kutta method to solve the value of the sensitivity trajectory equation Γ ^(k) (t) at each integration time, the solution formula is: <mrow><mtable><mtr><mtd><mrow><msub><mi>Q</mi><mn>1</mn></msub><mo>=</mo><mi>S</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>Q</mi><mn>2</mn></msub><mo>=</mo><mi>S</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><msub><mi>Q</mi><mn>1</mn></msub><mi>h</mi><mo>/</mo><mn>2</mn><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>/</mo><mn>2</mn><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>Q</mi><mn>3</mn></msub><mo>=</mo><mi>S</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><msub><mi>Q</mi><mn>2</mn></msub><mi>h</mi><mo>/</mo><mn>2</mn><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>/</mo><mn>2</mn><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>Q</mi><mn>4</mn></msub><mo>=</mo><mi>S</mi><mo>&amp;lsqb;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><msub><mi>Q</mi><mn>3</mn></msub><mi>h</mi><mo>,</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>+</mo><mi>h</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>+</mo><mfrac><mi>h</mi><mn>6</mn></mfrac><mrow><mo>(</mo><msub><mi>Q</mi><mn>1</mn></msub><mo>+</mo><mn>2</mn><msub><mi>Q</mi><mn>2</mn></msub><mo>+</mo><mn>2</mn><msub><mi>Q</mi><mn>3</mn></msub><mo>+</mo><msub><mi>Q</mi><mn>4</mn></msub><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow> Among them, t represents the time, t _i represents a certain time point in the control process selected by the Runge-Kutta method, h is the integral step size, x ^(k) (t _i ) represents the container at the time t _i in the k iteration The state information of , S(·) is the function describing the sensitivity equation, Q ₁ , Q ₂ , Q ₃ , Q ₄ respectively represent the function values of the four nodes in the integration process of the Runge-Kutta method. Step 3): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information dJ ^(k) of the objective function: <mrow><mtable><mtr><mtd><mrow><msup><mi>dJ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>=</mo><mfrac><mrow><mo>&amp;part;</mo><msup><mi>J</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>&amp;Phi;</mi><mn>0</mn></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>+</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>&amp;Phi;</mi><mn>0</mn></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>+</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi><mi>E</mi></mrow></munderover><msubsup><mo>&amp;Integral;</mo><msub><mi>t</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><msub><mi>t</mi><mi>i</mi></msub></msubsup><mo>{</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>L</mi><mn>0</mn></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mo>mrow><mrow><mo>&amp;part;</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>L</mi><mn>0</mn></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac><mo>}</mo><mi>d</mi><mi>t</mi></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mrow> Among them, Φ ₀ (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the objective function, and L ₀ (u ^(k) ,x ^(k) (t),t) represents the objective function integral item. Step 4): According to the obtained container state information x ^(k) (t) and the sensitivity trajectory equation Γ ^(k) (t), solve the gradient information g ^(k) of the constraints: <mrow><mtable><mtr><mtd><mrow><msup><msub><mi>g</mi><mi>j</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>=</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>&amp;Phi;</mi><mi>j</mi></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>+</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>&amp;Phi;</mi><mi>j</mi></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)< /mo ></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>+</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi><mi>E</mi></mrow></munderover><msubsup><mo>&amp;Integral;</mo><msub><mi>t</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><msub><mi>t</mi><mi>i</mi></msub></msubsup><mo>{</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>L</mi><mi>j</mi></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><msup><mi>&amp;Gamma;</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>+</mo><mfrac><mrow><mo>&amp;part;</mo><msub><mi>L</mi><mi>j</mi></msub><mrow><mo>(</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><msup><mi>u</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mfrac><mo>}</mo><mi>d</mi><mi>t</mi></mrow></mtd></mtr><mtr><mtd><mrow><msup><mi>g</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><mrow><msup><msub><mi>g</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><msup><msub><mi>g</mi><mi>j</mi></msub><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></mrow></mtd></mtr></mtable></mfenced><mo>,</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>...</mn><mo>,</mo><mi>m</mi></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow> Among them, Φ _j (u ^(k) ,x ^(k) (t),t _f ) represents the terminal constraint term of the jth constraint function, L _j (u ^(k) ,x ^(k) (t),t ) represents the integral term of the jth constraint function, and m represents the number of constraints. Described NLP problem solving module adopts the following steps to realize: Step 1): If the absolute value difference between the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration is less than the accuracy tol, it is judged that the convergence is satisfied, and the current iteration The speed control strategy of the traction motor is converted into the control command output of the traction motor; if the convergence is not satisfied, continue to perform step 2); Step 2): Overwrite the previous iteration u ^(k-1) , J ^(k-1) , dJ ^(k-1) with the values of u ^(k) , J ^(k) , dJ ^(k) , g ^(k ) , the value of g ^(k-1) , and increase the number of iterations k by 1; Step 3): take the motor speed control strategy u ^(k-1) as a certain point in the vector space, denoted as P ₁ , and the corresponding objective function value of P ₁ is J ^(k-1) ; Step 4): Starting from point P ₁ , according to the selected NLP algorithm and the gradient information dJ ^(k-1) of the objective function at point P ₁ and the gradient information g ^(k-1) of constraint conditions, construct a search vector space Optimal direction d ^(k-1) and step size α ^(k-1) ; Step 5): Construct another point P ₂ corresponding to u ^(k) in the vector space through the formula u ^(k) =u ^(k-1) +α ^(k-1) d ^(k-1) ; Step 6): Using optimization correction to obtain another point P ₃ corresponding to u ^(k) in the vector space, so that the objective function value J ^(k) corresponding to P ₃ is better than J ^(k-1) .