Cross-coupling global continuous robust control method

Abstract

The invention provides a cross-coupling global continuous robust control method, and relates to the technical field of motor control. The method comprises the steps that forklift physical parameters and controller parameters are initialized; the expected speeds of the two forklifts are determined according to the preset track; acquiring an actual speed and calculating a self-calibration error and a cross coupling error; constructing a state space model; determining an error vector and an error first-order derivative; establishing an objective function, setting a control coefficient, constructing a control function, and obtaining a global continuous robust control rate based on the control function; and the self-calibration error and the cross coupling error are substituted into the global continuous robust control rate, the steering angle and the accelerated speed are output to execution mechanisms of the first forklift and the second forklift, and global continuous and stable synchronous movement of the two forklifts is achieved. The sliding mode buffeting is eliminated by introducing the global continuous control signal, and the state model containing the lumped disturbance term and the Hurvetz polynomial stability verification mechanism are constructed, so that the global continuous stability of the system is realized.

Description

Technical Field

[0001] This application relates to the field of motor control technology, and in particular to a cross-coupled global continuous robust control method. Background Technology

[0002] In modern logistics warehousing and factory production transportation scenarios, electric pallet forklifts, as efficient handling equipment, often require multiple units to work together to complete tasks such as large cargo transfer and assembly line material replenishment. In these situations, the accuracy and stability of the synchronous motion control of the two forklifts directly determine transportation efficiency, operational safety, and cargo integrity. Currently, in the field of synchronous control of multiple motors or actuators, the cross-coupled PID (CC-PID) control method, which combines cross-coupled control with traditional PID control, is widely used. This method achieves basic motion control through the motor's own controller and then uses the cross-coupled controller to correct the positional deviations of multiple motors, demonstrating certain practicality in mechanical and electromechanical production processes.

[0003] However, the operating environment of electric pallet forklifts is significantly complex: on the one hand, the forklift faces real-time changes in ground friction (such as differences in ground material and fluctuations in friction coefficient caused by dust adhesion) and nonlinear disturbances such as backlash in the planetary gear transmission system during movement. Traditional CC-PID control is not robust to such dynamic disturbances and is prone to large fluctuations in synchronization error. On the other hand, the forklift's mass and center of gravity position change significantly under different working conditions such as no-load and 2T load. CC-PID control is difficult to adaptively adjust control parameters, resulting in a significant increase in synchronization error during critical movement stages such as steering. When no-load, the center of gravity synchronization error often fluctuates between -14 and 12 mm, and the mark point error fluctuates between -10 and 10 mm. When loaded with 2T, the error fluctuation range further expands to -25 to 58 mm, which cannot meet the requirements of high-precision synchronous handling.

[0004] To improve anti-interference capabilities, sliding mode control (SMC) technology has been introduced into multi-mechanism synchronous control. It features fast response and strong robustness. However, traditional sliding mode controllers are prone to chattering and struggle to balance the coordination of their own motion calibration and cross-coupling synchronous correction under complex forklift operating conditions. At the same time, existing control methods often lack global stability analysis and finite-time convergence design. In long-distance forklift transportation or frequent turning scenarios, synchronization accuracy is prone to accumulating deviations over time, making it impossible to guarantee continuous and stable synchronous motion performance. These problems restrict the efficiency and reliability of dual-machine collaborative operation of electric pallet forklifts. Summary of the Invention

[0005] This application provides a cross-coupled global continuous robust control method, which overcomes the shortcomings of existing electric pallet forklift dual-machine synchronous motion control methods, such as weak robustness to nonlinear disturbances, poor adaptability to different load conditions, large fluctuations in synchronization error, and lack of global stability. This method eliminates sliding mode chattering by introducing a global continuous control signal and constructs a state model with lumped disturbance terms and a Hurwitz polynomial stability verification mechanism to achieve global continuous stability of the system. This reduces the average synchronization error by about 4% under no-load conditions compared to cross-coupled input-output sliding mode control, and controls the error to about 2mm under 2T load, with an average synchronization error reduction of 42%, meeting the requirements for higher precision dual-forklift collaborative operation. This method adapts to the preset movement trajectory of the forklift, from the starting point a through the unloading points b, c, and d to the ending point e. It can also adaptively adjust physical and control parameters according to no-load / load conditions, ensuring stable and reliable synchronization performance during the acceleration process from the initial speed of 0 m / s to the target speed of 1.5 m / s, as well as during the turning processes from 10s to 25s, 55s to 60s, and 85s to 90s. This provides technical support for the collaborative handling of electric pallet forklifts.

[0006] This application provides a cross-coupled global continuous robust control method, the method comprising: Determine the physical parameters of the electric pallet forklift, including at least the forklift's mass. m Distance between front wheel and center of gravity l f Distance between rear wheel and center of gravity l r Front wheel lateral stiffness K f Rear wheel lateral stiffness K r and the moment of inertia of the center of mass during yaw. I z Set global continuous robust control parameters, which include the parameters of the self-global continuous robust controller SC-GCRC and the cross-coupled global continuous robust controller CC-GCRC; Based on the preset synchronous motion trajectory of the electric pallet forklift, the desired speed of the first forklift in the X-axis direction in the vehicle coordinate system is obtained. and the desired velocity in the Y-axis direction Based on the desired speed of the first forklift, the desired speed of the second forklift in the X-axis direction of the vehicle body coordinate system is calculated. and the desired velocity in the Y-axis direction ; Real-time acquisition of the actual position coordinates of the first forklift X 1. Y 1. Actual speed , and the actual position coordinates of the second forklift X 2.Y 2. Actual speed , ; Introducing external interference terms d 1. d 2. The external interference items include interference caused by changes in ground friction and forklift backlash vibration; Calculate self-calibration error: Let X 1d , Y 1d Let be the desired position coordinates of the first forklift in the ground reference coordinate system. X 2d , Y 2d Let be the desired position coordinates of the second forklift in the ground reference coordinate system; for the first forklift, the X-axis error of its own global continuous robust controller SC-GCRC1 is . X 1d - X 1. The Y-axis error is Y 1d - Y 1; For the second forklift, the X-axis error of its own globally continuous robust controller SC-GCRC2 is: X 2d - X 2. The Y-axis error is Y 2d - Y 2; Calculate the cross-coupling error: For the first forklift, the X-axis error of its cross-coupling global continuous robust controller CC-GCRC1 is... X 2- X 1. The Y-axis error is Y 2- Y 1; For the second forklift, the X-axis error of its cross-coupled global continuous robust controller CC-GCRC2 is: X 1- X 2. The Y-axis error is Y 1- Y 2; Construct a state-space model of the electric pallet forklift, and calculate the derivative of the velocity in the X-axis direction output by the state-space model. Y-axis velocity derivative Differentiate each component to obtain the acceleration in the X-axis direction. Y-axis acceleration Relationship with control input; wherein, the control input includes steering angle and acceleration ; set up X d , Yd The coordinates of the forklift's desired position are: , Determine the error vector and the first derivative of the error for the desired forklift speed; To drive the forklift to the desired speed , The objective is to effectively suppress forklift acceleration and jerk disturbances. A target function is established, control coefficients are set, a control function is constructed, and a global continuous robust control law is obtained based on the control function. Substituting the self-calibration error and cross-coupling error into the global continuous robust control law, the output steering angle is determined. and acceleration The actuators of the first and second forklifts are connected to achieve continuous and stable synchronous movement of the two forklifts.

[0007] Preferably, the state-space model of the electric pallet forklift is represented as follows: (18) (19) In the formula, Side slip angle, r The yaw rate is angular velocity. For heading angle, v For longitudinal velocity, The sideslip angular velocity, This is the yaw acceleration. The rate of change of heading angle, This is the longitudinal acceleration.

[0008] Preferably, the acceleration in the X-axis direction Y-axis acceleration The relationship with the control input is expressed by the following formulas (20) and (21) or formula (22): (20) (twenty one) (twenty two) In the formula, and It is a lumped disturbance term.

[0009] As a preferred option and Represented as: (twenty three) The lumped disturbance term and its derivative are bounded, satisfying: (twenty four) In the formula, D 1( t ) represents the lumped disturbance term in the X direction. D 2( t ) represents the lumped disturbance term in the Y direction. This is the upper bound of D1(t). This is the upper bound of D2(t). Let D2(t) be the time derivative. for The upper realm, for The upper boundary.

[0010] Preferably, the error vector and the first derivative of the error are expressed as follows: (25) In the formula, e X Let be the error vector in the X-axis direction of the forklift. e Y Let be the error vector in the Y-axis direction of the forklift. , for e X , e Y A first-order singular, , for e X , e Y The second derivative of .

[0011] Preferably, the objective function is expressed as: (26) In the formula, X ( t () represents the actual X-axis position of the forklift in the ground reference coordinate system. Y ( t () represents the actual Y-axis position of the forklift in the ground reference coordinate system. ( t ) represents the rate of change of position error in the X direction. ( t ) represents the rate of change of position error in the Y direction. ( t Let be the second derivative of the position error in the X direction. ( t ) represents the second derivative of the position error in the Y direction.

[0012] Preferably, the control function is expressed as: (29) In the formula, Let S1 be the first derivative of the sliding mode function S1 in the X direction. The first derivative of the sliding mode function S2 in the Y direction. The robust control gain coefficient in the X direction. The robust control gain coefficient in the Y direction. The smoothing coefficient for continuous control in the X direction. The smoothing coefficient is continuously controlled in the Y direction. e X ( T ) for at time T The position error in the X direction, ( T ) for at time T The velocity error in the X direction, ( T ) for at time T The velocity error in the Y direction.

[0013] Preferably, the globally continuous robust control law obtained based on the control function is expressed as follows: (30) In the formula, S 1 represents the sliding mode function in the X direction. S 2 is the sliding mode function in the Y direction. , , , All are positive control gains, and sgn is the sign function. t For time.

[0014] Preferably, in the output steering angle and acceleration After achieving globally continuous and stable synchronized movement of the two forklifts via their actuators, the method further includes a stability analysis step for the cross-coupled globally continuous robust controller synchronization system. This stability analysis step includes: Substituting equation (29) into equation (30) yields the following result. (31) In the formula, control gain , , , All are positive control gains, satisfying: (32) In the formula, It is an auxiliary parameter that satisfies the following relationship: (33) By introducing auxiliary parameters Rewrite equation (31) as (34) In the formula, S 1( t Let be the sliding mode function in the X direction at time t. S 2( t Let be the sliding mode function in the Y direction at time t. and These are the robust control gain coefficients in the X and Y directions, respectively. and These are the continuous control smoothing coefficients in the X and Y directions, respectively; Combining equations (32) and (34), we get: (35) From equations (27) and (35), we obtain that the control law satisfies the Herwitz polynomial, that is: (36)

[0015] The cross-coupled global continuous robust control method provided in this application has at least the following beneficial effects: 1) This application achieves active compensation for disturbances by defining a lumped disturbance term and designing a robust control gain. Compared with traditional CC-PID control, this method reduces the synchronization error fluctuation amplitude by more than 90% under no-load and 2T load conditions, and can stably resist dynamic disturbances under complex operating conditions.

[0016] 2) In cross-coupled global continuous robust control, the SC-GCRC and CC-GCRC parameters are matched with the physical parameters under a 2T load to ensure that the control system can still maintain high-precision synchronization when the load changes cause the centroid to shift, thus solving the problem of fixed parameters and poor adaptability of traditional methods.

[0017] 3) This application achieves global continuous stability through Hurwitz polynomial verification, reduces the average error under no-load by 4%, controls the error under 2T load to about 2mm, and eliminates sliding mode chatter. This method can accurately control the synchronization error of the centroid, head marker A, and tail marker B, meeting the high precision requirements of cargo alignment and path following in forklift handling.

[0018] 4) This application is designed based on the actual operating trajectory of forklifts. The initial conditions and motion process closely match industrial scenarios. Control parameters can be quickly calibrated through simulation and experimentation, and no large-scale modification of the forklift hardware structure is required, making it easy to upgrade and adapt to existing equipment. This application is particularly suitable for transporting precision instruments, significantly improving logistics efficiency and operational safety. Attached Figure Description

[0019] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0020] Figure 1 Block diagram of a cross-coupled controller in the prior art provided for embodiments of this application. Figure 2 A block diagram of the PID control principle in the prior art provided in the embodiments of this application; Figure 3 A block diagram of a cross-coupled input / output sliding mode controller provided in an embodiment of this application; Figure 4 This is an ideal motion trajectory diagram of the forklift synchronization control system provided in the embodiments of this application; Figure 5 A comparison diagram of the centroid synchronization error between the CC-IOSMC method and the CC-PID method under no-load conditions provided in the embodiments of this application; Figure 6 A comparison diagram of the synchronization error of marker point A between the CC-IOSMC method and the CC-PID method under no-load conditions provided in the embodiments of this application; Figure 7 A comparison diagram of the synchronization error at marker point B between the CC-IOSMC method and the CC-PID method under no-load conditions provided in the embodiments of this application; Figure 8 A comparison diagram of centroid synchronization error between the CC-IOSMC method and the CC-PID method under a 2T load state provided in the embodiments of this application; Figure 9 A comparison diagram of the synchronization error at marker point A between the CC-IOSMC method and the CC-PID method under a 2T load state provided in the embodiments of this application; Figure 10 A comparison diagram of the synchronization error at marker point B between the CC-IOSMC method and the CC-PID method under a 2T load state provided in the embodiments of this application; Figure 11 A block diagram of a cross-coupled global continuous robust controller provided in an embodiment of this application; Figure 12 A comparison diagram of the centroid synchronization error between the CC-IOSMC method and the CC-GCRC method under no-load conditions provided in the embodiments of this application; Figure 13 A comparison diagram of the synchronization error of marker point A between the CC-IOSMC method and the CC-GCRC method under no-load conditions provided in the embodiments of this application; Figure 14 A comparison diagram of the synchronization error of marker point B between the CC-IOSMC method and the CC-GCRC method under no-load conditions provided in the embodiments of this application; Figure 15 A comparison diagram of the centroid synchronization error between the CC-IOSMC method and the CC-GCRC method under a 2T load state provided in the embodiments of this application; Figure 16 A comparison diagram of the synchronization error of marker point A between the CC-IOSMC method and the CC-GCRC method under a 2T load state provided in the embodiments of this application; Figure 17 A comparison diagram of the synchronization error of marker point B between the CC-IOSMC method and the CC-GCRC method under a 2T load state provided in the embodiments of this application.

[0021] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0022] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0023] The collection, storage, use, processing, transmission, provision, and disclosure of financial data or user data involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0024] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0025] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0026] Cross-coupled controllers are widely used for position synchronization of multiple motors, offering advantages such as high synchronization accuracy and strong robustness. A block diagram of a cross-coupled controller is shown below. Figure 1As shown. The control objective is to synchronize the positions of the two motors. First, the basic motion control objective for the motor positions is achieved through the motor's own controllers (Controller 1 and Controller 2). Second, if the positions of the two motors are not synchronized, the motor position error is obtained by subtracting the actual positions of the two motors, and the motor position deviation is corrected through a cross-coupled controller.

[0027] Traditional PID control is widely used in production processes such as machinery, electromechanical engineering, chemical engineering, and metallurgy. It controls the controlled object by forming a control quantity through a linear combination of the proportional (P), integral (I), and derivative (D) values ​​of the deviation signal. Figure 2 This is a block diagram of the PID control principle.

[0028] exist Figure 2 middle, For the system's expected output, For the actual output of the system, the classic PID control law is as follows: (1) (2) In the above formula, This is the proportionality coefficient. The integral time constant is... is the differential time constant.

[0029] The functions of each linear component in a PID controller are as follows: (1) Proportional process: through the proportional coefficient The system deviation is proportionally amplified and fed back to the input of the controlled object. If a deviation occurs, the controller can then take control action to suppress the deviation.

[0030] (2) Integral element: used for error-free control of the control system. This module can eliminate the steady error of the system.

[0031] (1) Differential element: By feeding back the rate of change of the error signal, the drastic change of the deviation signal is suppressed, which helps to speed up the adjustment speed of the system and reduce the response time.

[0032] This embodiment introduces the basic control principles of cross-coupled control and classical PID, combining the two to obtain the cross-coupled PID (Cross-coupled PID) synchronous control method. This method has been widely used in solving motor control problems. Similarly, CC-PID control can also be used in the synchronous motion control of electric pallet forklifts. This method will also be used in subsequent embodiments for synchronous control algorithm comparison and simulation result analysis.

[0033] The above are existing control methods in the prior art. In the scenario of synchronous motion control of two electric pallet forklifts, there is room for further improvement in accuracy and stability. Based on this, this application provides a cross-coupled input-output sliding mode control and cross-coupled global continuous robust control method. The implementation steps, principles and effects are described in detail in the following embodiments 1 and 2.

[0034] Example 1: This application provides a cross-coupled input-output sliding mode control method. Sliding mode controllers (SMCs) have advantages such as fast response and strong robustness. They are also robust to disturbances caused by external angular jitter and changes in friction. This method fully combines the advantages of cross-coupled controllers and input-output sliding mode controllers. Considering the complex motion conditions of forklift movement (backlash and real-time changes in friction between the ground and tires), a "self-calibrating input-output sliding mode controller" is proposed to calibrate the angular jitter caused by planetary gears. Simultaneously, a control algorithm using a cross-coupled sliding mode controller is applied to eliminate the motion deviation between the two vehicles. The block diagram of the designed cross-coupled input-output sliding mode controller is shown below. Figure 3 As shown. The cross-coupled input-output sliding mode control method includes the following steps S101-S110.

[0035] S101: Determine the physical parameters of the electric pallet forklift, said physical parameters including at least the forklift mass. m Distance between front wheel and center of gravity l f Distance between rear wheel and center of gravity l r Front wheel lateral stiffness K f and rear wheel lateral stiffness K r Set synchronization control parameters, which include parameters of the self-calibrated input-output sliding mode controller SC-IOSMC and the cross-coupled input-output sliding mode controller CC-IOSMC.

[0036] In this embodiment, the parameters of SC-IOSMC are: w =-1、 q =1、 C 1=20、 C 2=20、 =1.8、 =0.85, the parameters of CC-IOSMC are w =-1、 q =1、 C 1=10\) C 2=10、 =3、 =3.5.

[0037] S102: Based on the preset synchronous motion trajectory of the electric pallet forklift, obtain the desired speed of the first forklift in the X-axis direction in the vehicle coordinate system. and the desired velocity in the Y-axis direction Based on the desired speed of the first forklift, the desired speed of the second forklift in the X-axis direction of the vehicle body coordinate system is calculated. and the desired velocity in the Y-axis direction .

[0038] like Figure 3 The block diagram of the cross-coupled input-output sliding mode controller is shown below. and These are the desired first forklift body coordinate systems. axial velocity and The velocity in the axial direction is used to calculate the body coordinate system of the second forklift based on the desired velocity of the first forklift. axial velocity and axial velocity .

[0039] S103: Real-time acquisition of the actual X-axis velocity of the first forklift. Actual Y-axis velocity And the actual X-axis velocity of the second forklift Actual Y-axis velocity .

[0040] S104: Calculate self-calibration error: For the first forklift, the X-axis error of its self-calibration input / output sliding mode controller SC-IOSMC1 is... and The difference, the Y-axis error is and The difference; for the second forklift, the X-axis error of its self-calibrated input / output sliding mode controller SC-IOSMC2 is... and The difference, the Y-axis error is and The difference.

[0041] like Figure 3 As shown, the motion controller section (SC-IOSMC 1) of the first forklift itself... Axial error input is obtained through the actual input of the first forklift. Axial velocity Expectations for the first forklift Axial velocity Subtraction yields SC-IOSMC 1 itself. Axial error input is obtained through the actual input of the first forklift. Axial velocity Expectations for the first forklift Axial velocity The difference is obtained by subtraction. Similarly, the error input method for the SC-IOSMC 2 controller of the second forklift is the same as that of the first forklift.

[0042] S105: Calculate the cross-coupling error: For the first forklift, the X-axis error of its cross-coupling input / output sliding mode controller CC-IOSMC1 is... and The difference, the Y-axis error is and The difference; for the second forklift, the X-axis error of its cross-coupled input / output sliding mode controller CC-IOSMC2 is... and The difference, the Y-axis error is and The difference.

[0043] like Figure 3 The dashed box shown represents the cross-coupling of the first forklift's own motion controller (CC-IOSMC 1) in the designed cross-coupled sliding mode controller. Axial error input is obtained through the actual input of the second forklift. Axial velocity The actual situation of the first forklift Axial velocity Subtraction yields CC-IOSMC 1 cross-coupling Axial error input is obtained through the actual input of the second forklift. Axial velocity The actual situation of the first forklift Axial velocity The difference is obtained by subtraction. Similarly, the error input method for the CC-IOSMC 2 controller of the second forklift is the same as that of the first forklift.

[0044] S106: Construct a state-space model of the electric pallet forklift and calculate the derivative of the velocity in the X-axis direction output by the model. Y-axis velocity derivative Differentiate each component to obtain the acceleration in the X-axis direction. Y-axis acceleration The mapping relationship between the control input and the steering angle; wherein the control input includes the steering angle. and acceleration .

[0045] In this embodiment, an input-output sliding mode controller is proposed. First, based on the forklift state-space model (3) and (4), the system output is controlled. , By taking the derivative, we obtain the first derivative of the output. , With input , The relationship between them.

[0046] (3) (4) In the formula, Side slip angle, For the vehicle body angle, v Forklift movement speed, r ω represents the yaw rate.

[0047] Arrange equations (3) and (4) to adjust the system input , Separation yields: (5) S107: with X , Y Used as the actual position coordinates of the forklift in the ground reference coordinate system. X d , Y d For the desired position coordinates of the forklift in the ground reference coordinate system, determine the error vector; wherein, the error vector includes the X-axis direction error vector. and Y-axis direction error vector .

[0048] In this embodiment, an error vector is defined. and for: (6) In the formula, , These are the actual position coordinates in the ground reference coordinate system. , Let be the desired position coordinates of the electric pallet forklift. and These are the error vectors along the X-axis and Y-axis, respectively.

[0049] S108: Determine the sliding mode function based on the error vector and the set control coefficients.

[0050] In this embodiment, the sliding mode function is defined as: (7) In the formula, S 1 and S2 represents the control gain coefficient in the sliding mode function, corresponding to the synchronization control intensity in the X and Y axes of the forklift, respectively. C 1 and C 2 is the control coefficient. and These are the error vectors in the X-axis direction and the Y-axis direction, respectively; and They are respectively and The first derivative.

[0051] S109: Adjust steering angle and acceleration Separating from the mapping relationship, a saturation function is introduced to construct the input-output sliding mode control law.

[0052] In this embodiment, the input vector is separated. , The input-output sliding mode control law is designed as follows: (8) In the formula, v 1 and v 2 is an auxiliary parameter. and It is a positive control parameter. Let saturation function be defined as follows: (9) In the formula, sat ( s ) represents the saturation function. s For the sliding surface variable, w These are the positive control parameters defined in the control law. q This represents the width of the saturation interval.

[0053] S110: Substitute the self-calibration error and cross-coupling error into the input-output sliding mode control rate, and output the steering angle. and acceleration The actuators of the first and second forklifts are connected; the stability of the system is analyzed using Lyapunov functions to ensure that the error vector converges to zero within a finite time, thus achieving synchronous movement of the two forklifts.

[0054] In step S110, a stability analysis of the cross-coupled input-output sliding mode controller synchronization system was performed. The specific analysis method is as follows: Take the Lyapunov function, represented as: (10) In the formula, V 1 and V2 are Lyapunov sub-functions related to the X-axis and Y-axis directions of the forklift, respectively; Define auxiliary parameters: (11) In the formula, and These are the second derivatives (expected accelerations) of the desired trajectory in the X and Y directions, respectively.

[0055] Differentiating equation (10) yields: (12) In the formula, and They are respectively V 1 and V The first derivative of 2, and They are respectively S 1 and S The first derivative of 2.

[0056] Substituting equation (5) and equation (8) into equation (12) in step four, and substituting the auxiliary parameter equation (11) into equation (12) in step five, we can obtain: (13) Assumption and If the number is positive, then: (14) According to the sliding condition, once the system state is constrained to a pre-specified state... Sliding modal regions, they can move along the sliding surface Slide towards the origin. Here, the sliding manifold is constructed in the cross-coupling error space, so the cross-coupling error will slide along... The sliding surface gradually converges to zero. It can be seen from equation (6) that when… hour and This indicates that both the self-position error and the cross-coupling synchronization error of the forklift synchronization system asymptotically converge to zero.

[0057] All of the IOSMC laws mentioned above are asymptotically stable control laws over a wide range. However, for practical systems, implementing finite-time (FT) tracking is more suitable for engineering applications. A proof of finite-time arrival will be given below.

[0058] Considering dynamic systems , If there exists a continuous positive definite function Satisfying differential inequalities (15) In the formula, for V ( x rate of change n The time scale for error convergence. V ( x ) is the energy function for analyzing stability.

[0059] Therefore, the dynamic system is stable in finite time, meaning that the trajectory of the dynamic system converges to zero in finite time. and It is a positive constant, among which .

[0060] The following is a finite-time convergence proof of the IOSMC control law, obtained from equation (3-10): (16) Differentiating equation (11) yields: (17) In the formula, If it is a positive number, it means that the trajectory of the dynamic system can converge to zero in a finite amount of time.

[0061] The feasibility and advancements of the aforementioned cross-coupled input-output sliding mode control method will be further illustrated below with simulation experiments of the cross-coupled input-output sliding mode controller synchronization system. These simulation experiments include no-load synchronization simulation and 2T load synchronization simulation of the cross-coupled input-output sliding mode controller.

[0062] Simulation Experiment 1: No-load synchronous simulation of cross-coupled input-output sliding mode controller.

[0063] The hardware platform used in this embodiment includes two electric pallet forklifts. The parameters of the electric pallet forklifts are shown in Table 1.

[0064] Table 1 Simulation Experiment Parameters of Electric Pallet Forklift

[0065] In Table 1, letters and These represent the front and rear wheels of an electric pallet forklift. and Representing the vehicle body coordinate system Axial direction and Axial direction.

[0066] Cross-coupled input-output sliding mode control is used to simulate a factory transportation environment. A forklift synchronization system starts from point a, loads and unloads goods at points b, c, and d, and finally terminates at point e. During this movement, synchronization between the two forklifts is maintained. The ideal trajectory of the forklift is as follows: Figure 4 As shown.

[0067] Figure 4 The circular markers indicate the outer contour points of the first and second forklifts. The blue circular marker A indicates the outer contour points of the heads of the two forklifts, and the green circular marker B indicates the outer contour points of the tails of the two forklifts. Unlike trolleys, forklifts are used to transport large machinery, and their contour points are used to evaluate synchronous motion performance indicators.

[0068] During simulation, the parameters of the self-calibrated input-output sliding mode controller (SC-IOSMC) of the dual forklift are: ; ; ; ; ; The parameters of the cross-coupled input / output sliding mode controller (CC-IOSMC) for two forklifts are as follows: ; ; ; ; ; .

[0069] In contrast, the parameters of the steering cross-coupled PID controller (CC-PID) are: ; ; The parameters of the straight-through cross-coupled PID controller are: ; ; .

[0070] The initial coordinates of the first forklift in the ground coordinate system are set to X=0; Y=0, and the initial body angle is 0°. The initial coordinates of the second forklift are X=0; Y=-1, and the initial body angle is 0°. The initial speed of the forklift is set to 0m / s, and the target speed is set to 1.5m / s. During the motion simulation, the forklift rotates 90° counterclockwise in the ground coordinate system at the 10s-25s, 55s-60s, and 85s-90s, respectively, to realize the turning motion of the forklift at points b, c, and d.

[0071] A comparison of the centroid synchronization errors of the CC-IOSMC method and the CC-PID method under no-load conditions is shown in the figure below. Figure 5 As shown.

[0072] The synchronization errors of marker points A and B of the two forklifts are respectively caused by: Figure 6 , Figure 7 As shown.

[0073] Under the control of the conventional cross-coupled PID control method, the mark point error fluctuates between -10 and 10 mm, the centroid synchronization error fluctuates between -14 and 12 mm, and the position synchronization error increases significantly when the forklift is synchronously turning.

[0074] Under the cross-coupled input-output sliding mode control strategy, the marker point error fluctuates between -4 and 4 mm, the centroid synchronization error fluctuates between -4 and 4 mm, and the fluctuation is smaller when the forklift is synchronously turning. The error amplitude is adjusted to 0 within a certain period of time.

[0075] Compared with the traditional cross-coupled PID control method, the cross-coupled input-output sliding mode control maintains the motion error of the forklift under no-load conditions at an accuracy of about 4 mm, significantly reduces the jitter amplitude, and converges the error in a finite time when the forklift is synchronously turning.

[0076] Simulation Experiment 2: Synchronous Simulation of Cross-coupled Input-Output Sliding Mode Controller with 2T Load.

[0077] Forklifts, as a type of logistics transportation vehicle, are an important indicator for measuring the cargo-carrying capacity of a synchronous system. Therefore, this embodiment studies them, and the following simulation experiment will simulate the synchronous performance of the second forklift T when it is carrying cargo.

[0078] Apply a 2-ton load to the forklift and modify the relevant parameters of the forklift as follows: Because the load is placed on the forks at the rear of the forklift, the vehicle's center of gravity will shift rearward, causing... , Meanwhile, other parameters of the forklifts remain unchanged, and the parameters of the self-calibration input-output sliding mode controllers (SC-IOSMC) of both forklifts are set as follows: ; ; ; ; ; The parameters of the cross-coupled input / output sliding mode controller (CC-IOSMC) for the two forklifts are set as follows: ; ; ; ; ; .

[0079] In contrast, the parameters of the cross-coupled PID controller (CC-PID) are: ; ; The parameters of the straight-through cross-coupled PID controller are: ; ; The system input remains constant during the simulation under load conditions.

[0080] The following is a comparison of the centroid synchronization errors of the CC-IOSMC method and the CC-PID method under a 2T load: Figure 8 As shown.

[0081] The synchronization errors of marker points A and B of the two forklifts are respectively caused by: Figure 9 , Figure 10 As shown.

[0082] The traditional cross-coupled PID control method has a marker point synchronization error of -25 to 58 mm, and the centroid synchronization error fluctuates between -25 and 58 mm with a large amplitude of jitter. The error fluctuates greatly during synchronous turning.

[0083] Under the cross-coupled input-output sliding mode control strategy, the marker point error fluctuates between -4 and 4 mm, the centroid synchronization error fluctuates between -4 and 4 mm, and the fluctuation is small and relatively stable when the forklift is synchronously turning.

[0084] Compared with the traditional cross-coupled PID control method, the cross-coupled input-output sliding mode control maintains the motion error of the forklift under different loads at an accuracy of about 4 mm, and the error curve fluctuates smoothly during the motion.

[0085] Under cross-coupled input-output sliding mode control, a small coordinate deviation can be obtained by adjusting the forklift's angle and acceleration input. The synchronization error between marker points B and C is controlled within an acceptable range, achieving the expected design goal.

[0086] Example 2: This application provides a cross-coupled global continuous robust control method. Global continuous robust control (GCRC) processing has the advantages of fast response and robustness against disturbances caused by external angular jitter and friction changes. The innovation of this method is as follows: (1) Global: It eliminates the adverse effects of the arrival phase on synchronous control.

[0087] (2) Continuity: The output of the GCRC controller is a continuous signal, which eliminates jitter and improves synchronization accuracy.

[0088] (1) Robustness: It can suppress the interference caused by complex motion conditions and has good robustness.

[0089] The cross-coupled global continuous robust control method proposed in this embodiment combines the advantages of cross-coupled control and global continuous robust control. It uses cross-coupled global continuous robust control (CC-GCRC) to achieve synchronous movement of the forklift, and demonstrates higher accuracy than cross-coupled input-output sliding mode control (CC-IOSMC) in simulation experiments.

[0090] This cross-coupled global continuous robust control method can be based on Figure 11 The cross-coupled global continuous robust controller implementation shown includes the following steps S201-S209.

[0091] S201: Determine the physical parameters of the electric pallet forklift, said physical parameters including at least the forklift mass. m Distance between front wheel and center of gravity l f Distance between rear wheel and center of gravity l r Front wheel lateral stiffness K f Rear wheel lateral stiffness K r and the moment of inertia of the center of mass during yaw. I z Set global continuous robust control parameters, which include the parameters of the self-global continuous robust controller SC-GCRC and the cross-coupled global continuous robust controller CC-GCRC.

[0092] For example, during no-load synchronous simulation, the parameters of both the dual forklift's own Global Continuous Robust Controller (SC-GCRC) and the cross-coupled Global Continuous Robust Controller (CC-GCRC) are set to [value missing]. ; ; ; ; ; ; ; ; ; ; ; .

[0093] S202: Based on the preset synchronous motion trajectory of the electric pallet forklift, obtain the desired speed of the first forklift in the X-axis direction in the vehicle coordinate system. and the desired velocity in the Y-axis direction Based on the desired speed of the first forklift, the desired speed of the second forklift in the X-axis direction of the vehicle body coordinate system is calculated. and the desired velocity in the Y-axis direction .

[0094] In this embodiment, as Figure 10As shown in the dashed box, the area inside the dashed box is the cross-coupled sliding mode controller. and Let X and Y be the desired velocities of the first forklift in the body coordinate system, respectively, along the X and Y axes. And let Y and Y be the desired velocities of the second forklift. Desired velocity in the axial direction and Desired velocity in the axial direction The desired speed of the first forklift is obtained by calculating it.

[0095] S203: Real-time acquisition of the actual position coordinates of the first forklift. X 1. Y 1. Actual speed , and the actual position coordinates of the second forklift X 2. Y 2. Actual speed , ; Introducing external interference terms d 1. d 2. The external interference items include interference caused by changes in ground friction and forklift backlash.

[0096] S204: Calculate self-calibration error: Let... X 1d , Y 1d Let be the desired position coordinates of the first forklift in the ground reference coordinate system. X 2d , Y 2d Let be the desired position coordinates of the second forklift in the ground reference coordinate system; for the first forklift, the X-axis error of its own global continuous robust controller SC-GCRC1 is . X 1d - X 1. The Y-axis error is Y 1d - Y 1; For the second forklift, the X-axis error of its own globally continuous robust controller SC-GCRC2 is: X 2d - X 2. The Y-axis error is Y 2d - Y 2.

[0097] S205: Calculate the cross-coupling error: For the first forklift, the X-axis error of its cross-coupling global continuous robust controller CC-GCRC1 is... X 2- X 1. The Y-axis error is Y 2- Y1; For the second forklift, the X-axis error of its cross-coupled global continuous robust controller CC-GCRC2 is: X 1- X 2. The Y-axis error is Y 1- Y 2.

[0098] It should be noted that steps S203-S205 above are for calculating the self-calibration error and cross-coupling error. The calculation principle is similar to the calculation principle of the corresponding error in the cross-coupling input-output sliding mode control method mentioned in Example 1, so it will not be repeated here.

[0099] S206: Construct a state-space model of the electric pallet forklift, and calculate the derivative of the velocity in the X-axis direction output by the state-space model. Y-axis velocity derivative Differentiate each component to obtain the acceleration in the X-axis direction. Y-axis acceleration Relationship with control input; wherein, the control input includes steering angle and acceleration .

[0100] In this embodiment, the state-space model of the electric pallet forklift is represented as follows: (18) (19) In the formula, Side slip angle, r The yaw rate is angular velocity. For heading angle, v For longitudinal velocity, The sideslip angular velocity, This is the yaw acceleration. The rate of change of heading angle, For longitudinal acceleration, and Interference items represent interference caused by external factors such as ground friction and forklift backlash.

[0101] Based on the forklift state-space model equations (18) and (19), the system output... , With system input , The relationship between them can be seen in the system output. , Differentiating, we get: (20) (twenty one) The above formula can be rewritten as follows: (twenty two) In the above formula and Defined as follows (twenty three) In the above formula, and This is the lumped disturbance term, representing the set of disturbances caused by the unmodeled dynamic system, external disturbances (variable friction from the ground, forklift backlash), and other factors. Due to the existence of actual physical constraints, the lumped disturbance term and its derivative are bounded, i.e. (twenty four): In the formula, D 1( t ) represents the lumped disturbance term in the X direction. D 2( t ) represents the lumped disturbance term in the Y direction. It is the upper bound (maximum absolute value) of D1(t). This is the upper bound of D2(t). Let D2(t) be the time derivative. for The upper realm, for The upper boundary.

[0102] S207: [Set] X d , Y d The coordinates of the forklift's desired position are: , To determine the desired speed of the forklift, define the error vector and the first derivative of the error.

[0103] In this embodiment, a new definition of error, namely the error vector and the first derivative of the error, are introduced as follows: (25) In the formula, e X Let be the error vector in the X-axis direction of the forklift. e Y Let be the error vector in the Y-axis direction of the forklift. , for e X , e Y A first-order singular, , for e X , eY The second derivative; , These are the actual coordinates in the ground reference coordinate system. , These are the desired coordinates for the forklift's ground reference coordinate system.

[0104] S208: To drive the forklift to the desired speed , The objective is to effectively suppress forklift acceleration and jerk disturbances. An objective function is established, control coefficients are set, a control function is constructed, and a global continuous robust control law is obtained based on the control function.

[0105] In this embodiment, the control objective of the forklift synchronization control system is to drive the forklift to the desired speed. , It effectively suppresses forklift acceleration and jerk disturbances, as detailed below. (26) In the formula, X ( t () represents the actual X-axis position of the forklift in the ground reference coordinate system. Y ( t () represents the actual Y-axis position of the forklift in the ground reference coordinate system. ( t ) represents the rate of change of position error in the X direction (velocity error). ( t ) represents the rate of change of position error in the Y direction (velocity error). ( t ) represents the second derivative of the position error in the X direction (acceleration error). ( t ) represents the second derivative of the position error in the Y direction (acceleration error).

[0106] Define a new function: (27) In the above formula, ,

[0107] Differentiating equation (27) above, we get: (28) Substituting equations (22) and (23) into equation (28), the control function is expressed as: (29) In the formula, Let S1 be the first derivative of the sliding mode function S1 in the X direction. The first derivative of the sliding mode function S2 in the Y direction. The robust control gain coefficient in the X direction. The robust control gain coefficient in the Y direction. The smoothing coefficient for continuous control in the X direction. The smoothing coefficient is continuously controlled in the Y direction. e X ( T ) for at time T The position error in the X direction, ( T ) for at time T The velocity error in the X direction, ( T ) for at time T The velocity error in the Y direction.

[0108] Equation (29) is rewritten to propose a globally continuous robust control law: (30) In the formula, S 1 represents the sliding mode function in the X direction. S 2 is the sliding mode function in the Y direction. , , , All are positive control gains, and sgn is the sign function. t For time.

[0109] S209: Substitute the self-calibration error and cross-coupling error into the global continuous robust control law, and output the steering angle. and acceleration The actuators of the first and second forklifts are connected to achieve continuous and stable synchronous movement of the two forklifts.

[0110] Following step S209, the cross-coupled global continuous robust control method further includes step S210.

[0111] S210: Stability analysis of a cross-coupled global continuous robust controller synchronization system.

[0112] Substituting equation (29) into equation (30), we easily obtain: (31) In the formula, control gain , , , All are positive control gains, and theoretically they should satisfy: (32) In the formula, It is an auxiliary parameter that satisfies the following relationship: (33) By introducing auxiliary parameters Equation (31) can be rewritten as: (34) In the formula, S 1( t Let be the sliding mode function in the X direction at time t. S 2( t Let be the sliding mode function in the Y direction at time t. and These are the robust control gain coefficients in the X and Y directions, respectively. and These are the continuous control smoothing coefficients in the X and Y directions, respectively.

[0113] Combining equations (32) and (34), we can obtain: (35) From equations (27) and (35), we obtain that the control law satisfies the Herwitz polynomial, that is: (36) In conclusion, the proposed controller can achieve the control objective and ensure that all signals in the system are closed-loop bounded.

[0114] The feasibility and advancement of the proposed cross-coupled global continuous robust control method will be further illustrated below with simulation experiments of the cross-coupled global continuous robust controller synchronization system.

[0115] The simulation experiment of the cross-coupled global continuous robust controller synchronization system compares the cross-coupled global continuous robust controller (CC-GCRC) with the cross-coupled input-output sliding mode controller (CC-IOSMC) designed in Example 1 under the same input and parameters using Simulink simulation to verify the synchronization performance of the designed cross-coupled global continuous robust controller. This simulation experiment includes no-load synchronization simulation and 2T load synchronization simulation of the cross-coupled global continuous robust controller.

[0116] Simulation Experiment 3: No-load synchronous simulation of a cross-coupled global continuous robust controller.

[0117] The prerequisites for the no-load simulation experiment are as follows: the ideal motion trajectory of the dual forklift synchronous control system is as follows. Figure 4As shown, the motion deviation of the center of gravity of the two forklifts, the motion deviation of the similar outer contour points of the heads of the two forklifts, and the motion deviation of the similar outer contour points of the tails of the two forklifts are also selected as indicators for evaluating synchronous motion performance. The relevant parameters of the forklift model are shown in Table 1 of Example 1.

[0118] The initial coordinates of the first forklift in the ground coordinate system are set to X=0; Y=0, and the initial body angle is 0°. The initial coordinates of the second forklift are X=0; Y=-1, and the initial body angle is 0°. The initial speed of the forklift is set to 0 m / s, and the target speed is set to 1.5 m / s. During the motion simulation, the forklift rotates 90° counterclockwise in the ground coordinate system at the 10s-25s, 55s-60s, and 85s-90s, respectively, to realize the turning motion of the forklift at points b, c, and d.

[0119] During the no-load synchronous simulation, the parameters of both the dual forklift's own Global Continuous Robust Controller (SC-GCRC) and the cross-coupled Global Continuous Robust Controller (CC-GCRC) are set to [value missing]. ; ; ; ; ; ; ; ; ; ; ; .

[0120] In comparison, the parameters of the self-calibrated input / output sliding mode controller (SC-IOSMC) for dual forklifts are: ; ; ; ; ; The parameters of the cross-coupled input / output sliding mode controller (CC-IOSMC) for two forklifts are as follows: ; ; ; ; ; .

[0121] The centroid synchronization error comparison between the CC-IOSMC method and the CC-GCRC method under no-load conditions is shown in the figure below. Figure 12 As shown.

[0122] The synchronization errors of marker points A and B of the two forklifts are respectively caused by: Figure 13 , Figure 14 As shown.

[0123] Compared with the CC-IOSMC method, the CC-GCRC method reduces the average motion error of the forklift under no-load conditions by about 4%, and significantly reduces the amplitude of synchronization error jitter.

[0124] Under the CC-GCRC method, by adjusting the forklift's angle and acceleration input, a smaller coordinate offset stability value can be obtained than that of CC-IOSMC. The synchronization error of marker points B and C is controlled within an acceptable range, achieving the expected design improvement goal.

[0125] Simulation Experiment 4: Simulation of 2T Load Synchronization of Cross-Coupled Global Continuous Robust Controller.

[0126] Similarly, forklifts, as logistics transport vehicles that carry goods, are an important indicator for measuring the cargo-carrying capacity of a synchronization system. Therefore, this embodiment will compare the load synchronization performance of the second forklift T using the CC-IOSMC method and the CC-GCRC method in the following simulation experiments.

[0127] Apply a 2-ton load to the forklift and modify the relevant parameters of the forklift as follows: ; ; Meanwhile, other parameters of the forklift remain unchanged.

[0128] The self-contained global continuous robust controller (SC-GCRC) and the cross-coupled global continuous robust controller (CC-GCRC) are configured as follows: ; ; ; ; ; ; ; ; ; ; ; .

[0129] In comparison, the parameter settings of the self-calibrated input / output sliding mode controllers (SC-IOSMC) of the two forklifts are as follows: ; ; ; ; ; The parameters of the cross-coupled input / output sliding mode controller (CC-IOSMC) for the two forklifts are set as follows: ; ; ; ; ; With the system inputs the same as in Example 1, a simulation under a 2T load condition is performed.

[0130] The centroid synchronization error comparison chart between the CC-IOSMC method and the CC-GCRC method under a 2T load is shown below. Figure 15 As shown.

[0131] The synchronization errors of marker points A and B of the two forklifts are respectively caused by: Figure 16 , Figure 17 As shown.

[0132] Compared to the ordinary CC-IOSMC control method, the CC-GCRC control method maintains the forklift motion error at around 2mm under a 2T load, and the average synchronization error is reduced by 42%. Furthermore, the synchronization error curve shows that the CC-GCRC control method significantly improves the accuracy of load synchronization during forklift movement.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A cross-coupled global continuous robust control method, characterized in that, The method includes: Determine the physical parameters of the electric pallet forklift, including at least the forklift's mass. m Distance between front wheel and center of gravity l f Distance between rear wheel and center of gravity l r Front wheel lateral stiffness K f Rear wheel lateral stiffness K r and the moment of inertia of the center of mass during yaw. I z Set global continuous robust control parameters, which include the parameters of the self-global continuous robust controller SC-GCRC and the cross-coupled global continuous robust controller CC-GCRC; Based on the preset synchronous motion trajectory of the electric pallet forklift, the desired speed of the first forklift in the X-axis direction in the vehicle coordinate system is obtained. and the desired velocity in the Y-axis direction Based on the desired speed of the first forklift, the desired speed of the second forklift in the X-axis direction of the vehicle body coordinate system is calculated. and the desired velocity in the Y-axis direction ; Real-time acquisition of the actual position coordinates of the first forklift X 1. Y 1. Actual speed , and the actual position coordinates of the second forklift X 2. Y 2. Actual speed , ; Introducing external interference terms d 1. d 2. The external interference items include interference caused by changes in ground friction and forklift backlash vibration; Calculate self-calibration error: Let X 1d , Y 1d Let be the desired position coordinates of the first forklift in the ground reference coordinate system. X 2d , Y 2d Let be the desired position coordinates of the second forklift in the ground reference coordinate system; for the first forklift, the X-axis error of its own global continuous robust controller SC-GCRC1 is . X 1d - X 1. The Y-axis error is Y 1d - Y 1; For the second forklift, the X-axis error of its own globally continuous robust controller SC-GCRC2 is: X 2d - X 2. The Y-axis error is Y 2d - Y 2; Calculate the cross-coupling error: For the first forklift, the X-axis error of its cross-coupling global continuous robust controller CC-GCRC1 is... X 2- X 1. The Y-axis error is Y 2- Y 1; For the second forklift, the X-axis error of its cross-coupled global continuous robust controller CC-GCRC2 is: X 1- X 2. The Y-axis error is Y 1- Y 2; Construct a state-space model of the electric pallet forklift, and calculate the derivative of the velocity in the X-axis direction output by the state-space model. Y-axis velocity derivative Differentiate each component to obtain the acceleration in the X-axis direction. Y-axis acceleration Relationship with control input; wherein, the control input includes steering angle and acceleration ; set up X d , Y d The coordinates of the forklift's desired position are: , Determine the error vector and the first derivative of the error for the desired forklift speed; To drive the forklift to the desired speed , The objective is to effectively suppress the disturbances of forklift acceleration and jerk, establish an objective function, set control coefficients, construct a control function, and obtain a global continuous robust control law based on the control function. Substituting the self-calibration error and cross-coupling error into the global continuous robust control law, the output steering angle is determined. and acceleration The actuators of the first and second forklifts are connected to achieve continuous and stable synchronous movement of the two forklifts.

2. The cross-coupled global continuous robust control method according to claim 1, characterized in that, The state-space model of the electric pallet forklift is represented as follows: (18) (19) In the formula, Side slip angle, r The yaw rate is angular velocity. For heading angle, v For longitudinal velocity, The sideslip angular velocity, This is the yaw acceleration. The rate of change of heading angle, This is the longitudinal acceleration.

3. The cross-coupled global continuous robust control method according to claim 2, characterized in that, The acceleration in the X-axis direction Y-axis acceleration The relationship with the control input is expressed by the following formulas (20) and (21) or formula (22): (20) (21) (22) In the formula, and It is a lumped disturbance term.

4. The cross-coupled global continuous robust control method according to claim 3, characterized in that, and Represented as: (23) The lumped disturbance term and its derivative are bounded, satisfying: (24) In the formula, D 1( t ) represents the lumped disturbance term in the X direction. D 2( t ) represents the lumped disturbance term in the Y direction. Let D1(t) be the upper bound. This is the upper bound of D2(t). The time derivative of D2(t) for The upper realm, for The upper boundary.

5. The cross-coupled global continuous robust control method according to claim 1, characterized in that, The error vector and the first derivative of the error are expressed as follows: (25) In the formula, e X Let be the error vector in the X-axis direction of the forklift. e Y Let be the error vector in the Y-axis direction of the forklift. , for e X , e Y A first-order singular, , for e X , e Y The second derivative of .

6. The cross-coupled global continuous robust control method according to claim 5, characterized in that, The objective function is expressed as: (26) In the formula, X ( t () represents the actual X-axis position of the forklift in the ground reference coordinate system. Y ( t () represents the actual Y-axis position of the forklift in the ground reference coordinate system. ( t ) represents the rate of change of position error in the X direction. ( t ) represents the rate of change of position error in the Y direction. ( t Let be the second derivative of the position error in the X direction. ( t ) represents the second derivative of the position error in the Y direction.

7. The cross-coupled global continuous robust control method according to claim 6, characterized in that, The control function is expressed as follows: (29) In the formula, Let S1 be the first derivative of the sliding mode function S1 in the X direction. The first derivative of the sliding mode function S2 in the Y direction. The robust control gain coefficient in the X direction. The robust control gain coefficient in the Y direction. The smoothing coefficient for continuous control in the X direction. The smoothing coefficient is continuously controlled in the Y direction. e X ( T ) for at time T The position error in the X direction, ( T ) for at time T The velocity error in the X direction, ( T ) for at time T The velocity error in the Y direction.

8. The cross-coupled global continuous robust control method according to claim 7, characterized in that, The globally continuous robust control law obtained based on the control function is expressed as follows: (30) In the formula, S 1 represents the sliding mode function in the X direction. S 2 is the sliding mode function in the Y direction. , , , All are positive control gains, and sgn is the sign function. t For time.

9. The cross-coupled global continuous robust control method according to claim 8, characterized in that, Output steering angle and acceleration After achieving globally continuous and stable synchronized movement of the two forklifts via their actuators, the method further includes a stability analysis step for the cross-coupled globally continuous robust controller synchronization system. This stability analysis step includes: Substituting equation (29) into equation (30) yields the following result. (31) In the formula, control gain , , , All are positive control gains, satisfying: (32) In the formula, It is an auxiliary parameter that satisfies the following relationship: (33) By introducing auxiliary parameters Rewrite equation (31) as (34) In the formula, S 1( t Let be the sliding mode function in the X direction at time t. S 2( t Let be the sliding mode function in the Y direction at time t. and These are the robust control gain coefficients in the X and Y directions, respectively. and These are the continuous control smoothing coefficients in the X and Y directions, respectively; Combining equations (32) and (34), we get: (35) From equations (27) and (35), we obtain that the control law satisfies the Herwitz polynomial, that is: (36)。

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