A Forklift Synchronous Control Method Based on Cross-Coupled Sliding Mode Control

Abstract

The present invention discloses a forklift synchronization control method based on cross-coupled sliding mode control, including the establishment of an input-output sliding mode controller and the establishment of a cross-coupled controller. The forklift synchronization method based on cross-coupled sliding mode control designed by the present invention achieves good control effects for the high-precision synchronization control of forklifts and the suppression of synchronization errors during the synchronized steering of two forklifts, and has good robustness in the presence of interference from complex operating conditions of forklifts.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric pallet forklifts, and particularly relates to a synchronous control method for forklifts with cross-coupled sliding mode control. Background Art

[0002] Forklifts are engineering vehicles widely used in ports, stations, airports, freight yards, factory workshops, warehouses, distribution centers and logistics centers. They are essential and efficient equipment for loading, unloading, handling, pallet transportation and container transportation of pallet goods in cabins, carriages and containers. Forklifts can generally be divided into two categories: internal combustion forklifts and electric forklifts. Affected by factors such as labor substitution, environmental protection upgrading and electrification upgrading, electric forklifts are becoming the mainstream transportation vehicles in the handling industry to replace internal combustion forklifts. However, it is difficult for electric forklifts to achieve precise motion control of the expected position of the forklift.

[0003] Patent Name: A Hybrid Electric Pallet Forklift and Its Motion Method (Patent Application No. 201910530060.7) proposed a hybrid electric pallet forklift and its motion method using a mechanical coupling method. However, this structure relies on hard synchronization of the mechanical structure, and there is a problem that the mechanical structure will be distorted when the motion is asynchronous. Summary of the Invention

[0004] The purpose of the present invention is to provide a synchronous control method for forklifts with cross-coupled sliding mode control to solve the precise motion control of the expected position of the forklift.

[0005] The technical solution provided by the present invention is as follows:

[0006] A synchronous control method for forklifts with cross-coupled sliding mode control,

[0007] Step 1, Establishment of the dynamic model of the electric pallet forklift

[0008] First, a fixed ground coordinate system marked with X and Y is established. Secondly, a vehicle body coordinate system is established with the center of mass P of the forklift as a particle, the x-axis as the longitudinal direction of the forklift movement, and the y-axis as the lateral direction of the forklift movement;

[0009] δ represents the steering angle of the front wheels of the forklift, and β f represents the side slip angle of the front wheels, and β r1 , β r2 represent the side slip angles of the two rear wheels. The side slip angle generates a lateral lateral force of F yf , F yr1 , F yr2 , and the tires control the lateral movement of the forklift under the action of the lateral lateral force;

[0010] The forces of each tire of the forklift act on the centroid P of the forklift. Let β represent the centroid sideslip angle of the forklift, ψ represent the course angle of the forklift centroid, U and V respectively represent the lateral and longitudinal speeds of the centroid P in the vehicle coordinate system, v represent the vector motion speed of the centroid P, r represent the yaw angular velocity of the forklift centroid, and l f represents the distance from the centroid to the center axis of the front wheels, lr represents the distance from the centroid to the center axis of the rear wheels, and d r represents the wheelbase of the two rear wheels of the forklift;

[0011] The following assumptions are made for the forklift tires,

[0012] 1) For a forklift moving at high speed, the lateral force of the tire is considered to increase linearly when the sideslip angle β f 、β r1 、β r2 is less than 4°;

[0013] 2) The sideslip angles β f 、β r1 、β r2 of the tires during the movement of the forklift are extremely small;

[0014] Based on the above assumptions, the following mathematical model of the forklift is obtained:

[0015] F y = m * α y (1)

[0016] where the lateral force of the tire is represented by F y , the mass of the forklift is represented by m, and the lateral acceleration is represented by α y ;

[0017] F = I z * α r (2)

[0018] where the resultant yaw moment of the forklift is represented by F, the yaw moment of inertia of the forklift body is represented by I z , and the yaw angular acceleration of the forklift body is represented by α r ;

[0019] Rewriting the above formula (1) gives

[0020]

[0021] Rewriting the above formula (2) gives

[0022]

[0023] From the linear relationship between the lateral force of the tire and the front wheel steering angle, we can get

[0024] F yr = K f*β f (5-1)

[0025] F yr1 =K r1 *β r1 (5-2)

[0026] F yr2 =K r2 *β r2 (5-3)

[0027] Among them, the lateral force of the front tire, the lateral force of the rear tire 1, and the lateral force of the rear tire 2 are represented by F yf , F yr1 , F yr2 respectively. The cornering stiffness of the front wheel, the cornering stiffness of the rear wheel 1, and the cornering stiffness of the rear wheel 2 are represented by K f , K r1 , K r2 respectively. The slip angle of the front wheel, the slip angle of the rear wheel 1, and the slip angle of the rear wheel 2 are represented by β f , β r1 , β r2 respectively.

[0028] Since the slip angle is very small during the actual driving of the forklift, it can be approximately considered that U = v * cosβ ≈ v, V = v * sinβ ≈ v * β. At the same time, d r is negligible compared with the driving length of the forklift. Let d r = 0, and the slip angles of the front wheel, the rear wheel 1, and the rear wheel 2 can be obtained

[0029]

[0030]

[0031]

[0032] Substituting equations (6) to (8) into the above equations (5-1), (5-2), and (5-3) gives

[0033]

[0034]

[0035]

[0036] The cornering stiffness K r1 of the rear wheel 1 and the cornering stiffness K r2 of the rear wheel 2 are the same. Therefore, F yr1 = F yr2 . In addition, let K r1 = K r2 = Kr , F yr = F yr1 = F yr2 ,

[0037] The above equation (3) can be rewritten as

[0038]

[0039] The above equation (4) can be rewritten as

[0040]

[0041] Since β f is very small when the forklift is moving, let sinβ f ≈ 0, cosβ f ≈ 1, the above equation (12) can be rewritten as

[0042]

[0043] Substituting equations (9), (10) and (11) into the above equations (13) and (14) gives

[0044]

[0045]

[0046] From the relationship between the forklift heading angle ψ and the yaw angular velocity r of the forklift's center of mass

[0047]

[0048] From the relationship between the forklift speed v and the acceleration α

[0049]

[0050] From the relationship between the vehicle body coordinate system and the ground coordinate system

[0051]

[0052]

[0053] Select the sideslip angle β of the center of mass, the yaw angular velocity f, the yaw angle ψ, and the velocity v of the center of mass movement as the state variables of the system; select the front wheel steering angle δ and the vehicle body acceleration α as the inputs of the system; select the velocity X in the X direction and the velocity Y in the Y direction of the forklift in the fixed coordinate system as the outputs of the system to establish the state space equation

[0054]

[0055]

[0056] Step 2: Establishment of the input-output sliding mode controller

[0057] Derive the output of the system in the above equations (21) and (22) to obtain

[0058]

[0059]

[0060] Rearrange the inputs δ and α in the above equations (23) and (24) to obtain

[0061]

[0062] Define the error

[0063]

[0064] where the X coordinate in the ground coordinate system is represented by X, the Y coordinate in the ground coordinate system is represented by Y, the desired X coordinate in the ground coordinate system is represented by X d and the desired Y coordinate in the ground coordinate system is represented by Y d . The deviation between the desired and actual coordinates on the X coordinate is represented by eX, and the deviation between the desired and actual coordinates on the Y coordinate is represented by eY;

[0065] Define the sliding mode function

[0066]

[0067] where the sliding mode function 1 is represented by S 1 and the sliding mode function 2 is represented by S 2 . The sliding mode convergence speed coefficient 1 is represented by C 1 and the sliding mode convergence speed coefficient 2 is represented by C 2 ;

[0068] Separate the input vectors δ and α, and design the input-output sliding mode control law to obtain

[0069]

[0070] where the switching term function is represented by sgn, the switching term coefficient 1 is represented by η 1 and the switching term coefficient 2 is represented by η 2 . v 1 and v 2 are obtained from equation (29);

[0071]

[0072] Step 3: Establishment of the cross-coupling controller

[0073] Given the expected X and Y axis speeds of forklift 1 simultaneously, the difference between this speed and the actual X and Y axis speeds of forklift 1 itself is used to obtain the self-movement error of forklift 1. The self-input-output sliding mode controller of forklift 1 controls the movement of forklift 1 through the self-movement error of forklift 1. Similarly, the expected X and Y axis speeds of forklift 2 are calculated from the expected X and Y axis speeds of forklift 1. The difference between this speed and the actual X and Y axis speeds of forklift 2 itself is used to obtain the self-movement error of forklift 2. The self-input-output sliding mode controller of forklift 2 controls the movement of forklift 2 through the self-movement error of forklift 2;

[0074] The difference between the actual X and Y axis speeds of forklift 1 and the actual X and Y axis speeds of forklift 2 is used to obtain the cross-coupling movement error of forklift 1. The cross-coupling input-output sliding mode controller of forklift 1 controls forklift 1 to complete synchronous deviation calibration through the cross-coupling movement error of forklift 1. Similarly, the difference between the actual X and Y axis speeds of forklift 2 and the actual X and Y axis speeds of forklift 1 is used to obtain the cross-coupling movement error of forklift 2. The cross-coupling input-output sliding mode controller of forklift 2 controls forklift 2 to complete synchronous deviation calibration through the cross-coupling movement error of forklift 2.

[0075] A forklift synchronous control method with cross-coupling sliding mode control according to the present invention application has achieved good control effects for the high-precision synchronous control of forklifts and the suppression of synchronous errors during double-forklift synchronous steering, and has good robustness in the presence of interference from complex operating conditions of forklifts. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a schematic structural diagram of an electric pallet forklift system according to the present invention;

[0077] Figure 2 It is a force analysis diagram of forklift dynamics according to the present invention;

[0078] Figure 3 It is a block diagram of a cross-coupling input-output sliding mode control method according to the present invention;

[0079] Figure 4 It is an ideal path diagram for forklift synchronous operation according to the present invention;

[0080] Figure 5 It is a simulation result diagram of no-load synchronous movement according to the present invention;

[0081] Figure 6 It is a simulation result diagram of 2T load synchronous movement according to the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0082] To make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the present invention will be further described below in conjunction with specific embodiments.

[0083] A synchronous control method for forklifts based on cross-coupled sliding mode control, including the establishment of an input-output sliding mode controller and the establishment of a cross-coupled controller.

[0084] The specific process of the cross-coupled sliding mode control method for electric pallet forklifts is as follows:

[0085] Step 1: Establishment of the dynamic model of the electric pallet forklift

[0086] The actual working conditions of the forklift operation scenario are complex. When the forklift is driving on different road surfaces, the changing tire-ground friction coefficient will affect the acceleration and deceleration of the forklift, and at the same time, the backlash jitter of the steering transmission structure will affect the steering movement of the forklift system. The sliding mode controller has a fast response speed and is robust to the interference caused by external angular jitter and friction changes. Therefore, an input-output sliding mode controller is adopted to cope with the complex operation conditions of the above forklift.

[0087] Refer to Figure 1 As shown in the structure of an electric pallet forklift system, it includes components such as the vehicle head 9, forklift forks 8, forklift front wheels 4, forklift rear wheels 7, steering servo motor 3, planetary reducer 2, planetary gear 1, sun gear 6, and straight-line servo motor 5. Among them, the steering servo motor 3 is decelerated by the planetary reducer 2 and then rotates on the sun gear 6 by the planetary gear 1 to realize the lateral rotation of the forklift front wheel 4; the main shaft of the straight-line servo motor 5 is connected to the central axis of the forklift front wheel 4, which is the power device for realizing the forward and backward movement of the forklift.

[0088] A force analysis diagram of a forklift is as Figure 2 shown,

[0089] First, establish a fixed ground coordinate system marked with X and Y. Secondly, establish a vehicle body coordinate system with the center of mass P of the forklift as the mass point, the x-axis as the longitudinal direction of the forklift movement, and the y-axis as the lateral direction of the forklift movement;

[0090] δ represents the steering angle of the forklift front wheel, β f represents the side slip angle of the front wheel, β r1 、β 2 represent the side slip angles of the two rear wheels. The side slip angle generates lateral lateral forces F yf 、F yr1 、F yr2 , and the tires control the lateral movement of the forklift under the action of the lateral lateral forces;

[0091] The above-mentioned forces of each tire of the forklift act on the center of mass P of the forklift. Use β to represent the center of mass side slip angle of the forklift, ψ to represent the course angle of the center of mass of the forklift, U and V respectively represent the lateral and longitudinal speeds of the center of mass P in the vehicle body coordinate system, v represents the vector movement speed of the center of mass P, r represents the yaw angular velocity of the forklift center of mass, l f represents the distance from the center of mass to the center axis of the front wheel, l rIt represents the distance from the centroid to the center axis of the rear wheels, d r It represents the wheelbase of the two rear wheels of the forklift;

[0092] The following assumptions are made for the forklift tires,

[0093] 1) For a forklift moving at high speed, the lateral force of the tire is considered to increase linearly when the sideslip angle β f 、β r1 、β r2 is less than 4°;

[0094] 2) During the movement of the forklift, the sideslip angles β f 、β r1 、β r2 are extremely small;

[0095] Based on the above assumptions, the following mathematical model of the forklift is obtained:

[0096] F y = m * α y (1)

[0097] where the lateral force of the tire is represented by F y , the mass of the forklift is represented by m, and the lateral acceleration is represented by α y ;

[0098] F = I z * α r (2)

[0099] where the resultant yaw moment of the forklift is represented by F, the yaw moment of inertia of the forklift body is represented by I z , and the yaw acceleration of the forklift body is represented by α r ;

[0100] Rewriting the above formula (1) gives

[0101]

[0102] Rewriting the above formula (2) gives

[0103]

[0104] From the linear relationship between the lateral force of the tire and the front wheel steering angle, we can get

[0105] F yr = K f * β f (5 - 1)

[0106] F yr1 = K r1 * β r1 (5 - 2)

[0107] Fyr2 = K r2 *β r2 (5 - 3)

[0108] Among them, the lateral force of the front tire, the lateral force of the rear tire 1, and the lateral force of the rear tire 2 are represented by F yf , F yr1 , F yr2 respectively. The cornering stiffness of the front wheel, the cornering stiffness of the rear wheel 1, and the cornering stiffness of the rear wheel 2 are represented by K f , K r1 , K r2 respectively. The sideslip angle of the front wheel, the sideslip angle of the rear wheel 1, and the sideslip angle of the rear wheel 2 are represented by β f , β r1 , β r2 respectively.

[0109] Since the sideslip angle is very small during the actual driving process of the forklift, it can be approximately considered that U = v * cosβ ≈ v, V = v * sinβ ≈ v * β. At the same time, d r is negligible in comparison with the driving length of the forklift. Let d r = 0, then β r1 ≈β r2 , and the sideslip angles of the front wheel, the rear wheel 1, and the rear wheel 2 can be obtained

[0110]

[0111]

[0112]

[0113] Substituting equations (6) to (8) into the above equations (5 - 1), (5 - 2), and (5 - 3) gives

[0114]

[0115]

[0116]

[0117] The cornering stiffness K r1 of the rear wheel 1 and the cornering stiffness K r2 of the rear wheel 2 are the same. Therefore, F yr1 = F yr2 . In addition, let K r1 = K r2 = K r , F yr = F yr1 = F yr2 .

[0118] Rewriting the above equation (3) gives

[0119]

[0120] The above formula (4) can be rewritten as

[0121]

[0122] Since β f is very small when the forklift is moving, let sinβ f ≈ 0 and cosβ f ≈ 1. The above formula (12) can be rewritten as

[0123]

[0124] Substituting formulas (9), (10) and (11) into the above formulas (13) and (14) gives

[0125]

[0126] From the relationship between the forklift heading angle ψ and the yaw angular velocity r of the forklift's center of mass, we get

[0127]

[0128] From the relationship between the forklift speed v and the acceleration α, we get

[0129]

[0130] From the relationship between the vehicle body coordinate system and the ground coordinate system, we get

[0131]

[0132]

[0133] Select the sideslip angle β of the center of mass, the yaw angular velocity r, the yaw angle ψ, and the moving speed v of the center of mass as the state variables of the system; select the front wheel steering angle δ and the vehicle body acceleration α as the inputs of the system; select the speed X in the X direction and the speed Y in the Y direction of the forklift in the fixed coordinate system as the outputs to establish the state space equation as

[0134]

[0135]

[0136] Step 2: Establishment of the input-output sliding mode controller

[0137] For the output of the system in the above formulas (21) and (22) Taking the derivative gives

[0138]

[0139]

[0140] For the above ([[]] 23 ), arranging the inputs δ and α in equations (24) gives

[0141]

[0142] Define the error

[0143]

[0144] Among them, the X coordinate of the ground coordinate system is represented by X, the Y coordinate of the ground coordinate system is represented by Y, the expected X coordinate of the ground coordinate system is represented by X d and the expected Y coordinate of the ground coordinate system is represented by Y d . The deviation between the expected coordinate and the actual coordinate on the X coordinate is represented by eX, and the deviation between the expected coordinate and the actual coordinate on the Y coordinate is represented by eY;

[0145] Define the sliding mode function

[0146]

[0147] Among them, the sliding mode function 1 is represented by S 1 and the sliding mode function 2 is represented by S 2 . The sliding mode convergence speed coefficient 1 is represented by C 1 and the sliding mode convergence speed coefficient 2 is represented by C 2 .

[0148] Separate the input vectors δ and α, and design the input-output sliding mode control law to obtain

[0149]

[0150] Among them, the switching term function is represented by sgn, the switching term coefficient 1 is represented by η 1 and the switching term coefficient 2 is represented by η 2 . v 1 , v 2 are obtained from equation (29)

[0151]

[0152] Furthermore, conduct a stability analysis of the forklift system

[0153] Take the Lyapunov function

[0154]

[0155]

[0156] Taking the derivative of the above equation (30) gives

[0157]

[0158] In the fourth step of the above equation (31), substituting equations (25) and (28), and in the fourth step, let

[0159]

[0160] Obviously, the following equation is obtained

[0161]

[0162] According to Lyapunov's theorem, it can be known that the system is Lyapunov stable. It is shown that in a finite time, S 1 → 0, S 2 → 0. The finite-time reachability of the sliding variable has been proven.

[0163] Furthermore, according to the sliding condition, once the system state is restricted to the pre-specified S = 0 sliding mode region, they can slide along the sliding surface S towards the origin. Here, the sliding manifold is constructed in the ground coordinate system error space, so the ground coordinate system error will asymptotically converge to zero along S. It can be seen from equation (33) that when t → ∞, e X → 0 and e Y → 0. It shows that both the self-position error and the cross-coupling synchronization error of the forklift synchronization system asymptotically converge to zero.

[0164] Step 3: Establishment of the cross-coupling controller

[0165] The cross-coupling controller is widely used in the position synchronization of multiple motors and has the advantages of high synchronization accuracy and strong robustness. The present invention applies a cross-coupling sliding mode controller to eliminate the motion deviation of two vehicles.

[0166] The block diagram of the cross-coupling input-output sliding mode control method of the present invention is as Figure 3 shown.

[0167] Referring to Figure 3 shown, while giving the desired X and Y axis speeds of forklift 1, the difference between this speed and the actual X and Y axis speeds of forklift 1 itself is used to obtain the self-motion error of forklift 1. The self-input-output sliding mode controller of forklift 1 controls the motion of forklift 1 through the self-motion error of forklift 1. Similarly, the desired X and Y axis speeds of forklift 2 are calculated from the desired X and Y axis speeds of forklift 1. The difference between this speed and the actual X and Y axis speeds of forklift 2 itself is used to obtain the self-motion error of forklift 2. The self-input-output sliding mode controller of forklift 2 controls the motion of forklift 2 through the self-motion error of forklift 2.

[0168] Further, the black dashed box represents the cross-coupling controller part. The actual X and Y axis speeds of forklift 1 are subtracted from those of forklift 2 to obtain the cross-coupling motion error of forklift 1. The cross-coupling input-output sliding mode controller of forklift 1 controls forklift 1 to complete the synchronization deviation calibration through the cross-coupling motion error of forklift 1. Similarly, the actual X and Y axis speeds of forklift 2 are subtracted from those of forklift 1 to obtain the cross-coupling motion error of forklift 2. The cross-coupling input-output sliding mode controller of forklift 2 controls forklift 2 to complete the synchronization deviation calibration through the cross-coupling motion error of forklift 2.

[0169] Next, simulation experiments are carried out to verify the accuracy of the present invention.

[0170] Experiment 1: Synchronous motion simulation experiment of two forklifts without load

[0171] The synchronous control method of forklifts with cross-coupling sliding mode control established according to the above method is used to conduct a simulation experiment on the forklift dynamics model to verify the effectiveness of this method.

[0172] Simulating the factory transportation environment, the forklift synchronization system starts from point a, loads and unloads goods at points b, c, and d, and finally terminates the movement at point e, maintaining synchronization between the two forklifts during the movement. The ideal path diagram of forklift synchronous operation is as Figure 4 shown. The center of mass P point of the two vehicles in the figure is used as an index for evaluating the motion synchronization performance in the following.

[0173] For equation (28) and Figure 3 the proposed synchronous control method of forklifts with cross-coupling sliding mode control is used to conduct a simulation of forklift no-load synchronization control on the forklift dynamics model.

[0174] Among them, the parameters of the self-calibration input-output sliding mode controllers of the two forklifts are both set to C 1 = 20; C 2 = 20; η 1 = 1.8; η 2 = 0.85. The parameters of the cross-coupling input-output sliding mode controllers of the two forklifts are both set to C 1 = 10; C 2 = 10; η 1 = 3; η 2 = 3.5.

[0175] The forklift system parameters are selected as follows: forklift mass m = 280 kg; distance from the center of mass to the rear wheels L f = 0.5 m; distance from the center of mass to the front wheels L r = 1 m; front wheel cornering stiffness K f = 4000 N*m / rad; rear wheel cornering stiffness K r = 1500 N*m / rad; yaw moment of inertia I of the whole vehicle about the center of massz = 69.488 kg / m^2; The longitudinal stiffness of the front wheel K x = 2000 N*m / rad; The unit lateral stiffness of the front wheel K y = 53333 N*m / rad; The acceleration due to gravity g = 9.8 N / kg; The reduction ratio i of the planetary reducer 1 = 0.025; The reduction ratio I of the steering gear and the sun gear 2 = 0.169; The backlash deviation e of the steering gear and the sun gear gear bacldach = 0.0074 rad.

[0176] Set the initial coordinates of forklift 1 in the ground coordinate system as X = 0; Y = 0, the initial body angle 0°, the initial coordinates of forklift 2 as X = 0; Y = -1, the initial body angle 0°, and set the target speed of the forklift as 3.5 m / s. Rotate counterclockwise by 90° in the ground coordinate system at the 25th s - 30th s, 55th s - 60th s, and 85th s - 90th s of the motion simulation to achieve the steering motion of the forklift at points b, c, and d.

[0177] For Experiment 1: The simulation result diagram of the no-load synchronous motion, as Figure 5 shown.

[0178] Refer to Figure 5 shown. It can be seen from the simulation diagram that under the forklift synchronization method of cross-coupled sliding mode control, the motion synchronization error of the centroid point P jitters between -3 and 3 mm, and the jitter is smaller during the synchronous steering of the forklifts. The error amplitude is adjusted to 0 within a certain period of time, achieving the goal of high-precision no-load synchronization of two forklifts.

[0179] Experiment 2: The synchronous motion simulation experiment of two 2T-load forklifts

[0180] Use the forklift synchronization control method of cross-coupled sliding mode control established by the above method to conduct a simulation experiment on the forklift dynamics model to verify the effectiveness of this method.

[0181] For equation (28) and Figure 3 the proposed forklift synchronization control method of cross-coupled sliding mode control is used to conduct a 2T-load synchronous control simulation on the forklift dynamics model.

[0182] Among them, the parameters of the self-calibration input-output sliding mode controllers of the two forklifts are both set to C 1 = 40; C 2 = 40; η 1 = 0.4η 2 = 0.3, and the parameters of the cross-coupled input-output sliding mode controllers of the two forklifts are both set to C 1 = 1; C 2 = 1; η 1 = 8; η2 = 8.

[0183] The forklift system parameters are selected as follows: the mass of the forklift m = 1280 kg; the distance from the center of mass to the rear wheels L f = 1 m; the distance from the center of mass to the front wheels L r = 0.5 m; the cornering stiffness of the front wheels K f = 4000 N*m / rad; the cornering stiffness of the rear wheels K r = 1500 N*m / rad; the yaw moment of inertia I of the whole vehicle about the center of mass z = 69.488 kg / m^2; the longitudinal stiffness of the front wheels K x = 2000 N*m / rad; the unit cornering stiffness of the front wheels K y = 53333 N*m / rad; the acceleration due to gravity g = 9.8 N / kg; the reduction ratio I of the planetary reducer 1 = 0.025; the reduction ratio I of the steering gear and the sun gear 2 = 0.169; the backlash deviation e between the steering gear and the sun gear gear bacldach = 0.0074.

[0184] The ideal trajectory is as Figure 4 shown. The initial coordinates of forklift 1 in the ground coordinate system are set as X = 0; Y = 0, the initial body angle is 0°, the initial coordinates of forklift 2 are X = 0; Y = -1, the initial body angle is 0°, and the target speed of the forklift is set as 3.5 m / s. It rotates counterclockwise by 90° in the ground coordinate system at the 25th s - 30th s, 55th s - 60th s, and 85th s - 90th s of the motion simulation to achieve the steering motion of the forklift at points b, c, and d.

[0185] For Experiment 2: The simulation results of the 2T load synchronous motion diagram are as Figure 6 shown.

[0186] Referring to Figure 6 shown, it can be seen from the simulation diagram that under the forklift synchronization method of cross-coupled sliding mode control, the synchronous error of the center of mass point P jitters between -6 and 4 mm, and the jitter is smaller during the synchronous steering of the forklifts. The error amplitude is adjusted to 0 within a certain period of time, achieving the goal of high-precision 2T load synchronization of double forklifts.

[0187] In summary of the above simulation results, the forklift synchronization method designed by the present invention with cross-coupled sliding mode control has achieved good control effects for the high-precision synchronous control of forklifts and the suppression of synchronous errors during the synchronous steering of double vehicles, and has good robustness in the presence of interference from complex operating conditions of forklifts.

Claims

1. A synchronous control method for forklifts based on cross - coupled sliding - mode control, characterized in that, Step 1: Establishment of the dynamic model of an electric pallet forklift Firstly, a fixed ground coordinate system marked by X and Y is established. Secondly, a vehicle body coordinate system is established with the center of mass P of the forklift as a particle, the x - axis as the longitudinal direction of the forklift movement, and the y - axis as the lateral direction of the forklift movement; δ represents the steering angle of the front wheels of the forklift, and β f represents the side slip angle of the front wheels, and β r1 , β r2 represents the side slip angles of the two rear wheels. The side slip angle generates a lateral force of F yf , F yr1 , F yr2 on the tires. Under the action of the lateral force, the tires control the lateral movement of the forklift; The forces of the tires of the above forklift act on the centroid P of the forklift. Let β represent the centroid sideslip angle of the forklift, ψ represent the heading angle of the forklift centroid, U and V respectively represent the lateral and longitudinal speeds of the centroid P in the vehicle coordinate system, v represent the vector motion speed of the centroid P, r represent the yaw angular velocity of the forklift centroid, and l f represents the distance from the centroid to the center axis of the front wheels, and l r represents the distance from the centroid to the center axis of the rear wheels, and d r represents the wheelbase of the two rear wheels of the forklift; Make the following assumptions about the forklift tires, 1) For a forklift moving at high speed, the lateral force of the tire is considered to increase linearly when the sideslip angles β f , β r1 , β r2 are less than 4°; 2) The side slip angle β of the forklift tire during movement f 、β r1 、β r2 is extremely small; Based on the above assumptions, the following mathematical model of the forklift is obtained: F y = m * α y (1) Among them, the lateral force of the tire is represented by F y The mass of the forklift is represented by m, and the lateral acceleration is represented by α y represented F = I z *α r (2) Among them, the resultant force of the forklift's yaw rotation is represented by F, and the yaw moment of inertia of the forklift body is represented by I z The yaw rotational acceleration of the forklift body is represented by α r represented By rewriting the above formula (1), we can get By rewriting the above formula (2), we can get From the linear relationship between the lateral force of the tire and the front - wheel steering angle, we can get F yr = K f * β f (5 - 1) F yr1 = K r1 * β r1 (5 - 2) F yr2 = / K r2 * β r2 (5 - 3) Among them, the lateral force of the front tire, the lateral force of the rear tire 1, and the lateral force of the rear tire 2 are represented by F yf , F yr1 , F yr2 respectively. The cornering stiffness of the front wheel, the cornering stiffness of the rear wheel 1, and the cornering stiffness of the rear wheel 2 are represented by K f , K r1 , K r2 respectively. The sideslip angle of the front wheel, the sideslip angle of the rear wheel 1, and the sideslip angle of the rear wheel 2 are represented by β f , β r1 , β r2 respectively. Since the sideslip angle is very small during the actual driving of the forklift, it can be approximately considered that U = v * cosβ ≈ v, V = v * sinβ ≈ v * β, and at the same time d r is negligible in comparison with the driving length of the forklift. Let d r = 0, and the sideslip angles of the front wheels, rear wheel 1, and rear wheel 2 can be obtained Substituting formulas (6) to (8) into the above formulas (5 - 1), (5 - 2), and (5 - 3), we can get Cornering stiffness K of the rear wheel 1 r1 and cornering stiffness K of the rear wheel 2 r2 are the same. Therefore, F yr1 = F yr2 In addition, let K r1 = K r2 = K r and F yr = F yr1 = F yr2 , By rewriting the above formula (3), we can get By rewriting the above formula (4), we can get Since β is very small when the forklift is moving f is very small, let sinβ f ≈ 0, cosβ f ≈ 1, the above equation (12) can be rewritten as Substituting formulas (9), (10), and (11) into the above formulas (13) and (14), we can get From the relationship between the heading angle ψ of the forklift and the yaw angular velocity r of the center of mass of the forklift, we can get From the relationship between the speed v of the forklift and the acceleration α, we can get From the relationship between the vehicle - body coordinate system and the ground coordinate system, we can get Select the sideslip angle β of the center of mass, the yaw angular velocity r, the yaw angle ψ, and the moving speed v of the center of mass as the state variables of the system; select the front - wheel steering angle δ and the vehicle - body acceleration α as the inputs of the system; select the speed X in the X - direction and the speed Y in the Y - direction of the forklift in the fixed coordinate system as the outputs of the system, and establish the state - space equation as follows Step 2: Establishment of the input - output sliding - mode controller Deriving the output of the system in the above equations (21) and (22) We can obtain by differentiation By organizing the inputs δ and α in the above formulas (23) and (24), we can get Define the error Among them, the X coordinate of the ground coordinate system is represented by X, the Y coordinate of the ground coordinate system is represented by Y, the expected X coordinate of the ground coordinate system is represented by X d represented, and the expected Y coordinate of the ground coordinate system is represented by Y d represented. The deviation between the expected coordinate and the actual coordinate on the X coordinate is represented by e X represented, and the deviation between the expected coordinate and the actual coordinate on the Y coordinate is represented by e Y represented; Define the sliding - mode function Among them, the sliding mode function 1 is represented by S 1 and the sliding mode function 2 is represented by S 2 ; the sliding mode convergence speed coefficient 1 is represented by C 1 and the sliding mode convergence speed coefficient 2 is represented by C 2 . Separate the input vectors δ and α, and design the input - output sliding - mode control law to get Among them, the switching term function is represented by sgn, the switching term coefficient 1 is represented by η 1 and the switching term coefficient 2 is represented by η 2 . v 1 and v 2 are obtained from equation (29); Step 3: Establishment of the cross - coupled controller Simultaneously give the expected X - axis and Y - axis speeds of forklift 1. The difference between this speed and the actual X - axis and Y - axis speeds of forklift 1 itself is used to obtain the self - motion error of forklift 1. The input - output sliding - mode controller of forklift 1 controls the movement of forklift 1 through the self - motion error of forklift 1. Similarly, the expected X - axis and Y - axis speeds of forklift 2 are calculated from the expected X - axis and Y - axis speeds of forklift 1. The difference between this speed and the actual X - axis and Y - axis speeds of forklift 2 itself is used to obtain the self - motion error of forklift 2. The input - output sliding - mode controller of forklift 2 controls the movement of forklift 2 through the self - motion error of forklift 2; The difference between the actual X - axis and Y - axis speeds of forklift 1 and the actual X - axis and Y - axis speeds of forklift 2 is used to obtain the cross - coupled motion error of forklift 1. The cross - coupled input - output sliding - mode controller of forklift 1 controls forklift 1 to complete the synchronous deviation calibration through the cross - coupled motion error of forklift 1. Similarly, the difference between the actual X - axis and Y - axis speeds of forklift 2 and the actual X - axis and Y - axis speeds of forklift 1 is used to obtain the cross - coupled motion error of forklift 2. The cross - coupled input - output sliding - mode controller of forklift 2 controls forklift 2 to complete the synchronous deviation calibration through the cross - coupled motion error of forklift 2.

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