A reclaimer bucket wheel position control method based on adaptive sliding mode controller

Abstract

The present invention discloses a method for controlling the position of a reclaimer bucket wheel based on an adaptive sliding mode controller. Aiming at the problem of reclaimer bucket wheel position control in complex environments, adaptive control and sliding mode control are combined to propose a method for controlling the position of a reclaimer bucket wheel based on an adaptive sliding mode controller. First, a three-degree-of-freedom bucket wheel reclaimer dynamics model is established. Then, a sliding mode surface is constructed based on this model and a sliding mode controller is designed. Then, in response to the chattering problem of the traditional sliding mode controller system, an adaptive law is designed to compensate for it, reducing output torque fluctuations and the impact of internal parameter uncertainty on the system. This improves bucket wheel positioning efficiency and meets the working requirements of the bucket wheel reclaimer for rapid positioning in complex environments such as load mass fluctuations.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial-grade reclaimers, and in particular relates to a reclaimer bucket wheel position control method based on an adaptive sliding mode controller. Background Art

[0002] Bucket-wheel reclaimers are large-scale reclaiming equipment widely used in material yards to reclaim materials. Because their booms are often over ten meters long, inaccurate position control can easily lead to collisions or motor stalls caused by the bucket wheel penetrating too deeply into the stockpile. Manual operation requires repeated adjustments to the bucket wheel's position, severely impacting positioning efficiency and posing safety risks. Therefore, research on a position control method for bucket-wheel reclaimers in complex environments is of great practical significance and value.

[0003] A bucket-wheel reclaimer features a gantry platform, a slew motor capable of rotating about the Z axis, and a hydraulic drive capable of pitching about the Y axis. This gives the bucket wheel at the end of the boom the ability to reclaim materials at a fixed point in space with three degrees of freedom. A bucket-wheel reclaimer is a nonlinear, tightly coupled system. This, combined with unfavorable factors such as parameter uncertainty caused by material mass variations and unmodeled dynamics, makes controlling the reclaimer's bucket wheel position quite difficult.

[0004] Currently, most material yards still use traditional PID methods to control bucket wheel position. This method struggles to overcome nonlinearities and interference, resulting in far from adequate bucket wheel positioning efficiency. Some control methods, such as neural networks and fuzzy PID control, which are independent of model parameters, have been used to address the strong nonlinear coupling of reclaimer bucket wheel positioning. However, significant changes in model parameters or the operating environment require readjustment of the rules or retraining, hindering practical industrial application. Others have used traditional sliding mode control to address interference in nonlinear systems, achieving some positioning control results but still failing to address system chattering caused by high-frequency switching.

[0005] Therefore, a bucket wheel position control method for a reclaimer based on an adaptive sliding mode controller is proposed to overcome the nonlinear dynamic characteristics of large inertia machinery, load mass fluctuations and other interferences, reduce torque fluctuations and system chattering, and improve bucket wheel positioning efficiency. Summary of the Invention

[0006] Purpose of the invention: In order to overcome the defects and shortcomings of the prior art, the present invention proposes a reclaimer bucket wheel position control method based on an adaptive sliding mode controller.

[0007] Technical solution: To achieve the above-mentioned purpose, the present invention adopts the following technical solution:

[0008] The method for controlling the bucket wheel position of a reclaimer based on an adaptive sliding mode controller includes the following steps:

[0009] Step 1) The bucket wheel at the end of the boom is equivalent to a three-degree-of-freedom robotic arm with translation-rotation-rotation, and a dynamic model of the bucket wheel's three-degree-of-freedom spatial positioning is established, and the dynamic model is converted into a second-order dynamic model;

[0010] Step 2) According to the given position θ d =[θ 0d θ 1d θ 2d ] T The error e between the actual position and the actual position is used to construct the sliding surface and design the control law of the sliding mode controller;

[0011] Step 3) Based on the control law of the sliding mode controller in step 2), an adaptive law is designed to compensate for the chattering term Ksign(s) of the sliding mode surface, and the control law parameters are tuned to obtain an adaptive sliding mode controller;

[0012] Step 4) The driving torque output by the adaptive sliding mode controller designed in step 3) is applied to three actuators: the driving wheel of the trolley platform, the rotary joint around the Z axis, and the pitch joint around the Y axis;

[0013] Step 5) Based on the position detection and posture recognition system, determine whether the three degrees of freedom are in place. If so, end the control process; otherwise, jump to step 3).

[0014] In step 1), the bucket wheel reclaimer is equivalent to a mechanical arm with three degrees of freedom: translation-rotation-rotation. The dynamic model is as follows:

[0015]

[0016] Where q = [x c θ1θ2] T , θ1 and θ2 are the angular positions of connecting rod 1 and connecting rod 2 respectively, and the motion equation of the trolley is rd is the diameter of the truck tire, is the angular velocity of the tire; take the basis of the null space of A(q)=[0 0 0]: v is the angular velocity of each actuator,

[0017]

[0018] Among them, M 11 =m0+m1+m2, M 12 =M 21 =-m2r2cosθ2sinθ1, M 13 =M 31 =-m2r2sinθ2cosθ1,

[0019]

[0020] in,

[0021] G( q )=[0 0 m2gr2 cos θ2] T

[0022]

[0023] Among them, τ=[τ1τ2τ3], τ1 is the driving torque on the driving wheel of the trolley platform, τ2 and τ3 are the driving torques of the two revolving joints, M(q)∈R 3×3 is the inertia matrix. is the centripetal force and Coriolis force matrix, G(q) is the gravitational vector, B(q) is the transformation matrix, τ∈R 3 is the input torque vector, A(q) is the additional constraint matrix, λ is the Lagrange multiplier; m0 is the mass of the trolley platform, m1 is the mass of link 1, m2 is the mass of link 2, and g is the acceleration of gravity; the lengths of link 1 and link 2 are l1 and l2, respectively, and their moments of inertia are J1 and J2, respectively; the distance from the center of mass of link 1 to the revolute joint is r1, and the distance from the center of mass of link 2 to the pitch joint is r2; θ1 and θ2 are the angular positions of link 1 and link 2, respectively. are the angular velocities of link 1 and link 2, respectively.

[0024] Considering the unmodeled dynamics of the system and the total disturbance, the system is converted into a second-order dynamic model:

[0025]

[0026] in, Represent the unmodeled dynamics and total disturbance of the manipulator system, simplifying the second-order dynamic model:

[0027]

[0028]

[0029] in, τ=[τ1τ2τ3], τ1 is the driving torque on the driving wheel of the trolley platform, τ2 and τ3 are the driving torques of the two rotating joints, q=[x c θ1θ2] T ,

[0030] The model under the unmodeled dynamics and total disturbance effects is expressed as:

[0031]

[0032]

[0033] In step 2) and step 3), an adaptive sliding mode controller is designed and the system output vector is selected as: θ = [θ0θ1θ2] T , where θ0 is the rotation angle of the truck tire, θ1 and θ2 are the angular positions of connecting rod 1 and connecting rod 2 respectively, and θ d =[θ 0d θ 1d θ 2d ] T The position is given by the above angle;

[0034] The position error is:

[0035] e=θ d -θ

[0036] According to the linear sliding surface:

[0037]

[0038] Where C = diag(c1, c2, c3), c i >0 (i=1, 2, 3) is the parameter to be adjusted,

[0039] Derivative of the sliding surface function have:

[0040]

[0041] The matrix parameters in the above formula may be affected by the uncertain mass m2 and are not equivalent to the nominal parameter matrix of the system, which can be expressed as It can be considered Satisfy the existence of their respective upper bounds, such that Then we have:

[0042]

[0043] where Θ=[m max v max g max ] T , against Estimates The designed adaptive law is:

[0044]

[0045] The matrices Γ and P are diagonal matrices of the positive eigenvalues of the parameters to be tuned. An adaptive law is added to compensate for the chattering term Ksign(s) on the sliding mode surface. The torque control law output by the controller is:

[0046]

[0047] Where sign is the sign function, ε is the sliding mode coefficient matrix, and the form of Λ is selected as:

[0048]

[0049] Therefore, the adaptive sliding mode controller is as follows:

[0050]

[0051] In actual situations, external disturbances cannot be accurately obtained and expressed, so the control law is written as:

[0052]

[0053] Adaptive sliding mode controller control law under quality parameter uncertainty You can write:

[0054]

[0055] in, and is the parameter matrix of the robot arm under nominal mass.

[0056] In step 5), the bucket-wheel reclaimer controller uses a PLC controller. Based on a calculated adaptive sliding mode control law, it drives three actuators: the gantry platform drive wheel, the Z-axis slewing joint, and the Y-axis pitching joint. The gantry's slewing angle is positioned using a circular Gray busbar system supplemented by redundant rotary encoders to improve interference immunity and stability. The bucket-wheel reclaimer's boom uses a non-contact inclination sensor to detect pitch angle. The installation of redundant inclination sensors ensures accurate and secure pitch angle measurement.

[0057] Compared with the prior art, the advantages of the present invention are as follows:

[0058] The present invention proposes a bucket wheel position control method for a reclaimer based on an adaptive sliding mode controller, which can solve the bucket wheel position control problem of the reclaimer in complex environments. At the same time, an adaptive law is designed for compensation, which alleviates the chattering problem of the traditional sliding mode controller system, reduces the output torque fluctuation, reduces the impact of internal parameter uncertainty on the system, improves the bucket wheel positioning efficiency, and meets the working requirements of the bucket wheel reclaimer for rapid positioning in complex environments such as fluctuations in load mass. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Flowchart of the bucket wheel position control method based on the adaptive sliding mode controller implemented in the present invention;

[0060] Figure 2 Schematic diagram of parameters of an equivalent three-degree-of-freedom robotic arm model implemented in the present invention;

[0061] Figure 3 This is a block diagram of the adaptive sliding mode controller implemented in the present invention;

[0062] Figure 4 θ2 response curves of the inaccurate mass sliding mode control, adaptive sliding mode control, and accurate mass sliding mode control implemented in the present invention;

[0063] Figure 5 The sliding mode controller and the adaptive sliding mode controller of the present invention are used to control the torque output of the mobile platform. DETAILED DESCRIPTION

[0064] The method of the present invention is described in detail below with reference to the accompanying drawings and specific implementation methods.

[0065] Example 1: A method for controlling the position of a bucket wheel of a reclaimer based on an adaptive sliding mode controller, comprising the following steps:

[0066] Step 1) The bucket wheel at the end of the boom is equivalent to a three-degree-of-freedom robotic arm with translation-rotation-rotation, and a dynamic model of the bucket wheel's three-degree-of-freedom spatial positioning is established, and the dynamic model is converted into a second-order dynamic model;

[0067] Step 2) According to the given position θ d =[θ 0d θ 1d θ 2d ] T The error e between the actual position and the actual position is used to construct the sliding surface and design the control law of the sliding mode controller;

[0068] Step 3) Based on the control law of the sliding mode controller in step 2), an adaptive law is designed to compensate for the chattering term Ksign(s) of the sliding mode surface, and the control law parameters are tuned to obtain an adaptive sliding mode controller;

[0069] Step 4) The driving torque output by the adaptive sliding mode controller designed in step 3) is applied to three actuators: the driving wheel of the trolley platform, the rotary joint around the Z axis, and the pitch joint around the Y axis;

[0070] Step 5) Based on the position detection and posture recognition system, determine whether the three degrees of freedom are in place. If so, end the control process; otherwise, jump to step 3). The details are as follows:

[0071] The overall process of the method of the present invention is as follows Figure 1The specific steps are as follows:

[0072] Bucket wheel reclaimer is equivalent to a robotic arm with three degrees of freedom: translation-rotation-rotation. Figure 2 As shown, its dynamic model is as follows:

[0073]

[0074] Where q = [x c θ1θ2] T , θ1 and θ2 are the angular positions of connecting rod 1 and connecting rod 2 respectively, and the motion equation of the trolley is r d is the diameter of the truck tire, is the angular velocity of the tire; take the basis of the null space of A(q)=[0 0 0]: v is the angular velocity of each actuator,

[0075]

[0076] Among them, M 11 =m0+m1+m2, M 12 =M 21 =-m2r2cosθ2sinθ1, M 13 =M 31 =-m2r2sinθ2cosθ1,

[0077]

[0078] in,

[0079] G( q )=[0 0 m2gr2 cosθ2] T

[0080]

[0081] Among them, τ=[τ1τ2τ3], τ1 is the driving torque on the driving wheel of the trolley platform, τ2 and τ3 are the driving torques of the two revolving joints, M(q)∈R 3×3 is the inertia matrix. is the centripetal force and Coriolis force matrix, G(q) is the gravitational vector, B(q) is the transformation matrix, τ∈R 3 is the input torque vector, A(q) is the additional constraint matrix, λ is the Lagrange multiplier; m0 is the mass of the trolley platform, m iis the mass of link 1, m2 is the mass of link 2, g is the acceleration of gravity, the lengths of link 1 and link 2 are l1 and l2 respectively, the moments of inertia are J1 and J2 respectively, the distance from the center of mass of link 1 to the revolute joint is r1, and the distance from the center of mass of link 2 to the pitch joint is r2; θ1 and θ2 are the angular positions of link 1 and link 2 respectively, are the angular velocities of link 1 and link 2, respectively.

[0082] Considering the unmodeled dynamics of the system and the total disturbance, the system is converted into a second-order dynamic model:

[0083]

[0084] in, Represent the unmodeled dynamics and total disturbance of the manipulator system, simplifying the second-order dynamic model:

[0085]

[0086]

[0087] in, τ=[τ1τ2τ3], τ1 is the driving torque on the driving wheel of the trolley platform, τ2 and τx are the driving torques of the two rotating joints, q=[x c θ1θ2] T , The model under the unmodeled dynamics and total disturbance effects is expressed as:

[0088]

[0089]

[0090] Design an adaptive sliding mode controller and select the system output vector as: θ=[θ0 θ1 θ2] T , where θ0 is the rotation angle of the truck tire, θ1 and θ2 are the angular positions of connecting rod 1 and connecting rod 2 respectively, and θ d =[θ 0d θ 1d θ 2d ] T is the position given by the above angle.

[0091] In this embodiment, the parameters of the robot arm model are selected as follows: m0 (nominal) = 3000 kg, m1 (nominal) = 2000 kg, m2 (nominal) = 1500 kg, m0 (real) = 3000 kg, m1 (real) = 2000 kg, m2 (real) = 1600 kg, l1 = 5 m, r1 = 2.5 m, l2 = 15 m, r2 = 7.5 m, rd=1m, J1(nominal)=1.25×10 4 kg·m 2 , J2(nominal)=8.4375×10 4 kg·m 2 , J2(real)=11.25×10 4 kg·m 2 .

[0092] During the actual reclaiming process of the bucket wheel reclaimer, the material carried on the boom fluctuates with the reclaiming speed, causing the boom mass parameter to differ from the nominal mass. Therefore, the actual m2 is selected to be different from the nominal mass.

[0093] The position error is:

[0094] e=θ d -θ

[0095] According to the linear sliding surface:

[0096]

[0097] Where C = diag(c1, c2, c3), c i >0 (i=1, 2, 3) is the parameter to be adjusted,

[0098] Derivative of the sliding surface function have:

[0099]

[0100] The matrix parameters in the above formula may be affected by the uncertain mass m2 and are not equivalent to the nominal parameter matrix of the system, which can be expressed as It can be considered Satisfy the existence of their respective upper bounds, such that Then we have:

[0101]

[0102] Where Θ=[m max v max g max ] T , against Estimates The designed adaptive law is:

[0103]

[0104] The matrices Γ and P are diagonal matrices of the positive eigenvalues of the parameters to be tuned. An adaptive law is added to compensate for the chattering term Ksign(s) on the sliding mode surface. The torque control law output by the controller is:

[0105]

[0106] Where sign is the sign function, ε is the sliding mode coefficient matrix, and the form of Λ is selected as:

[0107]

[0108] Therefore, the adaptive sliding mode controller (Adoptive Sliding Mode Controller) is as follows:

[0109]

[0110] In actual situations, external disturbances cannot be accurately obtained and expressed, so the control law is written as:

[0111]

[0112] Adaptive sliding mode controller control law under quality parameter uncertainty You can write:

[0113]

[0114] in, and is the parameter matrix of the robot arm under nominal mass.

[0115] The structure of the designed adaptive sliding mode controller is as follows: Figure 3 shown.

[0116] The parameters to be adjusted in an adaptive sliding mode controller are the sliding surface coefficient matrix ε, K, Γ, and P. K is the switching gain matrix. A larger K gain improves the system's anti-disturbance capability, but this also leads to greater torque fluctuations in the controller output and more pronounced system chattering. However, in practical systems, no form of sliding mode control can completely eliminate chattering, as eliminating chattering completely eliminates the sliding mode controller's anti-disturbance capability. The only way to compensate for the reduced K gain is to increase Λ.

[0117] The matrix parameters of the adaptive sliding mode controller are selected as ε = diag (1, 1, 1), K = diag (0.08, 0.08, 0.08), Γ = diag (0.2, 0.2, 0.2) and P = diag (0.1, 0.1, 0.1). For comparison, the matrix parameters of the sliding mode controller are selected as ε0 = diag (1, 1, 1), K0 = diag (1, 1, 1), and a constant torque disturbance is applied to the controlled object.

[0118] The obtained θ2 response curves of non-precise mass sliding mode control, adaptive sliding mode control and precise mass sliding mode control are shown as follows: Figure 4 As shown, the sliding mode controller and the adaptive sliding mode controller mobile platform torque control output are obtained as follows Figure 5 shown.

[0119] Depend on Figure 4 As can be seen, the adaptive sliding mode controller can further mitigate the negative impact of internal system parameter uncertainty on control performance. The system output tracks the desired angle with zero static error, ensuring the robustness of the control system and providing a certain degree of resistance to external constant disturbances. Compared with the traditional sliding mode controller, the bucket wheel positioning speed has been significantly improved, with the adjustment time reduced from 5 seconds to 3.8 seconds.

[0120] Depend on Figure 5 It can be seen that due to the addition of the adaptive control law, the switching gain matrix of the sign-even function is compensated, and the controller output torque fluctuation is significantly suppressed. Compared with the traditional sliding mode controller, the amplitude of the system chattering is significantly reduced, and the controller torque output chattering amplitude is reduced from 0.2×10 4 N·m 2 Reduced to 0.05×10 4 N·m 2 .

[0121] The bucket-wheel reclaimer's PLC controller utilizes the control module from Nanjing Sciyon's NT6000 DCS system. Based on a calculated adaptive sliding mode control law, it drives the three actuators: the gantry platform drive wheels, the Z-axis slewing joint, and the Y-axis pitch joint. The gantry's slewing angle is positioned using a GC2000 ring Gray busbar positioning system supplemented by redundant rotary encoders to enhance interference immunity and stability. The bucket-wheel reclaimer's boom utilizes a Witt Intelligent SINDT TTL / 232 sensor for non-contact pitch angle detection. This sensor features a wide single-axis measurement range, a wide temperature range, and excellent seismic resistance, ensuring accurate and secure pitch angle measurement.

[0122] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention, and equivalent changes or substitutions made on the basis of the above technical solutions fall within the scope of protection of the claims of the present invention.

Claims

1. A method for controlling the bucket wheel position of a reclaimer based on an adaptive sliding mode controller, characterized in that: The method comprises the following steps: Step 1) The bucket wheel at the end of the boom is equivalent to a three-degree-of-freedom robotic arm with translation-rotation-rotation, a three-degree-of-freedom spatial bucket wheel dynamic model is established, and the dynamic model is converted into a second-order dynamic model; Step 2) According to the given position θ d =[θ 0d θ 1d θ 2d ] T The error e between the actual position and the actual position is used to construct the sliding surface and design the control law of the sliding mode controller; Step 3) Based on the control law of the sliding mode controller in step 2), an adaptive law is designed to compensate for the chattering term Ksign(s) of the sliding mode surface, and the control law parameters are tuned to obtain an adaptive sliding mode controller; Step 4) applying the three-degree-of-freedom driving torque output by the adaptive sliding mode controller in step 3) to the three actuators of the vehicle platform driving wheel, the rotary joint around the Z axis, and the pitch joint around the Y axis; Step 5) Based on the position detection and posture recognition system, determine whether the three degrees of freedom are in place. If so, end the control process; otherwise, jump to step 2); In step 1), the bucket wheel reclaimer is considered as a mobile robot with three degrees of freedom to establish a dynamic model. The specific steps are as follows: The dynamic model of the bucket wheel reclaimer is equivalent to a robotic arm with three degrees of freedom: translation, rotation, and rotation. Where q = [x c θ1θ2] T , θ1 and θ2 are the angular positions of connecting rod 1 and connecting rod 2 respectively, and the motion equation of the trolley is r d is the diameter of the truck tire, is the angular velocity of the tire; take the basis of the null space of A(q)=[0 0 0]: v is the angular velocity of each actuator, where, M 11 = m0 + m1 + m2, M 12 = M 21 = -m2r2cosθ2sinθ1, M 13 = M 31 = -m2r2sinθ2cosθ1, in, G(q)=[00m2gr2cosθ2] Τ Among them, τ=[τ1τ2τ3], τ1 is the driving torque on the driving wheel of the trolley platform, τ2 and τ3 are the driving torques of the two revolving joints, M(q)∈R 3×3 is the inertia matrix, is the centripetal force and Coriolis force matrix, G(q) is the gravitational vector, B(q) is the transformation matrix, τ∈R 3 is the input torque vector, A(q) is the additional constraint matrix, λ is the Lagrange multiplier; m0 is the mass of the trolley platform, m1 is the mass of link 1, m2 is the mass of link 2, and g is the acceleration of gravity; the lengths of link 1 and link 2 are l1 and l2, respectively, and their moments of inertia are J1 and J2, respectively; the distance from the center of mass of link 1 to the revolute joint is r1, and the distance from the center of mass of link 2 to the pitch joint is r2; θ1 and θ2 are the angular positions of link 1 and link 2, respectively. are the angular velocities of link 1 and link 2 respectively; Considering the unmodeled dynamics and total disturbance of the system, the dynamic model is converted into a second-order dynamic model: in, Represent the unmodeled dynamics and total disturbance of the manipulator system, simplifying the second-order dynamic model: in, τ=[τ1τ2τ3], τ1 is the driving torque on the driving wheel of the trolley platform, τ2 and τ3 are the driving torques of the two rotating joints, q=[x c θ1θ2] T , 2. The method for controlling the bucket wheel position of a reclaimer based on an adaptive sliding mode controller according to claim 1, characterized in that: Step 2) and step 3) design the adaptive sliding mode controller. The specific steps are as follows: Select the system output vector as: θ=[θ0 θ1 θ2] T , where θ0 is the rotation angle of the truck tire, θ1 and θ2 are the angular positions of connecting rod 1 and connecting rod 2 respectively, and θ d =[θ 0d θ 1d θ 2d ] T is the given position in angle; The position error is: e=θ d -θ According to the linear sliding surface: Design the switching function of the system, where C = diag(c1, c2, c3), c i >0(i=1,2,3) is the parameter to be adjusted, Derivative of the sliding surface function have: The matrix parameters in the above formula are affected by the uncertain mass m2 and are not equivalent to the nominal parameter matrix of the system, which can be expressed as Satisfy the existence of their respective upper bounds, such that Then we have: Where Θ=[m max v max g max ] T , against Estimates The designed adaptive law is: The matrices Γ and P are diagonal matrices of the positive eigenvalues of the parameters to be tuned. An adaptive law is added to compensate for the chattering term Ksign(s) on the sliding mode surface. The torque control law output by the controller is: Where sign is the sign function, ε is the sliding mode coefficient matrix, and the form of Λ is selected as: Adaptive sliding mode controller control law under quality parameter uncertainty writing: in, and is the parameter matrix of the robot arm under nominal mass.

3. The method for controlling the position of a reclaimer bucket wheel based on an adaptive sliding mode controller according to claim 1, characterized in that: Step 5) Position detection and posture recognition system, the specific steps are as follows: The trolley rotation angle positioning uses annular Gray busbar positioning assisted by redundant rotary encoders to improve anti-interference ability and stability; the bucket wheel reclaimer arm uses a non-contact inclination sensor to detect the pitch angle, and the accuracy and safety of the pitch angle measurement are guaranteed by installing redundant inclination sensors; the controller uses a PLC controller, which drives the three actuators of the trolley platform drive wheel, the Z-axis rotation joint, and the Y-axis pitch joint according to the calculated adaptive sliding mode control law.

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