A Finite-Time Bounded Control Strategy for Standard Orchard Machinery Based on DOBC

Abstract

This invention discloses a finite-time bounded control strategy for standard orchard machinery based on DOBC (Digital Oscillator-Based Control). It describes the kinematic model of the rigid body structure of the standard orchard machinery; utilizes an extended state observer to monitor the system's state and disturbances; and designs a system control law based on the observer's results, ensuring the standard orchard machinery operates within a set range without harming the fruit trees. The finite-time bounded control strategy for standard orchard machinery based on DOBC proposed in this invention guarantees that the machinery's operating state remains within a specified range, and that the machinery operates stably under the provided controller. The design method of this invention is a systematic design scheme.

Description

Technical Field

[0001] This invention discloses a finite-time bounded control strategy for standard orchard machinery based on DOBC, belonging to the field of control technology for standard orchard machinery in agriculture. Background Technology

[0002] In standard orchards, agricultural machinery must navigate along the desired path and not exceed the designated area. A standard orchard refers to one with an area of ​​over 300 mu (approximately 20 hectares), complete infrastructure, and fruit trees planted at a specific row spacing, such as a standard pear orchard or a standard apple orchard. When agricultural machinery operates in a standard orchard, such as for mass agricultural operations like spraying pesticides, precision tillage, and harvesting and fertilizing, the machinery's travel range must not exceed the row spacing between the fruit trees; otherwise, it will damage the trees. Therefore, the machinery must operate only within a certain range.

[0003] Agricultural machinery operates within a defined range for a finite time period, making it susceptible to disturbances. Excessive disturbances can prevent the machinery from accurately tracking the intended path within the allotted time, causing it to exceed the row spacing of fruit trees and damage them. Therefore, a method is needed to mitigate the impact of disturbances on the machinery. Disturbance Observation-Based Control (DOBC) is a suitable approach. This invention addresses this issue... Figure 1 The standard orchard machinery navigation path shown is finite-time bounded. By drawing on the mathematical model proposed in the paper "Research on Intelligent Control Method of Multi-mode Variable Structure for Agricultural Machinery Navigation" [D] (Weiliguo, 2015), a finite-time bounded control strategy for standard orchard machinery based on DOBC is proposed.

[0004] Therefore, in the field of control technology for standard orchard agricultural machinery in existing agriculture, a control strategy that can solve the problem of finite-time bounded control of standard orchard agricultural machinery is proposed. Summary of the Invention

[0005] The purpose of this invention is to solve the finite-time bounded problem of standard orchard agricultural machinery and provide a finite-time bounded control strategy for standard orchards based on DOBC.

[0006] This invention provides a novel time-bounded control strategy for standard orchard machinery. To ensure that standard orchard machinery operates within the bounded spacing between fruit tree rows and avoids damage to the trees, it is necessary to reduce the impact of disturbances on the machinery, allowing it to travel within the required road area. This invention, through Time-Bounded Control (DOBC), ensures that the machinery's operating status remains within a certain safe range, thereby protecting the fruit trees.

[0007] The present invention makes the following main contributions: 1. It uses an extended state observer to observe the state of the system and can accurately estimate the disturbances of the system; 2. It uses the DOBC control strategy to ensure that the agricultural machinery is bounded in finite time.

[0008] This invention provides the following technical solution:

[0009] A finite-time bounded control strategy for standard orchard machinery based on DOBC, the control strategy comprising the following steps:

[0010] Step 1: Establish a mathematical model for the operation of standard orchard agricultural machinery, and initialize the system state and control parameters. The process is as follows:

[0011] 1.1 Design principles for standard orchard agricultural machinery operation control rules;

[0012] In order to avoid making the motion model of agricultural machinery too complex, while still accurately describing the operating state of the agricultural machinery, we make the following assumptions:

[0013] Assumption 1: The control variables of the motion model are the speed of the agricultural machinery and the front wheel steering angle;

[0014] Assumption 2: The two front wheels are equivalent to the virtual wheels between the two wheels, and the agricultural machinery is simplified into a two-wheel model;

[0015] Assumption 3: The agricultural machinery moves on a flat, level surface;

[0016] Assumption 4: The movement of agricultural machinery is pure rolling, with no slippage occurring;

[0017] The detailed notation for the kinematic model of agricultural machinery is as follows:

[0018] --S is a pre-defined path, defined within an absolute coordinate system [O, X, Y];

[0019] --M is the center of the rear wheel of the agricultural machinery;

[0020] --Q is the point on S that is closest to M, and Q is unique;

[0021] --p is the coordinate of point Q along the direction of S, c(p) represents the curvature of S at this point, and θ1 represents the tangent direction angle along the path S at this point relative to the coordinate system [O, X, Y].

[0022] --θ2 is the direction angle of the centerline of the agricultural machinery relative to the coordinate system [O, X, Y]; therefore, θ = θ1 - θ2 represents the heading deviation of the agricultural machinery relative to the path S;

[0023] --x is the lateral position deviation of the agricultural machinery relative to path S;

[0024] -- It is the linear velocity of the agricultural machinery at point M;

[0025] --δ is the front wheel direction angle relative to the center of the agricultural machinery;

[0026] --L is the wheelbase of the agricultural machinery;

[0027] 1.2 The kinematic system model of standard orchard agricultural machinery can be represented in the following form;

[0028]

[0029] For the following cases in system model (1):

[0030]

[0031] (2) means that the center point M of the rear wheel of the agricultural machinery coincides with the curvature center of the desired path S, and the kinematic model of the agricultural machinery is abnormal. Therefore, it is not necessary to consider it in actual operation because the curvature of the desired path is small. In actual normal operation, the center point M of the rear wheel of the agricultural machinery will not coincide with the curvature center of the desired path S.

[0032] Step 2: Establish a spatial state model of the standard orchard agricultural machinery operation system;

[0033] It should be noted that, in order for agricultural machinery to accurately track the desired path, it is only necessary to ensure that x and θ do not exceed certain limits. Therefore, it is only necessary to study the kinematic properties of x and θ, that is, to ensure X(t). T RX(t)≤c z , where X = [x, θ] T .

[0034] Define state variables x1 =x, x2=θ, x3=δ, agricultural machinery operating speed Constant, control quantity is In a standard orchard, the desired path S can be considered as a straight line, i.e., curvature c(p) = 0. Then, equation (1) can be rewritten in the following state-space form:

[0035]

[0036] Where y = x1 is the system output;

[0037] It can be seen that the kinematic model of agricultural machinery has strong nonlinearity. Designing a controller directly for it would be very difficult and hard to implement. Therefore, linearizing it yields the following form:

[0038]

[0039] During the operation of agricultural machinery, it is inevitably affected by multi-source disturbances such as model parameter perturbations and external disturbances. Therefore, (4) can be further rewritten as:

[0040]

[0041] That is

[0042]

[0043] where represents the total disturbance received by the system;

[0044] Step 3, design of the controller for the standard orchard agricultural machinery operation system;

[0045] Finite-time boundedness means that for the system

[0046]

[0047] Given c1, c2, T, d, c1 < c2, for we have:

[0048]

[0049] A sufficient condition for finite-time boundedness is that there exist a positive scalar α and two positive definite matrices Q1, Q2 such that

[0050]

[0051] Let T max be the maximum value of T (the time of finite-time boundedness) that can be taken to maintain the sufficiency condition. It can be seen from the condition that, on the premise that other quantities remain unchanged, T<​​​​​​​​​​​​​​​Based on the system's state-space equations, the following extended state observer can be established:

[0056]

[0057] Where z1, z2, and z3 represent the observations of states x1, x2, and x3, respectively, z4 represents the estimate of the disturbance ω, and e y The output error is represented by l1, l2, l3, and l4, which represent the observer gain.

[0058] 3.2 Design the controller;

[0059] For the above model, the feedback matrix is ​​constructed using the pole placement method. The system matrix, control matrix, and disturbance matrix of the above model are as follows:

[0060]

[0061] Let the feedback matrix K = [k1 k2 k3], then If the closed-loop poles are set to -1, then the closed-loop characteristic polynomial is λ. 3 +3λ 2 +3λ+1, so the feedback matrix

[0062] If the feedforward section is set to a disturbance gain of -1, then the controller... in Indicates the state observed by the observer. This represents the estimated disturbance. Therefore, the original system would become:

[0063]

[0064] Compared with the original system In comparison, the disturbance in the system at this time is from the original It became

[0065] The technical concept of this invention is as follows: In order to avoid damage to fruit trees caused by the operation of agricultural machinery exceeding the prescribed range in the standard orchard agricultural machinery operation system, a finite-time bounded control strategy for standard orchard agricultural machinery based on DOBC is designed. An extended state observer is used to estimate the disturbances encountered during the operation of the agricultural machinery and cancel them at the control end, so as to ensure that the state of the system can be limited within a certain range, thereby avoiding damage to fruit trees and economic losses to fruit farmers. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the operation of the agricultural machinery in a standard orchard according to the present invention;

[0067] Figure 2 This is a schematic diagram of the movement of the agricultural machinery according to the present invention;

[0068] Figure 3 It is a standard finite-time bounded control block diagram for orchard machinery based on DOBC;

[0069] Figure 4 Agricultural Machinery X without DOBC T RX-t diagram;

[0070] Figure 5 Agricultural Machinery X based on DOBC T RX-t diagram; Detailed Implementation

[0071] The invention will now be further described with reference to the accompanying drawings.

[0072] Reference Figures 1-5 A finite-time bounded control strategy for standard orchard machinery based on DOBC, the control strategy comprising the following steps:

[0073] Step 1: Establish a mathematical model for the operation of standard orchard agricultural machinery, and initialize the system state and control parameters. The process is as follows:

[0074] 1.1 Design principles for standard orchard agricultural machinery operation control rules;

[0075] In order to avoid making the motion model of agricultural machinery too complex, while still accurately describing the operating state of the agricultural machinery, we make the following assumptions:

[0076] Assumption 1: The control variables of the motion model are the speed of the agricultural machinery and the front wheel steering angle;

[0077] Assumption 2: The two front wheels are equivalent to the virtual wheels between the two wheels, and the agricultural machinery is simplified into a two-wheel model;

[0078] Assumption 3: The agricultural machinery moves on a flat, level surface;

[0079] Assumption 4: The movement of agricultural machinery is pure rolling, with no slippage occurring;

[0080] The detailed notation for the kinematic model of agricultural machinery is as follows:

[0081] --S is a pre-defined path, defined within an absolute coordinate system [O, X, Y];

[0082] --M is the center of the rear wheel of the agricultural machinery;

[0083] --Q is the point on S that is closest to M, and Q is unique;

[0084] --p is the coordinate of point Q along the direction of S, c(p) represents the curvature of S at this point, and θ1 represents the tangent direction angle along the path S at this point relative to the coordinate system [O, X, Y].

[0085] --θ2 is the direction angle of the centerline of the agricultural machinery relative to the coordinate system [0, X, Y]; therefore, θ=θ1-θ2 represents the heading deviation of the agricultural machinery relative to the path S;

[0086] --x is the lateral position deviation of the agricultural machinery relative to path S;

[0087] -- It is the linear velocity of the agricultural machinery at point M;

[0088] --δ is the front wheel direction angle relative to the center of the agricultural machinery;

[0089] --L is the wheelbase of the agricultural machinery;

[0090] 1.2 The kinematic system model of standard orchard agricultural machinery can be represented in the following form;

[0091]

[0092] For the following cases in system model (1):

[0093]

[0094] (2) means that the center point M of the rear wheel of the agricultural machinery coincides with the curvature center of the desired path S, and the kinematic model of the agricultural machinery is abnormal. Therefore, it is not necessary to consider it in actual operation because the curvature of the desired path is small. In actual normal operation, the center point M of the rear wheel of the agricultural machinery will not coincide with the curvature center of the desired path S.

[0095] Step 2: Establish a spatial state model of the standard orchard agricultural machinery operation system;

[0096] It should be noted that, in order for agricultural machinery to accurately track the desired path, it is only necessary to ensure that x and θ do not exceed certain limits. Therefore, it is only necessary to study the kinematic properties of x and θ, that is, to ensure X(t). T RX(t)≤c2, where X=[x,θ] T ;

[0097] Define state variables x1 = x, x2 = θ, x3 = δ, and the operating speed of the agricultural machinery. Constant, control quantity is In a standard orchard, the desired path S can be considered as a straight line, i.e., curvature c(p) = 0. Then, equation (1) can be rewritten in the following state-space form:

[0098]

[0099] Where y = x1 is the system output;

[0100] It can be seen that the kinematic model of agricultural machinery has strong nonlinearity. Designing a controller directly for it would be very difficult and hard to implement. Therefore, linearizing it yields the following form:

[0101]

[0102] During the operation of agricultural machinery, it is inevitable that it will be affected by multiple sources of interference, such as model parameter perturbation and external interference. Therefore, (4) can be further rewritten as:

[0103]

[0104] Right now

[0105]

[0106] in This represents the total disturbance experienced by the system;

[0107] Step 3, Design of the standard orchard agricultural machinery operation system controller;

[0108] Finite-time boundedness refers to the system

[0109]

[0110] Given c 1、 c2, T, d, c1 < c2, for have:

[0111]

[0112] A sufficient condition for finite-time boundedness is the existence of a positive scalar α and two positive definite matrices Q. 1、 Q2, making

[0113]

[0114] Let T max To maintain the maximum value of T (finite-time bounded time) that can be obtained while the sufficient condition holds, it can be seen from the condition that, assuming other quantities remain unchanged, T max It is negatively correlated with the magnitude d of the disturbance. Therefore, as long as a suitable controller is designed to cancel out disturbances and reduce d, the finite-time boundedness of the system can be guaranteed to a certain extent.

[0115] As can be seen from the finite-time bounded control block diagram based on DOBC, the control signal consists of two parts: a feedback part and a feedforward part. The feedback part constructs the feedback matrix through the pole placement method, while the feedforward part subtracts the estimated disturbance at the control end to cancel the influence of the disturbance on the system.

[0116] 3.1 Establish an extended state observer;

[0117] Since the state of the system and the disturbances it experiences cannot be directly measured, it is necessary to establish an extended state observer to observe the state of the system and estimate the disturbances it experiences.

[0118] Based on the system's state-space equations, the following extended state observer can be established:

[0119]

[0120] Where z1, z2, and z3 represent the observations of states x1, x2, and x3, respectively, z4 represents the estimate of the disturbance ω, and e y The output error is represented by l1, l2, l3, and l4, which represent the observer gain.

[0121] 3.2 Design the controller;

[0122] For the above model, the feedback matrix is ​​constructed using the pole placement method; the system matrix, control matrix, and disturbance matrix of the above model are as follows:

[0123]

[0124] Let the feedback matrix K = [k1 k2 k3], then If the closed-loop poles are set to -1, then the closed-loop characteristic polynomial is λ. 3 +3λ 2 +3λ+1, so the feedback matrix

[0125] If the feedforward section is set to a disturbance gain of -1, then the controller... in Indicates the state observed by the observer. This represents the estimated disturbance. Therefore, the original system would become:

[0126]

[0127] Compared with the original system In comparison, the disturbance in the system at this time is from the original It became

[0128] To verify the feasibility of the proposed method, this invention presents simulation results of the control strategy on the MATLAB simulation platform:

[0129] The parameters are given as follows: Considering a standard orchard with a length of 120m, taking the Dongfanghong ME504 wheeled tractor as an example, the wheelbase L = 1.830m, and the given operating speed of the tractor. Therefore, the simulation time is given as 60 seconds, and the system matrix, control matrix, and disturbance matrix are as follows:

[0130]

[0131] Set c1 = 1, c2 = 2, The perturbation is set to sin(0.5t), and the feedback matrix K = [-0.46 -2.75 -3].

[0132] Without using the DOBC control strategy, but only using feedback control, the simulation results are as follows: Figure 4 As shown, the X of the agricultural machinery T RX exceeded the specified limits;

[0133] Using the DOBC control strategy, it can be calculated that... Simulation results are as follows Figure 5 As shown, the X of the agricultural machinery T RX remains bounded over a finite time and stabilizes within a very small value over a short period of time, demonstrating good control performance.

[0134] The excellent optimization effect shown by the above-described embodiment of the present invention is obviously not limited to the above embodiment. Various modifications can be made to it without departing from the basic spirit of the present invention and without exceeding the scope of the substantive content of the present invention.

Claims

1. A finite-time bounded control strategy for standard orchard machinery based on DOBC, characterized by comprising the following steps: Step 1: Establish a mathematical model for the operation of standard orchard agricultural machinery, and initialize the system state and control parameters. The process is as follows: 1.1 Design principles for standard orchard agricultural machinery operation control rules; To avoid making the motion model of agricultural machinery too complex, while still accurately describing its operating state, we make the following assumptions: Assumption 1: The control variables of the motion model are the speed of the agricultural machinery and the front wheel steering angle; Assumption 2: The two front wheels are equivalent to the virtual wheels between the two wheels, and the agricultural machinery is simplified into a two-wheel model; Assumption 3: The agricultural machinery moves on a flat, level surface; Assumption 4: The movement of agricultural machinery is pure rolling, with no slippage occurring; The detailed notation for the kinematic model of agricultural machinery is as follows: --S is a pre-defined path, defined within an absolute coordinate system [O, X, Y]; --M is the center of the rear wheel of the agricultural machinery; --Q is the point on S that is closest to M, and Q is unique; --p is the coordinate of point Q along the direction of S, c(p) represents the curvature of S at this point, and θ1 represents the tangent direction angle along the path S at this point relative to the coordinate system [O, X, Y]. --θ2 is the direction angle of the agricultural machinery's centerline relative to the coordinate system [O, X, Y]; therefore, θ = θ1 - θ2 represents the heading deviation of the agricultural machinery relative to the path S; --x is the lateral position deviation of the agricultural machinery relative to path S; -- It is the linear velocity of the agricultural machinery at point M; --δ is the front wheel direction angle relative to the center of the agricultural machinery; --L is the wheelbase of the agricultural machinery; 1.2 The kinematic system model of standard orchard agricultural machinery can be represented in the following form; For the following cases in system model (1): (2) means that the center point M of the rear wheel of the agricultural machinery coincides with the curvature center of the desired path S, and the kinematic model of the agricultural machinery is abnormal. Therefore, it is not necessary to consider it in actual operation because the curvature of the desired path is small. In actual normal operation, the center point M of the rear wheel of the agricultural machinery will not coincide with the curvature center of the desired path S. Step 2: Establish a spatial state model of the standard orchard agricultural machinery operation system; It should be noted that, in order for agricultural machinery to accurately track the desired path, it is only necessary to ensure that x and θ do not exceed certain limits. Therefore, it is only necessary to study the kinematic properties of x and θ, that is, to ensure X(t). T RX(t)≤c2, where X=[x,θ] T ; Define state variables x1 = x, x2 = θ, x3 = δ, and the operating speed of the agricultural machinery. Constant, control quantity is In a standard orchard, the desired path S can be considered as a straight line, i.e., curvature c(p) = 0. Then, equation (1) can be rewritten in the following state-space form: in, y = x1 is the system output; It can be seen that the kinematic model of agricultural machinery has strong nonlinearity. Designing a controller directly for it would be very difficult and hard to implement. Therefore, linearizing it yields the following form: During the operation of agricultural machinery, it is inevitable that it will be affected by multiple sources of interference, such as model parameter perturbation and external interference. Therefore, (4) can be further rewritten as: Right now in This represents the total disturbance experienced by the system; Step 3, Design of the standard orchard agricultural machinery operation system controller; Finite-time boundedness refers to the system Given c1, c2, T, d, where c1 < c2, for have: A sufficient condition for finite-time boundedness is that there exists a positive scalar α and two positive definite matrices Q1 and Q2 such that... Let T max To maintain the maximum value of T (finite-time bounded time) that can be obtained while the sufficient condition holds, it can be seen from the condition that, assuming other quantities remain unchanged, T max It is negatively correlated with the magnitude d of the disturbance. Therefore, as long as a suitable controller is designed to cancel out disturbances and reduce their impact on the system, the finite-time boundedness of the system can be guaranteed to a certain extent. As can be seen from the finite-time bounded control block diagram based on DOBC, the control signal consists of two parts: a feedback part and a feedforward part. The feedback part constructs the feedback matrix through the pole placement method, while the feedforward part subtracts the estimated disturbance at the control end to cancel the influence of the disturbance on the system. 3.1 Establish an extended state observer; Since the state of the system and the disturbances it experiences cannot be directly measured, it is necessary to establish an extended state observer to observe the state of the system and estimate the disturbances it experiences. Based on the system's state-space equations, the following extended state observer can be established: Where z1, z2, and z3 represent the observations of states x1, x2, and x3, respectively, z4 represents the estimate of the disturbance ω, and e y L1 represents the output error, and L2, L3, and L4 represent the observer gain. 3.2 Design the controller; For the above model, the feedback matrix is ​​constructed using the pole placement method; the system matrix, control matrix, and disturbance matrix of the above model are as follows: Let the feedback matrix K = [k1 k2 k3], then If the closed-loop poles are set to -1, then the closed-loop characteristic polynomial is λ. 3 +7λ 2 +12λ+10, so the feedback matrix If the feedforward section is set to a disturbance gain of -1, then the controller... in Indicates the state observed by the observer. If we represent the estimated disturbance, then the original system would become: Compared with the original system In comparison, the disturbance in the system at this time is from the original It became

Images