Agricultural tractor path tracking sliding mode control method

Abstract

The application discloses a kind of agricultural tractor path tracking sliding mode control methods, belong to agricultural tractor path tracking control field.Main steps are:1, establish agricultural tractor straight-line navigation path tracking dynamics model;2, define agricultural tractor straight-line navigation state variable, establish system state equation;3, select sliding surface, establish sliding mode dynamics equation;4, design corresponding sliding mode disturbance observer, estimate disturbance;5, according to dynamics model, design three-order sliding mode controller.The application has the following advantages: firstly, using sliding mode controller controls agricultural tractor straight-line navigation problem, so that the system has strong anti-interference ability;Secondly, by adding disturbance observation device, disturbance can be effectively estimated, overestimation is avoided, control gain is reduced, and then chattering problem is reduced.

Description

Technical Field

[0001] This invention relates to a method for tracking agricultural machinery path based on sliding mode control, belonging to the field of intelligent agricultural machinery control technology. Background Technology

[0002] my country is a major agricultural country, and agriculture is the foundation of social and economic development and the guarantee of people's material life. In order to promote the improvement of agricultural productivity and realize the development of agricultural modernization, people have put forward the concept of precision agriculture. It mainly uses technologies such as navigation satellite positioning technology, sensor technology, and remote sensing control to complete the autonomous operation of agricultural machinery and achieve automated navigation. This effectively reduces the time spent in farmland cultivation, improves cultivation efficiency, and can replace manual labor to achieve automatic driving, alleviate driver fatigue, reduce the incidence of production accidents, and improve production safety.

[0003] Agricultural machinery path tracking, as a key technology for automated navigation in agricultural machinery, has always been a research hotspot in the field of intelligent agricultural machinery control. Existing agricultural machinery path tracking technologies mainly rely on the navigation and positioning technology of the upper-level computer system and the sensor accuracy and hydraulic steering of the lower-level computer system for control. This significantly increases the complexity of system design and the dependence on the control model, raising production costs, reducing production efficiency, and also resulting in poor adaptability to agricultural machinery operating environments. Therefore, optimizing a robust and highly accurate path tracking controller while simplifying the structure of the agricultural machinery automatic navigation system is crucial to achieving precision and intelligent agriculture. Summary of the Invention

[0004] This invention provides a path tracking control method for agricultural machinery based on sliding mode theory, which can stably and effectively track and control unmanned agricultural machinery even when the system model parameters are uncertain or the operating environment is highly volatile. This method ensures the stability and accuracy of the nonlinear feedback controller while simplifying the original hardware system structure.

[0005] The technical solution of this invention is: a sliding mode control method for path tracking of agricultural tractors, comprising the following steps:

[0006] Step 1: Establish a linearized dynamic model for the linear navigation path tracking of agricultural tractors;

[0007] Step 2: Define the state variables for the linear navigation of the agricultural tractor and establish the system state equations;

[0008] Step 3: Select the sliding surface and establish the sliding dynamics equations;

[0009] Step 4: Design a third-order sliding mode controller;

[0010] Step 5: Design a finite-time disturbance observer to estimate the disturbance;

[0011] Step 6: Based on the dynamic equations and combined with a finite-time disturbance observer, design a composite third-order sliding mode controller.

[0012] Furthermore, in step 1, the dynamic model for linear navigation path tracking of the agricultural tractor is linearized. The process of establishing the linearized model is as follows:

[0013] First, taking an agricultural tractor as the object of action, a dynamic model for linear navigation path tracking of an agricultural tractor is obtained:

[0014] Where ψ is the heading angle, δ is the steering wheel deflection angle, and V x Let L be the tractor's forward velocity, L be the wheelbase, x be the vehicle's position along the path, and y be the lateral deviation. This model exhibits nonlinearity and strong coupling, making direct control design for this model extremely difficult. Generally, to address this issue, the most common method is to linearize the model near its equilibrium point, resulting in the following linearized model:

[0015]

[0016] In the formula, u is the control input, i.e. the rate of change of wheel yaw angle, and d(t) is the external lumped disturbance.

[0017] Furthermore, in step 3, the design process of the sliding mode dynamics equations is as follows:

[0018] First, define the state variables, let x1 = y, x2 = V. x ψ, Then system (2) can be written in the following form:

[0019]

[0020] Here, d1(t) is the external lumped disturbance, and x1, x2, x3 are state variables;

[0021] Then select appropriate sliding variables as follows:

[0022]

[0023] Based on the sliding variable and the linearized state equation, design the corresponding third-order sliding mode dynamics equation:

[0024] Here, a(t, x) represents the total uncertainty of the system, including d(t) which represents the external lumped disturbance.

[0025] Furthermore, in step 4, the sliding mode controller is designed as follows:

[0026] Here, β3 is the control gain, r1, r2, and r3 are constants, β1, β2, and α are positive constants, s1, s2, and s3 are sliding variables, and τ > 0.

[0027] Furthermore, the controller parameters need to satisfy the following relationship:

[0028] ρ≥a≥r1>r2>r3, β1>0, r2=r1-τ, r3=r2-τ, β2>0, β3>0, ρ>0 (7)

[0029] Furthermore, in step 5, the finite-time perturbation observer is designed as follows:

[0030]

[0031] Where M = b(t, x), v0, v1, v2, z3 are auxiliary variables, L0, L1, L2, L3 are all positive constants, and z0, z1, z2 are the observed values ​​of x1, x2 and d1(t).

[0032] Furthermore, the observer parameters need to satisfy the following relationship:

[0033]

[0034] Here, l>0.

[0035] Theoretically, once the observer converges, the bound of d(t) can be determined; however, due to initial overshoot, a certain amount of observation error is usually required for convergence. Therefore, directly estimating the bound of d(t) using z3 is inaccurate. The approach taken here is to take... Because the observer's output will stabilize after t≥T.

[0036] Furthermore, in step 6, the composite third-order sliding mode controller is designed as follows:

[0037]

[0038] Here, β4 is the control gain, r1, r2, and r3 are constants, β1, β2, and a are positive constants, and s1, s2, and s3 are sliding variables.

[0039] Furthermore, the parameters of the sliding contactor need to satisfy the following relationship:

[0040] ρ≥a≥r1>r2>r3, β1>0, r2=r1-τ, r3=r2-τ, β2>0, β4>0 (11)

[0041] Here, it should be noted that the values ​​of β4 and β3 are different: adding a disturbance observer allows us to accurately know the upper bound of the disturbance, thus eliminating the need to estimate the upper bound of the disturbance and preventing overestimation of the gain; then, by combining the saturation technique with this controller, we can obtain a third-order nested saturated sliding mode controller:

[0042]

[0043] ∈>0 is an arbitrary constant.

[0044] The present invention has the following beneficial technical effects:

[0045] 1) For the problem of linear navigation of agricultural tractors, a sliding mode controller based on power integral is proposed for the first time.

[0046] 2) Adding a disturbance observer can estimate the disturbance to a limited extent, reduce the control gain, and thus reduce chattering.

[0047] 3) Use Lyapunov analysis instead of geometric or homogeneous methods to analyze closed-loop third-order sliding mode dynamics. It can provide finite-time stability rather than finite-time convergence.

[0048] 4) This sliding mode controller can give agricultural tractor linear navigation systems better anti-interference ability and convergence performance. Attached Figure Description

[0049] Figure 1 Block diagram of agricultural machinery linear navigation control principle;

[0050] Figure 2 Heading angle response curves under the action of third-order sliding mode control and first-order linear sliding mode controller;

[0051] Figure 3 Lateral deviation response curves under the action of third-order sliding mode control and first-order linear sliding mode controller;

[0052] Figure 4 Steering wheel deflection angle response curve under the action of third-order sliding mode control and first-order linear sliding mode controller;

[0053] Figure 5 Controller response curves under the action of third-order sliding mode control and first-order linear sliding mode controller;

[0054] Figure 6 Sliding mode variable response curves under the action of third-order sliding mode control and first-order linear sliding mode controller;

[0055] Figure 7 Under the addition of saturation function: response curves of lateral deviation, heading angle, and steering wheel deflection angle;

[0056] Figure 8Controller response curve under saturation function;

[0057] Figure 9 Heading angle response curves with and without an observer;

[0058] Figure 10 Lateral deviation response curves for adding and not adding an observer;

[0059] Figure 11 The effect of adding an observer versus not adding an observer on the control input response curve; Detailed Implementation

[0060] This invention provides a sliding mode control method for path tracking of agricultural tractors. To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention.

[0061] Figure 1 The diagram shown is a schematic diagram of the system relationship of the present invention, which includes 1. a dynamic model of linear navigation path tracking for agricultural tractors, 2. the state equation of the linearized system obtained by linearization, 3. sliding mode dynamic equation, 4. observer model, and 5. third-order sliding mode controller.

[0062] Based on the above system, the following specific implementation explains the linear navigation path tracking control method for agricultural tractors of the present invention:

[0063] 1. Based on Figure 1 The following diagram illustrates the linear navigation of an agricultural tractor. A dynamic model for the linear navigation path tracking of the agricultural tractor is established as follows:

[0064]

[0065] Where ψ is the heading angle, δ is the wheel yaw angle, and V x Let L be the forward velocity of the tractor, L be the wheelbase, x be the position of the tractor along the path, and y be the lateral deviation.

[0066] This model shows that the system is nonlinear and strongly coupled, making direct control design of this model extremely difficult. Generally, the most common approach to solve this problem is to linearize the model around its equilibrium point and then design the linearized system.

[0067] 2. Based on the linear navigation path tracking dynamics model of agricultural tractors (1), the linearized model is established as follows:

[0068]

[0069] In the formula, u is the control input, i.e. the rate of change of wheel yaw angle, and d(t) is the external lumped disturbance.

[0070] 3. Based on the linearized model (2), establish the state equations for the system:

[0071] Let x1 = y, After the above linear transformation, the system can be written as follows, and the system state equation is as follows:

[0072]

[0073] Here, d1(t) represents the external lumped disturbance.

[0074] 4. Based on state equation (3), the design process of the sliding mode dynamics equation is as follows:

[0075] Select sliding variable

[0076]

[0077] Design the corresponding third-order sliding mode dynamics equations based on the sliding variables and the system's state equations:

[0078]

[0079] 5. Based on the sliding mode dynamics equation (5), the finite-time disturbance observer is designed as follows:

[0080]

[0081] in L0 = 1.1L, M = b(t, x)u, v0, v1, v2, z3 are auxiliary variables, and z0, z1, z2 are the observed values ​​of x1, x2 and d1(t);

[0082] 6. Based on the sliding mode dynamics equation (5), design the corresponding sliding mode controller:

[0083]

[0084] Here, ρ≥a≥r1>r2>r3, β1>0, r2=r1-τ, r3=r2-τ, and β1, β2, and β3 are all positive constants. Then, by combining the saturation technique with this controller, we can obtain a third-order nested saturated sliding mode controller:

[0085]

[0086] ∈>0 is an arbitrary constant.

[0087] Specifically: the sampling time is 30 seconds, the Euler method is used for simulation, the step size is 0.001 seconds, and here d1(t) = 2sin(t). <D

[0088] Here we compare with first-order linear sliding mode: linear sliding surface: s=c1x1+c2x2+x3, c1, c2>0.

[0089] controller Choose c1 = c2 = 0.5, D = 2, k1 = 1.5.

[0090] Then, we compared a third-order sliding mode controller with a first-order linear sliding mode surface, and a third-order sliding mode controller with and without an observer: Figure 2 Heading angle response curves under the action of third-order sliding mode control and first-order linear sliding mode controller; Figure 3 Lateral deviation response curves under the action of third-order sliding mode control and first-order linear sliding mode controller; Figure 4 Steering wheel deflection angle response curve under the action of third-order sliding mode control and first-order linear sliding mode controller; Figure 5 Controller response curves under the action of third-order sliding mode control and first-order linear sliding mode controller; Figure 6 Sliding mode variable response curves under the action of third-order sliding mode control and first-order linear sliding mode controller; Figure 7 Under the addition of saturation function: response curves of lateral deviation, heading angle, and steering wheel deflection angle; Figure 8 Controller response curve under saturation function; Figure 9 Heading angle response curves with and without an observer; Figure 10 Lateral deviation response curves for adding and not adding an observer; Figure 11 The effect of adding an observer versus not adding an observer on the control input response curve;

[0091] from Figure 2-4 It can be seen that, under the presence of disturbances, both the first-order linear sliding mode controller and the third-order sliding mode controller proposed in this paper have good anti-interference capabilities when using a sliding mode controller. At the same time, it is easy to see that the third-order sliding mode controller performs better than the first-order linear sliding mode controller in terms of dynamic process: both overshoot and settling time are significantly better. Figure 7-8 It can be seen that by adding a saturation function, the controller system achieves continuous control, and the chattering problem is significantly improved. From Figure 9-11 It can be seen that adding an observer can estimate and compensate for disturbances at the same time, thereby reducing β4, thus reducing chattering and further improving the system's anti-interference capability.

[0092] In summary, this invention relates to a path tracking method for agricultural machinery based on sliding mode control, belonging to the field of intelligent control technology for agricultural machinery. First, a mathematical model for linear navigation path tracking of agricultural machinery is constructed. Then, the state variables for linear navigation path tracking are defined, and the state equations of the system are established. Next, a third-order sliding mode controller is designed. Finally, a finite-time saturation controller is designed for the aforementioned sliding mode controller, resulting in a composite controller.

[0093] The advantages of the controller proposed in this invention are that it proposes sliding mode control, which has strong anti-interference ability, good dynamic performance and good robustness; at the same time, it proposes a disturbance observer based on the sliding mode controller to further improve the anti-interference ability of the system.

[0094] The detailed descriptions listed above are merely specific descriptions of feasible embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.

Claims

1. A sliding mode control method for path tracking of agricultural tractors, characterized in that: Includes the following steps: Step 1: Establish a linearized dynamic model for the linear navigation path tracking of agricultural tractors; Step 2: Define the state variables for the linear navigation of the agricultural tractor and establish the system state equations; Step 3: Select the sliding surface and establish the sliding dynamics equations; Step 4: Design a third-order sliding mode controller; Step 5: Design a finite-time disturbance observer to estimate the disturbance; The finite-time perturbation observer is designed as follows: （8）； in , , Wheelbase , To control the input amount, , The speed in the forward direction of the tractor. As an auxiliary variable, for The observed values, where s1 is the sliding variable. Let x1 and x2 be the vehicle positions along the path, x1 and x2 be the state variables, and d1(t) be the external lumped disturbance. Step 6: Based on the dynamic equations and combined with a finite-time disturbance observer, design a composite third-order sliding mode controller.

2. The sliding mode control method for path tracking of an agricultural tractor according to claim 1, characterized in that, In step 1, the dynamic model for linear navigation path tracking of agricultural tractors is linearized. The process of establishing the linearized model is as follows: First, taking an agricultural tractor as the object of action, we obtain the dynamic model of the agricultural tractor's straight-line navigation path tracking system: （1）； in For heading angle, For the steering wheel deflection angle, The speed in the forward direction of the tractor. Wheelbase This represents the vehicle position along the path. For lateral deviation; from the dynamic model of formula (1), the agricultural tractor straight navigation path tracking system is nonlinear and strongly coupled. If the dynamic model of formula (1) is directly controlled and designed, it will be very difficult. In order to solve this problem, linearization is performed near the equilibrium point of the dynamic model of formula (1), and the linearized model is as follows: (2); In the formula, To control the input, i.e. the rate of change of wheel yaw angle, d1(t) is the external lumped disturbance.

3. The sliding mode control method for path tracking of an agricultural tractor according to claim 2, characterized in that, In step 3, the design process of the sliding mode dynamics equations is as follows: First, define the state variable, let Then formula (2) can be written in the following form: （3）； here For external lumped disturbances. For state variables; Then select appropriate sliding variables as follows: (4); Based on the sliding variable and the linearized state equation, design the corresponding third-order sliding mode dynamics equation: （5）； here Let be the total uncertainty of the system, including d1(t) as the external lumped disturbance. .

4. The sliding mode control method for path tracking of an agricultural tractor according to claim 1, characterized in that, In step 4, the sliding mode controller is designed as follows: （6）； here To control the gain, It is a constant. For positive integers, It is a sliding variable.

5. The sliding mode control method for path tracking of an agricultural tractor according to claim 4, characterized in that, The controller parameters need to satisfy the following relationship: （7）； Where τ>0.

6. The sliding mode control method for path tracking of an agricultural tractor according to claim 2, characterized in that, The observer parameters need to satisfy the following relationship: (9); Theoretically, once the observer converges, the bound of d1(t) can be determined; however, due to initial overshoot, a certain amount of observation error is usually required for convergence. Therefore, directly using... The estimated bound of d1(t) is inaccurate. The solution here is to take: Because the observer's output will It stabilized later.

7. The sliding mode control method for path tracking of an agricultural tractor according to claim 2, characterized in that, In step 6, the composite third-order sliding mode controller is designed as follows: （10）； here To control the gain, It is a constant. For positive integers, It is a sliding variable.

8. The sliding mode control method for path tracking of an agricultural tractor according to claim 7, characterized in that, The parameters of the sliding contactor need to satisfy the following relationship: （11）； Let me point out here, and The numerical values ​​differ: By adding a disturbance observer, the upper bound of the disturbance can be accurately determined, eliminating the need to estimate the upper bound and preventing overestimation of the gain; then, by combining saturation techniques with a composite third-order sliding mode controller, we can obtain a third-order nested saturated sliding mode controller: ； It is an arbitrary constant.

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