A path tracking method for agricultural machinery based on non-singular terminal sliding mode

Abstract

The application discloses a kind of agricultural machinery path tracking methods based on non-singular terminal sliding mode, belong to agricultural machinery navigation technical field.Main steps are:1. establish the path tracking model including disturbance, and transform into the state equation of strict feedback form;2. design second-order disturbance observer to estimate unknown state related to heading and aggregate disturbance;3. considering the goal of path tracking, select appropriate sliding surface;4. design non-singular terminal sliding mode controller, realize path tracking goal.The application has the advantages that:one, controller design only uses position deviation information, realizes path tracking control goal without using sensor to measure heading deviation information, reduces sensor cost;Two, the controller shortens system response time, improves tracking accuracy;Three, disturbance in the system is accurately estimated and compensated into the controller simultaneously, enhances the anti-interference performance of system.

Description

Technical Field

[0001] This invention relates to path-tracking control technology for the navigation system of an agricultural wheeled tractor. Specifically, it utilizes state observation technology and a non-singular terminal sliding mode control method to design a path-tracking algorithm for agricultural machinery. This technology aims to improve the transient performance, tracking accuracy, and stability of the agricultural wheeled tractor's navigation system, belonging to the field of agricultural machinery navigation technology. Background Art

[0002] my country is a major agricultural country with a population of nearly 1.5 billion. Agriculture is a fundamental industry supporting the construction and development of the national economy. Since the beginning of the 21st century, urbanization has led to a large influx of agricultural laborers into urban employment. Coupled with the increasingly aging population, the construction and development of modern agriculture faces a serious challenge of labor shortages, which will inevitably greatly increase the demand for agricultural machinery and equipment. Agricultural mechanization and automation are the foundation for the implementation of precision agriculture. The higher the degree of mechanization and automation in agricultural production, the more conducive it is to the implementation of precision agriculture technologies. Agricultural tractors, as a key power source for mechanized field operations, can be used with various agricultural implements to perform a range of field operations and field management tasks, and can also be used to tow trailers for transportation. However, the control performance of automatic navigation systems is affected by factors such as the mechanical structure of the agricultural machinery, its posture sensors, operating conditions, and control algorithms. This results in unsatisfactory tracking performance for automatic navigation systems of agricultural tractors in practice. To address this issue, a path tracking control algorithm for an agricultural machinery navigation system was developed to ensure that the automatic navigation system not only maintains operational accuracy but also improves its robustness to disturbances.

[0003] Generally, the design of a path tracking controller for an agricultural tractor navigation system requires the use of the agricultural machinery's position and heading information. However, since the sensors installed on the agricultural machinery for measuring heading are susceptible to measurement noise and vehicle body shaking, this can lead to large errors in the measured values ​​of the heading information, causing abnormal fluctuations in the control signal and affecting the path tracking effect. Therefore, the present invention proposes to use state observation technology to simultaneously observe the unknown system states related to the heading in real time and estimate the unknown lumped disturbance in real time; on this basis, the controller is designed using a non-singular terminal sliding mode control method. It is worth noting that the developed path tracking control strategy achieves path tracking control without using sensors to measure heading information when only the position information of the agricultural machinery is required; in addition, the control algorithm is effective in improving transient path tracking performance, eliminating steady-state errors, enhancing stability, and suppressing disturbance directions. Summary of the Invention

[0004] To address current challenges in agricultural machinery path tracking, this paper proposes a path tracking method based on a nonsingular terminal sliding mode. This method achieves path tracking control without using sensor-measured heading information. The designed path tracking control algorithm demonstrates effectiveness in improving the transient path tracking performance of a tractor navigation system, eliminating steady-state errors, enhancing stability, and suppressing disturbances.

[0005] The technical solution of the present invention is: a method for agricultural machinery path tracking based on a non-singular terminal sliding mode, comprising the following steps:

[0006] Step 1: Analyze the disturbance factors existing in the actual operation process of the agricultural wheeled tractor and construct a path tracking model including the disturbance, which is used as a reference model for the design of the path tracking controller;

[0007] Step 2: Introduce coordinate transformation to transform the path tracking model into a state equation in a strict feedback form that is convenient for controller design;

[0008] Step 3: Considering the goal of path tracking, the state equation is combined to construct a non-singular terminal sliding surface;

[0009] Step 4: Based on the non-singular terminal sliding mode surface, design a non-singular terminal sliding mode controller;

[0010] Step 5: Aiming at the unknown system state and unknown lumped disturbance in the state equation, a second-order disturbance observer is designed to simultaneously realize the real-time observation of the unknown state and the accurate estimation of the unknown lumped disturbance;

[0011] Step 6: Design a non-singular terminal sliding mode controller based on state observation technology and saturation technology;

[0012] Step seven, perform an inverse transformation based on the controller in step six to obtain the actual control input of the agricultural machinery front wheel steering angle.

[0013] Furthermore, considering that agricultural machinery may be affected by disturbances in actual working scenarios, a path tracking model including disturbances is established as follows:

[0014]

[0015] where l os and θ os They represent the lateral deviation and heading deviation between the actual path of the agricultural machinery and the reference path, and l os and θ os The first derivative of , σ is the direction coefficient, which is defined as negative clockwise, v is the longitudinal speed of the agricultural machinery, L is the wheelbase of the agricultural machinery, δ fis the front wheel steering angle of the agricultural machinery, R is the radius of the reference path, and d(t) is the lumped disturbance including system uncertainty and external interference;

[0016] In order to better reflect the complex interference and uncertainty factors in the actual working environment of agricultural machinery, a lumped disturbance d(t) including constant interference, ramp interference, sine interference and cosine interference is designed and expressed as follows:

[0017] d(t)=vcosθ os d0(t)

[0018] Among them, d0(t) is designed as follows:

[0019]

[0020] Where d0(t) is the designed perturbation set and t is the time constant;

[0021] To facilitate path design, the radius R of the reference path is converted into the curvature of the path. Assuming that the agricultural machine moves forward along the trajectory in a clockwise direction, that is, the direction coefficient σ = -1; then the state space equation for the system is established:

[0022]

[0023] where c o is the curvature of the reference path, x1=l os , x2=v sinθ os , x1 and x2 are system states, and are the first-order derivatives of the system states x1 and x2, respectively, u = tanδ f is the input of the virtual controller.

[0024] Furthermore, in order to facilitate the processing of unknown system state x2, the system is further expressed as follows:

[0025]

[0026] in represents the unknown lumped disturbance.

[0027] Furthermore, in step 3, considering the path tracking goal of the agricultural machinery, a non-singular terminal sliding mode surface is constructed as follows:

[0028]

[0029] Where s is the sliding surface function, β>0 is the constant to be designed, p and q are positive odd numbers and satisfy

[0030] Selecting a nonlinear function as the sliding surface enables the state tracking error to converge to zero faster within a finite time, has good robustness to the errors of the agricultural machinery model and external interference signals, and improves the control performance.

[0031] Furthermore, in step 4, to achieve the control objective, the non-singular terminal sliding mode controller u is designed as:

[0032]

[0033] Among them, K1, K2>0 and K2>||D||, Then s will be stable in finite time.

[0034] Furthermore, in step 5, a second-order disturbance observer is designed, and its structure is as follows:

[0035]

[0036] L1, L2, L3 are positive real number observation gains, z0, z1, z2 represent the observer output variables, are the first-order derivatives of z0, z1, and z2 respectively, It is worth pointing out that the output states z1 and z2 in the observer are used to observe the unknown state x2 and the unknown lumped disturbance D respectively. The application of the observer realizes the simultaneous observation of the unknown state and disturbance.

[0037] Furthermore, in step 6, the non-singular terminal sliding mode controller u based on the state observation technology is designed as:

[0038]

[0039] Furthermore, a non-singular terminal sliding mode controller with saturation technology is designed as follows:

[0040]

[0041] Among them, the saturation function is an arbitrary constant.

[0042] Furthermore, in step seven, by controlling the controller u=tanδ f Perform inverse transformation to obtain the front wheel steering angle δ of the agricultural machinery f for:

[0043]

[0044] By adjusting the front wheel steering angle δ f Control, the final lateral deviation l os and heading deviation θ os will converge to zero.

[0045] The present invention has the following beneficial technical effects:

[0046] 1. In the present invention, the path tracking model is converted into a state equation in a strict feedback form for control design, which reduces the difficulty of controller design. The controller design only uses position deviation information to achieve path tracking control without sensor-measured heading deviation information, reducing sensor costs.

[0047] 2. The path tracking algorithm in the present invention can not only ensure that the lateral deviation and heading deviation converge to zero within a limited time, but also achieve faster system response and higher tracking accuracy.

[0048] 3. The method of the present invention is simple and easy to implement. It estimates the disturbance in the system through a second-order finite-time disturbance observer and compensates it synchronously in the controller, thereby enhancing the system's robustness against disturbances and achieving better control effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a control block diagram of the agricultural tractor path tracking control system of the present invention.

[0050] Figure 2 Schematic diagram of the agricultural tractor path tracking of the present invention.

[0051] Figure 3 is the curve of the disturbance d(t) changing with time.

[0052] Figure 4 Response curve of lateral deviation under U-shaped path condition.

[0053] Figure 5 Response curves of heading deviation and heading deviation estimation under U-shaped path conditions.

[0054] Figure 6 This is the response curve of the front wheel steering angle without adding the saturation function under the U-shaped path condition.

[0055] Figure 7 The response curve of the front wheel steering angle after adding the saturation function under the U-shaped path condition.

[0056] Figure 8 It is the trajectory result of path tracking under the U-shaped path condition. DETAILED DESCRIPTION

[0057] The present invention provides a path tracking method for agricultural machinery based on a non-singular terminal sliding mode. To clarify and clarify the objectives, technical solutions, and effects of the present invention, the following provides a clear and complete description of the technical solutions in the embodiments of the present invention, combined with the accompanying drawings. It should be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention.

[0058] Figure 1 This is a control block diagram of the agricultural tractor path tracking control system of the present invention, which mainly includes two parts: a control link and an observation link. Figure 2 The figure below is a schematic diagram of the path tracking of an agricultural tractor according to the present invention. The reference speed v of the agricultural machine is 3 m / s, and the wheelbase L of the agricultural machine is 1.69 m. Furthermore, it is assumed that the agricultural machine travels clockwise to track the reference path, i.e., the directional coefficient σ is -1. A method for agricultural machine path tracking based on a nonsingular terminal sliding mode controller is implemented as follows:

[0059] Step 1: Establish an agricultural machinery path tracking model including disturbances as follows:

[0060]

[0061] where l os and θ os They represent the lateral deviation and heading deviation between the actual path of the agricultural machinery and the reference path, σ is the direction coefficient (defined as clockwise is negative), v is the longitudinal speed of the agricultural machinery, L is the wheelbase of the agricultural machinery, and δ f is the front wheel steering angle of the agricultural machinery, R is the radius of the reference path, and d(t) is the lumped disturbance including system uncertainty and external interference.

[0062] Step 2: Convert the path tracking model into a state equation in strict feedback form.

[0063] Let x1 = l os , x2=v sinθ os , u=tanδ f , Then the system can be re-expressed as follows:

[0064]

[0065] Among them, x1 and x2 are system states, u is the input of the virtual controller, and c o is the curvature of the reference path.

[0066] Furthermore, in order to facilitate the processing of unknown system state x2, the system is further expressed as follows:

[0067]

[0068] in, D represents the unknown lumped disturbance.

[0069] Step 3: Construct a non-singular terminal sliding surface.

[0070]

[0071] Among them, β>0 is the constant to be designed, p and q are positive odd numbers, and satisfy

[0072] Step 4: Design a non-singular terminal sliding mode controller.

[0073]

[0074] Among them, K1, K2>0 and K2>||D|| are the guidance law parameters to be designed, and the sliding variable s will be stable within a finite time.

[0075] Step 5: Design a second-order finite-time disturbance observer:

[0076]

[0077] L1, L2, L3 are positive real observation gains, z0, z1, z2 represent the observer output variables; it is worth noting that the output states z1 and z2 in the observer are used to observe the unknown state x2 and the unknown lumped disturbance D respectively.

[0078] Step 6: Design a non-singular terminal sliding mode controller based on disturbance observation technology and saturation technology.

[0079]

[0080] Among them, K1, K2>0 and K2>||D|| are the guidance law parameters to be designed, and the sliding variable s will be stable within a finite time.

[0081] Improve the controller by adding a saturation function:

[0082]

[0083] Among them, the saturation function is an arbitrary constant.

[0084] Step 7: Inverse transform to obtain the steering angle of the front wheel of the agricultural machinery.

[0085]

[0086] Final lateral deviation l os and heading deviation θ os will converge to zero.

[0087] To better verify the control effect of the proposed output feedback path tracking algorithm, a simulation platform based on Matlab software was built to verify the effectiveness of the controller in the presence of interference. The simulation used the Euler method and set the sampling period to 0.001ms.

[0088] Figure 3 is the curve of disturbance d(t) changing with time (time(sec)), Figure 4 is the curve of lateral deviation changing with time under U-shaped path condition, Figure 5 is the response curve of the actual and estimated heading deviation under the U-shaped path condition, Figure 6 is the response curve of the front wheel steering angle without adding saturation function under U-shaped path condition, Figure 7 The response curve of the front wheel steering angle with the saturation function added under the U-shaped path condition is shown below. Figure 8 It is the trajectory result of path tracking under the U-shaped path condition.

[0089] It can be seen from the simulation results that in the presence of interference, the non-singular terminal sliding mode controller designed in the present invention based on state observation technology can track the reference path and travel along the reference path in a relatively short time. At the same time, the proposed control algorithm has good robust performance.

[0090] Although the present invention has been described in terms of various specific embodiments, those skilled in the art will appreciate that the present invention may be implemented with modifications within the spirit of the claims. Therefore, any obvious improvements, substitutions, or modifications that a person skilled in the art can make without departing from the spirit of the present invention are within the scope of protection of the present invention.

Claims

1. A method for agricultural machinery path tracking based on non-singular terminal sliding mode, characterized in that , including the following steps: Step 1: Analyze the disturbance factors existing in the actual operation process of the agricultural wheeled tractor and construct a path tracking model including the disturbance, which is used as a reference model for the design of the path tracking controller; Step 2: Introduce coordinate transformation to transform the path tracking model into a state equation in a strict feedback form that is convenient for controller design; Step 3: Considering the goal of path tracking, the state equation is combined to construct a non-singular terminal sliding surface; Step 4: Based on the non-singular terminal sliding mode surface, design a non-singular terminal sliding mode controller; Step 5: Aiming at the unknown system state and unknown lumped disturbance in the state equation, a second-order disturbance observer is designed to simultaneously realize the real-time observation of the unknown state and the accurate estimation of the unknown lumped disturbance; Step 6: Design a non-singular terminal sliding mode controller based on state observation technology and saturation technology; Step 7: Perform an inverse transformation based on the controller in step 6 to obtain the actual control input of the front wheel steering angle of the agricultural machinery; In step 3, considering the path tracking goal of the agricultural machinery, the non-singular terminal sliding mode surface is constructed as follows: Where s is the sliding surface function, β>0 is the constant to be designed, p and q are positive odd numbers and satisfy Selecting a nonlinear function as the sliding surface allows the state tracking error to converge to zero faster within a finite time, has good robustness to the errors of the agricultural machinery model and external interference signals, and improves the control performance; In step 4, to achieve the control objective, the non-singular terminal sliding mode controller u is designed as: Among them, K1, K2>0 and K2>||D||, Then s will be stable in finite time; In step 5, a second-order disturbance observer is designed, and its structure is as follows: L1, L2, L3 are positive real number observation gains, z0, z1, z2 represent the observer output variables, are the first-order derivatives of z0, z1, and z2 respectively, v0 and v1 are intermediate variables. It is worth noting that the output states z1 and z2 in the observer are used to observe the unknown state x2 and the unknown lumped disturbance D, respectively. The application of the observer realizes the simultaneous observation of the unknown state and disturbance. In step 6, the non-singular terminal sliding mode controller u based on the state observation technology is designed as: The non-singular terminal sliding mode controller with saturation technology is designed as follows: Among them, the saturation function δ>0 is an arbitrary constant.

2. The agricultural machinery path tracking method based on non-singular terminal sliding mode according to claim 1, characterized in that: Considering that agricultural machinery may be affected by disturbances in actual working scenarios, a path tracking model including disturbances is established as follows: where l os and θ os They represent the lateral deviation and heading deviation between the actual path of the agricultural machinery and the reference path, and l os and θ os The first derivative of , σ is the direction coefficient, which is defined as negative clockwise, v is the longitudinal speed of the agricultural machinery, L is the wheelbase of the agricultural machinery, δ f is the front wheel steering angle of the agricultural machinery, R is the radius of the reference path, and d(t) is the lumped disturbance including system uncertainty and external interference; In order to better reflect the complex interference and uncertainty factors in the actual working environment of agricultural machinery, a lumped disturbance d(t) including constant interference, ramp interference, sine interference and cosine interference is designed and expressed as follows: d(t)=vcosθ os d0(t) Among them, d0(t) is designed as follows: Where d0(t) is the designed perturbation set and t is the time constant; To facilitate path design, the radius R of the reference path is converted into the curvature of the path. Assuming that the agricultural machine moves forward along the trajectory in a clockwise direction, that is, the direction coefficient σ = -1; then the state space equation for the system is established: where c o is the curvature of the reference path, x1=l os , x2=vsinθ os , x1 and x2 are system states, and are the first-order derivatives of the system states x1 and x2, respectively, u = tanδ f is the input of the virtual controller.

3. The agricultural machinery path tracking method based on non-singular terminal sliding mode according to claim 2, characterized in that: In order to facilitate the processing of unknown system state x2, the system is further expressed as follows: in represents the unknown lumped disturbance.

4. The agricultural machinery path tracking method based on non-singular terminal sliding mode according to claim 1, characterized in that: In step 7, by controlling the controller u=tanδ f Perform the inverse transformation to obtain the front wheel steering angle δ of the agricultural machinery f for: By adjusting the front wheel steering angle δ f Control, the final lateral deviation l os and heading deviation θ os will converge to zero.

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