Research on the Control System for the Conveying and Separation Experimental Platform of Tiger Nut Harvester Based on Sensing Technology and Control Algorithms

Abstract

Enhancing the intelligence of Tiger nut harvesting equipment with the advancement of agricultural machinery is imperative. Mismatches between excavation feed rate and conveying-separating capacities hinder the efficiency of Tiger nut harvesters. A visualized Tiger nut harvesting platform was designed to address this, incorporating parameters like conveying speed, torque, vibration frequency, and excavation depth. The platform features a mechanical execution part and an automatic control system with speed, torque, frequency, and depth control modules. Mechanical design analysis defined control parameters and methods for each module. An adaptive B-PID controller was proposed for trajectory tracking, combining backstepping and PID. A control model accounting for motion damping and error compensation was derived. Simulink simulations compared B-PID with backstepping controllers, showing B-PID’s robustness and effective trajectory tracking. Actual experiments assessed mechanical-control coordination using relative error metrics. The results showed that the maximum relative error of rotation speed was 3.8%, the maximum relative error of frequency was 3.67%, and the maximum relative error of excavation depth was 1.5%. Correction models for excavation depth and excitation frequency parameters were established. This study offers a theoretical framework to advance the intelligent design of tiger nut harvesting machinery.

1. Introduction

The Tiger nut, scientifically called Cyperus esculentus, represents a multifunctional economic crop that synergistically combines grain, oil, and animal husbandry. Characterized by its well-developed root systems, robust adaptability, and pronounced stress resistance, this species exhibits significant potential for agricultural and ecological applications [1,2,3]. The extensive cultivation of Tiger nuts on a large scale not only facilitates the amelioration of sandy land and the mitigation of wind and sand erosion but also significantly augments farmers’ economic revenue, thereby enhancing public living standards [4]. Xinjiang is an important production area for Tiger nuts in China, and harvesting is a crucial step in the production of Tiger nuts [5].

The conveying and separation mechanism constitutes a pivotal core technology within the framework of the Tiger nut harvester, garnering extensive scholarly attention and yielding notable advancements globally. Historically, the pioneering Tiger nut harvester introduced in Spain employed a vibrating screen configuration to separate Tiger nut, a design paradigm that continues to inform contemporary principles of operation [6]. Zhao et al. [7] presented a scraper-based apparatus for the transportation of Tiger nuts. He and collaborators [8] engineered a Tiger nut conveyance mechanism. Lv Zhijun et al. [9] designed a pulsating roll-cleaning device to improve the harvesting efficiency of Tiger nuts. Pei Minghao et al. [10] conducted mechanical testing and analysis on the interaction between a vibrating digging shovel and rotary blades on the root–sand complex of Cyperus esculentus to establish an optimized parameter combination model.

In recent years, a considerable body of research has focused on integrating mechanical components with sensor technology, control algorithms, and other advanced methodologies to enhance the intelligence of agricultural production processes [11,12,13,14,15]. In terms of electronic applications such as PLC or microcontroller, Cheng Pengfei et al. [16] used a distance sensor to collect the thickness signal of potato chunks during transportation. After being processed by a PLC control system, the program automatically controlled the frequency converter to adjust the frequency converter motor, achieving the constant sorting flow rate requirement for potato cleaning equipment. Lou Xiuhua et al. [17] proposed a dual objective joint control strategy and control algorithm. They built a corn joint harvester cleaning control system. Wei Dexin et al. [18] developed an online monitoring system for the cleaning loss of corn kernel harvesters. The average cleaning loss rates measured by the monitoring system were 1.41%, 1.58%, and 1.83% at working speeds of 0.8, 1.0, and 1.2 m∙s⁻¹, respectively. Mirzazadeh et al. [19] developed a grain cleaning system for combined harvesters and proposed an RSM model for the cleaning grain harvesting system. They determined the optimal conditions for grain particles to pass through the upper and upper screens: feed rate of 3.33 kg/s, fan speed of 742 rpm, aperture of 10 mm, and ideal value of 0.84. In terms of the application of the PID control algorithm, Chen Zhiwei et al. [20] built a measurement and control system for the Tiger nut separation and cleaning test bench, which achieved precise speed control, essential test data acquisition, feeding system control, and other functional requirements. According to the requirements of the test bench, the PID control algorithm was added to the blower speed control to achieve the goal of precise control. Shangguan Zechao et al. [21] designed a corn harvester monitoring and control system based on STM32 and implemented fuzzy PID control for nonlinear control systems.

Based on the above research, aiming at the problems of low efficiency caused by the mismatch between the amount of digging feed and the amount of conveying separation in the existing Tiger nut harvesting and conveying separation platform, we designed a Tiger nut harvesting and conveying separation platform, which can realize the functions of visualization and adjustment of operating parameters such as conveying speed, conveying torque, vibration frequency and digging depth. A torque sensor and dip angle sensor were used to obtain parameters such as auger torque and digging depth, and the B-PID adaptive controller was applied to track and detect the digging depth trajectory. On this basis, the relative error was finally taken as the evaluation index. The coordination between mechanical execution and automatic control was tested to support the development of intelligent harvesting apparatus for Tiger nuts in the Xinjiang sandy area.

2. Materials and Methods

2.1. Overall Instrument Structure and Mechanism of Action

2.1.1. Instrument Structure

The harvesting and conveying separation platform mainly consisted of a rotary till-age excavation device, a five-stage screw conveying device, a vibrating screen, an automatic control system, and a frame. Among them, the rotary tillage excavation device mainly comprised rotary tillage blades, shovels, depth-limiting wheels, etc. The five-stage screw device was composed of the first-stage screw, the second-stage screw, the third-stage screw, the fourth-stage screw, and the fifth-stage screw. The vibrating screen mainly comprised a vibrating front screen, a rear screen, and an excitation device. The automatic control system was mainly composed of a screw speed control module, a screw torque detection module, an excitation frequency control module, and an excavation depth detection module. The speed and excitation frequency parameters of each level of the helical screw were set through the Human–Machine Interaction Interface inside the control box. The screw torque detection module used torque sensors to measure the torque generated by each level of helical screw during operation. The excavation depth detection module mainly used the inclination angle of the depth limiting wheel measured by the inclination sensor to calculate the excavation depth of the rotary tiller, thereby reflecting the harvester’s material feeding amount per unit of time. The global structure is shown in Figure 1.

2.1.2. Mechanism of Operation

During the operation, the rotary tillage digging device propelled a mixture of tiger nuts, roots, soil aggregates, and sand onto the vibrating screen. This ejection was achieved via the axial movement of the screw within a given level and the radial movement between adjacent screw levels. The interaction between the excitation device and the anterior and posterior screen bodies separated the screen bodies. Simultaneously, the return spring facilitated their rapprochement, inducing a reciprocating periodic vibration in the screen bodies. Concurrently, the lower-monitor PLC received operational instructions from the upper-monitor HMI via the IO port, regulating the screw’s rotational speed and excavation depth. Subsequently, the PLC transmitted the specific speed and depth values to the HMI interface via analog signals.

The synergistic interaction between a spiral conveyor and a vibrating screen facilitated the loosening of the mixture. This promoted the percolation of sand through the screen apertures and disrupted the structural cohesion of the composite material. Consequently, this process enhanced the separation of tiger nuts and roots from the sand matrix. The operational parameters of the harvesting, conveying, and separation test platform are detailed in

Table 1. Technical parameters of harvesting, conveying, and separation test bench.

Parameters	Value
Length × width × height/(mm × mm × mm)	4900 × 2600 × 1600
Working width/(mm)	1600
Total power/(kW)	33
Frequency adjustment range/(Hz)	0~25
Adjustment range of conveying speed/(r∙min−1)	0~380
Mining depth adjustment range/(mm)	0~200

.

2.2. Design of Screw Conveyor Speed Control Module

2.2.1. Analysis of the Speed Range of Screw Conveyor

The single-stage helical screw conveyor blades were designed with both left-hand and right-hand configurations. The blades’ opposing helical directions achieved material conveyance towards the center. Each stage of the screw conveyor employed a symmetrical distribution of left-hand and right-hand helical blades. Specifically, the operational lengths of the left-hand and right-hand blades were identical. The combined action of these two helical blades facilitated the transfer of material to the subsequent screw conveyor stage, thereby enhancing the utilization rate of each stage. The dimensions of the helical screw conveyor are illustrated in Figure 2. The screw conveyor shaft measured 1834 mm in length. The operational lengths of the left-hand and right-hand helical blade sections were each 800 mm. The outer diameter of the screw conveyor shaft was 108 mm, while the outer diameter of the helical blades was 400 mm.

In the material ejection process, the screw’s preceding stage rotational speed dictated the subsequent stage’s feed line velocity. Specifically, increased screw speed resulted in a higher initial ejection velocity, as illustrated in Figure 3. When the initial ejection velocity (V_c1) was set to a lower value during sand ejection, gravitational effects resulted in a material trajectory (l₁) that did not directly intersect the screw’s axial action zone, leading to material accumulation at the screw’s lower extremity and hindering transport. Conversely, a high ejection velocity (V_c3) caused the sand to impact the machine casing at the screw’s upper end, resulting in rebound and preventing axial movement (trajectory l₃). An optimal initial ejection velocity (V_c2), intermediate between the aforementioned extremes, resulted in the sand being effectively projected into the screw for axial transport along trajectory l₂. To maximize sand throughput, extend material retention time within the screw, and enhance sand removal efficiency, trajectory l₂ was targeted. This necessitated a screw rotational speed that avoided both excessively high and low values. Subsequent experimental parameter selection involved the investigation of the screw’s rotational speed, with the variable range informed by prior research group findings, which established a maximum screw rotational speed of 280 r∙min⁻¹ [22].

Upon the ejection of materials, such as sand, into the subsequent screw conveyor level, an optimal material deposition zone was identified. Point D was designated as the coordinate origin (0,0). The following conditions were required to ensure seamless material transfer into this optimal zone.

$$\left\{\begin{array}{l}L=V_{x}t+R_{s}cos\alpha \\ H=V_{y}t-{\displaystyle \frac{1}{2}}g{t}^2\\ V_x=V_{c}cos\sigma \\ V_y=V_{c}sin\sigma \\ V_c=\left(1-\mu \right)V_q\end{array}\right.$$

(1)

In the formula, L represents the horizontal distance between the material and the screw shaft at its apogee, measuring 580 mm; H is the vertical distance from the material to the screw shaft at its highest point, ranging from 210 to 400 mm. The radius of the sieve, R_s, was 0.254 m. V_x denotes the X-direction component of the material’s initial velocity, while V_y indicates the Y-direction component of the same. The time for the material to reach its zenith is denoted by t; α is the angle between the machine and the ground, taken as 10°. σ signifies the angle between the material’s ejection velocity and the ground, measured at 65.5°. The coefficient of friction between sand and steel, μ, is 0.43. V_q is the linear velocity of the material at the periphery of the preceding screen body, and V_c is the initial velocity at which the material was ejected.

The initial velocity of the sand particles was calculated from Equation (1) to be 2.5~3.2 m∙s⁻¹. Subsequently, the linear velocity of the material at the edge of the preceding screen body was determined to be 4.5~5.7 m∙s⁻¹. The application of Equation (2) yielded a minimum rotational velocity of the screw of 169 r∙min⁻¹. However, owing to the presence of a significant gap between the actual screen body and the screw, filled with a substantial quantity of sand, soil, and other admixtures, the material’s linear velocity at point B was reduced during operation. Therefore, to achieve the target linear velocity, the minimum operational rotational speed of the screw was required to exceed 169 r∙min⁻¹.

$$n={\displaystyle \frac{30v_q}{\pi R_s}}$$

(2)

The variables v_q, n, and R_s are defined as follows:

v_q is the linear velocity of the material at the edge of the previous screen body, m∙s⁻¹; n is the rotational speed of the screw shaft, r∙min⁻¹; R_s os the rotational radius of the screen mesh, m.

2.2.2. Screw Speed Control System

During the operation of the screw device, the operator initially selected the requisite screw speed via the Human–Machine Interface (HMI). Subsequently, the upper computer HMI conveyed instructions to the lower computer Programmable Logic Controller (PLC) through a communication signal. Upon receiving this signal, the PLC transmitted the instruction to modulate the frequency converter, which in turn adjusted the speed of the motor by altering the frequency of its operational power supply, thus achieving the intended regulation of the screw’s rotational speed. The corresponding flow chart is presented in Figure 4.

The screw speed control device comprised a touchscreen, PLC, motor, inverter, and other hardware components. Given that tiger nuts are cultivated primarily in sandy soil and harvesting generates substantial dust, a review of relevant literature [23,24,25] informed the selection of a resistive touchscreen to ensure reliable operation in the harsh environment. This decision considered cost, functionality, and environmental robustness, ultimately leading to the selection of the MT6071IQ resistive touchscreen (Willcom, Shenzhen, China). PLC selection was based on the specific operational requirements, including input/output (I/O) counts, necessary functional modules, operating environment, and processing speed. After reviewing the pertinent literature [26,27,28,29,30], the DELTA DVP series ES2 host PLC (DELTA, Wujiang, China) was chosen for its suitability to the tiger nut harvester’s operational demands. This PLC was interfaced with the HMI via an RS422 port, connected to six frequency converters via an RS485 communication port, and linked to an analog expansion module via a dedicated communication line. To facilitate efficient control and reliable operation during the process of screw conveying and vibratory screening for the removal of tiger nuts and other plant material, a YE3 series three-phase induction motor was selected. Finally, considering the operational needs of the tiger nut harvester, a Canroon CV900G series frequency converter (Canroon, Shenzhen, China) was chosen to regulate the drive motor’s frequency.

2.3. Torque Detection Module for Screw

2.3.1. Modal Analysis of Screw Structure

The screw assembly comprised a screw shaft and left- and right-rotating spiral blades, which were welded together. Constructed from Q235 material, the screw shaft’s surface underwent a blackening treatment. During the conveyance of the tiger nut, root, and soil mixture, the high-speed rotation of the screw shaft and blades engendered significant vibration. This vibration, exacerbated by the vibratory screening process of the overall machine, induced vibrations within the screw components themselves. The potential for resonance-induced fatigue damage to structural components, impacting the screw’s operational efficiency and posing a safety risk, necessitated a modal analysis. This analysis was performed using Workbench software (2022 R1), yielding the first six natural frequencies of the screw. The maximum displacement deformation of the screw shaft and spiral blades at various frequencies was subsequently analyzed to evaluate the structural integrity and design rationality. A SolidWorks-generated screw model was imported into Workbench, assigned Q235 material properties, and meshed, resulting in a finite element model with 257,001 nodes and 105,018 elements. Constraints were applied at the bearing locations on both ends of the screw shaft, and the first six modes were subsequently solved. The numerical simulation results are shown in Figure 5 and

Table 2. Various modes and vibration modes of the transport screw.

Orders	Inherent Frequency/Hz	Maximum Deformation/mm	Vibration Mode Description
1	116.94	13.887	The opposite bending deformation of the left-handed and right-handed blades (Z-direction)
2	119.24	14.185	The bending deformation of the left-handed and right-handed blades in the same direction (Z-direction)
3	133.14	8.179	Bending deformation along the Y-direction
4	133.41	9.083	Bending deformation along the X-direction
5	255.34	23.44	Isotropic bending deformation of spacer blades (Z-direction)
6	264.53	21.33	The bending deformation of both ends of the blade and the middle blade in the same direction (Z-direction)

.

From Table 2, it was observed that the initial six natural frequencies of the screw ranged from 116.94 to 264.53 Hz, with the displacement deformation varying between 8.179 and 23.44 mm. The sixth-order mode exhibited the highest natural frequency at 264.53 Hz, whereas the fifth-order mode demonstrated the largest displacement deformation of 23.44 mm. Each of these natural frequencies was associated with its specific vibration mode. The distribution of vibration intensity across different parts of the screw and its vibrational response under each corresponding mode were analyzed. The intervals between adjacent frequencies were notably close within the first six natural frequencies. The natural frequencies corresponding to each other differed primarily in the direction of vibration, yet the configurations of the vibration modes remained strikingly similar. As depicted in Figure 4, the vibration of the screw predominantly involved the bending deformation of both the center of the screw shaft and the spiral blade. Under the first, second, fifth, and sixth-order vibration modes, the maximum deformation occurred at the outermost edge of the spiral blade. Conversely, under the conditions of the third and fourth-order vibration modes, the maximum deformation was centered at the screw shaft. This analysis underscores the complex vibrational behavior inherent to the screw’s structural dynamics.

A pre-determined screw rotational speed of 280 r∙min⁻¹ was employed, and the screw’s operational excitation frequency was subsequently calculated as 4.67 Hz using the intrinsic frequency formula, f = n/60. A comparative analysis of the simulation and theoretical results revealed that the operational excitation frequency was significantly lower than the first six natural frequencies of the screw’s vibration modes. This finding indicated an absence of resonance during operation and confirmed the design’s rationality.

2.3.2. Torque Measuring System for Screw

Screw torque was measured primarily to determine the working torque of the five-stage screw. A torque sensor was installed between the motor and the screw device via two couplings, as depicted in Figure 6. This sensor measured the working torque of the screw device, displaying the data on a human–computer interface (HCI) to facilitate analysis of the screw’s operational status within the vibrating screen. The HCI provided real-time torque values for each stage of screw operation and enabled button-controlled start and stop functionalities.

The lower computer of this system utilized the ES2 PLC from the DVP series of DELTA company (DELTA, Wujiang, China), while the upper computer employed the MT6071IQ resistive touch screen from Willcom Technology Co., Ltd. (Willcom, Shenzhen, China). The DY-300N Bengbu torque sensor (DaYang, Bengbu, China) was selected for measuring the operating torque of the screw. The Human–Machine Interface (HMI) was primarily composed of an operation status module and a parameter setting module, which enabled rotational speed and torque detection adjustments. The HMI interface was developed using DOPSoft software (1.01.10). The interface design is presented in Figure 7.

2.4. Excitation Frequency Control System

The vibrating screen was primarily composed of a front screen, a back screen, a vibration generator, connecting rods, and other components. The front and back screens, constructed from sieve bars and ribbed plates welded together, were connected to the frame via the connecting rods and vibration generator, which included an exciter, vibration rollers, and springs. An exciter roller was affixed to each of the front and rear screens. These rollers primarily drove the screen body’s movement away from the exciter. Conversely, the two screens, connected by springs, facilitated resetting the screen body towards the exciter. A schematic diagram of the vibrating screen body structure is presented in Figure 8. Given the operational requirements of processing a high-mass feed mixture and removing sand and soil, the cam design process necessitated consideration of both high-speed and heavy-load characteristics to enhance vibration frequency. A four-circular arc cam was employed for excitation. To ensure smooth and stable shaker-excitation roller contact and to meet screen body stroke requirements, the excitation roller contour was designed such that the cam’s ascending phase corresponded to a sinusoidal accelerating motion during the uplift phase of the excitation process.

The operation of a vibrating screen involved the exciter, which was driven by the power shaft, rotating and simultaneously displacing the vibration roller away from the exciter’s movement. This resulted in the sieve body moving away from the exciter, forcing the front screen. Both the front screen and the back sieve were transitioned from a static state to a state of motion when a certain distance was traversed. At this juncture, the spring reset the front screen and the back sieve, thereby initiating the reciprocating vibration of the sieve body. The vibration of the sieve body effectively separated Tiger nuts, roots, sand, and other mixtures. The material was loosened, with sand falling into the sieve bar gap and ultimately being removed from the system.

To optimize screening performance, a relationship between material particle size and screen body vibration parameters is employed: large particles are best separated using high-amplitude, low-frequency vibrations, and conversely, small particles are more effectively screened at low-amplitude, high-frequency settings [31]. The excitation frequency control system outputs commands via the PLC’s IO port to control the motor speed, thereby adjusting the speed of the excitation cam and eccentric wheel. Given that the screening material primarily consisted of sand and soil, a small amplitude and high frequency were employed. Studies [32,33,34,35] have reported a vibration frequency of 7 Hz for the intermediate test level value during the Tiger nut and castor clearing process.

In contrast, a paper [36] reported that the maximum vibration frequency value was 9 Hz in the potato soil separation process. This was relevant for scenarios where the sieve mesh aperture diameter was small and for sandy materials with fine particle sizes. In conjunction with the Tiger nut harvesting process, the sand and soil separation requirements, and the outcomes of the pre-experimentation, the maximum vibration frequency parameter was determined to be 9 Hz. The maximum value of the vibration frequency parameter stood at 9 Hz, and 7 Hz was adopted as the intermediate level for selecting experimental variable factors in the subsequent phase.

2.5. Digging Depth Detection Module

2.5.1. Determination of Digging Depth Parameters

The tiger nut–root–sandy soil complex was among the objects utilized in the study of harvesting implement geometry and its basic parameters, which necessitated the determination of dimensions such as the size of the complex. During the tiger nut harvesting period, the five-point method was employed to select the test area, wherein a 1 m × 1 m segment of the tiger nut–root–sandy soil complex was sampled. Vernier calipers (maximum measurement length: 150 mm, measurement accuracy: 0.02 mm) and a steel tape measure (maximum measurement length: 5000 mm, measurement accuracy: 1 mm) were used to ascertain the complex’s stalk diameter, stalk height, stubble growth depth, growth width, and other dimensional parameters. Simultaneously, the quality of the complex, the sand within it, as well as the tiger nut, roots, and soil were evaluated. The mass of the composite, the mass of sand and soil within it, and the mass of tiger nuts and roots were also determined. Subsequently, the mass ratios of sand and soil and tiger nuts and roots within the composite were calculated, respectively.

The results indicated that the average values of the composite’s stalk diameter, stalk height, growth depth, and width were 5.2 ± 0.77 mm, 84 ± 4.53 mm, 114 ± 3.47 mm, and 162 ± 7.02 mm, respectively. Consequently, it was observed that the average value of the composite’s stalk diameter was 5.2 ± 0.77 mm, and the width was 162 ± 7.02 mm. To ensure low damage excavation of tiger nuts, it was determined that the machine’s excavation depth should exceed 120 mm during operation.

2.5.2. Digging Depth Detection System

During operation, the rotary cutter of the harvester engaged the soil, performing the plowing action. The depth of this operation was regulated by a depth-limiting wheel. Contact between the depth-limiting wheel and the soil generated a reaction force, which, via the support bar, lifted the front end of the harvester (i.e., the rotary tillage device). An inclination sensor situated on the support bar measured the angle α between the support bar and the ground. This angular information was transduced into an electrical signal by a transmitter and subsequently transmitted to the controller. The plowing depth, h, of the rotary tillage knife was then computed using a pre-established geometric mathematical model relating to the plowing depth and the measured angle. This calculated depth was finally relayed to the Human–Machine Interface (HMI). The geometric relationship is depicted in Figure 9.

The hardware configuration of the digging depth detection system comprised an entry inclination sensor, a rotary tillage knife, a depth-limiting wheel, and a supporting frame. The entry inclination sensor utilized an LCA318T device, primarily tasked with measuring the rotary tiller’s digging depth. This soil inclination sensor was interfaced with the PLC’s analog input/output ports. During depth detection, the test bar was initially zeroed via the HMI interface before the depth value was acquired. This procedure is illustrated in Figure 10.

2.5.3. B-PID-Based Nonlinear Excavation Depth Trajectory Tracking and Regulation System

Principle of the Control System

• Lyapunov stability theory

In the active domain $\Omega$, an actual number δ > 0 exists for the system for any chosen actual number ε > 0. An equilibrium state is said to be stable in the sense of Lyapunov when it satisfies (3) and when the solutions from any x₀ satisfy (4) [37,38,39].

$$\left|\right|x_0-x_e\left|\right|\le \delta$$

(3)

$$\left|\right|\Omega -x_e\left|\right|\le \epsilon$$

(4)

In actual engineering problems, if the equilibrium state x_e is stable in the sense of Lyapunov and the stable state x_e is perturbed, it will eventually converge to x_e. According to Lyapunov’s second law, i.e., it reaches the Lyapunov’s function V is positive definite, and $\stackrel{•}{V}$ is negative definite.

2.

Barbalat’s lemma

Barbalat’s lemma is commonly used for nonautonomous systems in nonlinear systems [40,41]. Suppose a continuously derivable function f(t), as t tends to infinity, has a finite number of limit values, and the derivative of f(t) is uniformly continuous. In that case, the derivative of f(t) tends to zero as t tends to infinity.

3.

PID control principle

PID is one of the most used control algorithms in automatic control systems, in which the proportional control P outputs a proportional amount of control according to the size of the error between the controlled quantity and the set value. Increasing the proportion can shorten the adjustment time but will increase the overshooting amount. Integral control I outputs the control quantity according to the integral value of the error, which can eliminate the static error of the system but will increase the overshooting quantity and regulation time. Differential control D outputs the control quantity according to the negative value of the rate of change of the error, which can reduce the amount of overshot and the regulation time but will increase the system jitter for noise and other disturbances. The following equation can express the principle of action of the PID controller:

$$U(t)=K_p\times e(t)+K_i\times {\displaystyle \int e}(t)dt+K_d\times {\displaystyle \frac{de(t)}{dt}}$$

(5)

where U(t) denotes the control quantity, e(t) denotes the error, K_p denotes the proportionality coefficient, K_i denotes the integration coefficient, and K_d denotes the integration coefficient.

Structure of the Control System

This paper modeled the digging depth detection device as follows. The mass of the device was represented by m, the input driving force F was I, the displacement y₁ was y, and the velocity y₂ was $\stackrel{•}{y}$. Since the soil friction force on the detection device is a nonlinear force positively correlated with the velocity y₂ when detecting the digging depth [42], to facilitate the calculations, this paper assumed that the friction force f = cy₂³, where c was the scale factor. According to Newton’s second law, the following mathematical model can be established:

$$\stackrel{•}{y_1}=y_2$$

(6)

$$\stackrel{•}{y_2}=-{\displaystyle \frac{c}{m}}{y_2}^3+{\displaystyle \frac{I}{m}}$$

(7)

This paper proposed using a backstepping method in conjunction with PID control design to develop a controller for a depth regulation system in excavation. The following section provides a detailed explanation of this process. Assuming an ideal scenario where the operational displacement of the depth detection mechanism was denoted as y_1d, the displacement error was represented by e₁, and a Lyapunov function V₁ was defined for the displacement setting, the subsequent relationship can be derived as follows:

$$e_1=y_{1d}-y_1$$

(8)

$$V_1(e_1)={\displaystyle \frac{1}{2}}{e_1}^2$$

(9)

By taking the derivatives of V₁ and e₁, the following relationship can be obtained:

$$\stackrel{•}{V_1}=e_1(\stackrel{•}{y_{1d}-}{y}_2)$$

(10)

$$\stackrel{•}{e_1}=\stackrel{•}{y_{1d}-}{y}_2$$

(11)

Assuming that in an ideal state, the operating speed of the digging depth detection device was denoted by y_2d, and the velocity error was represented by e₂, if a Lyapunov function V₂ was defined for the displacement error and the velocity error, the following relationships can be derived:

$$e_2=y_{2d}-y_2=\stackrel{•}{y_{1d}}+k_1{e}_1-y_2$$

(12)

$$V_2(e_1,e_2)={\displaystyle \frac{1}{2}}{e_1}^2+{\displaystyle \frac{1}{2}}{e_2}^2$$

(13)

At this point, $\stackrel{•}{V_1}$ can be rewritten in the following form:

$$\stackrel{•}{V_1}=e_1\left(\stackrel{•}{y_{1d}-}{y}_{2d}+e_2\right)$$

(14)

According to Lyapunov’s second method, for the system to achieve equilibrium at this stage, the following relationship had to be satisfied:

$$y_{2d}=\stackrel{•}{y_{1d}}+k_1{e}_1$$

(15)

Herein, k₁ was an arbitrary non-zero constant. At this stage, differentiating e₂ yielded the following relationship:

$$\stackrel{•}{e_2}=\stackrel{••}{y_{1d}}+k_1\stackrel{•}{e_1}+{\displaystyle \frac{c{y}_2^3}{m}}-{\displaystyle \frac{I}{m}}$$

(16)

Differentiating V₂ with respect to its variable yielded the following relationship:

$$\stackrel{•}{V_2}=e_1\left(\stackrel{•}{y_{1d}-}{y}_{2d}+e_2\right)+e_2\left(\stackrel{••}{y_{1d}}+k_1\stackrel{•}{e_1}+{\displaystyle \frac{c{y}_2^3}{m}}-{\displaystyle \frac{I}{m}}\right)$$

(17)

According to Lyapunov’s second method, for the system to achieve equilibrium at this stage, the following conditions had to be satisfied:

$$-k_2{e}_2=\stackrel{••}{y_{1d}}+k_1\stackrel{•}{e_1}+{\displaystyle \frac{c{y}_2^3}{m}}-{\displaystyle \frac{I}{m}}+e_1$$

(18)

Herein, k₂ represented an arbitrary non-zero constant. Through simplification, the following equation can be obtained:

$$I=\stackrel{••}{m{y}_{1d}}+m{k}_1\stackrel{•}{e_1}+c{y}_2^3+m{e}_1+m{k}_2{e}_2$$

(19)

Given that the proportionality coefficient c was an indeterminate constant, its value within the present context was designated as the indeterminate constant $\stackrel{\wedge }{k}$. Consequently, the error $\tilde{k}$ and its corresponding derivatives were expressed as follows:

$$\tilde{k}=c-\stackrel{\wedge }{k}$$

(20)

$$\stackrel{•}{\stackrel{~}{k}}=-\stackrel{•}{\stackrel{\wedge }{k}}$$

(21)

A Lyapunov function V₃ was established for the displacement error, velocity error, and proportionality coefficient error. The derivative of this Lyapunov function, denoted as $\stackrel{•}{V_3}$, yielded the following equation:

$$V_3(e_1,e_2,\tilde{k})={\displaystyle \frac{1}{2}}{e_1}^2+{\displaystyle \frac{1}{2}}{e_2}^2+{\displaystyle \frac{1}{2}}{\tilde{k}}^2$$

(22)

$$\stackrel{•}{V_3}=-k_1{e_1}^2-k_2{e_2}^2+\tilde{k}\left({\displaystyle \frac{e_2}{m}}{y_2}^3-\stackrel{•}{\stackrel{\wedge }{k}}\right)$$

(23)

According to Barbalat’s Lemma, the following relationship can be derived:

$$\stackrel{•}{\stackrel{\wedge }{k}}={\displaystyle \frac{e_2}{m}}{y_2}^3$$

(24)

Integrating Equation (24) yielded the following relationship:

$$\stackrel{\wedge }{k}={\displaystyle {\int }_0^t\frac{e_2}{m}{y_2}^3}dt$$

(25)

Rearranging the above equation yielded the following relationship:

$$I=\stackrel{••}{m{y}_{1d}}+m{e}_1+m{k}_2{e}_2+m{k}_1(\stackrel{•}{y_{1d}-}{y}_2)+\stackrel{\wedge }{k}{y_2}^3$$

(26)

Up to this point, the design of the digging depth trajectory tracking controller had been completed. Figure 11 illustrates the constructed Simulink simulation model.

Simulation Experiment

This section validated the effectiveness of the proposed method. Given the highly nonlinear underground operating environment of the excavation depth device, this study employed Simulink modules within MATLAB 2017b to input sinusoidal and random displacements, enabling a comparative analysis of the proposed B-PID controller and a backstepping controller lacking PID integration. The objective was to observe the trajectory tracking performance of both controllers for y₁. Figure 12 and Figure 13 present the simulation results.

As depicted in Figure 12, for the sinusoidal motion curve, the B-PID controller exhibited superior steady in position tracking accuracy when compared to the backstepping controller without PID integration. Its fluctuations were more stable during changes in the curve. Conversely, the Non-PID exhibited relatively less stable performance and achieved an inferior approximation of the sinusoidal trajectory throughout the experimental phase compared to the B-PID. As shown in Figure 13, both the B-PID controller and the backstepping controller demonstrated strong steady for trajectories generated by random white noise.

To further investigate controller performance, this study compared the displacement error (e₁) and velocity error (e₂) generated by two controllers when tracking a sinusoidal trajectory, as illustrated in Figure 14 and Figure 15.

Analysis of Figure 14 and Figure 15 and

Table 3. Displacement errors and velocity errors in a specific time.

Error	Controller	5 s	10 s		15 s	20 s	25 s
Displacement Error (e1)	B-PID	−5.107 × 10−2	1.924		−4.989 × 10−2	−1.949	7.08 × 10−3
	Non-PID	−1.004 × 10−2	1.983		−5.284 × 10−2	−1.974	5.218 × 10−2
Velocity Error (e2)	B-PID	−2.745 × 10−2	1.97		2.94 × 10−2	−1.958	−2.931 × 10−2
	Non-PID	−3.657 × 10−2	1.993		3.69 × 10−2	−1.962	−3.558 × 10−2
Error	Controller	30 s	35 s	40 s	45 s	50 s	55 s
Displacement Error (e1)	B-PID	1.918	−4.59 × 10−2	−1.946	1.078 × 10−2	1.921	−4.234 × 10−2
	Non-PID	1.975	−5.23 × 10−2	−1.975	5.226 × 10−2	1.975	−5.226 × 10−2
Velocity Error (e2)	B-PID	1.959	2.931 × 10−2	−1.959	−2.931 × 10−2	1.959	2.931 × 10−2
	Non-PID	1.988	3.673 × 10−2	−1.964	−3.569 × 10−2	1.985	3.663 × 10−2
Error	Controller	Max	Min		RMS	Variance	Covariance
Displacement Error (e1)	B-PID	1.924	−1.949		5.636 × 10−1	1.6731	1.992
	Non-PID	1.983	−1.975		5.684 × 10−1	1.7728
Velocity Error (e2)	B-PID	2.571	−1.959		4.14 × 10−1	1.7259	1.833
	Non-PID	2.571	−1.964		4.14 × 10−1	1.8263

reveals that the B-PID controller exhibits significantly smaller displacement and velocity errors, with lower root mean square (RMS) and variance values compared to the Non-PID. This further substantiates the superior performance of the B-PID. Furthermore, the positive covariance between the displacement and velocity errors for both B-PID and Non-PID controllers indicates a positive correlation between these two variables.

To compare the robustness of the B-PID and Non-PID controllers, this study incorporated step disturbances into a trajectory generated with random white noise. The simulation results are illustrated in Figure 16. The displacement errors are illustrated in Figure 17.

The analysis of Figure 16 and Figure 17, along with

Table 4. Displacement errors at a specific time.

Error	Controller	5 s	15 s	25 s	35 s	45 s
Displacement Error (e1)	B-PID	1.496 × 10−1	1.669 × 10−1	−1.435 × 10−3	−8.028 × 10−8	7.901 × 10−12
	Non-PID	1.919 × 10−1	7.872 × 10−5	−1.029 × 10	5.713 × 10−1	−3.411
Error	Controller	Max	Min	Mean	RMS
Displacement Error (e1)	B-PID	8.354 × 10−1	−5.505 × 10−3	5.801 × 10−2	1.532 × 10−1
	Non-PID	1.344 × 10	−1.318 × 10	−3.543 × 10−1	5.707

, reveals that under the condition of step disturbances introduced into the system, the B-PID controller exhibits a smaller displacement error. Furthermore, the root mean square (RMS) of the displacement error for the B-PID controller, which is 1.532 × 10⁻¹, is significantly lower than that of the Non-PID controller, with an RMS value of 5.707. This indicates that the B-PID controller possesses superior robustness compared to the Non-PID controller.

The whole simulation results indicated that, compared to other controllers, the B-PID controller possessed significant advantages in tracking accuracy and robustness.

3. Experiment and Results Analysis

In May 2023, practical tests are conducted in the Soil Channel Performance Laboratory of the School of Mechanical and Electrical Engineering at Shihezi University to evaluate control modules for the screw speed of the conveying and separating device, the detection module for excavation depth, and the control module for vibration frequency. The test materials, including Tiger nut–root–sand complexes, are sourced from the Tiger nut planting base of the Second Company, 54th Regiment, Third Division of the Xinjiang Production and Construction Corps. Before tests, the soil in the soil channel test area is leveled and compacted using the flatting device, sprinkler device, and compaction device that are part of the soil channel test rig. The Tiger nut–root–sand complex materials are also laid out in the soil channel test area according to the planting pattern.

The experimental apparatus primarily includes the Soil Channel Test Vehicle (TCC-3.0), the tachometer (testo 470), a ruler, a shovel, and other tools. The device used in the experiment is a self-constructed conveying and separating platform for Tiger nut harvesting, as depicted in Figure 18. Electrical wiring of Tiger nut harvester is shown in Figure 19.

3.1. Rotational Speed Measurement of Helical Screw

The Tiger nut harvesting, conveying, and separation platform employs a multi-stage conveying screw combined with a vibrating screen system. The first stage conveying screw feeds on a mixture of Tiger nut, sand, and other materials excavated by the rotary tillage and digging device, characterized by the highest mass of conveyed materials. The second stage conveying screw processes the mixture after the first-stage screw has removed some of the sand. The third stage conveying screw primarily ensures the conveyance of Tiger nut while simultaneously removing sand. In the design of this stage, considerations must be made regarding the potential damage to Tiger nuts.

Given that the three-stage conveying screws have different operating objects and functions, their rotational speeds are designed to decrease progressively: the first-stage screw has the highest speed, the second-stage screw has the next highest speed, and the third-stage screw has the lowest speed. The fourth and fifth stage conveying screws mainly serves to remove residual sand and complete the conveyance of Tiger nuts. The rotational speeds of the third, fourth, and fifth stage conveying screws are set to be consistent.

The specific experimental procedures are detailed as follows: In the screw operation control interface, individual operations can be performed on the speed and vibration frequency of each level of the screw. The interface displays the torque and rotational speed for each level of the screw. The operational sequence commences by selecting the display box corresponding to the screw speed. Subsequently, the desired rotational speed for each screw stage is manually entered. Upon activation of the ‘Start all’ button located on the interface, the screw stages will initiate sequentially, progressing from stage 1 through stage 5. The rotational speed ratios between the first, second, and third stage conveying screws were set at 0.8, 0.9, and 1, respectively. After the equipment operated usually, the rotational speeds of each stage’s screw were measured using a tachometer. The results are shown in

Table 5. Test results of screw performance with different rotational speed ratios.

Rotational Speed Ratio	Project	First Stage Screw r∙min−1	Second Stage Screw r∙min−1	Third Stage Screw r∙min−1	Fourth Stage Screw r∙min−1	Fifth Stage Screw r∙min−1	Relative Error/%
0.8	Theoretical Value	280	224	179	179	179	3.80
	Measured Value	267	213	172	173	175
0.9	Theoretical Value	280	252	227	227	227	1.76
	Measured Value	273	246	224	225	223
1	Theoretical Value	280	280	280	280	280	2.49
	Measured Value	277	268	274	276	270

. According to the table, when the screw rotational speed ratios were 0.8, 0.9, and 1, the relative errors between the theoretical and measured values were 3.80%, 1.76%, and 2.49%, respectively. All relative errors are below 5%, meeting the requirements.

3.2. Excavation Depth Testing

The specific procedures for this experiment are as follows. Prior to the commencement of the experiment, zero calibration is required. The zero-point value for the excavation depth is denoted as l₀. Initially, the soil entry zero-point value can be provisionally set to 0. Subsequently, the length of the soil entry testing rod is defined as the aggregate length of the soil entry testing rod and the roller; this is denoted as l for computational expediency. With the apparatus situated on a level plane, when the rotary tillage blades are in incipient contact with the ground surface, the tillage depth value will be recorded as l_i. The zero-point value l₀ is then determined via the equation l₀ = l − l_i, and this calculated value is subsequently input into the soil entry zero-point setting field. Upon completion of this zeroing procedure, direct readings of tillage depth values can be obtained.

During the testing process, adjustments to the excavation depth were made on the HMI interface by inputting values of 129 mm, 127 mm, 125 mm, 123 mm, and 121 mm, respectively. Five test points were selected within the test area, and the excavation depth was measured using a ruler at each point. Each measurement was replicated thrice, and the arithmetic mean was recorded. The resultant data are presented in

Table 6. Excavation depth test results.

Serial Number	1	2	3	4	5
Theoretical Value/mm	129	127	125	123	121
Measured Value/mm	128.4	126.5	123.1	121.2	119.9
Relative Error/%	0.4	0.3	1.5	1.4	0.9

. As indicated by the table, the relative errors at the five test points were 0.4%, 0.3%, 1.5%, 1.4%, and 0.9%, respectively, with the maximum relative error being 1.5%, which meets the requirements. Additionally, a scatter plot was created with the theoretical values of the excavation depth on the x-axis and the measured values on the y-axis, and a mathematical relationship approximation curve was fitted to the data points, which can be seen in Figure 20. The resulting mathematical relationship between the theoretical and measured values is y = 1.115x − 15.555, with an R² value of 0.9768, indicating the reliability of the correction model.

3.3. Excitation Frequency Test

The rotational velocity of the exciter drive motor was regulated, such that the excitation cam achieved rotational velocities of 126 r∙min⁻¹, 108 r∙min⁻¹, 105 r∙min⁻¹, 120 r∙min⁻¹, and 135 r∙min⁻¹. By substituting the screw speed into the natural frequency calculation formula f = n/60, it can be determined that the excitation frequencies are 8.4 Hz, 7.2 Hz, 7 Hz, 8 Hz, and 9 Hz, respectively. Utilizing a high-speed camera (TS4100LR3C8512), the excitation process of the exciter cam on the front and rear screens was recorded. The motion of the front and rear screens was analyzed using the high-speed video dynamic analysis software Xcitex ProAnalyst (2023), obtaining the number of vibrations per minute, i.e., the excitation frequency, which cen be seen in Figure 21. Each experiment was conducted in triplicate, and the mean value was subsequently calculated. Since the exciter structure consists of four circular arc cams, the excitation frequencies of the front and rear screens are consistent. The experimental results in

Table 7. Excitation frequency test results.

Serial Number	1	2	3	4	5
Theoretical Value/Hz	8.4	7.2	7	8	9
Measured Value/Hz	8.3	7	6.89	7.94	8.67
Relative Error/%	1.19	2.78	1.57	0.75	3.67

show that the relative errors at the five test points are 1.19%, 2.78%, 1.57%, 0.75%, and 3.67%, respectively, with the maximum relative error being 3.67%, below 5%, meeting the requirements.

Additionally, the theoretical values of the excitation frequency were taken as the x-axis, and the measured values as the y-axis. A scatter plot formed by these values was subjected to mathematical relationship curve fitting, which can be seen in Figure 22. The mathematical relationship between the theoretical and measured values after fitting is given by the equation y = 0.9408x + 0.3092, with an R² value of 0.9852, indicating the reliability of the correction model.

4. Conclusions

(1) A visualized control platform was developed to address the low efficiency of Tiger nut harvesting in Xinjiang’s sandy regions, stemming from a mismatch between digging feed rate and conveying separation rate. This platform, incorporating screw speed, torque, vibration frequency, and digging depth control, integrates mechanical execution components and an automatic control system, thus contributing to the intellectualization of Tiger nut harvesting equipment;

(2) An adaptive controller integrating backstepping and PID (B-PID) techniques was proposed to enhance trajectory tracking and depth detection during Tiger nut harvesting. A comprehensive control model was developed, accounting for motion damping and displacement error compensation. Performance evaluation through Simulink simulations compared the B-PID controller with alternative control strategies. Results from these experiments demonstrate that the B-PID model significantly improves trajectory tracking, offering effective control for digging depth detection;

(3) Module testing experiments were conducted on the Tiger nut harvesting and conveying separation platform. The experimental results show that in the screw speed test, when the screw speed ratio is 0.8, 0.9, and 1, the relative errors between theoretical and measured values are 3.80%, 1.76%, and 2.49%, respectively; in the digging depth test, the relative errors at five test points are 0.4%, 0.3%, 1.5%, 1.4%, and 0.9%, with the maximum relative error being 1.5%; in the vibration frequency test, the relative errors at five test points are 1.19%, 2.78%, 1.57%, 0.75%, and 3.67%, with the maximum relative error being 3.67%. Based on these results, correction models for digging depth and vibration frequency parameter control were established.