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Design and Experimental Study of Tillage Depth Control System for Electric Rotary Tiller Based on IPSO-ADRC

Wei Tao1, Bin Chen1,*, Xinkun Yang1, Bo Guo1, Wanwan Xu1, Shaoye Ke1, Shenghong Huang1

Published in Journal of the ASABE 69(1): 53-66 (doi: 10.13031/ja.16239). Copyright 2026 American Society of Agricultural and Biological Engineers.

1 College of Mechanical and Electrical Engineering, Wuyi University, Wuyishan, Fujian, China.

* Correspondence: binchen2009@gmail.com

The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/

Submitted for review on 28 October 2024 as manuscript number ITSC 16239; approved for publication as a Research Article by Associate Editor Dr. Kyeong Hwan Lee and Community Editor Dr. Seung Chul Yoon of the Information Technology, Sensors, & Control Systems Community of ASABE on 15 December 2025.

Citation: Tao, W., Chen, B., Yang, X., Guo, B., Xu, W., Ke, S. & Huang, S. (2026). Design and experimental study of tillage depth control system for electric rotary tiller based on IPSO-ADRC. J. ASABE, 69(1), 53-66. https://doi.org/10.13031/ja.16239

Highlights

ABSTRACT. To address the accuracy issue of tillage depth in self-propelled electric rotary tillers, this study proposes a real-time tillage depth control system based on an active disturbance rejection control (ADRC) method optimized with an improved particle swarm optimization (IPSO) algorithm. The system integrates signal data from body posture sensors to establish a mathematical model of the hybrid stepping motor and utilizes the improved particle swarm optimization algorithm to fine-tune the parameters of the state observer and nonlinear state error compensator. Additionally, new nonlinear functions are designed to enhance the control efficiency of the extended state observer and nonlinear state error compensator. The tuned ADRC control signals are employed to drive the hybrid stepping motor, enabling precise tillage depth control. To evaluate the system's performance, field experiments were conducted in a tea plantation at operating speeds of 0.72 km/h and 1.2 km/h with preset tillage depths of 50 mm and 90 mm. The experimental results indicate that the IPSO-ADRC-controlled system maintains an average tillage depth standard deviation within 0.85 mm. Compared to traditional fuzzy PID control and ADRC, IPSO-ADRC reduces the coefficient of variation (CV) in tillage stability by 83.7% and 70.0%, respectively. The IPSO-ADRC control enhances the hybrid stepping motor with faster response speed, improved tracking accuracy, and stronger anti-interference capability, significantly improving control performance and ensuring higher tillage quality in tea plantation operations.

Keywords.Electric rotary tiller, IPSO-ADRC, Tillage depth control system.

With the advancement of modern agricultural technology, the degree of agricultural mechanization has been increasing. As an important piece of agricultural machinery, electric rotary tillers play an indispensable role in enhancing tillage efficiency and quality (Fargnoli et al., 2024; Mousazadeh et al., 2011). Tillage depth control is a key factor in ensuring tillage quality, directly influencing soil turnover, seed planting depth, and seed-soil contact. These factors significantly affect crop growth and yield (Fawzia et al., 2019). Traditional tillage depth adjustment methods mainly rely on manual regulation, which suffers from issues such as insufficient precision and slow response, failing to meet the demands for precision farming in modern agriculture. To address these issues and enhance the accuracy and timeliness of tillage depth control, modern electric rotary tillers widely incorporate intelligent control systems. The system can monitor and dynamically adjust tillage depth in real-time under complex and changing environments, thereby effectively improving work quality and efficiency (Jia et al., 2016; Kim et al., 2020).

Currently, tillage depth adjustment remains a core task in the mechanical automation control technology of electric rotary tillers (Luo et al., 2023; Romaneckas et al., 2022). Hu et al. (2024) developed a tillage depth stabilization control system based on electro-hydraulic control, using the fuzzy adaptive PID (FAPID) method, which effectively improves the response speed and anti-interference capability of the electro-hydraulic system. The goal is to improve the operational quality of tillage machinery and address the current issues of low accuracy and slow response in existing tillage depth control methods. Xiao et al. (2023) proposed applying the fuzzy PID control method to the rotary tiller depth adjustment system, using real-time detection from resistance and angle sensors. The controller operates the electro-hydraulic system, achieving dual-parameter control of tillage depth. This method is significant for improving the quality and efficiency of greenhouse rotary tillage operations while reducing operator labor intensity and operational risks. Gao et al. (2021) proposed a variable universe fuzzy PID controller (VUFPID) based on tillage depth error and depth error rate, which exhibits good adaptability and anti-interference capability in tillage depth control. This method allows for fast and accurate adjustment of tractor implement tillage depth, adapting to the complex and variable agricultural environment. Wang et al. (2024) proposed an improved tillage depth control strategy for complex farmland terrain, using mechanical angle sensors to accurately measure the hydraulic lift arm angle and associating it with the tillage angle to achieve high-precision control. The introduced Hybrid Extended State Observer Back-Stepping Smoothing Mode Control (HESO-Back Stepping SMC) effectively estimates unmeasured variables and disturbances. It provides continuous, smooth control signals while reducing oscillations. Comprehensive simulations and field tillage tests have demonstrated that the HESO-Back Stepping SMC offers precision and reliability in complex agricultural environments. Tao et al. (2025) proposed an adaptive real-time tillage depth control system for electric rotary tillers based on Linear Active Disturbance Rejection Control (LADRC), integrating body posture sensor data and using the LADRC controller to drive a hybrid stepping motor to control the tiller’s lift, achieving precise depth control. Field experiments at speeds of 0.5 km/h and 0.8 km/h were conducted, confirming the accuracy and reliability of the system. Other research teams have achieved precise tillage depth control using improved fuzzy PID control strategies, sliding mode adaptive control, and sliding mode control algorithms. Most of these studies focus on fieldwork environments, where rotary tiller control systems primarily use traditional hydraulic control methods (Liu et al., 2023; Che et al., 2024; Li et al., 2021; Sun et al., 2023). These studies indicate that depth regulation remains the central task in the automation control technology of electric rotary tillers. Current research primarily employs strategies such as Fuzzy-PID control and LADRC. However, in the practical context of tea plantation operations, these methods face distinct bottlenecks: (1) Fuzzy-PID control relies on expert experience and utilizes fixed parameters, leading to slow response times, limited adjustment accuracy, and significant tillage depth fluctuations when confronting strong nonlinear and time-varying disturbances, such as abrupt changes in soil resistance and machine body vibrations. (2) Although standard LADRC estimates the total disturbance via an Extended State Observer, its parameters (e.g., the ESO gain ß) typically depend on empirical tuning. This process is not only cumbersome but also unlikely to yield a globally optimal parameter set, thus constraining its potential in dynamic environments and leaving room for improvement in response speed. Consequently, developing an intelligent control algorithm capable of adaptive optimization, rapid response, and strong anti-interference ability is imperative for achieving high-precision depth control in electric rotary tillers used in tea plantations.

To overcome the aforementioned bottlenecks, this study proposes a novel tillage depth control strategy based on IPSO-ADRC. The core academic innovation of this work lies not merely in the application of an existing algorithm to a new scenario but in the targeted enhancement of the IPSO algorithm itself, specifically tailored to the dynamic characteristics of the tillage depth control system. We introduced two key improvements to the standard PSO: a nonlinear adaptive inertia weight strategy and dynamically adjusted cognitive and social learning factors. This enhanced IPSO algorithm is then synergistically integrated with an ADRC controller that incorporates a refined nonlinear function, nfal, for the ESO and NLSEF. This deep integration is designed to achieve automatic global optimization of the ADRC parameters, thereby significantly improving the system's response speed, tracking accuracy, and anti-interference capability. We hypothesize that the proposed IPSO-ADRC system will achieve a faster settling time with minimal overshoot compared to both Fuzzy-PID and standard LADRC, and will demonstrate a lower CV in tillage depth stability during field experiments, directly addressing the precision and consistency challenges in tea plantation operations.

Materials and Methods

Working Principle of the Tillage Depth Control System

The structure of the adaptive real-time tillage depth control system consists of three main units: the rotary posture sensor, control unit, and stepping motor lead screw slide. The rotary posture sensor is primarily used to detect the posture changes of the rotary tiller when the electric rotary tiller moves over uneven terrain. The control unit uses the STM32F407 control chip, with the microprocessor integrating input data from the sensors performing extended Kalman filtering and prediction processing. The corresponding pulse control signals are then transmitted to the stepping motor driver through the IPSO-ADRC controller. The stepping motor lead screw slide controls the lifting of the rotary tiller head, and the tillage depth signal transmitted in real-time by the grating sensor is fed back to the control unit, completing adaptive real-time tillage depth control. The adaptive real-time tillage depth control system achieves precise rotary tillage depth control through the following steps. The workflow is shown in figure 1.

Figure 1. Tillage depth control system workflow diagram.

  1. The control unit, based on the remotely preset rotary tillage depth target value, sends the information via wireless communication to the rotary tiller control system, calculates and sends pulse signals to the stepping motor, and drives the lead screw slide to lower to the set depth. The grating sensor mounted on the guide rail monitors the displacement of the lead screw in real-time and compares it with the preset rotary tiller depth signal to ensure the target tillage depth is achieved.
  2. In response to uneven working environments, the control unit utilizes the signal from the rotary posture sensor to perform extended Kalman filtering for preprocessing, addressing external disturbances such as jitter and vehicle body deviation during the electric rotary tiller’s movement. The control unit calculates the required adjustment amounts and converts these into pulse signals sent to the stepping motor, driving the lead screw slide to control the tiller’s lift and maintain the correct rotary position.

After the stepping motor completes the lifting and lowering actions, the control unit collects real-time displacement signals from the grating sensor as the actual tillage depth measurement. By comparing and feeding back the actual tillage depth signal with the preset value, the control unit adapts and corrects the error based on IPSO-ADRC, forming a complete closed-loop control process to ensure the accuracy and stability of the tillage depth.

Real-Time Adaptive Tillage Depth Control Method

Automatic Tillage Depth Control System and Method

In traditional tillage depth control methods, both position-based and force-based adjustments have their advantages and limitations. Force-based adjustment is not affected by fluctuations in the terrain, but errors in real-time soil resistance detection can lead to inconsistent tillage depth. While position-based adjustment is not influenced by soil resistance, it can produce large errors in the presence of severe terrain fluctuations, requiring additional sensors to mitigate these errors (Kim et al., 2022; Zhang et al., 2023; Zhou et al., 2023). There are typically two methods for tillage depth control: switch switching and control coefficients. The control coefficient method, through the setting of parameters widely studied and practiced, can achieve better control performance. Since the electric rotary tiller operates in tea gardens where terrain fluctuations are minimal, the control coefficient method is advantageous for utilizing the benefits of position adjustment.

After comprehensive consideration, this study adopts a combined measurement method using posture sensors and grating scale sensors, significantly reducing jitter and external disturbances in the electric rotary tiller. The innovative use of the IPSO-ADRC controller further reduces errors, and the mechanical structure of the hybrid stepping motor enables stable and precise control of tillage depth. The rotary posture sensor is used to detect surface unevenness in real-time. After filtering and preprocessing using the extended Kalman filter algorithm, the desired tillage depth is compared with the actual depth to calculate the real-time adjustment needed. This is processed by the IPSO-ADRC controller and converted into pulse control signals to drive the stepping motor. The grating scale sensor then detects the tillage depth in real-time and feeds it back to the IPSO-ADRC controller. The entire tillage control system completes real-time adaptive adjustment of the rotary tiller's depth.

The sensor installation positions are shown in figure 2, and the schematic of the control system is shown in figure 3.

A stepping motor is an open-loop control element that converts electrical pulse signals into angular or linear displacement. The motor's speed and stopping position depend solely on the frequency and number of pulse signals. For each pulse signal received, the stepper driver rotates the stepper motor by a fixed angle in the set direction. The main parameters of the stepper motor are calculated as follows:

(1)

where

N = number of steps of the stepper motor (related to the motor driver)

? = motor’s working rotation angle (°)

K0 = pulse count

l = slide travel (mm)

P = lead of the lead screw (mm)

f = pulse signal frequency (Hz)

v = slide speed (mm/s).

When the electric rotary tiller encounters uneven terrain, the rotary tiller experiences positional shifts during operation. The controller adjusts the stepping motor in real-time based on the position changes detected by the posture sensor, adapting to the direction of the tillage depth variation.

Figure 2. Schematic diagram of automatic tillage depth control system.

Figure 3. IPSO-ADRC regulation principle diagram.

(2)

where

?K = number of varying pulse signals

?L = actual adjusted rotary tillage depth by the stepper motor, calculated from pitch and roll angle offsets measured by the tillage depth attitude sensor

La = assumed actual working depth of the rotary tiller after stepper motor adjustment based on ?K

Ld = real-time adjustment error of tillage depth.

Based on the defined parameters, the real-time adjustment error of tillage depth is calculated as shown in equation 3.

(3)

The rotary tillage depth is dynamically corrected by the feedback controller, with Le asymptotically approaching zero within the minimum achievable time frame. This real-time terrain-adaptive depth adjustment methodology is demonstrated to achieve superior performance in the environments with limited topographic variations. The terrain roughness during tillage operations is continuously monitored by the onboard attitude sensor mounted on the rotary tiller. Let the initial pitch angle be defined as a, with the subsequently detected pitch angle denoted as a'. The distance between the centroid O of the tiller and the center of mass P of the rotary assembly is designated as x, as illustrated in figure 4.

The depth variation z' induced by pitch angle changes can therefore be derived through geometric principles, as formulated in equation 4:

(4)

In addition to the pitch angle-induced tillage depth variation, the rotary tillage process is further influenced by roll angle dynamics. As depicted in figure 5, the roll angle variation-induced depth modification is quantified as z'', as expressed in equation 5:

(5)

where

y = implement chassis width

ß = roll angle measured by the attitude sensor.

By combining equations 4 and 5, the real-time tillage depth variation?L can be derived as follows:

(6)

Figure 4. Geometric plot of tillage depth versus attitude angle.

Figure 5. ADRC basic structure diagram (x denotes input signal, d represents total external disturbance, and y corresponds to actual output).

The two-phase hybrid stepper motor employed in this study is composed of a stator and rotor assembly. A magnetic field is generated by the stator poles, which interacts with the rotor poles to achieve synchronous rotation between the stator and rotor magnetic fields. Both stator and rotor are fabricated with permanent magnet materials. The stator is configured with eight uniformly distributed magnetic poles, forming two-phase windings where each phase contains four poles (Lai et al., 2021). During the mathematical modeling process, the following effects are systematically neglected:

  1. Interpolar leakage flux in the stator
  2. Permanent magnet leakage in the rotor
  3. Hysteresis and eddy current losses
  4. Harmonic components induced by stator coil self-inductance

Phase-equivalent mathematical models are established based on the electromagnetic circuit configuration. When a pulse signal ?i is received, the stepper motor is rotated, with the actual rotation angle recorded as ?o. The voltage balance equations for the two-phase hybrid stepper motor are formulated as follows:

(7)

where

Ua and Ub = phase voltages of the two windings

ia and ib = winding currents in respective phases

L = average self-inductance component

? = angular displacement of the stepper motor

R = phase resistance of both windings

J = moment of inertia

B = viscous damping coefficient

TE = electromagnetic torque

TL = load torque

Zr = number of rotor teeth

Km = motor constant.

Based on equation 7 and the dynamic characteristics of the stepper motor, taking single-phase excitation as an example with the assumption of zero load torque, the following relationships can be derived during motor energization:

(8)

At the initial moment, the stepper motor is maintained in an equilibrium state where the stepping-angle variation rate approximates zero, and the incremental motion equation for the stepping angle can be established as follows:

(9)

where ?? denotes the angular increment defined as ?? = ?0 - ??. Given the infinitesimal magnitude of ??, a linearized infinitesimal extremum approximation yields:

(10)

Applying the Laplace transform to both sides of the equation under zero initial conditions yields equation 11.

(11)

The transfer function of the two-phase hybrid stepper motor is expressed as shown in equation 12.

(12)

The parameters of the stepper motor utilized in this study (model JK86HS115-4208, manufactured by JKONG MOTOR Co., Ltd., Changzhou, China) are summarized in table 1.

Table 1. Main parameters of the stepper motor.
Parameter NameParameter Values
Number of rotor teeth Zr50
Phase current ia/A4.2
Viscous damping coefficient B/N·m·s0.05
Moment of inertia J/g*cm22700
Phase inductance L/mH6.0

Substituting the aforementioned parameters into the transfer function given in equation 12 yields:

(13)

ADRC Controller Design

ADRC, an advanced control strategy pioneered by Jingqing Han (Han et al., 2023), operates on the principle of treating both internal and external system uncertainties as a generalized disturbance. This disturbance is dynamically estimated and compensated through an Extended State Observer (ESO). The ADRC architecture consists of three core components (Gao and Huang, 2023; Jin and Gao, 2023):

The fundamental architecture of ADRC is schematically illustrated in figure 5.

The Tracking Differentiator (TD) achieves smooth approximation of the generalized derivative for input signals through nonlinear functions within the ADRC framework. The discrete-time formulation of a second-order TD algorithm is expressed as:

(14)

where

T = integration step size

r = velocity factor

?F = filtering coefficient

v1 = tracking signal of the input x0

v2 = differential signal of v1

fhan(·) = nonlinear time-optimal synthesis function that suppresses overshoot in transient processes.

The piecewise-defined fhan(·) function is structured as follows to satisfy control requirements:

(15)

The core component of the Extended State Observer (ESO) incorporates a nonlinear function that effectively mitigates disturbance impacts while maintaining stable regulation around the target value. In conventional ADRC implementations, the fal function has been predominantly adopted as the fundamental nonlinear element. Characterized by its piecewise nonlinear structure, the fal function is mathematically defined as:

(16)

where

e = error signal

a = nonlinearity factor typically constrained within 0<a<1

d = filtering coefficient.

The conventional fal function suffers from an inflection point near the origin, resulting in compromised smoothness characteristics. To address this limitation, this study introduces an optimized nonlinear function, denoted as nfal, formulated as:

(17)

Both the fal and nfal nonlinear functions are symmetric with respect to the origin, but the transition process of the nfal function curve is smoother. In this study, the nfal function is used to design the active disturbance rejection controller.

The Extended State Observer (ESO) operates through compensatory feedback mechanisms to estimate both unknown disturbances and unmodeled dynamics, thereby enabling state reconstruction by generating real-time estimates of each system state. For a second-order system, the ESO is formulated as given in equation 18.

(18)

where

z1 = observed angular velocity of the stepper motor

z2 = total disturbance estimate

e = observation error

b = compensation factor.

To further enhance the control performance of the ADRC, a third-order Extended State Observer (ESO) is redesigned based on the newly formulated nonlinear function nfal, with its discrete-time algorithm expressed as:

(19)

where

z1 =input variable

z2 = differential term of the input variable

z3 = total disturbance estimate

h0 = sampling step size

ß10, ß20, ß30 = tunable nonlinear gain coefficients of the ESO.

The Nonlinear State Error Feedback (NLSEF) constitutes a novel control law independent of the plant's mathematical model. Leveraging the enhanced nonlinear function nfal, the NLSEF algorithm is synthesized in equation 20.

(20)

where u0 is defined as the nonlinear compensation module synthesizing proportional-derivative actions, z3(k)/b constitutes the disturbance compensation term dynamically eliminating observed perturbations.

Particle Swarm Optimization Enhancement

PSO is a stochastic population-based optimization algorithm that emulates the social behaviors of biological swarms (Eberhart and Yuhui, 2001). Through dynamic updates of particle velocities and positions driven by environmental feedback, this method satisfies both proximity and quality criteria. Owing to its simplicity, computational efficiency, robust convergence properties, and global search capabilities, PSO has been demonstrated as one of the most effective nature-inspired algorithms for solving constrained/unconstrained single-multi-objective global optimization problems (Ministry of Agriculture of the People's Republic of China, 2003).

By selecting an appropriate fitness function as the evaluation metric, each particle identifies its personal best position (pbest) at iteration k. The global best position (gbest) is subsequently determined by comparing all pbest solutions across the swarm. The velocity Vi(k + 1) and position Xi(k + 1) of particle i at iteration k + 1 are governed by equation 21:

(21)

where

? = inertia weight governing momentum preservation between successive iterations

c1 = individual cognitive coefficient quantifying self-experience influence

c2 = social cognitive coefficient reflecting swarm intelligence interactions

vi(k) = velocity of particle i at the k-th iteration

xi(k) = positional coordinates of particle i during the k-th iteration.

The core academic innovation of this research involves significant enhancements to the standard Particle Swarm Optimization (PSO) algorithm, making it particularly suitable for optimizing the high-dimensional and nonlinear parameter set of the ADRC controller in a dynamic tillage depth control application. The standard PSO algorithm often struggles to balance global exploration and local exploitation when solving complex engineering optimization problems, primarily due to its fixed inertia weight and learning factors. This frequently leads to premature convergence to local optima, a significant drawback when optimizing the highly coupled parameters of an ADRC controller for a system with time-varying dynamics and strong external disturbances.

The hybrid stepper motor control system integrating IPSO-ADRC is architecturally depicted in figure 6, where IPSO denotes the refined algorithm implementation.

During the initial transient phase of ADRC, the system response is predominantly governed by the TD dynamics. Consequently, the fitness function is defined as the cumulative error integral between the system response y(t) and the desired trajectory yref(t) over the time interval spanning from the rise time tr to the sampling termination T, mathematically formulated as:

(22)

where tr denotes the rise time of the step response, and T represents the sampling period.

Figure 6. Block diagram of IPSO-ADRC.

In conventional PSO, the inertia weight (?) is typically constrained within 0.4=?=0.95. To balance global exploration and local exploitation capabilities, ? is generally implemented through a linear decreasing strategy, mathematically expressed as:

(23)

where

kmax = maximum iteration count

?max = upper bounds of the inertia weight

?min = lower bounds of the inertia weight.

A larger inertia weight ? enhances the particle swarm's global exploration capability by expanding the search space, whereas a smaller ? strengthens local exploitation precision through concentrated neighborhood searches. During the initial phase of optimization, a higher ? value is allocated to prioritize global exploration. As the search progresses and the optimal solution region is approached, ? is adaptively reduced to refine local convergence.

To address the limitations of linear inertia weight adjustment in conventional PSO, this study introduces a nonlinear sigmoid-based adaptation mechanism, where the inertia weight is governed by:

(24)

Here, ? is the sigmoid shaping coefficient that modulates the transition steepness between exploration and exploitation phases. Through coefficient calibration, the operational range of ? is constrained within [0.4, 0.95], ensuring compatibility with empirical PSO configurations.

In conventional PSO, the learning factors c1 and c2 remain constant throughout the search process. Improper selection of these parameters can severely degrade optimization performance. To further enhance the capabilities of the IPSO algorithm, c1 and c2 are dynamically adjusted through linear adaptation based on iteration progress, governed by the following relationships:

(25)

The proposed IPSO algorithm introduces two critical enhancements over conventional PSO to address exploration-exploitation trade-offs and enhance interpretability (Eberhart and Yuhui, 2001; Zhang et al., 2018):

  1. Nonlinear Inertia Weight Adaptation

The inertia weight ? is dynamically adjusted using a sigmoid function (eq. 24), enabling smooth transitions between global exploration and local exploitation phases. This contrasts with linear weight decay strategies that often exhibit abrupt behavioral shifts. The sigmoid-based adaptation provides:

This strategy maintains a higher inertia weight in the early iterations, promoting extensive global exploration to avoid local optima. In later iterations, the weight nonlinearly decreases to a lower value, facilitating fine-tuned local search around the promising regions. This adaptive mechanism provides a more intelligent balance between "exploration" and "exploitation" throughout the optimization process, which is crucial for effectively tuning the ADRC parameters.

  1. Cognitively Balanced Learning Factors

The learning factors c1 and c2 follow antagonistic linear trajectories (eq. 25).

This design ensures that social learning is emphasized in the early-stage (c2 dominant) and that individual cognition is prioritized in the later-stage (c1 dominant), with local refinement around the suspected optimal region.

This design ensures that in the early stages, social learning (emphasized by a larger c2) guides the swarm to converge rapidly towards a promising region. In the later stages, individual cognition (emphasized by a larger c1) is prioritized to refine the solution. This cognitively balanced approach guides the IPSO more effectively in locating the global optimal parameter set for the ADRC, which simultaneously satisfies the requirements for rapid response, stability, and robustness.

Applying the enhanced IPSO to ADRC parameter tuning provides an automated, efficient, and reliable global optimization method tailored to the specific challenges of tillage depth control. The improvements enable the algorithm to find a superior set of parameters that allows the ESO to estimate composite disturbances more accurately and the NLSEF to correct errors more rapidly. This directly addresses the bottlenecks of existing methods in handling nonlinearity and strong disturbances, as stated earlier. Therefore, the contribution of this study is not merely an empirical application but a substantiated algorithmic advancement that tangibly enhances control system performance.

Results and Discussion

Simulation-Based Validation of the IPSO-ADRC Control Strategy

Based on the adaptive tillage depth IPSO-ADRC control methodology, a high-fidelity simulation model was developed in Simulink (MATLAB 2023a) to validate the proposed control strategy. The architectural schematic of the IPSO-ADRC control system is illustrated in figure 7, with critical design parameters enumerated in table 2.

Figure 7. Simulation model with IPSO-ADRC controller.

To verify the core hypothesis that IPSO-enabled parameter optimization enhances the transient response and disturbance-rejection capability of ADRC, a high-fidelity Simulink model was developed. Figure 8 presents the step responses of the three control strategies under a 50-mm reference input. As summarized in table 3, the IPSO-ADRC controller achieved the shortest settling time (0.137 s)—a 27.5% reduction compared with LADRC (0.189 s)—while maintaining zero overshoot and the smallest steady-state error.

To further examine robustness, a ±20 mm sinusoidal disturbance was introduced to simulate terrain fluctuations. As shown in figure 9, the IPSO-ADRC controller constrained the depth deviation within ±3.0 mm, significantly outperforming LADRC (±7.0 mm) and Fuzzy-PID (±12.0 mm). These results confirm that IPSO effectively optimizes the ESO and NLSEF parameters, thereby enhancing the controller’s ability to estimate and compensate for unknown disturbances during transient and steady-state conditions.

Field Performance: Depth Accuracy and Stability

A comparative field study was conducted to evaluate the performance of three control systems (Fuzzy-PID, ADRC, and IPSO-ADRC) for regulating the tillage depth of an electric rotary tiller under varying operational conditions. The field performance of these automated depth-control systems was systematically assessed, with emphasis on their ability to maintain agronomic requirements for depth uniformity and stability (Abduvakhobov et al., 2022; Tao et al., 2025). Key evaluation metrics included:

As illustrated in figure 10, the electric rotary tiller was specifically designed for tea-soybean intercropping systems in tea plantations. The experimental plot spanned 30 meters in length, with the rotary blades operating at an average rotational speed of 150 r/min (Zhong et al., 2022). To address challenges associated with the lightweight design and limited power output of self-propelled electric tillers—where excessive rotational speeds combined with deeper tillage depths may induce blade slippage, incomplete soil fragmentation, and operational anomalies (Mohammadi et al., 2022). Two operational speed levels (0.72 km/h and 1.2 km/h) were systematically evaluated.

Given the agronomic requirements for soybean cultivation (30–50 mm planting depth) and the need to ensure adequate soil preparation (50–100 mm tillage depth), predefined tillage depth settings of 50 mm and 90 mm were implemented under each speed condition. This resulted in four experimental combinations (table 4), designed to quantify performance trade-offs between energy efficiency and soil processing quality.

Table 2. Main design parameters of IPSO-ADRC controller.
Controller ModulesParametersValues
TDr500
?F0.01
T0.0001
ESOh00.001
d0.05
a10.5
a20.5
ß1030
ß20300
ß301000
b2
NLSEFd10.05
a30.25
a40.25
ß14000
ß2140

Table 3. Performance of different controllers and tillage depth step response.
Tillage Depth
(mm)		Controller
Types		Settling Time
(s)		Overshoot
(s%)
50IPSO-ADRC0.1370
50LADRC0.1890
50Fuzzy-PID0.23115.4

The tillage depth regulation system was evaluated under four operational configurations (table 4). A 20-meter central zone was designated as the stabilized working area, with 5-meter buffer segments at both ends to account for depth establishment transients. Each configuration underwent triplicate trials, with mean values calculated for statistical analysis. Comparative testing of ADRC and IPSO-ADRC controllers was conducted through the following standardized procedure:

Figure 8. Step response plots for different tillage depths.

Figure 9. Effect of real-time control of different tillage depths under disturbing signals.

Step 1: System Calibration

Pre-trial verification included:

Step 2: Control Algorithm Implementation

Step 3: Operational Execution

Upon timer initiation:

Step 4: Spatial Sampling

Step 5: Post-Process Verification

Field experiments were conducted under four operating conditions combining two target depths (50 and 90 mm) and two travel speeds (0.72 and 1.20 km·h?¹). Depth trajectories for each control method are shown in figure 12, and the quantitative results are summarized in table 5.

Across all operating conditions, the IPSO-ADRC controller consistently achieved the highest depth accuracy, maintaining:

In comparison, LADRC recorded CV values of 2.7–5.9%, and Fuzzy-PID reached up to 8.5% at higher speeds. These results demonstrate that IPSO-ADRC not only complies with but significantly exceeds the NY/T 740-2003 depth-uniformity requirement (CV = 8%), validating its practical effectiveness in real tillage environments with soil disturbance and posture variation.

Figure 10. Self-propelled electric tiller working experiment diagram.

Figure 11. Tillage depth data collection.

Table 4. Combination of test conditions of the tiller.
Working Condition
Number		Target Tillage Depth
(mm)		Working Speed
(km·h-1)
1500.72
2900.72
3501.20
4901.20

Robustness Under Varying Travel Speeds and Soil Disturbances

The robustness of the three controllers was evaluated by comparing their performance across different travel speeds. As shown in table 5, increasing the speed from 0.72 to 1.20 km·h?¹ caused noticeable degradation in the Fuzzy-PID controller (CV increased from 4.4% to 8.5%). LADRC showed moderate robustness, with CV increasing from 2.7% to 3.3%.

In contrast, IPSO-ADRC maintained nearly stable performance, with CV only increasing from 0.6% to 1.6%. This superior consistency indicates that the IPSO-optimized ESO gains enable accurate estimation of terrain-induced disturbances, while the optimized NLSEF parameters enhance the controller’s response to rapid posture changes and vibration effects during high-speed tillage.

Discussion: Linking Empirical Findings with Theoretical Contributions

The results from both simulation and field experiments strongly validate the theoretical advantages of the proposed IPSO-ADRC framework. Several mechanisms explain the observed performance improvements:

  1. Enhanced ESO disturbance estimation
  2. The nonlinear inertia-weight and adaptive learning-factor strategies of IPSO ensure a proper balance between global search and local refinement, resulting in observer gains that better match real-time soil resistance and chassis posture dynamics.
  3. Improved tracking precision via NLSEF optimization
  4. The proposed nfal function provides smoother nonlinear compensation than the traditional fal. IPSO further tunes its shape parameters to minimize steady-state error during continuous tillage operations.
  5. Stronger robustness across operating conditions
  6. Unlike LADRC—which relies on manually tuned bandwidth parameters—the IPSO-ADRC framework automatically adapts to terrain fluctuations, maintaining depth stability across different soil conditions and forward speeds.
  7. Clear hypothesis validation
  8. The significant reduction in CV (83.7% vs Fuzzy-PID and 70.0% vs LADRC) empirically confirms that intelligent optimization of ADRC parameters is essential for achieving high-precision and high-stability tillage depth control.

Overall, the results demonstrate that the IPSO-ADRC controller offers both substantial engineering performance benefits and meaningful theoretical contributions by integrating swarm-intelligent optimization with modern disturbance-rejection control theory.

Figure 12. Rotary tillage depth under different control methods.

Table 5. Comparison of tillage depth control performance under different methods.
No.Control MethodWorking
Speed
(km·h–1)		Target
Tillage
Depth
(mm)		Average
Tillage
Depth
(mm)		Standard
Deviation of
Tillage Depth
(mm)		Tillage Depth
Stability Coefficient
of Variation
(%)
1Fuzzy-PID0.725051.92.34.4
2LADRC0.725051.11.42.7
3IPSO-ADRC0.725050.30.30.6
4Fuzzy-PID0.729093.34.34.6
5LADRC0.729092.53.13.4
6IPSO-ADRC0.729090.50.60.6
7Fuzzy-PID1.25054.04.68.5
8LADRC1.25051.41.73.3
9IPSO-ADRC1.25050.70.81.6
10Fuzzy-PID1.29096.27.37.6
11LADRC1.29094.65.65.9
12IPSO-ADRC1.29091.41.61.8

Conclusions

To address the uneven tillage depth control in self-propelled electric rotary tillers during operation, this study proposes a novel depth control system integrating vehicle attitude sensors, hybrid stepper motors, and an STM32 microcontroller-based control unit. The system employs an IPSO-ADRC strategy, achieving rapid response (0.137 s settling time), high precision (maximum deviation: 2.5 mm), and minimal fluctuation (standard deviation: 0.85 mm) in depth regulation. Implementation of the IPSO-ADRC strategy ensured consistent tillage depth throughout operations, reducing the CV for depth stability by 83.7% compared to conventional Fuzzy-PID controllers and 70.0% compared to standard ADRC. These improvements significantly enhanced depth uniformity, meeting stringent agricultural requirements for tillage consistency. The closed-loop control architecture, enabled by real-time depth monitoring via displacement sensors and feedback correction against preset target depths, demonstrated robust accuracy and reliability. Field validations confirmed the system's practical applicability across 0.72–1.2 km/h operational speeds. This work provides a technically viable solution for precision tillage control and offers valuable insights for research in agricultural automation and precision farming technologies. Future work will extend this approach to larger-scale trials and other crop systems.

Acknowledgments

This research was supported by the Natural Science Foundation of Fujian Province (Grant Nos. 2023J011041 and 2024J01909), the Fujian Provincial Key Science and Technology Project: Key Technologies and Equipment for Continuous and Intelligent Production of Bamboo Scrimber (Grant No. 2024HZ026011), the Nanping Science and Technology Plan Project (Grant Nos. N2023Z001, N2023Z002, and N2024Z001), the Nature Science Foundation of Nanping, China (Grant Nos. N2023J001, N2025J001, N2025J002) and the Horizontal Projects of Wuyi University (Grant Nos. 2024-WHFW-030, 2025-WHFW-043).

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