Nonlinear Control Method Research Articles

Control of a Directional Downhole Drilling System Using a State Barrier Avoidance Based Method

Abstract Vibrations such as bit-bouncing, stick–slip, and whirl motion can significantly reduce downhole drilling's performance and efficiency. These phenomena are likely to arise once the dynamical states of drilling fall into undesired operating regimes, as verified by both theoretical analyses and experimental studies. To effectively avoid such undesired operating conditions of a downhole drilling process, this paper introduces an advanced nonlinear state-constrained control method to formulate a setpoint tracking problem of high-order directional drilling dynamics under state constraints. These constraints are carefully defined using the field test results, and their shapes are in complex state-space regions, causing additional complexity to the control design. Moreover, unlike vertical drilling, the directional drilling system requires modeling of coupled axial and torsional dynamics with a higher degree-of-freedom (DOF). In this study, the proposed method will tackle these challenges by converting the original high-order constrained control problem into a standard nonlinear control problem. Leveraging on the linear parameter varying (LPV) method that is applied to the converted system, we can actively prevent drilling from falling into the undesired regimes, to achieve the constrained control objective.

Sliding mode-based direct power control of unified power quality conditioner

The Unified Power Quality Conditioner (UPQC) is a promising solution for mitigating multiple Power Quality(PQ) issues in distribution systems, including harmonics, poor power factor, voltage sag/swell and voltage imbalance. The conventional Sliding Mode Controller (SMC) in UPQCs suffers from wide switching frequency variations, chattering problems, and inherent active and reactive power coupling. This study proposes a nonlinear control method, Sliding Mode-based Direct Power Control (SMC-DPC), for the simultaneous regulation of the shunt and series compensators in a UPQC. By optimizing voltage vector selection based on real-time power errors, the proposed method effectively mitigates chattering, and reduces switching frequency variations, and ensures precise tracking of instantaneous active and reactive powers even in the presence of coupling effects. The proposed approach simplifies the system design and improves steady state and dynamic power tracking. The simulation results in MATLAB Simulink® on a 20 kVA system demonstrate that the proposed method achieves a source current THD of 1.52%, compared to 2.31% for conventional SMC and 5.11% for linear controller. Furthermore, the method is robust to grid parameter variations and demonstrates satisfactory performance in both strong and weak grids. In weak grids, the proposed method reduces the line losses by 13.71% and 14.54% compared to SMC and linear controller respectively. The reported results comply with international standards such as IEEE-519 and IEC 61000-3-12, confirming effectiveness of SMC-DPC for enhancing PQ in distribution system.

Improve LVRT capability of organic solar arrays by using chaos-based NMPC

Electric utilities are continuously scheduling to develop power grids in order to supply the electrical energy demanded by their consumers. The common method is the construction of traditional power plants or development of existing infrastructures. The challenges associated with using fossil fuel, such as environmental pollution and climate changing like glacier melting and rising sea levels, highlight the importance of using green energy sources like photovoltaic systems. In other side, extracting the maximum power under intermittent generated power has a great importance. So, a novel chaotic-based nonlinear model predictive control method is introduced for tracking the maximum power point of organic photovoltaic cells. The proposed approach involves estimating a reference point and adjusting the operating point by using a Lagrangian function. Also, chaotic-based nonlinear model predictive controller is used for controlling the operation of boost converter. According to obtained results, the proposed approach capable of fast tracking as well as improving the ride through capacity.

Information fusion-based three-dimensional two-stage optimal cooperative predictive guidance law

A three-dimensional (3D) two-stage optimal cooperative predictive guidance law based on information fusion theory is proposed to intercept a highly maneuverable target. This guidance law integrates an Adaptive Predictive Horizon Nonlinear Model Predictive Control (ANMPC) method and a Distributed Anti-Saturation Extended State Observer (DASESO) algorithm. The combined approach aims to minimize the three-dimensional nonlinear zero-effort-miss. By considering zero-effort-miss, the guidance process can be divided into two stages: rapid convergence to maintain state and fine-tuning. The two-stage method allows missile fuel and computational resources to be allocated more targetedly. In the guidance process, a two-stage switching distance is established based on the initial conditions of the missiles and the target. The DASESO algorithm cooperatively processes information from each missile to accurately estimate the target's maneuvering acceleration. Subsequently, an ANMPC method is employed to generate the optimal guidance command. Additionally, the convexity of the optimization problem has been analyzed to ensure its feasibility in practical applications. Through numerical simulation and comparative analysis, it has been proven that this method can effectively intercept and optimize fuel use, even when dealing with highly maneuverable targets with maneuverability similar to that of the missiles.

A nonlinear model predictive control method for ship path following in waves

ABSTRACT With the development of intelligent ships, the problem of ship path following has attracted much attention in recent years. Ship motion is inevitably affected by an external environment and thus the design of the ship control system in currents or waves, etc. has always been a challenging work. In the present work, a Nonlinear Model Predictive Control (NMPC) method is proposed for ship path following in waves. The NMPC controller can obtain the desired rudder angle of nonlinear ship system by solving an open-loop optimisation problem. The NMPC controller integrated with a Line-of-Sight (LOS) guidance is proposed and applied for a container ship which is controlled to follow two desired paths in both calm water and waves. The simulation results demonstrate the more effectiveness and greater anti-interference of the proposed NMPC method, compared with that the results by using a traditional Proportional-Derivative (PD) control method.

Active disturbance rejection control for piezoelectric cantilever beam with time delay

This Letter presents an active control method for the vibration of piezoelectric structures. First, a controller based on nonlinear extended state observer is designed to improve the disturbance rejection capability of the vibration structure. Additionally, an improved nonlinear active disturbance rejection control (IMNADRC) method is combined with Smith predictor for time delay compensation, resulting in Smith predictor-based IMNADRC. Finally, numerical simulations and experiments are carried out for active vibration suppression of piezoelectric beam under fixed harmonic excitation and variable harmonic excitation, respectively. The results show that the proposed method has good control effect on structural vibration suppression and is highly adaptable to various external excitations.

A time-efficient nonlinear control method for the hyperchaotic finance system synchronization

Irregular and complex behavior in the financial system can disrupt stability and smooth economic growth. It causes randomness within the system, generating chaos; hindering synchronization behaviour. Achieving smooth and rapid synchronization between two coupled hyperchaotic finance (HF) systems with lessened fluctuation of input and output signals is vital for continuing financial stability and fostering economic growth, a challenge addressed in this article. The paper proposes a novel time-efficient nonlinear control (TENLC) technique and investigates HF systems synchronization using the drive-response system (DRS) arrangement. The proposed TENLC strategy realizes fast and smooth synchronization behaviour between two coupled HF systems, reducing closed-loop state-variable trajectory oscillations. The controller is designed to retain the nonlinear components within the closed-loop system and does not depend on the system's parameters, simplifying the design and analysis process. The Lyapunov stability technique confirms the closed-loop's global stability at the origin. Proofs of mathematical analysis and computer-based simulation results validate the theoretical findings, showing that the presented TENLC strategy converges the state error trajectories to zero in a short transient time with lessened fluctuations for all signals. The comparative computer-based simulation analysis confirms that the presented TENLC approach outperforms other synchronization control techniques.

Modeling and Control of Multi‐Stack Fuel Cell Air System based on Nonlinear Model Predictive Control Method

Hydrogen is crucial for achieving SDGs by driving energy transition and combating climate change. Proton exchange membrane fuel cell technology, leveraging hydrogen, faces challenges in meeting high‐power demands. The multistack fuel cell system (MFCS) tackles this by integrating multiple substacks, yet its air supply needs meticulous control. Proportional integral derivative (PID) decoupling from single‐stack falls short of MFCS. This article proposes nonlinear model predictive control (NMPC) for optimized air flow and pressure decoupling. Modeling MFCS's air system and designing a predictive model, it is aimed to ensuring precise control of air flow and pressure in each substack. The decoupling experiments show that NMPC outperforms PID, accurately managing air flow and pressure and reducing load fluctuations. For air mass flow, NMPC cuts mean‐absolute error (MAE) by 64.56% and root‐mean‐square error (RMSE) by 81.36%. For pressure, MAE drops 81.23% and RMSE 83.59%. Comprehensive step load tests confirm NMPC's precise, dynamic regulation too, compared to PID, NMPC lowers average MAE for air mass by 20.67%, pressure by 32.22%. RMSE improvements of 31.08% and 33.23% highlight NMPC's strength. NMPC's quick response mitigates coupling issues, enhancing vehicle load adaptability.

Quadrotor Trajectory Tracking Via SMC-Embedded Wild Horse Optimization

This study provides an integrated control strategy with proportional derivative (PD) and sliding mode control (SMC) for a quadrotor. For inner loop control, the SMC, a robust nonlinear control method, is used to increase the system's resistance to uncertainty and shocks. By using high-speed switching in variable structure control, it reduces tracking mistakes. In the meantime, the PD control concentrates on tracking a helical path while controlling the outer loop for trajectory tracking. The PD and SMC parameters (k1, k2, and k3) could not be manually adjusted to produce acceptable results at first. As a result, this work presents an improvement by optimizing these control parameters using the Wild Horse Optimization (WHO) algorithm, a modern and cutting-edge optimization technique. This improvement shows good results in improving the quadrotor's tracking precision and stability, and it also greatly increases system performance.All simulations were performed in MATLAB, which facilitated detailed analysis and validation of the proposed control strategy.

Lyapunov-based model predictive control for trajectory tracking of hovercraft with actuator constraints and external disturbances

In this study, a Lyapunov-based model predictive control (LMPC) method is developed to address the trajectory tracking problem of autonomous hovercrafts subjected to unknown complex disturbances from ocean environments and practical constraints of marine surface vessels, such as actuator increment limitations and saturation. Initially, the novel LMPC algorithm is applied to enhance tracking performance through rolling optimization and online optimization. Subsequently, a nonlinear disturbance observer is designed to estimate external disturbances caused by wind and dynamics uncertainties. Furthermore, to theoretically ensure control stability, contraction constraints are established using the nonlinear backstepping control method. This approach provides the essential conditions for the system's robustness and stability. Finally, the superiority and robustness of the designed LMPC trajectory tracking method are demonstrated through numerical simulations conducted in a marine environment.

Robust Speed Control of Permanent Magnet Synchronous Motor Drive System Using Sliding-Mode Disturbance Observer-Based Variable-Gain Fractional-Order Super-Twisting Sliding-Mode Control

This paper proposes a novel nonlinear speed control method for permanent magnet synchronous motors that enhances their robustness and tracking performance. This technique integrates a sliding-mode disturbance observer and variable-gain fractional-order super-twisting sliding-mode control within a vector-control framework. The proposed control scheme employs a sliding-mode control method to mitigate chattering and improve dynamics by implementing fractional-order theory with a variable-gain super-twisting sliding manifold design while regulating the speed of the considered motor system. The aforementioned observer is suggested to enhance the control accuracy by estimating and compensating for the lumped disturbances. The proposed methodology demonstrates its superiority over other control schemes such as traditional sliding-mode control, super-twisting sliding-mode control, and the proposed technique. MATLAB/Simulink simulations and real-time implementation validate its performance, showing its potential as a reliable and efficient control approach for the system under study in practical applications.

Research on Variable Parameter Color Image Encryption Based on Five-Dimensional Tri-Valued Memristor Chaotic System.

To construct a chaotic system with complex characteristics and to improve the security of image data, a five-dimensional tri-valued memristor chaotic system with high complexity is innovatively constructed. Firstly, a pressure-controlled tri-valued memristor on Liu's pseudo-four-wing chaotic system is introduced. Through analytical methods, such as Lyapunov exponential map, bifurcation map and attractor phase diagram, it is demonstrated that the new system has rich dynamical behaviors with periodic limit rings varying with the coupling parameter of the system, variable airfoil phenomenon as well as transient chaotic phenomenon of chaos-periodic depending on the system parameter and chaos-quasi-periodic depending on the memristor parameter. The system is simulated with dynamic circuits based on Simulink. Secondly, the differently structured synchronous controls of chaotic systems are realized using a nonlinear feedback control method. Finally, based on the newly constructed five-dimensional chaotic system, a variable parameter color image encryption scheme is proposed to iteratively generate varying chaotic pseudo-random sequences by varying the system parameters, which will be used for repetition-free disambiguation, additive modulo left-shift diffusion and DNA encryption for the three components of RGB of the color image after chunking. The simulation results are analyzed by histogram, information entropy, adjacent pixel correlation, etc., and the images are tested using differential attack, noise attack and geometric attack, as well as analyzing the PSNR and SSIM of the decrypted image quality. The results show that the encryption method has a certain degree of security and can be applied to medical, military and financial fields with more complex environmental requirements.

Energy enhancement in grid-connected photovoltaic generation systems using adaptive control technique

This research paper presents an innovative adaptive control technique for enhancing energy efficiency in grid-connected photovoltaic (PV) generation systems. By integrating an advanced high-gain DC-DC converter with adaptive and non-linear control methods, the proposed system ensures optimal power absorption from various renewable resources and maintains robust power transfer efficiency and reliability. Key results from the implementation at the Union Territory of Puducherry substation demonstrate significant improvements: the adaptive control system dynamically adjusts to changes in source voltage and load conditions, maintaining a constant output voltage with minimized steady-state error and low overshoot. The feedback controller effectively responds to fluctuations in duty cycle and output load, ensuring stable operation under varying environmental conditions. These enhancements contribute to a reliable and efficient integration of renewable energy sources into the power grid, addressing critical challenges in renewable energy technology.

Robust Geometric Control for a Quadrotor UAV with Extended Kalman Filter Estimation

This study proposes a robust geometric controller tailored for quadrotor unmanned aerial vehicles (UAVs). The original geometric controller exhibits excellent performance in quadrotor UAV maneuvers. However, as a model-based nonlinear control method, it is sensitive to system model parameters. By integrating a novel extended Kalman filter (EKF)-based estimator for real-time, online estimation of the quadrotor’s inertia parameters, the controller adeptly handles internal uncertainties and external perturbations during flight maneuvers. This approach significantly improves the robustness of the control system against model inaccuracies. Empirical evidence is provided through both simulation and extensive real-world flight tests, demonstrating the controller’s effectiveness and its practical applicability in dynamic environments. The results confirm that this integration substantially enhances system reliability and performance under varied operational conditions.

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

A Dual-FSM GI LiDAR Imaging Control Method Based on Two-Dimensional Flexible Turntable Composite Axis Tracking

In this study, a tracking and pointing control system with a dual-FSM (fast steering mirror) two-dimensional flexible turntable composite axis is proposed. It is applied to the target-tracking accuracy control in a GI LiDAR (ghost imaging LiDAR) system. Ghost imaging is a multi-measurement imaging method; the dual-FSM GI LiDAR tracking and pointing imaging control system proposed in this study mainly solves the problems of the high-resolution remote sensing imaging of high-speed moving targets and various nonlinear disturbances when this technology is transformed into practical applications. Addressing the detrimental effects of nonlinear disturbances originating from internal flexible mechanisms and assorted external environmental factors on motion control’s velocity, stability, and tracking accuracy, a nonlinear active disturbance rejection control (NLADRC) method based on artificial neural networks is advanced. Additionally, to overcome the limitations imposed by receiving aperture constraints in GI LiDAR systems, a novel optical path design for the dual-FSM GI LiDAR tracking and imaging system is put forth. The implementation of the described methodologies culminated in the development of a dual-FSM GI LiDAR tracking and imaging system, which, upon thorough experimental validation, demonstrated significant improvements. Notably, it achieved an improvement in the coarse tracking accuracy from 193.29 μrad (3σ) to 87.21 μrad (3σ) and enhanced the tracking accuracy from 10.1 μrad (σ) to 1.5 μrad (σ) under specified operational parameters. Furthermore, the method notably diminished the overshoot during the target capture process from 28.85% to 12.8%, concurrently facilitating clear recognition of the target contour. This research contributes significantly to the advancement of GI LiDAR technology for practical application, showcasing the potential of the proposed control and design strategies in enhancing system performance in the face of complex disturbances.

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Robust tracking control of flexible manipulators using hybrid backstepping/nonlinear reduced-order active disturbance rejection control

This study presents a novel hybrid control strategy for single-link flexible-joint robot manipulators, addressing inherent uncertainties and nonlinear dynamics. By integrating nonlinear reduced-order active disturbance rejection control (NRADRC) with backstepping control, the proposed method effectively estimates and mitigates nonlinear dynamics and external disturbances. Utilizing a nonlinear reduced-order extended state observer (NRESO) enhances resilience to internal and external uncertainties. The global stability of the proposed controller is rigorously established using the Lyapunov approach. Numerical comparisons with state-of-the-art nonlinear control methods demonstrate the superior efficiency and robustness of the proposed approach, especially under varying payloads and disturbances, advancing robotic control solutions.

Characteristics analysis and nonlinear control of a digital hydraulic pressure tracking system for high-speed helicopter wet friction clutch

The reliability and control precision of the engagement and disengagement of wet friction clutch are crucial to the transmission of high-speed helicopters. In contrast to the traditional proportional hydraulic system, the digital hydraulic system provides a viable solution due to the use of several fast switching valves (FSVs). In this research, a digital hydraulic pressure tracking system using two fast switching valve arrays (DHPTS-FSVA) is proposed and its nonlinear model is established. First, the static and dynamic characteristics of the DHPTS-FSVA are deeply analyzed by virtue of the half-bridge resistance theory. Moreover, a novel pressure control strategy is proposed, which consists of nonlinear adaptive control method, differential pulse width modulation (PWM) with pressure compensation, and logic allocation strategy of PWM duty ratio. Finally, comparative simulation and experimental results indicate that the maximum, average, and standard deviation of the errors are reduced by at least 16.1%, 45.1%, and 39.5%, respectively, at the tracking frequencies of 1 and 2 Hz, which proves that the proposed controller exhibits better tracking performance at low frequencies.

Backstepping Control of an AC/DC/AC Converter in a Grid Connected Wind Power System

The contribution of this paper is to study a nonlinear control approach known as the backstepping control method to manage reactive and active power using new parametric values for the grid connected wind power generation system. Specifically, the research focuses on a system containing a wind turbine system, a permanent magnet synchronous generator (PMSG), and a grid connected via AC/DC/AC converter. A comprehensive mathematical model for both the wind turbine system, PMSG, and the grid connected via AC/DC/AC converter was developed for this purpose. The Simulation results of the grid-connected wind power generation system are presented and analyzed to show the performance of the nonlinear backstepping control method. The characteristics of the response to variations in generator speed and the power injected into the grid show the highlight of the performance of the backstepping method, under varying wind conditions.