Nonlinear Control Method Research Articles

Nonlinear Optimal Control of an H‐Type Gantry Crane Driven by Dual PMLSMs

ABSTRACTGantry cranes of the H‐type with dual electric‐motor actuation are widely used in industry. In this article, the control problem of an H‐type gantry crane which is driven by a pair of linear permanent magnet synchronous motors (dual PMLSMs) is considered. The integrated system that comprises the H‐type gantry crane and its two LPMSMs is proven to be differentially flat. The control problem for this robotic system is solved with the use of a nonlinear optimal control method. To apply the nonlinear optimal control method, the dynamic model of the H‐type gantry crane with dual LPMSM undergoes approximate linearization at each sampling instant with the use of first‐order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization point is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time‐step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. The proposed control scheme achieves stabilization of the H‐type gantry crane with dual LPMSMs without the need of diffeomorphisms and complicated state‐space model transformations.

Linear and Non-Linear Optimal Control Methods to Determine the Best Chemotherapy Schedule for Most Effectively Inhibiting Tumor Growth

Background/Objectives: Cancer is a dynamic and complex disease that remains largely untreated despite major advances in oncology and treatment. In this context, we aimed here to investigate optimal control techniques in the management of tumor growth inhibition, with a particular focus on cancer chemotherapy treatment strategies. Methods: Using both linear autoregressive with exogenous inputs (ARX) and advanced non-linear tumor growth inhibition (TGI) modeling approaches, we investigated various single-agent treatment protocols, including continuous, periodic, and intermittent chemotherapy schedules. By integrating advanced mathematical modeling with optimal control theory and methods, namely the Linear Quadratic Regulator (LQR) and the “pseudo-linear” state-space equivalent representation and suboptimal control of a non-linear dynamic system known as the State-Dependent Riccati Equation (SDRE) approach, this work explores and evaluates successfully, more effective chemotherapy treatment strategies at the computer simulation level, using real preclinical data which increases the expectation to be applied in the clinical practice of oncology. Results: The integration of these methods provides insights into how different drug administration schedules may affect tumor response at the preclinical level. This work uses mathematical modeling to evaluate the efficacy of various periodic and intermittent chemotherapy treatment strategies, with a focus on optimizing drug doses while minimizing the potential side effects of chemotherapy due to the administration of less effective chemotherapeutic doses. Conclusions: The treatment scenarios tested in this study could effectively stop tumor growth or even lead to tumor regression to a negligible or near-zero size. This approach highlights the importance of computational tools for more effective treatment strategies in chemotherapy and offers a promising direction for future research and more efficient clinical applications in oncology as part of a more individualized approach.

Mechanism analysis and structural design of parallel-driven hydraulic wrist joint

Purpose This study aims to design a novel 3 degree-of-freedom parallel-driven hydraulic wrist (PHW) joint, characterized by a compact structure, heavy payload capacity and spherical workspace. Design/methodology/approach In this paper, the kinematics and dynamics mathematical model of PHW is analyzed based on the closed-loop vector method, screw theory and virtual work principle. And the key parameters of PHW are determined based on the singularity analysis. The integrated design method of hydraulic and mechanical systems is used, thereby enabling a hose-less configuration that fosters a low-leakage hydraulic system structure with reduced self-weight. Additionally, this research proposed a dynamic nonlinear compensation control methodology predicated on a payload model to enhance the stability and precision of trajectory tracking for PHW. Finally, several experiments have been conducted to evaluate and validate the performance of the proposed approach and the payload capacity of PHW. Findings Experiment results show that PHW has a payload-to-self-weight ratio of 4(payload 14 kg with self-weight 3.5 kg) under supply pressure 7 MPa. The experimental assessment of payload capacity substantiates the efficacy of the dynamic nonlinear compensation control method for PHW. Remarkably, the trajectory tracking errors for PHW remain under 0.03 rad, even when subjected to payloads of 10.5 and 14 kg. Originality/value This study presents an effective parallel hydraulic-driven wrist structure. This parallel structure provides a spherical workspace with flexible motion, and larger payload capacity compared with the existing robot wrist.

Fuzzy Control of Multivariable Nonlinear Systems Using T–S Fuzzy Model and Principal Component Analysis Technique

In this work, a new nonlinear control method is proposed, which integrates the Takagi–Sugeno (T–S) fuzzy model with the Principal Component Analysis (PCA) technique. The approach uses PCA to reduce the system’s dimensionality, minimizing the number of fuzzy rules required in the T–S fuzzy model. This reduction not only simplifies the system variables but also decreases the computational complexity, resulting in a more efficient control with smooth transient responses and zero steady-state error. To validate the performance of this PCA-based approach for both system identification and control, an interconnected double-tank system was employed. The results demonstrate the method’s capacity to maintain control accuracy while reducing computational load, making it a promising solution for applications in industrial and engineering systems that require robust, efficient control mechanisms.

An adaptive NMPC for ROVs trajectory tracking with environmental disturbances and model uncertainties

A novel hybrid adaptive control method is presented for trajectory tracking of remotely operated underwater vehicles (ROVs) that addresses unknown disturbances and model uncertainties in this paper. Traditional nonlinear control methods struggle to handle external disturbances and uncertainty in system model. To address the trajectory tracking control needs of ROVs in complex underwater environments, a kinematic and dynamic model is first developed for a fully actuated ROV with six degrees of freedom (6-DOF). The trajectory tracking problem is formulated as an online, nonlinear receding horizon optimization process. Control increments are computed as inputs to this nonlinear optimization problem. An L1 adaptive control method (L1AC) is then developed, incorporating a state observer, adaptive control law, and time filter. The framework retains the rolling optimization process of nonlinear model predictive control (NMPC) while integrating the L1 adaptive component for instant compensation of unknown disturbances and model parameter mismatches. Numerical simulations were conducted to compare the trajectory tracking performance of the proposed hybrid adaptive method with the NMPC method under various disturbances, including ocean currents, waves, random forces, and model uncertainties. The results confirm that the proposed hybrid adaptive control scheme is more effective and robust than the standalone NMPC approach across various scenarios.

Nonlinear Adaptive Optimal Control Design and Implementation for Trajectory Tracking of Four-Wheeled Mecanum Mobile Robots

This study proposes a nonlinear adaptive optimal control method, the adaptive H2 control method, applied to the trajectory tracking problem of the wheeled mobile robot (WMR) with four-wheel mecanum wheels. From the perspective of solving mathematical problems, finding an analytical adaptive control solution that satisfies the adaptive H2 performance criterion for the trajectory tracking problem of the WMR with four-wheel mecanum wheels is an extremely challenging task due to the high complexity of the dynamic system. To analytically derive the control law and adaptive control law for this trajectory tracking problem, a proportional-derivative (PD) type transformation is employed to formalize the trajectory tracking error dynamics between the WMR and the desired trajectory (DT). Based on an in-depth analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from the highly complex nonlinear dynamic system equations. This control law provides a solution to the trajectory tracking problem of the WMR while satisfying the adaptive H2 performance criterion. The proposed adaptive nonlinear control method offers a simple control structure and advantages such as improved energy efficiency. Finally, simulations and experimental implementations were conducted to verify the performance of the proposed adaptive H2 control method and the H2 control method in tracking the DT. The results demonstrate that, compared to the H2 control method, the adaptive H2 control method exhibits superior trajectory tracking performance, particularly in the presence of significant model uncertainties.

Nonlinear Optimal and Multi-Loop Flatness-Basedcontrol of Omnidirectional 3-Wheel Mobile Robots

In this article, the control problem for omnidirectional 3-wheel autonomous mobile robots is solved with the use of (i) a nonlinear optimal control method (ii) a flatness-based control approach which is implemented in successive loops. To apply method (i) that is nonlinear optimal control, the dynamic model of the omnidirectional 3-wheel autonomous mobile robots undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrix. The linearization point is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. To implement control method (ii), that is flatness-based control in successive loops, the state-space model of the omnidirectional 3-wheel autonomous mobile robot is separated into chained subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input-output linearized flat systems. The state variables of the preceding (i-th) subsystem become virtual control inputs for the subsequent (i+1-th) subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves trajectory tracking and autonomous navigation for the omnidirectional 3-wheel autonomous mobile robots without the need of diffeomorphisms and complicated state-space model transformations.

Single-input and Multi-objective-state Control Problem of AGV With High-frequency Interference: A Nonlinear Concurrent Control Method

Single-input and Multi-objective-state Control Problem of AGV With High-frequency Interference: A Nonlinear Concurrent Control Method

The Path Tracking Control of Unmanned Surface Vehicles Based on an Improved Non-Dominated Sorting Genetic Algorithm II-Based Multi-Objective Nonlinear Model Predictive Control Method

This paper proposes a multi-objective nonlinear model predictive control (MOMPC) method based on an improved non-dominated sorting genetic algorithm II (NSGAII) for the path tracking problem of unmanned surface vehicles (USVs). To enhance performance in cross-track error, a varying look-ahead distance is utilized in the line of sight (LOS) algorithm, which allows the MPC control algorithm to compute the look-ahead distance and desired speed rather than directly calculating the control input. Since the cost function of the MPC algorithm includes multiple objective terms, a multi-objective model predictive control algorithm is employed to improve overall control performance. Additionally, an adaptive rotation-based simulated binary crossover (ARSBX) is integrated into the NSGAII algorithm, and the non-dominated sorting method is optimized to reduce computation time. These enhancements increase diversity and exploration in the solution space, enabling the algorithm to find the optimal solution more efficiently. Simulations conducted in two different scenarios demonstrate that the nonlinear MPC method based on the improved NSGAII successfully tracks the desired path; it achieved an improvement of approximately 41% in time performance and about 5% in path-tracking error performance, exhibiting strong control performance and robustness.

Research on nonlinear second-order multi-agent systems containment control method with inherent time-delay based on compensator

In this study, a nonlinear second-order multi-agent systems containment control method based on compensator is discussed. In order to deal with nonlinear systems with inherent time delay, a new compensator-based control algorithm is proposed. The fully distributed compensator is designed to effectively converge the states of all followers to the convex hull formed by the states of leaders. By introducing a compensator, the errors in the system can be corrected and the influence of time delay on the system can be compensated to ensure that the system can achieve the desired performance and stability. Then, the original system is transformed into an error system by using matrix theory, and the stability of the error system is analyzed by using Lyapunov method, and the sufficient conditions for the solvability of the control problem are obtained. Finally, the effectiveness of the control algorithm is verified by matlab simulation.

Optimal Driving Torque Control Strategy for Front and Rear Independently Driven Electric Vehicles Based on Online Real-Time Model Predictive Control

This paper presents a novel driving torque control strategy for the front and rear independently driven electric vehicle (FRIDEV) to reduce energy consumption and enhance vehicle stability. The strategy is built on a comprehensive vehicle model that integrates vertical load transfer, tire slip dynamics, and an electric system model that accounts for losses in induction motors (IMs), permanent magnet synchronous motors (PMSMs), inverters, and batteries. The torque control problem is framed with a nonlinear model predictive control (MPC) method, utilizing state-space equations as representations of vehicle dynamics. The optimization targets adjust in real-time based on road traction conditions, with the slip rate of front and rear wheels determining the torque control strategy. Active slip control is applied when slip rates exceed critical thresholds, while under normal conditions, torque distribution is optimized to minimize energy losses. To enable online real-time implementation, an improved sparrow search algorithm (SSA) is designed. Simulations in MATLAB/Simulink confirm that the proposed online strategy reduces energy consumption by 2.3% under the China light-duty vehicle test cycle-passenger cars (CLTC-P) compared to a rule-based strategy. Under low-adhesion conditions, the proposed online strategy effectively manages slip ratios, ensuring stability and performance. Improved SSA also enhances computational efficiency by approximately 44%–52%, making the online strategy viable for real-time applications.

Hybrid self-learning model for the prediction and control of sintering furnace temperature

Ternary cathode materials are important components of lithium-ion batteries. However, the sintering process during manufacturing is challenging to control due to the inaccessibility of key dynamic variables and the frequent fluctuations in operating conditions. These lead to high energy consumption and inconsistent product quality. In this paper, we propose a hybrid self-learning prediction model and control method for sintering furnace temperature based on both first-principle and process data. Firstly, a mechanism model with temperature time delay is established based on energy flow analysis in the furnace. To capture the tail gas temperature dynamic in the mechanism model, a Ventingformer-based prediction data-driven model is proposed. In this model, a memory updating technique and an autoregressive module based on the Transformer framework are developed to identify long-time dependencies and respond to variations in input sequences. Then, a hybrid self-learning modeling framework is designed. Based on the established hybrid model, a multiscale objective function-based nonlinear model predictive control (MSCF-NMPC) method is proposed to achieve precise tracking control of the internal temperature in the furnace. A multiscale objective function with short-term cost in terms of energy consumption and tracking accuracy as well as long-term cost in terms of energy loss is constructing in the control optimization problem. Finally, the proposed hybrid self-learning model and MSCF-NMPC method are verified using the actual process data from a sintering furnace, demonstrating the effectiveness of the proposed method. The results offer practical guidance for industrial applications.

Prediction-based controller radial neural network for the traction control system

One of the systems needed to improve vehicle safety is the traction control system (TCS). This control mechanism keeps the wheels from slipping too much when the car accelerates, especially when it moves quickly. Because of the significant nonlinear behavior of the tire during acceleration and the unknown impacts of the road surface, it might be difficult to maintain wheel slip in an acceptable range, especially in bad weather. However, some uncertainties, such as unmodeled dynamics and vehicle parameter uncertainty, should be taken into account when designing the controller. Consequently, TCS requires the existence of a strong nonlinear control law. In this study, an analytical design for a TCS controller is made using the method of nonlinear predictive control. The control system’s resistance is then increased by employing an adaptive radial basis neural network (RFNN) to predict the system’s unknown uncertainties. In this study, the controller was designed using half car and quarter car models, respectively. The behavior of the suggested control system for tracking the reference wheel’s slip in the face of uncertainty for various movements is examined in the simulation results that follow. The resulting results have been compared with the simulation results generated from the nonlinear sliding mode controller response used in valid articles in order to provide a more thorough examination of the suggested control system. The findings demonstrate the effective performance of the suggested control mechanism against nonlinear effects and uncertainties.

Vibration control of Stewart platform based on an improved nonlinear proportional-derivative control method

This paper proposes an improved switching nonlinear proportional-derivative (S-NPD) control algorithm for a six-degree-of-freedom Stewart platform which has strong nonlinearity and uncertainty characteristics, designed to achieve vibration isolation and suppression over a wide bandwidth range while solving the problem of the difficulty in parameter tuning. The controller is designed based on the idea of variable-structure control, which achieves independent real-time adjustments of the control gains of the six legs and takes the sign of the proportional and differential errors as the switching function to realize the feed-forward correction of the proportional gain. This control input can track the expected value more precisely, thus strengthening the system's ability to cope with high dynamics. To validate the results of the proposed approach, numerical simulations are compared with those obtained from PD and NPD controls. The findings confirmed that the designed S-NPD controller shows commendable stability and robustness, and the vibration attenuation of the upper platform under low- and medium-frequency conditions is substantially improved. In addition, it obtains smoother vibration waveforms and lower control force under random disturbance conditions. Consequently, it is proved that the S-NPD control can obtain better regulation accuracy. Compared with the PD and NPD controls, the S-NPD control achieves up to 64% and 31.4% relative performance improvement in vibration attenuation rate, respectively.

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.