Nonlinear Control Research Articles

Pitching Stabilization Control for Super Large Ships Based on Double Nonlinear Positive Feedback under Rough Sea Conditions

Due to the rapid development of a global navigation satellite system and the rapid growth of ships, the traditional control algorithms are not suitable; hence, the longitudinal rocking phenomenon generated by external disturbances is more serious when a ship is sailing. This paper takes a mathematical model of the super large oil tanker “KVLCC2”’s longitudinal motion as the controlled plant, establishing a multi-input multi-output instability control system, using the root trajectory shaping method and a weighting matrix to ensure the stability of its transfer function’s mathematical model. An improved closed-loop gain-shaping algorithm is utilized to design a simple robust controller. And a dual nonlinear positive feedback control algorithm is added to the control system to further improve the controller’s pitching stabilization performance and reduce the controller’s output energy. In order to verify that the controller has a consistently strong robustness, simulation experiments are carried out by adding a level 6, 7 and 8 wind wave model and a perturbation link to the control system, respectively. The results show that when the value of the hysteresis constant is taken as 0.25, the output values of the heave displacement and the pitch angle are greatly reduced, and the longitudinal rocking phenomenon is significantly improved. The dual nonlinear positive feedback control algorithm enhances the ship’s pitching stabilization control capability and further reduces the controller’s output energy, which provides technical support for the smooth and efficient sailing of super large ships under changing sea conditions. Combined with a global navigation satellite system, this algorithm provides a new method for pitching stabilization control of super large ships.

Non-linear bending analysis and control of graphene-platelets-reinforced porous sandwich plates with piezoelectric layer subjected to electromechanical loading

Piezoelectric materials as the controlling element have been widely utilized to produce intelligent engineering structures, while these smart structures may fail to realize effective control of composite structures with large deformations. However, investigations on such issues are less reported in published literature, as an accurate and efficient model is required to well forecast the geometrically nonlinear behaviors of smart sandwich structures. As a result, a novel sinusoidal Legendre global-local higher-order shear deformation plate theory (SLHSDT) has been developed to accurately capture geometrically nonlinear behaviors of piezoelectric sandwich plates. The proposed model can fulfill the compatible conditions of transverse shear stresses and contain transverse normal strain, which can ensure precision in predicting electromechanical behaviors. The multi-patch isogeometric analysis (IGA) method for sandwich plates partially bonded with piezoelectric layers is proposed to overcome C1-continuity between patches for the first time. Moreover, the Newmark-β method and Newton-Raphson technique are attempted to solve the nonlinear equations. The present model has been utilized to investigate electromechanical behaviors of laminated structures with piezoelectric layers, which has been compared with the published results. In addition, experiments on macro fiber composite (MFC) integrated sandwich plates have been also carried out in the present work, which can effectively verify the performance of proposed model. Subsequently, the proposed model is employed to study electromechanical behaviors of the five-layer piezoelectric sandwich plates containing internal pores and graphene platelets. Then, influences of the porosity coefficient and GPLs weight fraction on the nonlinear electromechanical behaviors of sandwich plates are investigated. Eventually, the active control on nonlinear behaviors of piezoelectric porous sandwich plates with GPLs reinforcement is studied by using a closed-loop control system, and an effective approach slowing down large deformation has been proposed by selecting an appropriate distribution of GPLs along the thickness direction.

Robust Intelligent Nonlinear Predictive Control Based on Artificial Neural Network for Optimizing PMSM Drive Performance

In the realm of high-performance motor drive systems, achieving stable and optimal motor operation is crucial, particularly in environments characterized by disturbances. The implementation of model predictive control (MPC) represents a strategic methodology. However, conventional predictive controllers frequently encounter challenges due to uncertainties regarding the motor's internal parameters and external load characteristics, subsequently impacting the effectiveness of the control algorithm. This paper proposes a new robust predictive control combined with an artificial neural network (RMPC-ANN) approach applied to a permanent magnet synchronous motor (PMSM) to tackle challenges posed by external perturbations and parameter variations. The development of the proposed robust predictive controller involves optimizing a novel finite horizon cost function based on Taylor series expansion, which incorporates dual integral action into the control law. Crucially, this approach eliminates the necessity for measuring and observing external perturbations and parameter uncertainties. Additionally, for attaining high-precision speed control, the speed loop regulation relies on a multi-layer feedforward ANN algorithm. A comprehensive comparison was conducted using MATLAB/SIMULINK, assessing performance across diverse operating conditions. To further substantiate the numerical simulation results, a hardware-in-the-loop (HIL) configuration is implemented on the OPAL-RT platform, demonstrating the robustness and efficiency of the proposed control strategy.

Neural network-based nonlinear model predictive control with anti-dead-zone function for magnetic shape memory alloy actuator

Neural network-based nonlinear model predictive control with anti-dead-zone function for magnetic shape memory alloy actuator

A stacking sequence optimization strategy for process‐induced deformation of multi‐layer thick asymmetric laminates

AbstractThe occurrence of process‐induced deformations of composites laminates is challenging for assembly accuracy and may lead to a service life reduction of parts. However, it can be obviously mitigated through different optimization strategies on the basis of the accurate curing process simulation. In this study, a stacking sequence optimization strategy is proposed and applied to multi‐layer thick asymmetric laminates. The shapes of deformed laminate plates are experimentally investigated in virtue of the three‐dimensional coordinate measuring machine. The thermo‐chemical–mechanical behaviors of plates are first verified through the comparisons of model predicted and experimental process‐induced deformations. Then the nonlinear control formula achieved through the regression model is proposed for the direct relationship between stacking sequences and process‐induced deformations. Finally, the required solutions are generated by solving the control formula. With the comparisons between the average deformations before and after optimizations, it is found that the magnitudes of deformations are significantly reduced, especially when the unoptimizated deformations are large.Highlights The thermo‐chemical–mechanical behavior can be described in the curing process simulation model. The deformed shapes of multi‐layer thick asymmetric laminate plates are measured by a three‐dimensional coordinate measuring machine. The stacking sequence optimization strategy is implemented by introducing a nonlinear control formula.

Stability enhancement for seamless control in networked microgrids with energy storage: Nonlinear spatio-temporal control perspective

The integration of distributed energy resources into modernized networked microgrids, combined with the increasing variability in load dynamics, presents significant stability challenges. This research offers a comprehensive analysis of the stability of cascaded interactions in nonlinear multi-timescale systems, including grid-following and grid-forming inverters. The proposed grid-forming controller, integrated with energy storage systems and a nonlinear Lyapunov function, facilitates seamless control and stabilization of these inverters. This approach addresses challenges related to nonlinear plant and network dynamics, uncertainties in state variables, and unmodeled system dynamics. The closed-loop control system ensures asymptotic spatio-temporal dynamical stability through constrained time state convergence to stable equilibrium points while minimizing control oscillations. Comparative analysis and high-fidelity hardware-in-loop emulations demonstrate the superior performance of the proposed controller over traditional ones in diverse dynamic scenarios. Its ability to rapidly reject disturbances, minimize overshoot, converge efficiently, and enhance power quality confirms its effectiveness and highlights its potential for real-world applications.

An improve nonlinear robust control approach for robotic manipulators with PSO-based global optimization strategy

During the trajectory tracking of robotic manipulators, many factors including dead zones, saturation, and uncertain dynamics, greatly increase the modeling and control difficulty. Aiming for this issue, a nonlinear active disturbance rejection control (NADRC)-based control strategy is proposed for robotic manipulators. In this controller, an extended state observer is introduced on basis of the dynamic model, to observe the extend state of model uncertainties and external disturbances. Then, in combination with the nonlinear feedback control structure, the robust trajectory tracking of robotic manipulators is achieved. Furthermore, to optimize the key parameters of the controller, an improved particle swarm optimization algorithm (IPSO) is designed using chaos theory, which improves the tracking accuracy of the proposed NDRC strategy effectively. Finally, using comparative studies, the effectiveness of the proposed control strategy is demonstrated by comparing with several commonly used controllers.

Autonomous Lunar rendezvous trajectory planning and control using nonlinear MPC and Pontryagin’s principle

This paper explores the application of Nonlinear Model Predictive Control (NMPC) techniques, based on the Pontryagin Minimum Principle, for a minimum-propellant autonomous rendezvous maneuver in non-Keplerian Lunar orbits. The relative motion between the chaser and the target is described by the nonlinear dynamics of the circular restricted three body-problem, posing unique challenges due to the complex and unstable dynamics of near-rectilinear halo orbits. Key aspects of the proposed NMPC include trajectory optimization, maneuver planning, and real-time control, leveraging on its ability to satisfy complex mission requirements while ensuring safe and efficient spacecraft operations and in the presence of input and nonlinear/non-convex state constraints. The proposed formulation allows the design of a minimum-propellant controller, whose optimal control signal results to be bang–bang in time. A case study based on the Artemis III mission – where the docking of the Orion spacecraft to the Gateway station is planned – is illustrated in order to demonstrate the efficiency of the proposed approach, showcasing its potential for enhancing target tracking accuracy, while reducing propellant consumption.

Nonlinear optimal frequency control for dynamic vibration absorber and its application

A principal limitation of passive dynamic vibration absorber (DVA) lies in its intrinsic design constraint, as it is tuned to a specific resonant frequency, rendering it less effective at mitigating vibrations over a variable frequency range. To ensure that the DVA retains its vibration reduction capability under loads with time-varying frequencies, this paper proposes a method for designing the optimal suspension frequency based on the external load frequency. The approach involves altering the stiffness of the DVA through semi-active or active control to achieve the optimal suspension frequency and the best vibration reduction performance. In this study, the ratio R between the optimal suspension frequency and the load frequency is defined, and the nonlinear characteristic of R, based on the lowest vibration transmission rate, is studied using a two degree-of-freedom DVA model. Furthermore, an optimal suspension frequency variation control strategy based on load frequency identification is presented. Combined with the typical load with time-varying frequency encountered in metro vehicles, a multi-body dynamics theoretical model and a rigid–flexible coupling dynamics model are established to verify the effectiveness of the nonlinear optimal frequency control. Finally, the full-size railway vehicle roller rig is used to verify the correctness of the principle of optimal frequency curve. The research results show that when the mass ratio is 0.1, compared with rigid suspension, the nonlinear optimal frequency control can reduce the root mean square (RMS) value of the carbody’s entire time period acceleration during variable speed operation by 62.2%, and the maximum RMS value is reduced by 83.6%. In nonlinear control, unlike passive DVA, the vibration is never higher than that of rigid suspension within a specific velocity range. Compared with linear control strategy, nonlinearity can further reduce the elastic vibration. The test results from roller rig indicate that the semi-active DVA can effectively reduce the elastic vibrations of the carbody, while also validating the correctness of the nonlinear optimal suspension frequency principle. Therefore, the nonlinear frequency control in this study can provide reference for structural vibration control under loads with time-varying frequencies.

Dynamically adjusted cell fate decisions and resilience to mutant invasion during steady-state hematopoiesis revealed by an experimentally parameterized mathematical model

A major next step in hematopoietic stem cell (HSC) biology is to enhance our quantitative understanding of cellular and evolutionary dynamics involved in undisturbed hematopoiesis. Mathematical models have been and continue to be key in this respect, and are most powerful when parameterized experimentally and containing sufficient biological complexity. In this paper, we use data from label propagation experiments in mice to parameterize a mathematical model of hematopoiesis that includes homeostatic control mechanisms as well as clonal evolution. We find that nonlinear feedback control can drastically change the interpretation of kinetic estimates at homeostasis. This suggests that short-term HSC and multipotent progenitors can dynamically adjust to sustain themselves temporarily in the absence of long-term HSCs, even if they differentiate more often than they self-renew in undisturbed homeostasis. Additionally, the presence of feedback control in the model renders the system resilient against mutant invasion. Invasion barriers, however, can be overcome by a combination of age-related changes in stem cell differentiation and evolutionary niche construction dynamics based on a mutant-associated inflammatory environment. This helps us understand the evolution of e.g., TET2 or DNMT3A mutants, and how to potentially reduce mutant burden.

2D Path Following Control of Motor Graders

Optimal ground conditions in mining are crucial for operational efficiency and safety. Motor graders play a crucial role in achieving precise grading of passages; however, unlike many other mining vehicles, they have not yet been commercially automated. The redundant kinematics of motor graders, including articulation, front axle steering, and blade operations, pose significant challenges for automation. This research explores path following with a 2D kinematic model of motor graders and uses simulation to evaluate and compare the performance of these controllers in terms of step response and operational effectiveness. To address kinematic redundancy, two methods are proposed: Rear Offset Control, which defines the articulation angle using a lateral offset between the front and rear axles, and Single Track Control, which utilizes steering redundancy to adapt existing automation approaches to articulated vehicles. Simulation tests were conducted using two controllers: a Feedback Linearized PD controller (FBL+PD) and a Feedback Linearized Model Predictive Controller (FBL+MPC). Both were tuned for optimal performance on a step input path, with performance assessed based on Root Mean Square Error (RMSE) and control effort. This work introduces two methodologies—Rear Offset Control and Single Track Control—for autonomous motor grader operation. These were implemented with FBL+PD and FBL+MPC controllers on a 2D kinematic model. Future research will focus on dynamic modeling, implementing a Non-Linear Model-Predictive Controller, refining tuning methodologies for Feedback Linearized systems, and integrating these approaches with live vehicles.

Efficient predictive control method for ORC waste heat recovery system based on recurrent neural network

The model predictive control performs well in regulating operating parameters and ensuring system safety when the organic Rankine cycles are operating with variable heat sources. However, traditional nonlinear predictive control based on the organic Rankine cycle mechanism model involves significant computational complexity, making it challenging to quickly find a control solution. This limitation hinders its application in the organic Rankine cycle for rapid response control. To address this issue, a fast model predictive control method is proposed in this work. A recurrent neural network model is well-trained using the input–output data of the organic Rankine cycle process, and it is used as a surrogate model in the design of the model predictive controller for the control of organic Rankine cycle operating parameters. The formulated optimal control problem is then transformed into a mixed integer linear programming problem, which can obtain high-quality and fast solutions during the control process. Through comparison with recurrent neural network-based nonlinear predictive control and pseudo-sequential method-based fast nonlinear predictive control, the results show that the designed controller can effectively accomplish the control of organic Rankine cycle operating parameters with smaller overshoot. Moreover, its average control solution time is shorter by 89.59% and 93.27% respectively while the total net output power of the system during the control process is 0.54% and 1.3% higher than that of the other two controllers. It exhibits superior control performance, even under variable waste heat conditions.

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.

Fault tolerant control of uncertain hydraulic system against actuator fault based on redesign Lyapunov approach

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. This paper proposes the design of fault tolerant control for a class of uncertain nonlinear systems with actuator faults based on Lyapunov redesign principle. First, an assumption is introduced to design the control of the nominal system. Then, a new control law has been introduced to handle the difficulty caused by actuator failures. It is shown that the actuator faults can be completely compensated by the proposed nonlinear controller. Finally, the method will be applied to a hydraulic system to show its effectiveness.

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.

A novel memristive chaotic jerk circuit and its microcontroller-based sliding mode control

Due to the experimental realization of memristor circuit elements, research on memristors and memristor-based circuits has surged. Because of their nonvolatile and nonlinear behavior, memristors can be easily applied to chaotic circuits. This study introduces a novel memristive 3D chaotic jerk system, comprising only seven terms, along with its electronic model and microcontroller-based control. The flux-controlled memristor-based jerk system exhibits complex dynamics, which were analyzed through various properties such as phase portraits, the Jacobian matrix, equilibria, eigenvalues, Lyapunov spectra, bifurcation diagrams, and transient chaos behavior. Three controllers, namely, nonlinear feedback, classical sliding mode, and integral sliding mode were designed to control the chaotic jerk oscillator. Lyapunov functions were used to synthesize the nonlinear feedback controller and ensure system stability with the sliding mode technique. Numerical tests under various performance criteria and disturbance conditions showed that the sliding mode controller outperforms the nonlinear feedback controller due to its single-state control structure. The chaotic jerk oscillator hardware circuit was designed and implemented, operating easily with initial conditions set to zero and low DC supply voltages, with all output voltages within ±6V. Both theoretical and simulation results demonstrate the system’s complexity and applicability, with experimental results aligning well with simulations. Consequently, effective microcontroller-based control was achieved using a single-state controller.

Experimental Implementation of a TD3 Agent Based Speed Controller for Direct Torque Control of PMSM Drives

This manuscript presents a novel control approach for Permanent Magnet Synchronous Motors (PMSMs) by integrating the widely used Direct Torque Control (DTC) method with Deep Reinforcement Learning (DRL), specifically the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm. The TD3 algorithm is well-suited to address the challenges posed by high-dimensional state and action spaces in PMSM drives. The conventional Proportional–Integral (PI) controller in the outer loop of DTC is replaced with the DRL based TD3 agent to overcome the limitations of traditional PI controllers, such as model dependency and complex parameter tuning. The DRL technique allows the agent to learn optimal control policies from experience, making it suitable for complex and nonlinear control problems. Extensive simulation studies demonstrate the effectiveness of the TD3-based control in achieving accurate speed tracking under varying operating conditions. Real-time experimental validation using a TMS320F28379D digital signal processor confirms the feasibility of the proposed DRL based approach. The research offers new insights into improving the performance of PMSM drives and paves the way for future advancements in electric drive control.

Dynamic uncertainty propagation analysis framework for nonlinear control problem based on manifold learning and optimal polynomial method and its application on active suspension system

A novel uncertainty propagation method based on manifold learning and optimal polynomial model is proposed to quantify and analyze the dynamic uncertainties of the nonlinear feedback control system. To deal with the multiple objectives and constraints of the nonlinear control problem, a barrier Lyapunov-function-based nonlinear filtered backstepping controller is developed and applied to active suspension system to obtain superior ride comfort performance under limited structural constraints. Considering the errors in the production, manufacturing, and assembly, the probability density function is employed to quantify the structural parameter uncertainties in the nonlinear control system. Moreover, to reveal the dynamic propagation mechanism of uncertainties in the system with nonlinearity, the manifold learning method is proposed to reduce the dimensionality of the dynamic system to avoid the complexity of uncertainty propagation. Simultaneously, data-driven optimal polynomial model is utilized to accurately approximate the internal mechanism of nonlinear filtered backstepping control system. Based on that, the response uncertainties of the nonlinear control system are accurately and quickly quantified through dynamic moment information and uncertain fluctuation space. Finally, an active suspension system with nonlinearities and uncertainties is developed to verify the effectiveness of the controller with improved ride comfort and better handling safety and the superiority of the framework in terms of efficiency and accuracy of the dynamic uncertainty propagation analysis for nonlinear control problem.

A nonlinear control in αβ reference frame for single-stage three-phase grid-connected photovoltaic systems with an LCL-filter

A nonlinear control in αβ reference frame for single-stage three-phase grid-connected photovoltaic systems with an LCL-filter

A Novel Approach for Trajectory Tracking Control of an Under-Actuated Quad-Rotor UAV

A novel Udwadia-Kalaba approach for the trajectory tracking control of an under-actuated quad-rotor unmanned aerial vehicle (UAV) is presented. Compared to standard control approaches, the desired trajectories are treated as constraints called trajectory tracking constraints in this approach. Neither making any approximations or linearization of the nonlinear system nor imposing any a priori structure on the nature of the nonlinear controller, this methodology provides closedform nonlinear control. The control inputs satisfying the desired trajectory requirements can be obtained explicitly in compact closed form by solving Udwadia-Kalaba equation. Nonlinear dynamics modeling of a quad-rotor UAV is processed and a desired trajectory is given in this paper to illustrate this approach. The theoretical analysis and MATLAB simulation results verify the validity and efficiency of this approach. The real-time servo constraint forces are obtained conveniently and the quad-rotor UAV's movement meets the designed trajectory precisely.