Nonlinear Control Research Articles

Nonlinear control of three level NPC inverter used in PV/grid system: comparison of topologies and control methods

With the passage of time, the importance of using renewable energy systems to overcome energy consumption and improve the quality of the grid has emerged through the use of nonlinear control techniques and reliance on advanced types of inverters such as multi-level inverters. This research is focused on comparing two grid-connected converter topologies in a photovoltaic (PV) generation system connected to a three-phase grid that serves a non-linear load. Additionally, the study explores two different control techniques applied to this converter, evaluating their effects on the total harmonic distortion coefficient. A comparison has been made between the traditional inverter and the three-level inverter type neutral point clamped (NPC) inverter, with the use of integral backstepping (IBS) technique which was also compared with the proportional integral (PI) controller. The simulation results in MATLAB/Simulink are presented illustrating the performances and the strong effectiveness of the three-level NPC inverter controlled by the proposed technique (IBS).

Vector Control of Brushless Doubly-Fed Induction Machines Based on Highly Efficient Nonlinear Controllers

Vector Control of Brushless Doubly-Fed Induction Machines Based on Highly Efficient Nonlinear Controllers

A Lyapunov-based control design for centralised networked control systems under false-data-injection attacks

ABSTRACT A central processing unit receives data from all agents and transmits control commands in a Networked Control System (NCS) which is centralised. Centralised NCSs have numerous applications in industrial settings due to their efficiency, simplicity and cost-effective design. However, centralised NCSs are vulnerable to false data injection (FDI) attacks. Despite the fact that researchers have developed detection and mitigation defense mechanisms during past several years, most of these methods have focused on systems with linear dynamics. Furthermore, the existing literature only assumes the injection of FDI attacks on measurement signals. In this paper, we assume that an adversary has injected the FDI attack into both state measurements and control signals with nonlinear dynamics while considering communication noises and disturbances. We propose a secure nonlinear control design that mitigates FDI attacks in real time by combining learning and model-based approaches. We used Lyapunov stability analysis to design the controller, estimator and updating laws of the neural network (NN). In addition, we selected a network of two robots with Euler–Lagrange dynamics to illustrate the robustness of the proposed controller and estimator.

Simulation modeling of PMBLDC motor speed control in electric propulsion of EV system using adaptive nonlinear fuzzy sliding mode controller (ANF-SMC)

In the current scenario of transportation system, vehicles of conventional are replaced with Electric Vehicles (EVs) with Permanent Magnet Brushless Direct Control Motors (PMBLDCMs) because of the many advantages of the usage of such motors in EVs. Despite the many advantages of the usage of EVs with PMBLDCMs, there were some disadvantages, among them were speed control and dealing with uncertainty problems in the usage of PMBLDCMs in EVs. In rectifying the above-mentioned problems, this work proposed and implemented an ideology of using the nonlinear controller strategy Adaptive Neuro-Fuzzy Sliding Mode Control (ANF-SMC) in the Electric Propulsion Subsystem (EPSS) of EVs with the usage of the proposed nonlinear controller under not loaded and fully loaded vehicles with constant, variable and sudden disturbance in speed conditions. Simulation was carried out using MATLAB version R2020b with Fuzzy Tool Kit (FTK) and simulation performance comparison was done with the existing four (one linear and three nonlinear) controllers. Comparative simulation results infer that the proposed nonlinear controller performs well with zero overshoot and less settling time than that of the existing four (one linear and three nonlinear controllers).

Nonlinear Robust Control of Vehicle Stabilization System with Uncertainty Based on Neural Network

To effectively suppress the effects of uncertainties including unmodeled dynamics and external disturbances in the vehicle stabilization system, a nonlinear robust control strategy based on a multilayer neural network is proposed in this paper. First, the mechanical and electrical coupling dynamics model of the vehicle stabilization system, considering model uncertainty and actuator dynamics, is refined. Second, the lumped uncertainty of the vehicle stabilization system is estimated by a multi-layer neural network and compensated by feedforward control. The high robustness of the system is ensured by constructing the sliding mode feedback control law. The proposed control method overcomes the limitations of sliding mode technology and the neural network and is naturally applied to the vehicle stabilization system, avoiding the adverse effects of high-gain feedback. Based on Lyapunov theory, it is demonstrated that the proposed controller is able to achieve the desired stability tracking performance. Finally, the effectiveness of the proposed control strategy is verified by co-simulation and comparative experiments.

Terminal Synergetic Control for Plate Heat Exchanger

Terminal synergetic control (TSC) is proposed as a control strategy for the temperature management of a plate heat exchanger. The controller is designed by incorporating a selected macro variable with a time-varying sliding surface. The primary objective is to maintain precise control over the outlet temperature of the cold water. To assess the convergence characteristics of the newly proposed TSC approach, the simulation results achieved using TSC featuring a time-varying macro variable are compared to those obtained from the conventional synergetic control (SC) method. With an appropriate macro variable, the simulation results indicate a notable improvement in the convergence rate provided by our designed TSC method, compared to the conventional one. The desirable property of control input, the chattering-free condition, achieved by both TSC and SC approaches emphasizes the advantage of the synergetic control-based techniques over the conventional sliding mode controller. In conclusion, synergetic control-based techniques offer superior potential solutions for nonlinear feedback control problems.

Improved linear/nonlinear active disturbance rejection switching control for bearingless induction motor

ABSTRACT To achieve high-performance operation control for bearingless induction motor (BIM) systems, an improved linear/nonlinear active disturbance rejection switching control strategy is proposed (SADRC). The key innovation lies in the automatic switching between linear and nonlinear control modes based on system stability and disturbance magnitude. First of all, based on the principle of air-gap magnetic field directional control of the BIM, the first-order and second-order ADRC are designed for the rotating and suspending parts of the BIM, respectively. In addition, the nonlinear active disturbance rejection control (NLADRC) has the shortcoming of tracking performance degradation when the disturbance amplitude is large. Then, an active disturbance rejection controller that can automatically switch between linear and nonlinear based on the stability of the system and the magnitude of the disturbance is designed with the introduction of linear active disturbance rejection control (LADRC). The trigonometric function is introduced to improve the fal function to optimise the abrupt change at the linear interval and the high-frequency chattering phenomenon at the origin. The unknown parameters are rectified using the bandwidth method and the particle swarm algorithm, respectively, to ensure the robustness and adaptiveness of the control strategy. Finally, both simulation and experimental results show that the proposed SADRC strategy not only combines the advantages of linear and nonlinear self-anti-disturbance control but also improves the BIM rotor suspension performance and anti-disturbance capability.

Feedback Stabilization of Quasi-One-Sided Lipschitz Nonlinear Discrete-Time Systems with Reduced-Order Observer

The feedback stabilization problem for nonlinear discrete-time systems with a reduced-order observer is investigated, in which the nonlinear terms of the systems satisfy the quasi-one-sided Lipschitz condition. First, a discrete-time reduced-order observer for nonlinear systems is designed. Then, a feedback controller with a reduced-order observer is designed for realizing the stabilization of nonlinear discrete-time systems. We prove that the design of a feedback controller and reduced-order observer of systems can be carried out independently in the case of discrete-time with nonlinear terms, which largely reduces the computational complexity of the observer and controller. The introduction of the quasi-one-sided Lipschitz condition simultaneously enhances the robustness and stability of nonlinear control systems. Finally, the feasibility and effectiveness of the proposed design approach is verified by a numerical simulation.

Real-Time Co-optimization of Gear Shifting and Engine Torque for Predictive Cruise Control of Heavy-Duty Trucks

Fuel consumption is one of the main concerns for heavy-duty trucks. Predictive cruise control (PCC) provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information. In this study, a real-time implementable PCC, which simultaneously optimizes engine torque and gear shifting, is proposed for heavy-duty trucks. To minimize fuel consumption, the problem of the PCC is formulated as a nonlinear model predictive control (MPC), in which the upcoming road elevation information is used. Finding the solution of the nonlinear MPC is time consuming; thus, a real-time implementable solver is developed based on Pontryagin’s maximum principle and indirect shooting method. Dynamic programming (DP) algorithm, as a global optimization algorithm, is used as a performance benchmark for the proposed solver. Simulation, hardware-in-the-loop and real-truck experiments are conducted to verify the performance of the proposed controller. The results demonstrate that the MPC-based solution performs nearly as well as the DP-based solution, with less than 1% deviation for testing roads. Moreover, the proposed co-optimization controller is implementable in a real-truck, and the proposed MPC-based PCC algorithm achieves a fuel-saving rate of 7.9% without compromising the truck’s travel time.

Enhanced Traffic Light Guidance for Safe and Energy-Efficient Driving: A Study on Multiple Traffic Light Advisor (MTLA) and 5G Integration

This paper presents Multiple Traffic Light Advisor (MTLA), a novel Green Light Optimal Speed Advisory (GLOSA) system that leverages 5G communication technology. GLOSA systems are emerging as a key component in intelligent transportation systems, thanks to the development of effective communication technologies. At its core, MTLA serves as a guidance system for drivers, providing real-time instructions to adjust vehicle speed to optimize the utilization of current and future states of traffic lights along their route.The work addresses several limitations in the current state-of-the-art approaches, including the use of an overly simplified velocity profile, the omission of potential grip and jerk in problem formulation, and the absence of a detailed description of the algorithm’s implementation aspects. Initially, we comprehensively present an optimization-free implementation of the overall control architecture based on an unconventional speed profile. Subsequently, MTLA is improved within a non-linear Model Predictive Control (MPC) framework which uses the latter nonoptimal solution as an initial guess and considers potential grip and jerk in the problem formulation. The developed systems are numerically tested and compared within a high-fidelity simulation environment using the IPG CarMaker simulator. The results demonstrate promising performance in terms of energy savings, with a significant reduction of 37% in energy usage, as well as improved overall comfort with respect to the case where no guidance is given to the driver. These findings suggest a high potential for future developments in this domain.

Self-Organizing Type-2 Fuzzy Double Loop Recurrent Neural Network for Uncertain Nonlinear System Control.

Nonlinear systems, such as robotic systems, play an increasingly important role in our modern daily life and have become more dominant in many industries; however, robotic control still faces various challenges due to diverse and unstructured work environments. This article proposes a double-loop recurrent neural network (DLRNN) with the support of a Type-2 fuzzy system and a self-organizing mechanism for improved performance in nonlinear dynamic robot control. The proposed network has a double-loop recurrent structure, which enables better dynamic mapping. In addition, the network combines a Type-2 fuzzy system with a double-loop recurrent structure to improve the ability to deal with uncertain environments. To achieve an efficient system response, a self-organizing mechanism is proposed to adaptively adjust the number of layers in a DLRNN. This work integrates the proposed network into a conventional sliding mode control (SMC) system to theoretically and empirically prove its stability. The proposed system is applied to a three-joint robot manipulator, leading to a comparative study that considers several existing control approaches. The experimental results confirm the superiority of the proposed system and its effectiveness and robustness in response to various external system disturbances.

Nonlinear Active Disturbance Rejection Controller Design for Drag-Free Satellite with Two Test Massess

Nonlinear Active Disturbance Rejection Controller Design for Drag-Free Satellite with Two Test Massess

Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Recent connections in the adaptive control literature to continuous-time analogs of Nesterov's accelerated gradient method have led to the development of new real-time adaptation laws based on accelerated gradient methods. However, previous results assume that the system's uncertainties are linear-in-the-parameters (LIP). To compensate for non-LIP uncertainties, our preliminary results developed a neural network (NN)-based accelerated gradient adaptive controller to achieve trajectory tracking for nonlinear systems; however, the development and analysis only considered single-hidden-layer NNs. In this article, a generalized deep NN (DNN) architecture with an arbitrary number of hidden layers is considered, and a new DNN-based accelerated gradient adaptation scheme is developed to generate estimates of all the DNN weights in real-time. A nonsmooth Lyapunov-based analysis is used to guarantee the developed accelerated gradient-based DNN adaptation design achieves global asymptotic tracking error convergence for general nonlinear control affine systems subject to unknown (non-LIP) drift dynamics and exogenous disturbances. A comprehensive set of simulation studies are conducted on a two-state nonlinear system, a robotic manipulator, and a complex 20-D nonlinear system to demonstrate the improved performance of the developed method. Our simulation studies demonstrate enhanced tracking and function approximation performance from both DNN architectures and accelerated gradient adaptation.

Optimal control in models of virus propagation

Based on the SEIRD model, we consider that when multiple viruses of different virulence coexist, the more virulent virus will reinfect nodes already infected by the less virulent virus, which we call here Superexposed. Based on the state transitions, the corresponding differential equations and cost functions are established, then building the corresponding optimal control problem, where the vaccine efficiency and drug efficiency are controlled variables. This nonlinear optimal control problem is solved by Pontryagin’s maximum principle to finding the structure of the optimal control strategies. Based on the definition of the basic regeneration number, yielding the R0 value for the model, then discussed the final epidemic size. In the numerical analysis section, we validate the accuracy of the structure, fitting the behavior of each state and the effect of different parameter values.

Design and analysis of state-constrained nonlinear finite-time control algorithm with application to buck converter

Design and analysis of state-constrained nonlinear finite-time control algorithm with application to buck converter

Learning Lyapunov terminal costs from data for complexity reduction in nonlinear model predictive control

AbstractA classic way to design a nonlinear model predictive control (NMPC) scheme with guaranteed stability is to incorporate a terminal cost and a terminal constraint into the problem formulation. While a long prediction horizon is often desirable to obtain a large domain of attraction and good closed‐loop performance, the related computational burden can hinder its real‐time deployment. In this article, we propose an NMPC scheme with prediction horizon and no terminal constraint to drastically decrease the numerical complexity without significantly impacting closed‐loop stability and performance. This is attained by constructing a suitable terminal cost from data that estimates the cost‐to‐go of a given NMPC scheme with long prediction horizon. We demonstrate the advantages of the proposed control scheme in two benchmark control problems.

A Nonlinear Control Design for Cooperative Adaptive Cruise Control with Time-Varying Communication Delay

Cooperative adaptive cruise control (CACC) is one of the main features of connected and autonomous vehicles (CAVs), which uses connectivity to improve the efficiency of adaptive cruise control (ACC). The addition of reliable communication systems to ACC reduces fuel consumption, maximizes road capacity, and ensures traffic safety. However, the performance, stability, and safety of CACC could be affected by the transmission of outdated data caused by communication delays. This paper proposes a Lyapunov-based nonlinear controller to mitigate the impact of time-varying delays in the communication channel of CACC. This paper uses Lyapunov–Krasovskii functionals in the stability analysis to ensure semi-global uniformly ultimately bounded tracking. The efficaciousness of the proposed CACC algorithm is demonstrated in simulation and through experimental implementation.

An accurate trajectory tracking method for low-speed unmanned vehicles based on model predictive control

Trajectory tracking on a low-speed vehicle using the model predictive control (MPC) algorithm usually assumes a simple road terrain. This assumption does not correspond to the actual road situation, leading to low tracking accuracy. Therefore, a trajectory tracking method considering road curvature based on MPC is proposed in this paper. In this method, the controller can automatically switch between MPC types. Linear model predictive control (LMPC) is selected for small road curvatures, while nonlinear model predictive control (NMPC) is employed for large road curvatures. In addition, the NMPC algorithm in this work considers the effect of road curvature on tracking accuracy, making it suitable for tracking time-varying curvature roads. To verify the feasibility of the algorithm, simulation comparisons with the basic MPC model were carried out at different testing roads and vehicle longitudinal speeds. The results indicate that the method significantly improves trajectory tracking accuracy, all while ensuring real-time calculations. The intelligent switching capability of control models based on road curvature allows its application to track trajectories on arbitrarily complex roads.

Continuous adaptive nonlinear model predictive control using spiking neural networks and real-time learning

Model predictive control (MPC) is a prominent control paradigm providing accurate state prediction and subsequent control actions for intricate dynamical systems with applications ranging from autonomous driving to star tracking. However, there is an apparent discrepancy between the model’s mathematical description and its behavior in real-world conditions, affecting its performance in real-time. In this work, we propose a novel neuromorphic (brain-inspired) spiking neural network for continuous adaptive non-linear MPC. Utilizing real-time learning, our design significantly reduces dynamic error and augments model accuracy, while simultaneously addressing unforeseen situations. We evaluated our framework using real-world scenarios in autonomous driving, implemented in a physics-driven simulation. We tested our design with various vehicles (from a Tesla Model 3 to an Ambulance) experiencing malfunctioning and swift steering scenarios. We demonstrate significant improvements in dynamic error rate compared with traditional MPC implementation with up to 89.15% median prediction error reduction with 5 spiking neurons and up to 96.08% with 5,000 neurons. Our results may pave the way for novel applications in real-time control and stimulate further studies in the adaptive control realm with spiking neural networks.

Enhancing the trustworthiness of chaos and synchronization of chaotic satellite model: a practice of discrete fractional-order approaches

Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.