Nonlinear Control Research Articles

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.

Complete Controllability of Nonlinear Neural Network Control Systems

Complete Controllability of Nonlinear Neural Network Control Systems

Dynamic Nonlinear Droop Control (DNDC): A Novel Primary Control Method for DC Microgrids

Dynamic Nonlinear Droop Control (DNDC): A Novel Primary Control Method for DC Microgrids

Efficient and robust nonlinear control MPPT based on artificial neural network for PV system

Efficient and robust nonlinear control MPPT based on artificial neural network for PV system

A novel nonlinear controller design of three-phase grid-tied photovoltaic system

A novel nonlinear controller design of three-phase grid-tied photovoltaic system

Robust Nonlinear Control with Estimation of Disturbances and Parameter Uncertainties for UAVs and Integrated Brushless DC Motors

Robust Nonlinear Control with Estimation of Disturbances and Parameter Uncertainties for UAVs and Integrated Brushless DC Motors

Sliding mode control for doubly fed induction generators system-based a wind turbine

This paper presents a contribution to the control of a Doubly-Fed Induction Generator (DFIG) integrated into a wind turbine using nonlinear control. The parameters involved in this study are the active and reactive powers exchanged between the DFIG stator and the grid. For this purpose, the modeling of the DFIG with the cascaded rectifier-inverter PWM structure was established. A numerical simulation of the DFIG, powered by the cascaded structure and controlled by the developed strategies, was performed. The simulation results show that the sliding mode control (SMC) provides a better transient response , with a shorter response time and reduced overshoot. Furthermore, it maintains good performance and stability in the presence of parameter variations such as resistance and inductance. The proposed control algorithm is also robust against parameter variations and the resulting dynamic response is fast. The simulation results confirm the validity of the mentioned advantages and the effectiveness of the proposed method. The effectiveness and robustness of the control technique were implemented and tested under MATLAB/Simulink environment.

Fuzzy Adaptive Approaches for Robust Containment Control in Nonlinear Multi-Agent Systems under False Data Injection Attacks

This study addresses the problem of fractional-order nonlinear containment control of heterogeneous multi-agent systems within a leader–follower framework, focusing on the impact of False Data Injection (FDI) attacks. By employing adaptive mechanisms and fuzzy logic, the suggested method enhances system resilience, ensuring reliable coordination and stability even in the presence of deceptive disturbances. To deal with these uncertainties, our controller makes use of interval type-II (IT2) fuzzy sets, and we create matrix equalities and inequalities to account for the asymmetry of Laplace matrices. Also, we use the Lyapunov functions for the stability analysis of our system. Lastly, we explain the numerical simulations for the effectiveness of our theoretical results, and these simulated examples are used to verify the effectiveness of our approach and designed model.

Nonlinear steering control law under input magnitude and rate constraints with exponential convergence

AbstractA ship steering control law is designed for a nonlinear maneuvering model whose rudder manipulation is constrained in both magnitude and rate. In our method, the tracking problem of the target heading angle with input constraints is converted into the tracking problem for a strict-feedback system without any input constraints. To derive this system, hyperbolic tangent ($$\tanh$$ tanh ) function and auxiliary variables are introduced to deal with the input constraints. Furthermore, using the feature of the derivative of $$\tanh$$ tanh function, auxiliary systems are successfully derived in the strict-feedback form. The backstepping method is utilized to construct the control input for the resulting cascade system. The proposed steering control law is verified in numerical experiments, and the result shows that the tracking of the target heading angle is successful using the proposed control law.

A novel successive convexification framework with symplectic pseudospectral solutions for nonlinear optimal control problems of constrained pantograph delay systems

This paper proposes a novel symplectic pseudospectral iteration framework for the nonlinear optimal control problem (OCP) of a pantograph delay system with inequality constraints. Traditional numerical algorithms for OCPs with pantograph delay systems have predominantly focused on unconstrained scenarios, neglecting constrained problems. Therefore, we propose a novel symplectic pseudospectral iteration framework for constrained problems. First, we employ the successive convexification (SCvx) method to transform the original problem into a series of linear quadratic (LQ) problems, addressing nonlinearity. Then, leveraging time-scale transformations and parametric variational principles, we derive the first-order necessary conditions (FONCs) for these convexified problems, including a Hamiltonian two-point boundary value problem (HTBVP) with stretching terms and a linear complementarity problem. To handle pantograph time delays effectively, we employ a local Legendre-Gauss-Lobatto (LGL) pseudospectral method with proportional grid discretization. Finally, employing a symplectic indirect algorithm, we develop a symplectic pseudospectral method (SPM) for solving the transformed LQ problems, converting them into a system of sparse linear algebraic equations and a linear complementarity problem. Validation of the framework is performed using diverse illustrative examples, demonstrating strong agreement between SCvx and SPM in computational efficiency. Numerical experiments confirm the sparsity of the core matrix and robustness to initial guesses.

A new hybrid learning control system for robots based on spiking neural networks

This paper presents a new hybrid learning and control method that can tune their parameters based on reinforcement learning. In the new proposed method, nonlinear controllers are considered multi-input multi-output functions and then the functions are replaced with SNNs with reinforcement learning algorithms. Dopamine-modulated spike-timing-dependent plasticity (STDP) is used for reinforcement learning and manipulating the synaptic weights between the input and output of neuronal groups (for parameter adjustment). Details of the method are presented and some case studies are done on nonlinear controllers such as Fractional Order PID (FOPID) and Feedback Linearization. The structure and the dynamic equations for learning are presented, and the proposed algorithm is tested on robots and results are compared with other works. Moreover, to demonstrate the effectiveness of SNNFOPID, we conducted rigorous testing on a variety of systems including a two-wheel mobile robot, a double inverted pendulum, and a four-link manipulator robot. The results revealed impressively low errors of 0.01 m, 0.03 rad, and 0.03 rad for each system, respectively. The method is tested on another controller named Feedback Linearization, which provides acceptable results. Results show that the new method has better performance in terms of Integral Absolute Error (IAE) and is highly useful in hardware implementation due to its low energy consumption, high speed, and accuracy. The duration necessary for achieving full and stable proficiency in the control of various robotic systems using SNNFOPD, and SNNFL on an Asus Core i5 system within Simulink’s Simscape environment is as follows:– Two-link robot manipulator with SNNFOPID: 19.85656 hours– Two-link robot manipulator with SNNFL: 0.45828 hours– Double inverted pendulum with SNNFOPID: 3.455 hours– Mobile robot with SNNFOPID: 3.71948 hours– Four-link robot manipulator with SNNFOPID: 16.6789 hours.This method can be generalized to other controllers and systems like robots.

Robust and fast emulation of PV panels using FSL algorithm and nonlinear power stage controller

The effective implementation of Photovoltaic (PV) systems relies heavily on controlled testing using Photovoltaic Emulator (PVE). This paper presents a novel PVE for rapid and robust testing of PV systems. A fifteen segments linearization (FSL) methodology is put-forward to resolve the nonlinear current-voltage (I-V) equations of PV modules. The I-V curve is precisely segmented into 15 linear elements, whose coordinates are used to construct a suitable reference voltage for the PVE. To ensure a robust and fast emulation of the solar panel, a nonlinear power stage controller (NPSC) is designed to maximize the Buck converter-power stage of the PVE. Several experiments have been performed under diverse environmental and load testing profiles, revealing a mean error and maximum error of less than 0.2 %, and less than 0.6 % respectively for three classes of commercial PV modules (multicrystal KC200GT, poly-crystalline MSX-60, and mono-crystalline CS6K-280 M). The high computation accuracy of the FSL position the proposed PVE as a simple but powerful emulation tool for PV systems. By evaluating its performance and comparing it to the state-of-the-art emulators, this paper aims to demonstrate the effectiveness and superiority of the FSL-NPSC-PVE in achieving rapid and robust emulation of different commercial solar panels.

Control of DC-DC boost converter in discontinuous conduction mode feeding a constant power load

This article presents a new control strategy for a DC-DC boost converter used to supply a constant power load. The designed controller allows regulates the converter output voltage to a required reference value. By designing the controller based on the reduced order averaged model of the converter and using a nonlinear control technique based on feedback linearization, a simple-to-implement and stable controller for both operating modes of the converter (continuous and discontinuous conduction modes respectively) is obtained. The designed control strategy is validated through simulation and experimental results, demonstrating good dynamic performance and stability in both conduction modes, under variations in reference values and significant load changes. In addition, a comparison of the performance and implementation costs between the control strategy proposed in this paper and two strategies proposed by other authors is included.

Experimental test of optimizing maximum power point tracking performance in solar photovoltaic arrays based on backstepping control and optimized by genetic algorithm

Maximum Power Point Tracking (MPPT) is a key component of modern solar photovoltaic (PV) systems. It improves the efficiency of PV power generation systems by inevitably reducing power losses. The most developed MPPT methods adopted like hybrid approaches combine algorithms with nonlinear controllers, such as backstepping controller (BSC). Despite their prevalence, there is still a lack of standardized procedures for tuning the parameters of these nonlinear controllers. In response to this challenge, a proposed method is adopted to identify the optimal gains using Genetic Algorithm (GA) for an efficient power tracking. The advantage of this strategy is established by real-time testing with the GA-BSC technique, which validates its capacity to generate appropriate controller gains for improved tracking performance. Experimental comparisons reveal that the modified GA-BSC approach significantly outperforms the conventional GA-BSC strategy. The conventional GA-BSC method falls short due to its use of non-optimal gains, leading to less effective reference voltage tracking and lower overall performance. In contrast, the proposed method benefits from optimal gains, resulting in enhanced stability and faster response times—achieving maximum power point tracking in 0.2 s compared to 0.6 s for the P&O-BSC method. Another experiment was conducted to test the robustness of the proposed method under variable irradiation profile. The results demonstrated the efficiency of the improved GA-BSC approach compared to other methods, which was more stable and faster. These improvements highlight the capability of the proposed method to enhance hybrid method efficiency, thereby leading to increased efficiency and reliability in photovoltaic systems.

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.

Multivariable adaptive decoupling control based on stochastic configuration networks with serial-parallel switching distribution

A multivariable adaptive decoupling control scheme is proposed based on stochastic configuration networks with serial-parallel switching distribution (SPSCN). Firstly, a linear controller is designed by combining a PID controller, feedback decoupling, and one-step optimal control. Secondly, a nonlinear controller is presented to deal with higher-order nonlinear terms and unknown external perturbations. SPSCN is used to improve the prediction accuracy of unmodeled dynamics. It combines uniform and normal search strategies in a serial-parallel fashion, aiming at improving the node quality and reducing the model complexity. The approximation performance of the SPSCN algorithm is demonstrated by performing approximation experiments with two functions and four benchmark datasets. Compared with the generalized minimum variance control (GMVC) algorithm in controlling the process of cement raw material decomposition, our proposed control scheme outperforms.

Adaptive sliding mode control with nonlinear MPC-based obstacle avoidance using LiDAR for an autonomous surface vehicle under disturbances

This manuscript proposes a path-following and collision avoidance guidance and control system for an autonomous surface vehicle operating in cluttered environments under perturbations. A nonlinear model predictive control strategy handles the state and control constraints for obtaining a guidance law. The approach considers the vessel sideslip angle to provide the desired heading angle, satisfying path-following and obstacle avoidance. Additionally, to solve the nonlinear optimization problem for obtaining the guidance law in real-time, the acados software package is used. Furthermore, in order to guarantee that the vehicle tracks the guidance in presence of model uncertainties and external disturbances, a robust adaptive sliding mode low-level controller is adopted. This controller is finite time convergent, and dynamically adapts its control gain to use only the necessary control inputs. Furthermore, a low-memory and computationally-light obstacle detection strategy employing a LiDAR sensor is presented and proven to run in real-time. Simulation and experimental tests conducted using a customized prototype validate the advantages of the proposed strategy and demonstrate the effectiveness of the path following while evading multiple obstacles in the presence of external disturbances and model discrepancies.

Self-stabilizing economic nonlinear model predictive control applied to modular systems

Recent advances have been made in self-stabilizing Economic Nonlinear Model Predictive Control (eNMPC) formulation without pre-calculated setpoints, which leverages norm-based steady-state optimality conditions to enhance system robustness. To enable practical implementation, a generalized time-domain formulation is proposed, accommodating the discrete-time nature of control instrumentation and the continuous-time nature of first-principles models. A case study involving a modular membrane reactor illustrates the applicability of self-stabilizing eNMPC in real-world industrial scenarios.

Collision Avoidance Path Planning and Tracking Control for Autonomous Vehicles Based on Model Predictive Control.

In response to the fact that autonomous vehicles cannot avoid obstacles by emergency braking alone, this paper proposes an active collision avoidance method for autonomous vehicles based on model predictive control (MPC). The method includes trajectory tracking, adaptive cruise control (ACC), and active obstacle avoidance under high vehicle speed. Firstly, an MPC-based trajectory tracking controller is designed based on the vehicle dynamics model. Then, the MPC was combined with ACC to design the control strategies for vehicle braking to avoid collisions. Additionally, active steering for collision avoidance was developed based on the safety distance model. Finally, considering the distance between the vehicle and the obstacle and the relative speed, an obstacle avoidance function is constructed. A path planning controller based on nonlinear model predictive control (NMPC) is designed. In addition, the alternating direction multiplier method (ADMM) is used to accelerate the solution process and further ensure the safety of the obstacle avoidance process. The proposed algorithm is tested on the Simulink and CarSim co-simulation platform in both static and dynamic obstacle scenarios. Results show that the method effectively achieves collision avoidance through braking. It also demonstrates good stability and robustness in steering to avoid collisions at high speeds. The experiments confirm that the vehicle can return to the desired path after avoiding obstacles, verifying the effectiveness of the algorithm.