Nonlinear Backstepping Control Research Articles

Performance improvement of the variable speed wind turbine driving a DFIG using nonlinear control strategies

In this research paper, a nonlinear Backstepping controller has been proposed in order to improve the dynamic performance of a doubly fed induction generator (DFIG) based Wind Energy conversion System, connected to the grid through a back-to-back converter. Firstly, an overall modeling of proposed system has been presented. Thereafter, three control techniques namely backstepping (BSC), sliding mode (SMC) and field-oriented control (FOC) using a conventional PI regulator have been designed in order to control the stator active and reactive powers of the DFIG. In addition, the maximum power point tracking (MPPT) strategy has been investigated in this work with three mechanical speed controllers: BSC, SMC and PI controller with the aim of making a synthesis and a comparison between their performances to determine which of those three techniques is more efficient to extract the maximum power. Finally, a thorough comparison between the adopted techniques for the DFIG control has been established in terms of response time, rise time, total harmonic distortion THD (%) of the stator current, static errors and robustness. The effectiveness and robustness of each control approach has been implemented and tested under MATLAB/Simulink environment by using a 1.5 MW wind system model.

Analysis of Optimal Oxygen Excess Ratio and Nonlinear Tracking Control of Vehicle PEMFC Air Supply System

To a large extent, the efficiency and durability of the proton exchange membrane fuel cell (PEMFC) depend on the effective control of air supply system. However, dynamic load scenarios, internal and external disturbances, and the characteristics of strong nonlinearity make the control of complex air supply systems challenging. This paper mainly studies the modeling of PEMFC air supply system and the design of a nonlinear controller for oxygen excess ratio tracking control. First, we analyze and calibrate the system’s optimal oxygen excess ratio control target and explore how the system temperature and humidity impact it, respectively; second, a second-order affine oriented control model which can represent the static and dynamic characteristics of the air supply system is derived, and a disturbance observer is designed to estimate and compensate the “lumped error” online. Then, aiming at the problem of unmeasurable cathode pressure, a state observer based on Kalman optimal estimation algorithm is proposed to realize the real-time estimation of cathode pressure; finally, a dynamic output feedback control system based on observer and backstepping nonlinear controller is proposed, and the comparison and evaluation of two control strategies based on constant oxygen excess ratio tracking and optimal oxygen excess ratio tracking are carried out. The simulation results show the effectiveness and superiority of the designed control system compared with the reference controller.

Nonlinear backstepping controller design for bridge‐type fault current limiter to enhance the transient performance of hybrid power systems

Nonlinear backstepping controller design for <scp>bridge‐type</scp> fault current limiter to enhance the transient performance of hybrid power systems

Active slip control of a vehicle using fuzzy control and active suspension

This paper presents an active slip control system (ASCS) for a four-wheel drive electric vehicle (EV) using an active suspension of the vehicle. The integrated control mechanism is designed using a combination of a fuzzy controller and a nonlinear back-stepping controller to control the slip of the individual wheels with the help of the active suspension of the vehicle. In this research, the presented control mechanism is implemented in two steps. In the first step, based on the friction coefficient calculated from a nonlinear tire model, the fuzzy controller will generate the vehicle roll and pitch angles required to reduce the slipping of the individual wheels by changing the vertical load of the individual wheel. In the second step, a nonlinear back-stepping controller is used to track the required roll and pitch angles using the active suspension of the vehicle. A linear seven degree of freedom (DOF) vertical mathematical model is used for the design of the nonlinear back-stepping controller, while the rules of the fuzzy controller are interpreted from the friction coefficients of the tyre model. The performance of the presented control mechanism is verified using a 14-DOF nonlinear model with nonlinear tyre dynamics. The simulations using a nonlinear vehicle model show that the presented controller can successfully improve vehicle stability by reducing the slipping of the individual wheel.

Linear-based gain-determining method for adaptive backstepping controller

This paper presents a linear-based gain-determining method for nonlinear adaptive backstepping controllers. Usually, the gains for nonlinear controllers are tuned by the trial and error method. This method becomes more difficult as the number of gains increases. A user-friendly method is proposed in this work to deal with the problem. Firstly, a linear auxiliary system is formed by separating the linear parts from the nonlinear system. Then, linear state-space techniques are used to determine the gains for state-feedback by the linear auxiliary system. After that, by converting the state-feedback gains to backstepping gains, the gains of the nonlinear backstepping controller can be determined. The proficiency of the gain-determining method is proved by simulations with two linear techniques.

Optimal game theoretic solution of the pursuit‐evasion intercept problem using on‐policy reinforcement learning

AbstractThis article presents a rigorous formulation for the pursuit‐evasion (PE) game when velocity constraints are imposed on agents of the game or players. The game is formulated as an infinite‐horizon problem using a non‐quadratic functional, then sufficient conditions are derived to prove capture in a finite‐time. A novel tracking Hamilton–Jacobi–Isaacs (HJI) equation associated with the non‐quadratic value function is employed, which is solved for Nash equilibrium velocity policies for each agent with arbitrary nonlinear dynamics. In contrast to the existing remedies for proof of capture in PE game, the proposed method does not assume players are moving with their maximum velocities and considers the velocity constraints a priori. Attaining the optimal actions requires the solution of HJI equations online and in real‐time. We overcome this problem by presenting the on‐policy iteration of integral reinforcement learning (IRL) technique. The persistence of excitation for IRL to work is satisfied inherently until capture occurs, at which time the game ends. Furthermore, a nonlinear backstepping control method is proposed to track desired optimal velocity trajectories for players with generalized Newtonian dynamics. Simulation results are provided to show the validity of the proposed methods.

New Diagnosis and Fault-Tolerant Control Strategy for Photovoltaic System

This paper discusses open-circuit fault (OCF) diagnosis and fault-tolerant control strategy (FTCS) of a nonisolated DC-DC converter. The photovoltaic power conversion structure (PPCS) consists of a photovoltaic generator and an interleaved Boost converter (IBC). The maximum power point tracking (MPPT) control of the IBC ensures operation at maximum power. The design of the nonlinear Backstepping control is detailed based on the equivalent average model of IBC, and the stability is studied using Lyapunov’s theorem. The proposed OCF fault detection is based on sampling the voltage across the inductor at a much higher frequency than the switching frequency. In an OCF situation occurrence and a high control signal state, the detection of three negative samples is a condition for signaling the presence of an OCF fault; the photovoltaic system continues its normal operation. The simulation results show the validity of the proposed FTCS. The proposed diagnosis and control strategy improves the performance of the IBC in terms of cost, reliability, and service continuity.

Backstepping Control of an Unmanned Helicopter Subjected to External Disturbance and Model Uncertainty

A helicopter is a highly nonlinear system. Its mathematical model is difficult to establish accurately, especially the complicated flapping dynamics. In addition, the forces and moments exerted on the fuselage are very vulnerable to external disturbances like wind gust when flying in the outdoor environment. This paper proposes a composite control scheme which consists of a nonlinear backstepping controller and an extended state observer (ESO) to handle the above problems. The stability of the closed-loop system can be guaranteed based on Lyapunov theory. The external disturbances and model nonlinearities are treated as a lumped disturbance. Meanwhile, the ESO is employed to compensate the influence by estimating the lumped disturbance in real-time. Numerical simulation results are presented to demonstrate that the algorithm can achieve accurate and agile attitude tracking under the external wind gust disturbances even with model uncertainties. When coming to the flight test, a block dropping device was designed to generate a quantifiable and replicable disturbance, and the experimental results indicate that the algorithm introduced above can reject the external disturbance rapidly and track the given attitude command precisely.

Lyapunov-based model predictive control trajectory tracking for an autonomous underwater vehicle with external disturbances

This paper focus on the trajectory tracking of autonomous underwater vehicles (AUVs) in complex ocean environments. A novel Lyapunov-based Model Predictive Control (LMPC) framework is designed for AUV, which improves the performance of trajectory tracking through online optimization. By incorporating salient features of Lyapunov-based nonlinear backstepping control, the contraction constraint is constructed to ensure the closed-loop stability. Within this framework, the actual limitation of executor saturation could be clearly considered. Next, the recursive feasibility and closed-loop stability of the LMPC-based control are rigorously proved. Also, the guaranteed region of attraction (ROA) is clearly described. Finally, the simulation results demonstrate the feasibility and robustness of the designed LMPC trajectory tracking method.

A Nonlinear Backstepping Controller Design for High-Precision Tracking Applications with Input-Delay Gimbal Systems

This paper proposes a novel nonlinear control approach for a two-axis gimbal to achieve accurate real-time tracking performance in maritime surveillance applications. For this objective, the control system must overcome system complexities and limitations, including nonlinear dynamics, coupled Euler angle-based measurements, and delay time constraints. The nonlinear backstepping controller was designed, taking into consideration the nonlinearities and system couplings to preserve the system stability. Then, an extra backstep was incorporated to minimize the control errors due to the delay time. The proposed control scheme enhances the tracking performances and expands the system’s bandwidth, which is validated in the simulations and experimental studies in comparison with a super-twisting sliding mode controller introduced in a previous study.

Electrical control strategy for an ocean energy conversion system

Globally abundant wave energy for power generation attracts ever increasing attention. Because of non-linear dynamics and potential uncertainties in ocean energy conversion systems, generation productivity needs to be increased by applying robust control algorithms. This paper focuses on control strategies for a small ocean energy conversion system based on a direct driven permanent magnet synchronous generator (PMSG). It evaluates the performance of two kinds of control strategies, i.e., traditional field-oriented control (FOC) and robust adaptive control. The proposed adaptive control successfully achieves maximum velocity and stable power production, with reduced speed tracking error and system response time. The adaptive control also guarantees global system stability and its superiority over FOC by using a non-linear back-stepping control technique offering a better optimization solution. The robustness of the ocean energy conversion system is further enhanced by investigating the Lyapunov method and the use of a DC-DC boost converter. To overcome system complexity, turbine-generator based power take-off (PTO) is considered. A Matlab/Simulink study verifies the advantages of a non-linear control strategy for an Oscillating Water Column (OWC) based power generation system.

A robust nonlinear control strategy of a PV System connected to the three-phase grid based on backstepping and PSO technique

This article presents a robust non-linear control technique of the three-phase photovoltaic system. The structure chosen for this PV system is that of two power converters and DC voltage intermediate bus. The two power converters are: the DC-DC converter and the three-phase inverter, which requires two main controllers. These controllers have three main objectives. The first objective is to impose the PV voltage generated by the photovoltaic panel, in order to follow a maximum reference voltage provided by the MPPT block. The second one is to maintain the DC link voltage to a constant value, in order to optimize the transfer of energy between the two power converters. The last objective is to inject a three-phase sinusoidal current into the grid, while respecting a unit power factor. With the intention to achieve these three objectives, we designed cascading nonlinear controllers by using the technique of non-linear backstepping control in the synthesis of these two controllers, based on the Lyapunov function, with regard to maximise the PVG output voltage, in order to have a unitary power factor at the grid side. In order to regulate DC-link voltage, we developed an integral proportional controller (PI) with parameters that are optimized by the Particle Swarm Optimization (PSO) method. The robustness of the controller designed approach is tested by a simulation in MATLAB/Simulink software, that improves the performances of each controller whatever conditions of climate.

Design of Nonlinear Backstepping Control Strategy of PMSG for Hydropower Plant Power Generation

In this paper, renewable hydropower plant generators with permanent magnet synchronous generator are coupled via a diode bridge rectifier - DC/DC boost converter and three-phase inverter to a power grid. This paper studies a new control structure focused a backstepping control of the energy generation system.The proposed methods for adjusting the active and reactive power by adjusting the currents, the DC bus voltage on the main side converter, as well as the voltage at the output of the DC-DC boost converter. The main objective of this control is to obtain purely sinusoidal and symmetrical grid current signals, to suppress oscillations in reactive power and to cancel active power chattering in the event of grid imbalance. In order to optimize the energy flow in the different parts of the production process, an energy control algorithm is developed in order to attenuate the fluctuations in the water flow, the grid system of the hydropower plant considered has been implemented in Matlab/Simulink, the results show the effectiveness of the proposed method. To analyze our approach, a prototype is modeled, simulated and can be performed in an experimental test setup.

A Robust Nonlinear Controller for PMSG Wind Turbines

In this paper, a nonlinear backstepping controller is proposed to manage the performance of a full-variable permanent magnet synchronous generator wind turbine. This nonlinear controller achieves a rotational speed objective for the generator and is validated through Lyapunov-based stability analysis. Additionally, this objective is accomplished without a measurement for wind speed that influences the wind torque. The proposed scheme is compared to a typical linear controller through simulation results. Simulation tests are performed to compare the response time and average error of each controller in both a drastic and realistic dynamic wind environment. These results demonstrate that the proposed controller is far more robust to wind turbulence than traditional control schemes. The simulation results of this study indicate a 1000% increase in response time and 3000% decrease in average controller error.

Non-linear backstepping speed control for Asian electric scooter uses

The electric scooter has become very popular especially in large European and Asian urban areas, thanks to its some advantages. While its popularity is increasing, studies about these electric scooters are also increasing. The main objective of this study is to introduce the design of an autonomy extended electric three-wheeled scooter. For this aim, a model is obtained firstly and it is driven by two BLDC motors placed on the rear wheels independently controlled by a non-linear controller named as Backstepping. Indeed, it contains a powerful electronic differential system to ensure the security of passenger while entering the curved road. The studied model is simulated through the MATLAB Simulink environment where interesting results are shown in results.

Performance improvement of modern variable-velocity wind turbines technology based on the doubly-fed induction generator (DFIG)

In the latest decades, Green energies received significant support from the international community and became the key solution for the global environmental issues caused by the increasing consumption of fossil fuels. One of the cleanest sources of renewable energy that allow producing green energy is wind power which is developing with a fast rate and becoming mature and more economically competitive due to the advanced techniques for extraction. Today, the modern wind power systems technology is based on the variable-velocity Doubly Fed Induction Generators (DFIGs). To improve the operation, the production and the stability of the modern variable-velocity wind turbines technology, the current paper proposes an adaptive backstepping control structure for a wind power system based on the doubly-fed Induction generator (DFIG) in power grid-connected mode. This adaptive nonlinear control structure is proposed to cope with nonlinearity and effects of the parameter uncertainties and variations in the DFIG wind power system under study, whose main purpose is the power extract optimization from variable-velocity DFIG wind turbine while enhancing the stability of the whole system. Design of the adaptive nonlinear backstepping control system as rotational velocity and rotor current regulators have been implemented based on the wind power system dynamic model with unknown parameters. The system’s unknown parameters are dynamically estimated through the parameters adaptive update laws formulated during the design process, and these estimation laws together with the control actions for the DFIG-wind turbine are derived in such a way that the stability of the whole system according to the Lyapunov stability theory is ensured. Numerical simulation tests were conducted to evaluate the robustness and effectiveness of the proposed adaptive control structure. The obtained results show clearly that the proposed method has advanced robustness to cope with the system parameter variations and uncertainties.

Nonlinear controllers for fuel cell, photovoltaic cell and battery based hybrid energy management system

Abstract Due to limitations of conventional energy sources like petrol, diesel, hydro, nuclear etc., hybridization of green energy sources like photovoltaic cell, wind, fuel cell etc. has become a challenging task. In this research photovoltaic (PV) and fuel cells (FC) have been considered as primary sources of energy while battery as a storage unit for a Hybrid Energy Storage System (HESS). Extraction of maximum power from PV panel and output voltage regulation is another challenge due to its nonlinear characteristics. In this paper, single stage multi input multi output (MIMO) buck converter has been considered and four controllers: Fuzzy Logic Based (FLB) robust, nonlinear Backstepping (BS), Integral Backstepping (IBS) and Synergetic controllers have been proposed to track the output voltage, to control the battery charging and to extract maximum power from the PV cell. Asymptotic stability of the proposed controllers has been proved using Lyapunov theory. The performance of nonlinear controllers has been checked under input power and load variations on the converter having only one inductor and two input sources. They have been compared with each other and conventional PID controller under different operating conditions by simulations in MATLAB/Simulink. The results have also been validated by an experimental setup on a lab prototype.

DSPACE‐based implementation for observer backstepping power control of DFIG wind turbine

This work develops a real-time implementation on the DSPACE environment of an adaptive non-linear control strategy for a wind energy conversion system (WECS) based on the doubly-fed induction generator (DFIG). The DSPACE-DS1104 board is directly associated with an experimental bench of a wind power system. The non-linear backstepping controller has been realised to control the active and reactive powers of the DFIG connected directly to the electricity grid via two converters (grid side and machine side). First, a full review of the WECS is discussed. Subsequently, a detailed description of the backstepping control laws based on the Lyapunov stability technique is reported. Consequently, a simulation on the Matlab & Simulink environment was carried out to test the proposed control model in terms of performance and robustness. The second part of this work was devoted to the experimental validation of the adaptive backstepping control algorithm on a test bench to prove its efficiency. The results obtained show a perfect correlation between simulations and experiments (in static and dynamic regime) even for fluctuating wind speed.

Novel nonlinear control structure for vector control of SPIM drive using BS PCH

This paper presents a novel structure combining the port-controlled Hamiltonian (PCH) and Backstepping (BS) nonlinear control for the vector control of the six-phase induction motor (SPIM). In this new scheme, to improve the outer loop’s robustness, the BS technique using the integral tracking errors action is proposed in the speed and flux controllers design. The advantage of this proposed control law is not to increase the complexity of differential equation resolution due to being not increased system states numbers. To enhance more the performance of SPIM drives (SPIMD), port-controlled Hamiltonian (PCH) scheme is used in the inner current loop controllers. In this proposed PCH current controller, the stabilization of controller is achieved via system passivity. In that, the interconnection and damping matrix functions of PCH system are shaped so that the physical (Hamiltonian) system structure is preserved at the closed loop level and the closed loop energy function is equal to the difference between the physical energy of the system and the energy supplied by the controller. The proposed control design is based on combination PCH and BS techniques improve significantly performance and robustness. The proposed speed control scheme is validated by Matlab-Simulink software.

Simulation and experimental validation of single-phase series active power filter using PI and backstepping nonlinear controllers

&lt;p&gt;Nowadays, power distribution networks are focus mainly on power quality issues. Among the power disturbances, sag, swell and voltage harmonics are studied and deliberated in this research paper. These problems have negative impacts especially on the sensitive load, which have to be protected and secured against these problems. Therefore, to solve such disturbances, the series active power filter (SAPF) can be an efficient solution, which is used to compensate the voltage difference and to reduce the problem’s effects on the power system. In this paper, the SAPF is simulated and experimentally validated, where two control methods are used to control the applied disturbances; which are classical proportional integral PI and nonlinear backstepping controllers. The control structure of the SAPF aims to reduce the error of the injection voltage closed loop, in addition to reduce the total harmonic distortion (THD) values below 5% and within the specified ranges of the international IEEE-519 standard. From simulation results, the backstepping nonlinear controller has reacted more robustly and efficiently than the conventional PI controller.&lt;/p&gt;