Nonlinear Integral Backstepping Research Articles

Nonlinear integral backstepping control based on particle swarm optimization for a grid-connected variable wind energy conversion system during voltage dips

Double-fed induction generator (DFIG) wind turbines connected to the grid are particularly subject to grid problems such as voltage dips. Because of this, it might be challenging to maintain system stability and prevent system disconnections when using a Proportional-Integral (PI) Controller to operate this system. This paper applies the Integral Backstepping Control for the wind power plant system connected to the power grid. The Integral Backstepping is a nonlinear and recursive method that employs the Lyapunov theory to ensure the system's stability. The best selection of gain values for the Lyapunov function guarantees improved system control. These gains are frequently adjusted using the trial-and-error strategy, which is time-consuming and inefficient. This technique becomes more complex when many parameters need to be determined. It also limits the system's performance and restricts this nonlinear approach's advantages. The objective is to apply the particle swarm optimization for computing several constant values of the nonlinear approach by minimizing an integral absolute error criterion index. The weighted sum of errors is employed to solve the multiple objective problems. The proposed controller tracks the maximum power point, maintains the voltage of the DC-Link constant, and controls active and reactive power. The robustness of this method is verified in critical conditions, including system parameter variation and asymmetrical and symmetrical grid faults. The simulation findings highlight the effectiveness and robustness of the combination of Integral Backstepping with Particle Swarm Optimization in terms of reducing response time from 10.6 (ms) to 2 (ms), canceling static error, and improving overshoot compared to the vector control based on PI regulator. Besides, the DC-Link voltage ripples during the asymmetrical grid faults are reduced to ±1 (V) using the suggested controller. The latter can be implemented thanks to advancements in Central Processor Unit technology.

Nonlinear control of two-stage single-phase standalone photovoltaic system.

This paper presents a single-phase Photovoltaic (PV) inverter with its superior and robust control in a standalone mode. Initially, modeling and layout of the Buck-Boost DC-DC converter by adopting a non-linear Robust Integral Back-stepping controller (RIBSC) is provided. The controller makes use of a reference voltage generated through the regression plane so that the operating point corresponding to the maximum power point (MPP) could be achieved through the converter under changing climatic conditions. The other main purpose of the Buck-Boost converter is to act like a transformer and produce an increased voltage at the inverter input whenever desired. By not using a transformer makes the circuit size more compact and cost-effective. The proposed RIBSC is applied to an H-bridge inverter with an LC filter to produce the sinusoidal wave in the presence of variations in the output to minimize the difference between the output voltage and the reference voltage. Lyapunov stability criterion has been used to verify the stability and finite-time convergence of the overall system. The overall system is simulated in MATLAB/Simulink to test the system performance with different loads, varying climatic conditions and inverter reference voltages. The proposed methodology is compared with a back-stepping controller and Proportional Integral Derivative (PID) controller under rapidly varying climatic conditions. Results demonstrated that the proposed technique yielded a tracking time of 0.01s, a total harmonic distortion of 9.71% and a root means square error of 0.3998 in the case of resistive load thus showing superior control performance compared to the state-of-the-art control techniques.

Nonlinear position control of electro-hydraulic servo system based on lyapunov robust integral backstepping controller

In electro-hydraulic servo systems (EHSS), high nonlinearity and time-varying features limit the hydraulic actuator performance. In feedback-based systems, linearization reduces nonlinearities. Their cancellation may produce instability when modeling uncertainty exists. This work uses a robust nonlinear controller based on Lyapunov theory to control the nonlinear position of the electro-hydraulic servo system (EHSS). The dynamics of the system were modeled as extensively as possible, and then a simplified mathematical model based on the EHSS dynamics was created for the controller design. Integral backstepping was used to design the nonlinear robust controller utilizing the Lyapunov theory of nonlinear systems. Lyapunov functions theoretically ensured closed-loop stability. Comparative simulation analysis and experimental investigation in real-time with the proportional integral derivative (PID) controller optimized offline for position tracking control were carried out. Besides tracking performance and steady-state error, the mean square error (MSE), the root mean square error (RMSE), the maximum absolute value of tracking errors and the standard deviation of tracking errors (σ) was utilized to evaluate the controllers’ performance. The simulation analysis and experimental verification were accomplished under various sinusoidal trajectories using different testing conditions (amplitudes, frequencies, and external disturbance), in all testing conditions the effectiveness of the robust nonlinear integral backstepping controller was demonstrated.

Neuromorphic deep learning frequency regulation in stand-alone microgrids

Frequency instability has been a growing problem in recent years due to the rising penetration of distributed generating systems in the format of Microgrids (MGs), which are powered by renewable energy sources (RESs) with an unpredictable nature. The provision of an effective load frequency control (LFC) to an MG model under such conditions contributes significantly to the restoration regarding the unconfigured power system’s stability. An MG structure is employed, which combines renewable energy sources like solar and wind, as well as biologically renewable sustainable energy sources like wastewater, agricultural and domestic wastes, and contains appropriate battery systems and is suited to achieve both energy and waste control in this study. In addition, redox flow battery (RFB), an innovative battery storage system with a fast dynamic response in this MG structure, has been considered as one of the energy storage devices. A nonlinear integral backstepping (NIB) controller is adopted to stabilize the frequency deviation of the integrated MG system with RFB under various level of load disturbances and randomness of RESs. In particular, a spike neural network (SNN) based on neuromorphic platform is proposed to adjust the coefficients of NIB controller. Furthermore, real time analyses are performed with OPAL-RT to validate the feasibility of the proposed strategy from a systematical viewpoint. As a result of this study, the proposed controller for load disturbance, RES power changes, and contingency circumstances in bio renewable MG is determined to be flexible enough to satisfy the efficient frequency regulation for these grids.

An Integral-Backstepping Controller for Interleaved Boost Converter based on Photovoltaic Systems

Photovoltaic systems are one of the most widely used technologies for sustainable energy production due to their various advantages, such as being clean, free, and renewable energy sources. However, the power generated by the PV systems is strongly dependent on the atmospheric conditions. In addition, a suitable DC/DC converter must be used with a robust controller to facilitate system operation point changes associated with the changed climate conditions. In this paper, to deal with this challenge, a photovoltaic system based on four leg interleaved boost converter (FLIBC) has been proposed and studied. For robustness, the presented system is controlled using nonlinear integral backstepping control (IBSC) to track the maximum power point (MPP) and ensure an equal sharing current among the FLIBC legs. Moreover, the particle swarm optimization algorithm is used to find the optimum gains of the proposed IBSC. The entire system is simulated and validated using MATLAB/ Simulink environment. The simulation results demonstrate the efficiency of the proposed system based on the optimized IBSC (OIBSC) controller in terms of MPP tracking speed, overshoot and undershoot reduction, power ripple, and optimization of the performance term integral time square error (ITSE).

A New Hybrid MPPT Based on Incremental Conductance-Integral Backstepping Controller Applied to a PV System under Fast-Changing Operating Conditions

Maximum power point tracking (MPPT) is becoming more and more important in the optimization of photovoltaic systems. Several MPPT algorithms and nonlinear controllers have been developed for improving the energy yield of PV systems. On the one hand, most of the conventional algorithms such as the incremental conductance (INC) demonstrate a good affinity for the maximum power point (MPP) but often fail to ensure acceptable stability and robustness of the PV system against fast-changing operating conditions. On the other hand, the MPPT nonlinear controllers can palliate the robust limitations of the algorithms. However, most of these controllers rely on expensive solar irradiance measurement systems or complex and relatively less accurate methods to seek the maximum power voltage. In this paper, we propose a new hybrid MPPT based on the incremental conductance algorithm and the integral backstepping controller. The hybrid scheme exploits the benefits of the INC algorithm in seeking the maximum power voltage and feeds a nonlinear integral backstepping controller whose stability was ensured by the Lyapunov theory. Therefore, in terms of characteristics, the overall system is a blend of the MPP-seeking potential of the INC and the nonlinear and robust potentials of the integral backstepping controller (IBSC). It was noted that the hybrid system successfully palliates the conventional limitations of the isolated INC and relieves the PV system from the expensive burden of solar irradiance measurement. The proposed hybrid system increased the operational efficiency of the PV system to 99.94% and was found better than the INC MPPT algorithm and 8 other recently published MPPT methods. An extended validation under experimental environmental conditions showed that the hybrid system is approximately four times faster than the INC in tracking the maximum power with better energy yield than the latter.

Virtual Hardware-in-the-Loop FMU Co-Simulation Based Digital Twins for Heating, Ventilation, and Air-Conditioning (HVAC) Systems

In this paper, a novel self-adaptive control method based on a digital twin is developed and investigated for a multi-input multi-output (MIMO) nonlinear system, which is a heating, ventilation, and air-conditioning system. For this purpose, hardware-in-loop (HIL) and software-in-loop (SIL) are integrated to develop the digital twin control concept in a straightforward manner. A nonlinear integral backstepping (NIB) model-free control technique is integrated with the HIL (implemented as a physical controller) and SIL (implemented as a virtual controller) controllers to control the HVAC system without the need for dynamic feature identification. The main goal is to design the virtual controller to minimize the distinction between system outputs in the SIL and HIL setups. For this purpose, Deep Reinforcement Learning (DRL) is applied to update the NIB controller coefficients of the virtual controller based on the measured data of the physical controller. Since the temperature and humidity of HVAC systems should be regulated, the NIB controllers in the HIL and SIL are designed by the DRL algorithm in a multi-objective scheme (MO). In particular, the simulations of the HIL and SIL environments are coupled by a new advanced tool: function mockup interface (FMI) standard. The Functional Mock-up Unit (FMU) is adopted into the FMI interface for data exchange. The extensive research of HIL and SIL controllers shows that the system outputs of the virtual controller are controlled exactly according to the physical controller.

Power Factor Improvement and MPPT of the Grid-Connected Solar Photovoltaic System Using Nonlinear Integral Backstepping Controller

Power Factor Improvement and MPPT of the Grid-Connected Solar Photovoltaic System Using Nonlinear Integral Backstepping Controller

An integral backstepping controller design for compensated distribution networks with rapid earth fault current limiters in bushfire prone areas

AbstractThis paper presents a nonlinear integral backstepping controller (I‐BSC) design scheme for a T‐type residual current compensation (RCC) inverter used in compensated distribution networks with rapid earth fault current limiters (REFCLs). The major control task for the proposed scheme is to reduce the fault current to a value suitable for the mitigation of powerline bushfires due to single phase‐to‐ground faults in compensated distribution networks. The key distinct feature of the proposed I‐BSC over the traditional backstepping controller (T‐BSC) is that it introduces an integral action for analyzing the dynamic of the tracking error which minimizes its steady‐state value and ensures better dynamic performance. In order to prove the global asymptotic stability of the RCC inverter with the proposed integral backstepping controller (I‐BSC), the Lyapunov function‐based theory is used. Finally, the performance of the I‐BSC is analyzed on the MATLAB/Simulink environment and compared with a T‐BSC. The performance of both I‐ and T‐BSCs is assessed in terms of transient behaviors of the injected current to the neutral, fault current, and line‐to‐ground voltage of the faulty phase to ensure the standard operational criteria for self‐extinguishing powerline bushfires. Simulation results clearly demonstrate that both controllers fulfill operational standards for REFCL‐compensated networks though the I‐BSC archives better transient behaviors while comparing with the T‐BSC. Results from the processor‐in‐loop (PIL) validations are also included to further justify the applicability of the newly proposed scheme in the real‐time environment.

Grid Synchronization of Equivalent Wind Farm Equipped with DFIG Model for Transient Stability by Using Nonlinear Integral Backstepping Control

Grid Synchronization of Equivalent Wind Farm Equipped with DFIG Model for Transient Stability by Using Nonlinear Integral Backstepping Control

Smart Emergency EV-to-EV Portable Battery Charger

With the increase in the number of electric vehicles (EVs) and developments in their related charging infrastructures, consumers have still some concerns about some limiting factors in the EV industry such as battery life, charging station availability, electric grid capacity, limited driving range, and slow charging of batteries. Although some solutions are proposed for these limitations, they are not sufficiently efficient and cost-effective. Moreover, charging of EVs on-the-road is still a challenging issue which requires more innovation. This paper proposes a novel battery charger, known as an Emergency EV-to-EV Portable Battery Charger (EPBC), which provides a cost-effective solution for charging EVs on-the-road in emergency mode. The suggested smart charger can charge another EV based on the state of charge (SOC), capacity, and other important technical specifications of batteries in a safe and reliable manner. The smart charger can regulate the output voltage and the injected current to the EV simultaneously. To realize these features, a model free nonlinear integral backstepping control (MF-NIBC) is adopted to regulate the output voltage of the battery charger. By utilizing the actor and critic networks, a deep deterministic policy gradient (DDPG) is adopted to adjust the MF-NIBC controller. Finally, real-time tests based on the OPAL-RT setup are conducted to confirm the applicability and feasibility of the proposed EV-to-EV portable battery charger.

An Advanced Nonlinear Controller for the LCL-Type Three-Phase Grid-Connected Solar Photovoltaic System With a DC–DC Converter

In this article, an advanced nonlinear control scheme is proposed for a three-phase grid-connected inverter and a solar photovoltaic (PV) system connected dc–dc converter. The proposed control scheme is based on a nonlinear adaptive integral backstepping approach. The robustness of the proposed control scheme is achieved through maintaining stability of the overall system, extacting maximum power from the solar PV, and controlling active power. Moreover, the injection of less harmonic components into the grid, the superior performance against different atmospheric conditions, and external disturbances enduring capability are also key features of the controller. The stability of the overall system is achieved through the negative-definite control Lyapunov functions of the proposed control scheme. An adaptive law of the proposed control scheme on external disturbances provides the undergoing capability against the external disturbances. Maximum dc power from the solar PV system is obtained using the proposed control scheme on the dc–dc converter along with the incremental conductance algorithm. The proposed control scheme embedded in the three-phase grid-connected inverter with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -type filter provides maximum active power in the presence of external disturbances, controls reactive power, and injects less harmonic current into the grid. The simulation results under different atmospheric conditions further demonstrate the robustness of the proposed control scheme. The laboratory scale experiments validate the superiority of the proposed control scheme.

Adaptive integral backstepping control of a reconfigurable quadrotor with variable parameters’ estimation

This work presents the control of a quadrotor capable of changing its configuration while flying. The designed controller should handle several arising issues since the drone geometric parameters are varying over time. This variation has a great influence on the quadrotor control, which prompts us to propose an efficient nonlinear adaptive integral backstepping controller. The control architecture includes an estimator of the inertia and other specific blocks to calculate the center of gravity and the mixing matrix. The performance of the proposed control approach has been compared with the conventional integral backstepping controller in two cases, with and without disturbances. The obtained results of the inertias and the center of gravity are also compared and confirmed with those calculated using Computer-Assisted Design–based model.

Hybrid Control using Adaptive Particle Swarm Optimization and Integral Backstepping Control of Grid-connected Doubly Fed Induction Generator

We proposed an analysis of a hybrid control of active and reactive power for a doubly-fed induction generator for variable velocity wind energy injection into the electrical grid using a combination of adaptive particle swarm optimization and integral backstepping control in this paper. The stability of the Lyapunov function is utilized to establish the latter. Six controllers are developed as part of the proposed control process: The first is concerned with the maximum PowerPoint. The stator powers are managed by the second and third regulators, which are performed by the optimal PI controller using adaptive particle swarm optimization. The DC link voltage is kept constant by the fourth controller. The fifth and sixth are employed to pilot the rotor powers and ensure that the power factor is maintained to 1. These three controllers are synthesized by using the nonlinear integral backstepping control. These control strategies show excellent results compared to field-oriented control under a variable wind speed profile and changing generator settings in a Matlab/Simulink environment. According to the test findings, using integral backstepping, the overshoot of the DC-link voltage is decreased by 99.16 %. Furthermore, the particle swarm optimization reduces its time to reach the equilibrium state to 4.3 m s and demonstrates robustness against parameter generator changes.&#x0D; HIGHLIGHTS&#x0D; &#x0D; The regulation of the produced power by the wind energy conversion system (WECS) based on a doubly-fed induction generator is becoming increasingly important to researchers. This system is modeled and simulated in the Matlab/Simulink software environment to apply the proposed control&#x0D; In order to extract the maximum power from the variable wind source, a maximum power point tracking method is developed based on the PI controller&#x0D; For piloting the wind energy system conversion (WECS) based on a DFIG, a combination of the integrated Backstepping controller and adaptive PSO is proposed and realized in this paper&#x0D; Robustness tests are established by adjusting the generator parameters, and a comparative study is conducted to verify the superiority of the suggested control over the indirect vector control&#x0D; &#x0D; GRAPHICAL ABSTRACT

Lyapunov Function Based Flux and Speed Observer Using Advanced Non-linear Backstepping DVC for PWM-Rectifier Connected Wind-turbine-driven PM Generator

In this paper, modeling, and speed/position sensor-less designed Direct Voltage Control (DVC) approach based on the Lyapunov function are studied for three-phase voltage source Space Vector Pulse Width Modulation (SVPWM) Rectifier Connected to a Permanent Magnet Synchronous Generator (PMSG) Variable Speed Wind Power Generation System (VS-WPGS). This control strategy is based on voltage orientation technique without mechanical speed sensor. Advanced Non-linear Integral Backstepping Control (IBSC) of the Generator Side Converter (GSC) has the ability to have a good regulation of the DC link voltage to meet the requirements necessary to achieve optimal system operation, regardless of the disturbances caused by the characteristics of the drive train or some changes into the DC load. The estimation of the speed is based on Model Reference Adaptive System (MRAS) method. This method consists in developing two models one of reference and the other adjustable for the estimation of the two d-q axis components of the stator flux from the measurement of currents, the speed estimated is obtained by canceling the difference between the reference stator flux and the adjustable one using Lyapunov criterion of hyper-stability. Some results of simulation using Matlab/Simulink® are presented, discussed to prove the efficiency and robustness of the system control policy for WPGS against external and internal perturbations.

Adaptive Control of Wind Turbine Generators for Power Capture Optimization by Using Integral Backstepping Approach During Partial-Load Operation

The paper proposes an effective nonlinear integral backstepping approach strategy (IBS) through the use of a new adaptive power control algorithm for variable-speed wind turbine generators (VS-WTGs) to optimize the power extracted from the WTGs. The suggested approach is applied to one of the most frequently used maximum power control methods called as tip speed ratio (TSR) during partial-load operation considering the effects of the variations in wind velocity profile and unmodeled system dynamics such as external disturbances. The proposed method of control is known to scale-back the mechanical stress at the level of the GT shafts (generator and turbine). Furthermore, the IBS approach is relatively simple, which significantly reduces the online computational time and cost. Some numerical simulation results prove, under different wind speed models, that the proposed AC-TSR-IBS method works well on the level of the improved efficiency and the rapid system response compared to conventional TSR-PI method.

A Nonlinear Integral Backstepping Controller to Regulate the Voltage and Frequency of an Islanded Microgrid Inverter

The islanded operation mode of a microgrid system is usually affected by the system uncertainties, such as the load, source, and parameter variations. In such systems, the voltage and frequency must be regulated to maintain the power quality during islanded operation. As an approach to control the voltage and frequency, in this study, a decentralized nonlinear integral backstepping controller for the voltage source inverter used in an islanded microgrid is developed. First, the dynamical model of the inverter-based distribution generations (DGs) in microgrid system is developed. Subsequently, the model-based controller for the microgrid is built using dynamics of inverter-based DGs and Lyapunov theory, which could eliminate the voltage and frequency deviations in the system under different uncertainties. To ensure the system stability, a control Lyapunov function is adopted. Considering the influence of irradiations and other meteorological variables fluctuations a battery energy storage (BESS) is applied on the DC side to suppress the fluctuations of output power of DGs. Furthermore, the efficiency of the designed controller was validated through simulations in the MATLAB/Simulink environment under different scenarios and effectiveness of the proposed framework is further validated by real-time hardware in loop (HIL) experiments. In addition, the performance of the proposed controller is compared with a conventional backstepping (BS) controller. The comparison results demonstrate that the efficiency of the designed controller in terms of obtaining steady-state operating conditions is better than that of the BS controller.

A Novel Deep Learning Backstepping Controller-Based Digital Twins Technology for Pitch Angle Control of Variable Speed Wind Turbine

This paper proposes a deep deterministic policy gradient (DDPG) based nonlinear integral backstepping (NIB) in combination with model free control (MFC) for pitch angle control of variable speed wind turbine. In particular, the controller has been presented as a digital twin (DT) concept, which is an increasingly growing method in a variety of applications. In DDPG-NIB-MFC, the pitch angle is considered as the control input that depends on the optimal rotor speed, which is usually derived from effective wind speed. The system stability according to the Lyapunov theory can be achieved by the recursive nature of the backstepping theory and the integral action has been used to compensate for the steady-state error. Moreover, due to the nonlinear characteristics of wind turbines, the MFC aims to handle the un-modeled system dynamics and disturbances. The DDPG algorithm with actor-critic structure has been added in the proposed control structure to efficiently and adaptively tune the controller parameters embedded in the NIB controller. Under this effort, a digital twin of a presented controller is defined as a real-time and probabilistic model which is implemented on the digital signal processor (DSP) computing device. To ensure the performance of the proposed approach and output behavior of the system, software-in-loop (SIL) and hardware-in-loop (HIL) testing procedures have been considered. From the simulation and implementation outcomes, it can be concluded that the proposed backstepping controller based DDPG is more effective, robust, and adaptive than the backstepping and proportional-integral (PI) controllers optimized by particle swarm optimization (PSO) in the presence of uncertainties and disturbances.

Nonlinear robust integral backstepping based MPPT control for stand-alone photovoltaic system.

PV (Photovoltaic) cells have nonlinear current-voltage (I − V) and power-voltage (P − V) characteristics with a distinct maximum power point (MPP) that entirely depends on the ambient meteorological conditions (i.e. solar irradiance and temperature). Hence, to continuously extract and deliver the maximum possible power from the PV system, under given meteorological conditions, the maximum power point tracking (MPPT) control strategy needs to be formulated that continuously operates the PV system at its MPP. To achieve this goal, a hybrid nonlinear, very fast and efficient MPPT control strategy, based on the robust integral backstepping (RIB) control, is formulated in this research article. The simulation testbed comprises a standalone PV array, a non-inverting buck-boost (NIBB) DC-DC power converter, a purely resistive and a dynamic load (sound system). The proposed MPPT control scheme consists of two loops, where the first loop generates the real-time offline reference peak power voltage through an adaptive neuro-fuzzy inference system (ANFIS) network, which is then utilized in the second loop as a set-point value for generating a control signal and then forcing the PV system to be operated at this set-point by continuously adjusting the duty ratio of the power converter. This control strategy exhibits no overshoot, fast convergence, good transient response, fast rising and settling times and minimum output tracking error. The MATLAB/Simulink platform is used to test the performance of the proposed MPPT strategy against varying meteorological conditions, plant current and voltage faults and plant parametric uncertainties. To validate the superiority of the proposed control strategy, a comparative analysis of the proposed control strategy is presented with the nonlinear backstepping (B), integral backstepping controller (IB) and conventional PID and P&O based MPPT controllers.

Nonsingular Fast Terminal Sliding Mode Based Model-Free Control: Application to Glycemia Regulation Systems

A new Model-Free Control (MFC) is derived to enhance the control performance of the well-known Nonlinear Integral Backstepping based MFC (NIB-MFC). A Nonsingular Fast Terminal Sliding Mode (NFTSM) component is added to NIB-MFC, which makes possible to compensate the estimation error of the time-delay estimation module of NIB-MFC. The obtained in this way new control structure is called NFTSM-MFC. The system stability with NFTSM-MFC is proved and the application of NFTSM-MFC for glycemia regulation is considered. The performances of NFTSM-MFC are compared with those of the NIB-MFC and the intelligent proportional control for a glucose-insulin model of type 1 diabetes patients under a long term simulation.