Nonlinear Backstepping Control Research Articles

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

<p>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.</p>

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

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

An integrated scheme of speed control and vibration suppression for spiral spring energy storage system driven by PMSM based on backstepping control with minimum electrical loss

The operational performance of the spiral spring energy storage system is affected by the vibration of the spiral spring and the electrical loss of the permanent magnet synchronous motor. It is important to eliminate vibration and reduce electrical loss. A unified control scenario for speed regulation and vibration suppression based on the minimum electrical loss is proposed. First, the spiral spring is equivalent to an Euler–Bernoulli beam and its dynamic model suitable for control is established via the Lagrange equation. Then, the unified control scenario is proposed through nonlinear backstepping control. The speed controller and current controller including modal vibration suppression and minimum electrical loss operation of the system are established, and the stability of the controller is theoretically proved. Moreover, for unknown vibration mode of the spiral spring, a vibration mode–based estimation method with the least-squares algorithm is designed. Aiming at the uncertainty of the permanent magnet synchronous motor’s iron loss resistance, an estimation algorithm based on an adaptive neural fuzzy inference system is designed. The experimental results verify the correctness and effectiveness of the proposed control scheme. In comparison with traditional backstepping control, the proposed control method can effectively suppress the vibration of the spiral spring and realize the stable and highly efficient energy storage operation of the system.

Nonlinear backstepping control for PMSG wind turbine used on the real wind profile of the Dakhla‐Morocco city

Nonlinear backstepping control for PMSG wind turbine used on the real wind profile of the Dakhla‐Morocco city

A direct power control of a DFIG based-WECS during symmetrical voltage dips

The Wind Energy Conversion System (WECS) based Doubly Fed Induction Generator (DFIG) has experienced a rapid development in the world, which leads to an increasing insertion of this source of energy in the electrical grids. The sudden and temporary drop of voltage at the network can affect the operation of the DFIG; the voltage dips produce high peak currents on the stator and rotor circuits, without protection, the rotor side converter (RSC) will suffer also from over-current limit, consequently, the RSC may even be destroyed and the generator be damaged. In this paper a new Direct Power Control (DPC) method was developed, in order to control the stator powers and help the operation of the aero-generator during the faults grid; by injecting the reactive power into the network to contribute to the return of voltage, and set the active power to the optimum value to suppress the high peak currents. The DPC method was designed using the nonlinear Backstepping (BS) controller associated with the Lyapunov function to ensure the stability and robustness of the system. A comparison study was undertaken to verify the robustness and effectiveness of the DPC-BS to that of the classical vector control (VC) using Proportional-Integral (PI) correctors. All were simulated under the Simulink® software.

Nonlinear Backstepping Control of Electro-Hydraulic Brake System Based on Bond Graph Model

EHB (electro-hydraulic brake system) can provide active and decoupled brake for electric intelligent vehicles. However, modelling and control of automotive electro-hydraulic brake systems are always challenging due to the complex and highly nonlinear dynamic characteristics of the braking process. In this paper, a nonlinear backstepping control algorithm for EHB based on the bond graph model is introduced. A nonlinear, single-wheel brake system model is constructed using the bond graph method, in which the capacitive effect of the hydraulic fluid and the damping and inertia effects of calipers are considered. Based on this nonlinear model, a backstepping controller with good robustness is designed, and the control signals of the inlet and outlet valves are described by a unified expression. Moreover, the effects of the controller parameters on brake-pressure control are discussed in details, and suitable design parameters are chosen. Finally, the proposed algorithm is verified by the simulation and hardware-in-the-loop tests. The results show that valves are properly regulated by the backstepping controller, and the brake pressure follows the desired value rapidly and accurately.

Control of an Off-Grid PV System based on the Backstepping MPPT Controller

This work presents the modeling and the control of an Off-grid Photovoltaic (PV) system which consisted of a monocristalline PV module, a DC load, a DC-DC boost converter and a maximum power point tracking (MPPT) bloc. The output characteristic of the PV module is nonlinear and changes with solar irradiance and temperature. So, for given climatic conditions, the PV module output power is maximal when its voltage equals to a certain value. When temperature and solar irradiance change, the duty cycle of the converter considered as the control law is continuously adjusted to track the maximum power point (MPP) of the module. This paper highlights the non-linear Backstepping controller to extract the maximum power from the PV system. Asymptotic stability of the system is verified through Lyapunov stability analysis. The simulations results show that the proposed controller offers fast and accurate tracking of the MPP whatever is the change of the climatic conditions.

Nonlinear Control of Wind Energy Conversion System Based on DFIG with a Mechanical Torque Observer

In this paper, an advanced nonlinear backstepping control approach is developed and applied to the whole nonlinear system including the AC/DC/AC converters combined with the doubly-fed induction generator(DFIG). A high gain observer is synthesized, in order to provide an estimated value of the mechanical torque whereas, a wind speed estimation block is designed based on roots polynomial method; followed by sensorless maximum power point tracking (MPPT). The control objectives are fourfold: (i) Forcing the generator speed to track the reference signal given by the MPPT block, (ii) adjusting the stator reactive power injected into the grid to be null, (iii) Regulating the DC-link voltage between the rotor side and the grid side converters at the desired level, (iv) assuring a unitary power factor in the grid side. The achievement of these control objectives leans on a multi-loop regulator which shows a satisfying performance as far as it concerns the simulation results.

Nonlinear control by backstepping applied to the web winding system

The key system in the reversible cold rolling mill is the web winding system (WWS). The WWS is a complex process characterized by multiple variables with varying parameters in time, a strong coupling and a non-linearity, various operating conditions. For many products, such as thin film tapes, highly precise control of web tension and web velocity to prevent bending or breaking of the web is of paramount importance throughout the manufacturing process. Because of the radius variation and broad range of roller inertia, the dynamic system changes strongly during the winding process. In this work, we present the design of a new version of the nonlinear backstepping control law for the WWS, in order to guarantee that the final product does not undergo deformations or breaks. It is an adaptive control approach of backstepping with introduction of integral actions. Using Lyapunov stability theory, we verify that trajectory dynamics are asymptotically stable. Simulation studies with the MATLAB/SIMULINK environment are presented to exemplify the effectiveness and performances of the proposed controllers.

Modeling and Design of Single-Phase PV Inverter with MPPT Algorithm Applied to the Boost Converter Using Back-Stepping Control in Standalone Mode

We propose a high-performance and robust control of a transformerless, single-phase PV inverter in the standalone mode. First, modeling and design of a DC-DC boost converter using a nonlinear back-stepping control was presented. The proposed converter uses a reference voltage that is generated by the Perturb and Observe (P&O) algorithm in order to extract the maximum power point (MPP) by responding accurately to varying atmospheric conditions. Another goal for using the boost converter is to raise the voltage at the input of the inverter without using a transformer in this system, thus making the system more compact and less expensive. Secondly, the single-phase H-bridge inverter was controlled by using back-stepping control in order to eliminate the error between the output voltage of the inverter and the desired value, even if there is acute load variation at the output of the inverter. The stability of the boost converter and H-bridge inverter was validated by using Lyapunov’s stability theory. Simulation results show that the proposed PV system with back-stepping controllers has a good extraction of the MPP with an efficiency of 99.93% and 1 ms of response time. In addition, the sinusoidal form of the output voltage of the inverter is fixed to 220 V and the total harmonic distortion of the output voltage was found to be less than 1%.

Nonlinear Backstepping Control of a Quadrotor-Slung Load System

This paper presents a nonlinear backstepping controller designed for an underactuated quadrotor-slung load system that drives the load to a predefined trajectory. The quadrotor and the load are modeled as a rigid body and a point mass, respectively. The controller is designed through Lyapunov and backstepping techniques, and the control laws for thrust and angular velocity are presented, which guarantee the closed-loop system to be asymptotically stable. Experimental results are provided to assess the validity and performance of the proposed controller.

Dspace DS1104 implementation of a robust nonlinear controller applied for DFIG driven by wind turbine

This research paper deals whit the control of a doubly fed induction generator (DFIG) driven in rotation by wind turbine, the objective of this work is to control the electromagnetic torque of the generator and have a specified reactive stator power generated whatever perturbations, the MPPT method was used to extract the maximum of the power for different wind speed variations. To control the system studied we have used the Nonlinear Backstepping Controller with Lyapunov function, the robustness of our controller is tested in terms of reference tracking under perturbed conditions (generator parameters variations and voltage dips). All were implemented on dSPACE DS1104 Controller card Real-Time Interface (RTI), which runs in Simulink/MATLAB environment and ControlDesk 4.2 graphical interfaces. Hardware simulation results show and validate the performances and robustness of our controller.

DSP in the Loop Implementation of a Backstepping Controller for Wind Energy Conversion System Based on a Doubly Fed Induction Generator Connected to Grid

This paper deals with the design and implementation of the control strategy of a grid connected Doubly Fed Induction Generator wind turbine on a TMS320F28335 Digital Signal Processor (DSP). The synthesized controller is a nonlinear Backstepping control law whose stability is guaranteed in the context of Lyapunov stability theory. The control aim is to optimize the power extracted by the generator for large wind speed variations through Maximum Power Point Tracking (MPPT) and Unity Power Factor (UPF) control. These command strategies are implemented in order to achieve the following specifications: good static precision for optimal energy conversion; electrical dynamics as high as possible regardless of slow mechanical dynamics, smooth transient without overshoots that could damage the lifecycle of the machine and converters, rapid disturbance isolation and robustness to any parametric variations or uncertainties. The results of the Hardware in the Loop (HIL) implementation on DSP show satisfactory performance in terms of response time, setpoint tracking, stability, and robustness under stochastic wind speed profile and parameter variations.

Advanced non-linear backstepping control design for variable speed wind turbine power maximization based on tip-speed-ratio approach during partial load operation

This study suggests an effective non-linear control scheme to improve wind energy production for getting maximum output power during partial load operation from a variable speed wind turbine generator. The proposed control strategy is based on an integral backstepping control using Tip-Speed-Ratio approach (TSR) for Wind Turbine Generators applications to optimize the wind energy captured by the system operating under rating wind speed. The proposed method has a fast and robust tracking capability. In addition, it is not necessary to know the parameters of the generator so as to get the control signal. This control method is known to scale back the mechanical stress on the generator and turbine shafts. Moreover, the Integral Backstepping Control (IBSC) policy is relatively simple, that considerably reduces the online computational cost and time. The time-domain simulation results prove the efficient operation of the proposed TSR-IBSC with fast system response compared to standard TSR approach.

Switched reluctance motor circuit drive system using adaptive nonlinear backstepping control with mended recurrent Romanovski polynomials neural network and mended particle swarm optimization

AbstractA switched reluctance motor (SRM) circuit drive system caused many nonlinear effects due to convex construction. The linear control methods were hard to achieve good performance for the SRM circuit drive. The adaptive nonlinear backstepping control system using switching function is proposed for controlling the SRM drive system to obtain good performance. To reduce chattering of control effort, the adaptive nonlinear backstepping control system using adaptive law is proposed to estimate the required lumped uncertainty. When the inertia of the counterweight is varying, this proposed method cannot get a satisfactory performance. The adaptive nonlinear backstepping control system using mended recurrent Romanovski polynomials neural network with adaptive law and error‐estimated law is proposed for controlling the SRM drive system to raise robustness of the SRM drive system. Furthermore, two variable learning rates in the mended recurrent Romanovski polynomials neural network are adopted by using mended particle swarm optimization (PSO) algorithm to speed up parameter's convergence.Finally, comparative performances through some experimental results are verified that the proposed control system has better control performances than those of the proposed methods for the SRM drive system.

Retracted: Adaptive nonlinear backstepping control using mended recurrent Romanovski polynomials neural network and mended particle swarm optimization for switched reluctance motor drive system

A switched reluctance motor (SRM) drive system has highly nonlinear uncertainties owing to a convex construction. It is hard for the linear control methods to achieve good performance for the SRM drive system. An adaptive nonlinear backstepping control system using the mended recurrent Romanovski polynomials neural network and mended PSO with an adaptive law and an error estimated law is proposed to estimate the lumped uncertainty and to compensate the estimated error in order to enhance the robustness of the SRM drive system. Additionally, in accordance with the Lyapunov stability theorem, the adaptive law in the mended recurrent Romanovski polynomials neural network and the error estimated law are established. Furthermore, to help improve convergence and to obtain better learning performance, the mended particle swarm optimization (PSO) algorithm is utilized for adjusting the two varied learning rates of the two parameters in the mended recurrent Romanovski polynomials neural network. Finally, some experimental results and a comparative analysis are verified that the proposed control scheme has better control performances for controlling the SRM drive system.

Investigation on SVM-Backstepping sensorless control of five-phase open-end winding induction motor based on model reference adaptive system and parameter estimation

This paper deals with a new control technique applied to five-phase induction motor under open-end stator winding (FPIM-OESW) topology using the backstepping nonlinear control. The main objective is to improve the dynamics of this kind of machine, which is intended to be used in high power industrial application, where the maintenance is difficult and the fault tolerant is needed to ensure the continuous motor operating mode with minimized number of interruption. This control technique is combined with the Space Vector Pulse Width Modulation (SVPWM) to maintain a fixed switching frequency. In addition, the Model Reference Adaptive System (MRAS) concept is used for the estimation of the load torque, the rotor flux and the rotor speed to overcome the main drawbacks presented with the previous sensorless systems concepts. However, the great sensitivity to the changes of the motor internal parameters and it operating instability problems, especially in low-speed operating region, that causes an estimation error of the rotor speed, is the most disadvantage of the MRAS technique. Therefore, to solve this problem, an estimation method of the motor internal parameters such as the rotor resistance, the stator resistance and the magnetizing inductance, is proposed in this paper. Where, the main aim is to improve furthermore the control performance, to reduce the computational complexity and to minimize the rotor speed estimation error. The obtained simulation results confirm the enhanced performance and the clear efficacy of the proposed control technique under a variety of cases of different operating conditions.

Fractional Order Fuzzy Dynamic Backstepping Sliding Mode Controller Design for Triaxial MEMS Gyroscope Based on High-gain and Disturbance Observers

In this paper, a dynamic backstepping sliding mode controller with a fractional order sliding surface, which has a fuzzy boundary layer, is designed based on high-gain and disturbance observers for controlling the performance of a micro-electro-mechanical triaxial gyroscope. To compensate uncertainties of a system, a combination of sliding mode and robust nonlinear backstepping controller is used. In this design, in order to increase the degree of freedom of the controller, the sliding surface is selected to be of fractional order. in this paper, in order to significantly reduce the chattering phenomenon in the control signal, a new dynamic sliding surface in addition to the initial sliding surface and also fuzzy control theory to controllig the boundary layer are used. In addition, a high-gain observer and a disturbance observer are used to estimate the system states and incoming disturbances to the system. The asymptotic stability of the closed-loop system is proven by Lyapunov stability theorem. In order to evaluate the performance of the designed controller, this controller is compared with other sliding mode controllers. Simulation results show that the proposed controller has much less chattering phenomenon in control signal, increasing system stability, reducing the rise time and better tracking.

A second-order slip model for constraint backstepping control of antilock braking system based on Burckhardt’s model

ABSTRACTThis paper is concerned with the problem of constraint control for an Antilock Braking System (ABS) with asymmetric slip ratio constraints. A nonlinear backstepping control method based on Barrier Lyapunov Function (BLF) is proposed not only to track the optimal slip ratio but also to guarantee no violation on the slip ratio constraints. A second order slip rate model is established based on a quarter vehicle braking model and a Burckhardt’s tire model. The Asymmetric Barrier Lyapunov Function (ABLF) is introduced into the backstepping controller for solving the asymmetric slip ratio constraint problems. The proposed controller can implement ABS zero steady state error tracking of the optimal wheel slip ratio and make slip ratio constraints flexible for various runway surfaces and runway transitions. Simulation results show that the control scheme can guarantee no violation on slip ratio constraints and avoid self-locking.

Nonlinear Backstepping Control Design for Coupled Nonlinear Systems under External Disturbances

A nonlinear backstepping control is proposed for the coupled normal form of nonlinear systems. The proposed method is designed by combining the sliding‐mode control and backstepping control with a disturbance observer (DOB). The key idea behind the proposed method is that the linear terms of state variables of the second subsystem are lumped into the virtual input in the first subsystem. A DOB is developed to estimate the external disturbances. Auxiliary state variables are used to avoid amplification of the measurement noise in the DOB. For output tracking and unmatched disturbance cancellation in the first subsystem, the desired virtual input is derived via the backstepping procedure. The actual input in the second subsystem is developed to guarantee the convergence of the virtual input to the desired virtual input by using a sliding‐mode control. The stability of the closed‐loop is verified by using the input‐to‐state stable (ISS) property. The performance of the proposed method is validated via numerical simulations and an application to a vehicle system based on CarSim platform.