The paper presents the method of control of an induction squirrel-cage machine supplied by a voltage source converter. The presented idea is based on an innovative method of the voltage source converter control, consisting in direct joining of the motor control system with the voltage source rectifier control system. The combined control system gives good dc-bus voltage stabilization. In the applied control system the limits of the reference variables have been introduced. A correction of the estimated machine load torque is proposed. The new proposed solutions are confirmed by mathematical dependences, simulation and experimental results.

In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.

In this paper, we propose sensorless backstepping control of a double-star induction machine (DSIM). First, the backstepping approach is designed to steer the flux and speed variables to their references and to compensate uncertainties. Lyapunov”s theory is used and it demonstrates that the dynamic tracking of trajectories tracking is asymptotically stable. Second, unfortunately, this law control called sophisticated is a major problem which leads to the necessity of using a mechanical sensor (speed, load torque). This imposes an additional cost and increases the complexity of the montage. In practice, this variable is unknown and its measurement is expensive. To restrain this problem we estimate speed and load torque by using a Luenberger observer (LO). Simulation results are provided to illustrate the performance of the proposed approach in high and low variable speeds and load torque disturbance.

This paper presents a comparative study between the conventional PI (Proportional Integral) and backstepping controllers applied to the DFIG (Doubly Fed Induction Generator) used in WECS (Wind Energy Conversion System). These two different control strategies proposed in this work are developed to control the active and reactive power of the DFIG on the one hand, and to maintain the DC-link voltage constant for the inverting function on the other hand. This is ensured by generating control signals for two power electronic converters, RSC (Rotor Side Converter) and GSC (Grid Side Converter). In order to optimise the power production in the WT (Wind Turbine), an MPPT (Maximum Power Point Tracking) algorithm is applied along with each control technique. To simulate the effectiveness of the proposed controllers, MATLAB/Simulink Software is used, and the obtained results are analysed and discussed to compare PI and backstepping controllers in terms of robustness against wind speed variations and tracking performance in dynamic and steady states.

A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to be a hidden attractor when its basin of attraction has no intersection with small neighborhoods of equilibrium points of the system. Thus, our new non-equilibrium hyperjerk system possesses a hidden attractor. Chaos in the system has been observed in phase portraits and verified by positive Lyapunov exponents. Adaptive backstepping controller is designed for the global chaos control of the non-equilibrium hyperjerk system with a hidden attractor. An electronic circuit for realizing the non-equilibrium hyperjerk system is also introduced, which validates the theoretical chaotic model of the hyperjerk system with a hidden chaotic attractor.

J.L. Hindmarsh, R.M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.

Quadcopter unmanned aerial vehicle is a multivariable, coupled, unstable, and underactuated system with inherent nonlinearity. It is gaining popularity in various applications and has been the subject of numerous research studies. However, modelling and controlling a quadcopter to follow a trajectory is a challenging issue for which there is no unique solution. This study proposes an optimal hybrid quadcopter control with MPC-based backstepping control for following a reference trajectory. The outer-loop controller (backstepping controller) regulates the quadcopter’s position, whereas the inner-loop controller (Model Predictive Control) regulates its attitude. The translational and rotational dynamics of the quadcopter are analyzed utilizing the Newton-Euler method. After that, the backstepping controller (BC) is created, which is a recurrent control method according to Lyapunov’s theory that utilizes a genetic algorithm (GA) to choose the controller parameters automatically. In order to apply a linear control technique in the presence of nonlinearities in the quadcopter dynamics, Linear Parameter Varying (LPV) Model Predictive Control (MPC) structure is developed. Simulation validated the dynamic performance of the proposed optimal hybrid MPC-based backstepping controller of the quadcopter in following a given reference trajectory. The simulations demonstrate the fact that using a command control input in trajectory tracking, the proposed control algorithm offers suitable tracking over the assigned position references with maximum appropriate tracking errors of 0.1 m for the �� and �� positions and 0.15 m for the �� position.

Due to high performance demands of grid-connected pulse-width modulation (PWM) converters in power applications, backstepping control (BSC) has drawn wide research interest for its advantages, including high robustness against parametric variations and external disturbances. In order to guarantee these advantages while providing high static and dynamic responses, in this work, a robust BSC (RBSC) with consideration of grid-connected PWM converter parameter uncertainties is proposed for three-phase grid-connected four-leg voltage source rectifiers (GC-FLVSR). The proposed RBSC for GC-FLVSR is composed of four independent controllers based on the Lyabonov theory that control DC bus voltage and input currents simultaneously. As a result, unit power factor, stable DC-bus voltage, sinusoidal four-leg rectifier input currents with lower harmonics and zero-sequence (ZS), and natural currents can be accurately achieved. Furthermore, the stability and robustness against load, DC capacitor, and filter inductance variations can be tested. The effectiveness and superiority of the proposed RBSC compared to the PI control (PIC) have been validated by processor-inthe- loop (PIL) co-simulation using the STM32F407 discovery-development-board as an experimental study.