The collector and brushless electronic commutation machines based on the working principle of the direct current machines have been widely used in industrial applications through the help of the developments in power electronics, microelectronics, permanent magnets, microprocessors&control, digital signal processing technologies, etc. Internal permanent magnet synchronous motors (IPMSMs) are used in increasing numbers due to their advantages such as high torque/current and torque/inertia, robust construction, high efficiency, reliability, etc. The problems brought by position sensors, especially in terms of application, performance, mass production, and cost, have made sensorless control a necessity in drive systems and applications.This paper presents a backstepping control method for speed sensorless IPMSM based on an extended Kalman filter (EKF). First, a comprehensive nonlinear dynamical model of the IPMSM in the direct and quadrature ( ) rotor frame is derived and its state-space representation is obtained. Then, the rotor speed and current tracking backstepping controllers are designed to achieve precise tracking and anti-disturbance performance. The designed controllers are embedded into the field-oriented control (FOC) scheme. The asymptotic stability condition for the backstepping controller is guaranteed through the Lyapunov stability theorem. Finally, An EKF is designed for estimating the immeasurable mechanical parameters of IPMSM and tracking the system states in a finite time with high steady-state precision. The effectiveness of the proposed methodology is proved by conducting simulations having various dynamic operating conditions such as sudden torque load change, command speed change, and parameter variation.

To address the trajectory tracking issue for quadrotors working under the influence of external disturbances, a control scheme is designed for position and attitude trajectory tracking. Firstly, the quadrotor dynamic model is derived for control design. Secondly, adaptive integral backstepping control (AIBS) is employed in the position loop in which adaptive estimation is used to estimate the upper bounds of disturbances. Subsequently, a new adaptive backstepping fast nonsingular integral terminal sliding mode control (ABFNITSM) is proposed to follow desired Euler angles. The intro-duction of fast nonsingular terminal sliding mode and integral element is to realize fast convergence and accurate tracking. Dead zone technique is applied to minimize estimation errors. Besides, a saturation function is utilized to eliminate chattering phenomenon. Finally, simulation experiments are conducted under the Simulink environment. The proposed control is verified by comparing it with traditional integral terminal sliding mode control (ITSM) and integral backstepping control (IBS).

This paper investigates the roll parameter estimation of periodic disturbances where the amplitude, frequency, offset, and phase are hardly recognized in real practice. The key problem is to make an estimation that could eliminate the unknown disturbance parameters. An adaptive mechanism applies these four parameters to the globally exponential convergence using linear second-order filters and parameter estimation errors. Then, a backstepping controller is employed to make an exponential convergence to zero of the state variables. Moreover, reservoir computing is used to forecast chaotic roll motions to support predictability using Lyapunov exponents and the Poincaré map. Numerical simulations are demonstrated to validate the dynamical behaviors and efficacy of the proposed control scheme with machine learning.