Linear State Error Feedback Control Research Articles

Sensorless control of permanent magnet synchronous motor based on adaptive enhanced extended state observer

SummaryThis article proposes an enhanced adaptive disturbance rejection control strategy for sensorless control of permanent magnet synchronous motor. The traditional fixed bandwidth quadrature phase‐locked loop (Q‐PLL) is insufficient to meet system dynamics in the event of sudden speed changes or motor disturbances, resulting in a significant decrease in control performance. Meanwhile, conventional extended state observers usually rely on a fixed high gain for fast convergence, which raises concerns about their sensitivity to noise. To overcome these challenges, the proposed method introduces a third‐order adaptive cascaded linear extended state observer (ACLESO) in place of the conventional PLL to accurately estimate the speed, phase, and overall disturbances, ensuring timely and accurate estimation of the total disturbance. Then, a speed controller based on linear state error feedback control law (LSEFCL) was designed to enhance the dynamic performance of the system. Based on the stability analysis using the Lyapunov function, finally, extensive experimental tests were carried out to verify the validity of the proposed method.

Transient Response Characteristics Improvement of Permanent Magnet Synchronous Motor Based on Enhanced Linear Active Disturbance Rejection Sensorless Control

The compactness, cost decrease, and reliability of the auxiliary drive permanent magnet synchronous motors (PMSMs) for battery electric commercial vehicles can be further improved by adopting the position sensorless control technique. The conventional extended back electromotive force (EEMF) based sensorless control algorithm usually requires a phase-locked loop (PLL) and low pass filter to postprocess the estimated rotor position, which deteriorates the transient response of the PMSM significantly. To solve this problem, this article proposes an active disturbance rejection control based EEMF sensorless control method. By designing an extended state observer (ESO) considering the differential term of the position estimation error, timely and accurate estimation of the load disturbance and rotor position can be achieved simultaneously. The adaptive mechanism of the ESO exhibits sound system antidisturbance performance. Moreover, a linear state error feedback controller and feedforward compensation of load disturbance can replace the speed loop PI controller accordingly. Through stability and tracking performance analysis, the proposed method is superior in both steady-state performance and transient-state performance. The proposed scheme is experimentally validated by a 3 kW automotive power steering oil pump motor drive system. The results show that the transient response characteristics are obviously enhanced compared with the conventional methods. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>

DC-Link Voltage Research of Photovoltaic Grid-Connected Inverter Using Improved Active Disturbance Rejection Control

In this paper, a robust DC-link voltage control scheme is proposed to improve the tolerance of photovoltaic (PV) grid-connected inverter to disturbances. The sensitive characteristic of the DC-link voltage complicates the dynamics of the inverter control system and limits its overall performance, especially when uncertain disturbances are considered. To cope with this issue, a voltage controller based on the linear active disturbance rejection control (LADRC) is designed. By exploring the principle of deviation regulation, an improved linear extended state observer (LESO) is established to ensure that the total disturbance can be estimated in a relatively timely manner. The linear state error feedback (LSEF) control law is generated to compensate for the total disturbance, which reduces the plant to approximate the canonical cascaded double integrator. The stability and disturbance rejection capability of the improved LADRC are further analyzed in frequency domain. Finally, theoretical analysis and experimental results confirm the feasibility of the proposed control scheme.

Linear Active Disturbance Rejection Control of a Two-Degrees-of-Freedom Manipulator

This paper presents linear active disturbance rejection control (LADRC) for a two-degrees-of-freedom (2-DOF) manipulator system to achieve trajectory tracking. The system is widely used in engineering applications and exhibits the characteristics of high nonlinearity, strong coupling, and large uncertainty with two inputs and two outputs. First, the problem of dynamic coupling in the model of the 2-DOF manipulator is addressed by considering the dynamic coupling, model uncertainties, and external disturbances as total disturbances. Second, a linear extended state observer is designed to estimate the total disturbances, while a linear state error feedback control law is designed to compensate these disturbances. The main contribution is that the stability of the closed-loop system with two inputs and two outputs is analyzed, and the relationship between the performance of the closed-loop system and the controller parameters is established. The joint simulation of SolidWorks and Matlab/Simulink is conducted. The simulation and experimental results clearly indicate the superiority of LADRC over the PID for trajectory tracking and dynamic performance.

Second-Order Linear Active Disturbance Rejection Control and Stability Analysis of Energy Storage Grid-Connected Inverter

At present, which has gradually become a technical development trend that the energy storage grid-connected inverter system is connected to the grid to ensure the stable operation of the whole system. However, the stability of the energy storage system itself is also very important for the safe operation of the power grid. Therefore, improving the stability of grid-connected energy storage system is still the key technology of current research. Aiming at the strong coupling and low-voltage ride-through fault of grid-connected system, a second-order mathematical model of grid-connected control system is established. Based on its state space model, a linear extended state observer (LESO) for state observation and a linear state error feedback (LSEF) control law for disturbance estimation are designed. The second-order linear active disturbance rejection control (LADRC) is introduced into the voltage loop, the stability of the second-order LADRC controller is proved by the Lyapunov stability theory, and the stability conditions are given. Finally, the simulation model of the grid-connected energy storage system is built on the MATLAB/Simulink digital platform, and the low-voltage ride-through fault is designed on the grid-side. The simulation results show that the effect of the second-order LADRC control is better than that of the traditional PI control obviously, which reflects the superiority of the second-order LADRC in controlling the grid-side low-voltage ride-through fault.

Master-Slave Synchronization of Chaotic Φ6 Duffing Oscillators by Linear State Error Feedback Control

This paper is concerned with master-slave synchronization of chaotic Φ6 Duffing oscillators by using linear state error feedback control. Compared with some existing methods and results, this paper estimates the bound of the first trajectory (variable) of the controlled slave system and uses this bound to derive synchronization criteria for two chaotic Φ6 Duffing oscillators. The effectiveness of synchronization criteria is illustrated by three simulation examples.

Optimized linear active disturbance rejection control for pneumatic servo systems via least squares support vector machine

This paper presents an optimized linear active disturbance rejection controller to improve the response rapidity and anti-interference ability of a pneumatic servo system. Both a linear extended state observer and a least squares support vector machine are established to estimate and compensate total nonlinearity of the system. Moreover, a linear state error feedback controller is designed to ensure good performances of the closed-loop system. In addition, estimation error and tracking error are bounded and decrease with the increase of their respective eigenvalues. Lastly, simulation results show that the optimized controller has the better response rapidity and anti-interference ability than the traditional controller.

Frequency-domain criterion for the chaos synchronization of time-delay power systems under linear feedback control

This paper studies the global synchronization of non-autonomous, time-delay, chaotic power systems via linear state-error feedback control. The frequency domain criterion and the LMI criterion are proposed and applied to design the coupling matrix. Some algebraic criteria via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. The effectiveness of the new criteria is illustrated with numerical examples.

Finite-Time Combination-Combination Synchronization of Hyperchaotic Systems and its Application in Secure Communication

Global finite time synchronization of a class of combination-combination chaotic systems via master-slave coupling is investigated. A nonlinear feedback controller and a continuous generalized linear state-error feedback controller with simple structure are introduced in the synchronization scheme. They are applied to a practical master-slave synchronization scheme for combination-combination systems, which consist of the Chen chaotic system, hyperchaotic Chen system and hyperchaotic Lorenz system. Numerical simulations are provided to illustrate the effectiveness of the new synchronization criteria.

Master-Slave Global Synchronization for Froude Pendulums via Linear State Error Feedback Control

This paper deals with the global chaos synchronization of master-slave Froude pendulums coupled by linear state error feedback control. A master-slave synchronization scheme of the Froude pendulums under linear feedback control is presented. Based on this scheme, some sufficient criteria for global synchronization are proved and optimized. A numerical example is provided to demonstrate the effectiveness of the criteria obtained.

Global finite-time synchronization of a class of the non-autonomous chaotic systems

This paper investigates the global finite-time synchronization of a class of the second-order nonautonomous chaotic systems via a master–slave coupling. A continuous generalized linear state-error feedback controller with simple structure is introduced into the synchronization scheme. Some easily implemented algebraic criteria for achieving the global finite-time synchronization are proven and then optimized for the purposes of improving their sharpness. The optimized criteria are applied to a practical master–slave synchronization scheme for the single-machine-infinite-bus (SMIB) systems, obtaining the precise corresponding synchronization conditions. Several numerical examples are provided to illustrate the effectiveness of the new synchronization criteria.

The sufficient criteria for global synchronization of chaotic power systems under linear state-error feedback control

This paper investigates global complete synchronization of two identical power systems and global robust synchronization of two power systems with parameter mismatch and external disturbance, both under the master–slave linear state-error feedback control. Some criteria for achieving the synchronization via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. These algebraic criteria are further optimized so as to improve their performances. The effectiveness of the new algebraic criteria is illustrated by the numerical examples.

Bidirectionally coupled synchronization of the generalized Lorenz systems

Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices (diagonal matrices, so-called dislocated coupling matrices, and so on) are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system (Chaos, Solitons, and Fractals, 2005). The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics

We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators (DDOs). Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues — a signature of mode locking phenomenon are found.

Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control

This paper investigates the global synchronization of a class of third-order non-autonomous chaotic systems via the master–slave linear state error feedback control. A sufficient global synchronization criterion of linear matrix inequality (LMI) and several algebraic synchronization criteria for single-variable coupling are proven. These LMI and algebraic synchronization criteria are then applied to two classes of well-known third-order chaotic systems, the generalized Lorenz systems and the gyrostat systems, proving that the local synchronization criteria for the chaotic generalized Lorenz systems developed in the existing literature can actually be extended to describe global synchronization and obtaining some easily implemented synchronization criteria for the gyrostat systems.

Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control

We propose a fractional-order WINDMI system, as a generalization of an integer-order system developed by Sprott (2003). The considered synchronization scheme consists of identical master and slave fractional-order WINDMI systems coupled by linear state error variables. Based on the stability theory of nonlinear fractional-order systems, linear state error feedback control technique is applied to achieve chaos synchronization, and a linear control law is derived analytically to achieve synchronization of the chaotic fractional-order WINDMI system. Numerical simulations validate the main results of this work.

A new Lyapunov approach for global synchronization of non-autonomous chaotic systems

This paper proposes a new approach for finding the Lyapunov function to study the sufficient global synchronization criterion of master-slave non-autonomous chaotic systems via linear state error feedback control. The approach is first demonstrated in a synchronization scheme for the second-order non-autonomous chaotic systems and then generalized to the schemes for the nth-order non-autonomous chaotic systems. Some algebraic synchronization criteria for the second-order chaotic systems are obtained. The sharpness of the new criteria is compared with that of the existing criteria of the same type by numerical examples.

Chaotic synchronization by the intermittent feedback method

This paper studies the synchronization of chaotic systems by the intermittent feedback method which is efficient. A sufficient synchronization criterion for a general intermittent linear state error feedback control is obtained by using a Lyapunov function and differential inequalities. Numerical simulations for the chaotic Chua oscillator are presented to illustrate the theoretical results.

Robust synchronization of chaotic horizontal platform systems with phase difference

This paper studies a robust synchronization of non-autonomous chaotic systems with parameter mismatch. In the synchronization scheme, a linear state error feedback control is used to couple the master and slave horizontal platform systems excited by harmonic external forces, between which there exists a phase mismatch. A new definition of global synchronization with error bound is introduced. Using Lyapunov's stability theory, the sufficient synchronization criteria for the scheme are proven and the corresponding synchronization error bound is estimated. The synchronization criteria are further optimized by optimally designing a quadratic Lyapunov function to more precisely estimate the synchronization error bound. The illustrative simulations verify the effectiveness of these criteria. The estimated synchronization error bound is compared with numerical one in the examples.