Ultimate stability analysis of active disturbance rejection control with a high-gain observer

Nonlinear active disturbance rejection control is much more effective than linear active disturbance rejection control in tolerance to uncertainties and disturbances. However, it brings a great challenge for theoretical analysis, especially the stability analysis. This article proposes a linear matrix inequality method to analyze the absolute stability of generalized nonlinear active disturbance rejection control form which contains multiple nonlinearities with different parameters in both extended state observer and control law for single-input single-output systems. The generalized nonlinear active disturbance rejection control algorithm and the single-input single-output system are transformed into a direct multiple-input multiple-output Lurie system. A sufficient condition to determine its absolute stability based on linear matrix inequality method is given. The Lyapunov function of the Lurie system exists when the group of linear matrix inequalities is feasible. The free parameters and coefficients in Lyapunov function are given by the solution of these linear matrix inequalities. The electromagnetic valve actuator system in camless engine is presented as an application to illustrate how to perform the proposed method for absolute stability analysis and the stable region of parameter perturbations is obtained via the method. Simulation results show that the linear matrix inequality–based method is convenient and effective to determine whether the closed-loop system is absolutely stable.

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Sliding Mode Active Disturbance Rejection Control for Magnetorheological Impact Buffer System

Frontiers in Materials ◽

10.3389/fmats.2021.682215 ◽

2021 ◽

Vol 8 ◽

Author(s):

Bin Wang ◽

Wanjun Wang ◽

Zhaochun Li

Keyword(s):

Pid Control ◽

Disturbance Rejection ◽

Sliding Mode ◽

Mr Damper ◽

High Gain ◽

Buffer System ◽

Active Disturbance Rejection Control ◽

Active Disturbance Rejection ◽

Disturbance Rejection Control ◽

Hysteresis Nonlinearity

In the magnetorheological (MR) impact buffer system, the internal or external disturbance of the MR damper is one of the main factors that affect the buffer performance of the system. This study aims to suppress or eliminate the influence of the disturbance of the MR damper. The continuous terminal sliding mode control (CTSMC) strategy with a high gain has a strong antidisturbance ability. However, the high gain may cause fluctuation of the damping force of the system. Therefore, a composite control strategy of sliding mode active disturbance rejection control (ADRC) based on an extended state observer (ESO) is proposed in this study. The total disturbance of the system is estimated by the ESO in real time, and the estimated disturbance is used as a feedforward compensation to the controller to reduce the influence of disturbance on the system. The gain of the CTSMC law of the closed-loop system can be reduced. In addition, the Lyapunov stability criterion is used to ensure the stability of the proposed controller. In order to verify the performance of the proposed CTSMC controller on response speed, overshoot, and hysteresis suppression ability, the window function, square wave function, and multistep function are given as the inputs of the control system. To verify the performance of the proposed sliding mode ADRC for the MR impact buffer system, the mechanical model and the control model are established and simulated using MATLAB/Simulink. The simulation results show that the CTSMC controller has the fastest response time and no overshoot and can suppress the hysteresis nonlinearity of the MR device compared with the open-loop control, PID control, and fractional order PID control. The MR impact buffer system with the sliding mode ADRC obtained the minimum peak value of 4350N within the permitted buffer displacement range compared with the other three traditional control methods. That means the proposed control method in this study has the advantage on buffer performance for the MR impact buffer system.

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