Xiangjun Li

Stability Analysis of Second-Order Sliding Mode Control Systems With Input-Delay Using Poincaré Map

This note discusses the stability of dynamical systems with input-delay under the second-order sliding mode control algorithm. Poincaré Map is constructed to analyze the switching dynamics and to derive the stability conditions. Different parameter setting options are given for ensuring stability. Simulation examples are presented to verify the theoretical results.

Stability analysis of time-delayed single-input sliding mode control systems

This paper presents stability analysis of the time-delayed equivalent control based single input sliding mode control systems using an LMI approach. Conditions to guarantee the boundedness of the control system trajectories under the time-delayed equivalent control based sliding mode control are obtained. Maximum upper bound of the delay time to guarantee stability is estimated. Digital simulations are conducted to verify the theoretical results.

Modeling and Simulation of Digital Closed-loop Fiber Optic Gyroscope

Computer modeling and simulation are important for the researches and applications of the fiber optic gyroscope (FOG). In the paper, the dynamic model and stochastic model of digital closed-loop FOG are developed. With a number of reasonable approximations, the nonlinear dynamic model is simplified into a linear discrete dynamic model. The digital control algorithm in the closed-loop control is analyzed, and the dynamic simulation is conducted. In the stochastic modeling, different stochastic processes are built to simulate the various types of random gyro noise. A novel method is investigated to simulate 1/f noise with the orthogonal wavelet transform. The stochastic simulations are conducted and the effectiveness of the stochastic model is validated with Allan variance analysis

Time-delay effect on equivalent control based single-input sliding mode control systems

This paper studies the time-delay effect on the equivalent control based sliding mode control. Conditions to guarantee the boundedness of the control system steady states under the time delayed equivalent control based sliding mode control are obtained. Maximum upper bound of the delay time to guarantee boundedness is estimated. Simulations are conducted to verify the theoretical results.

Periodic Input Response of a Second-Order Digital Filter With Two's Complement Arithmetic

The dynamic behaviors of a nonlinear second-order digital filter with twos complement arithmetic under periodic inputs are explored. The conditions for avoiding overflow are derived. Various dynamic periodic responses are analyzed, accompanied by numerous simulation examples.

Chattering analysis of time-delayed second-order sliding mode control systems using Poincaré map

In this paper, chattering in a time-delayed second order sliding mode control (2-SMC) system is analyzed using the Poincaré map method. Convergence of the system under arbitrary time-delay is proved. The switching patterns are explored. The existence and uniqueness of the periodic orbit are shown. Simulations are done to support the theoretical results.

Digital Redesign of Sliding Mode Control of LTI Systems

In this paper, a new sliding mode controller design is proposed for sampled-data LTI systems based on the digital redesign methodology. With this controller, chattering is eliminated. LMI (linear matrix inequality) is employed to derive the controller. The simulation results have demonstrated the effectiveness of the proposed algorithm

A networked sliding mode controller for servomechanical systems

This paper proposes a networked sliding mode controller for servomechanical systems. Asymptotic stability is analyzed. Saturation function is used to eliminate chattering. Sensitivity of the zero eigenvalue with respect to the gain of the saturation function in linear interval is analyzed. Conditions for the choice of the gain and time delay are proposed. Simulations are conducted to verify the theoretical results.

Stabilization of oscillators with bounded delayed input: Sliding mode control method

Oscillators with bounded delayed input are stabilized by a sliding mode control law. In the control law, sign function is replaced by high gain function to avoid chattering in the presence of time delay. A condition is developed to determine the gain. Simulation is conducted to show the effectiveness of the theoretical analysis.

Time-delay effect on continuous approximation of sliding mode control

In this paper, time-delay effect on continuous approximation of sliding mode control (SMC) systems is studied in depth. The switching band that bound the zigzagging behaviors due to control switching around the switching manifold is constructed. Robust control theory is employed to develop a sufficient condition for the asymptotical stability of the system. Simulation is conducted to verify the theoretical results.