Second‐order sliding mode controller design subject to mismatched unbounded perturbations

The paper proposes a novel control design for nonlinear systems with multiple uncertainties and nonlinear measurement. The output linearization is utilized to handle the nonlinearities in system dynamics and measurement. Firstly, the integrator chain for nonlinear systems with multiple uncertainties is analyzed. Based on the fundamental integrator chain form, the equivalent total effect of multiple uncertainties is summarized as total disturbance. By timely estimating and compensating for the total disturbance, an active disturbance rejection control design to handle both multiple uncertainties and nonlinear measurement is proposed. Moreover, the transient performance of the corresponding closed-loop system is rigorously studied, which theoretically reveals the high consistence of the tracking performance despite various multiple uncertainties. K E Y W O R D Sactive disturbance rejection control, extended state observer, mismatched uncertainty, multiple uncertainties, nonlinear uncertain system, total disturbance

Section: A Numerical Examplementioning

confidence: 99%

mentioning

confidence: 99%

On active disturbance rejection control for nonlinear systems with multiple uncertainties and nonlinear measurement

Chen

Xue

Huang

2020

“…As we know, the effect of control input u is to eliminate the adverse impact of lumped disturbance d(t) such that the system states can converge to the origin. For this purpose, the conventional SMC method can be adopted here for system (1). According to the SMC theory, a linear sliding surface should be constructed before designing the reaching law.…”

Section: Problem Formulation and Motivationmentioning

confidence: 99%

“…Although many mathematical or engineering tools can be used for modeling, some discrepancies will always exist between the mathematical model used for describing the dynamic behaviors of a practical system and its actual plant. This is because these discrepancies are usually derived from some unknown external disturbances, parameter perturbations, or system uncertainties, which will heavily affect the performance of the considered system . To this end, designing a controller to provide the desired performance for the considered system is a very essential and challenging task.…”

Section: Introductionmentioning

confidence: 99%

“…This is because these discrepancies are usually derived from some unknown external disturbances, parameter perturbations, or system uncertainties, which will heavily affect the performance of the considered system. 1,2 To this end, designing a controller to provide the desired performance for the considered system is a very essential and challenging task. On this basis, the research on different types of nonlinear control methods has been paid much attention in the past several decades, such as backstepping method, [3][4][5] adaptive technique, [6][7][8]  ∞ method, 9,10 fuzzy control, 11,12 and sliding mode control (SMC).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A novel adaptive nonsingular terminal sliding mode controller design and its application to active front steering system

Ding

Liu

Park

2019

Self Cite

Summary Note that the amplitude of chattering existing in the sliding mode control method is proportional to the magnitude of the control gain. Therefore, the key issue to diminish the chattering is to decrease the value of sliding mode controller's gain to an acceptable minimal level defined by the so‐called reaching condition for the sliding mode's existence. For this reason, the nonsingular terminal sliding mode (NTSM) control method and the adaptive technique have been considered in this paper to develop a novel adaptive NTSM control method, which can be used to search the minimal value of the control gain automatically in the presence of the external disturbances. Meanwhile, the average value of a high‐frequency switching signal in the adaptive law can be provided by Arie Levant's differentiator rather than a low‐pass filter. The rigorous mathematical proof verifies that the system states can converge to the origin within a finite time under the proposed adaptive NTSM controller. Both the academic example and the practical application to an active front steering system are illustrated to show that the presented adaptive NTSM controller has better control performance than the conventional sliding mode controller.

Disturbance observer‐based two‐Layer control strategy design to deal with both matched and mismatched uncertainties

Shafei

Bahrami

Talebi

2020

This study presents a novel control strategy for managing nonlinear systems in the presence of mismatched uncertainties. Dealing with the uncertainties that do not satisfy the so‐called matching conditions is an ongoing issue in control engineering. In this regard, and for the first time, a disturbance observer (DO)‐based hybrid control system, which considers robustness as well as control signal optimality, is developed in this article. For this purpose, and with the aim of robustly managing uncertain nonlinear systems and achieving optimized control effort, an optimal control law based on the state‐dependent Riccati equation is integrated with a DO‐based second‐order sliding mode controller. The Lyapunov stability theory is applied to verify the asymptotic stability of the designed control system. Computer simulations are performed to demonstrate the efficacy and the superiority of our novel controller over two other existing methods (DO‐based sliding mode control [SMC] and DO‐based adaptive SMC). The simulation results show that the presented method is capable of managing uncertain nonlinear systems robustly and with much less control effort than the two mentioned methods.