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liuSecondOrderSlidingMode2021

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文献标题

Second-Order Sliding Mode Control Design Subject to an Asymmetric Output Constraint

Abstract

In this brief, a novel second-order sliding mode (SOSM) control method is developed to solve the asymmetric output constraint problem by using a power integrator and barrier Lyapunov function (BLF). The new BLF is first constructed based on the asymmetric constraint condition. A novel SOSM algorithm is then constructed for the nonlinear systems with an asymmetric output constraint. Under the proposed SOSM algorithm, the output of the resulting closed-loop system will never escape from the asymmetric constraint. Finally, a pendulum system is adopted to verify the validity of the theoretical results.

Contents

问题描述

问题背景

1. First order sliding mode (FOSM) has 2 obstacles
   1. Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
   2. Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
      1. especially for high-order nonlinear systems
2. pratical system has confined outputs
   1. eg. the sideslip angle of an electric vehicle should be constrained within a small range

问题难点

Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output

前人工作

results can be divided into 2 types:

1. Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
   1. complicated since implementation depend on computationally intensive algorithms
2. Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
   1. Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output^blf-fault

Inspired by ^blf-fault

• Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
  • Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output

本文工作

• Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
  • Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
  • Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
  • Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output

本文意义

• Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
• Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output
• Liu et al_2021_Second-Order Sliding Mode Control Design Subject to an Asymmetric Output

实验方法

Preliminaries and Problem Statement

Notion:

• ${\delta }_1$ and ${\delta }_2$ are positive constants
• ${\mathbb{D}}_1=\left\{s_1:-{\delta }_1<s_1<{\delta }_2\right\}$
• ${\mathbb{D}}_2={\mathbb{D}}_1\times \mathbb{R}$
• $\lfloor x{\rceil }^{\alpha }$ denotes ${\left|x\right|}^{\alpha }\mathrm{sign}\left(x\right)$
  • $\alpha >0$

Preliminaries

• 

Problem Statement

nonlinear system:

$$\dot{x}=G\left(t,x\right)+H\left(t,x\right)u,s=s\left(t,x\right)$$

^eqn-nonlinear-system

where $x\in {\mathbb{R}}^n,u\in \mathbb{R}$ is state and input, $s(t,x)$ is output function(i.e., the sliding variable)

Construct BLF and SOSM Controller

Application to Pendulum System

优点缺点

优点

缺点

个人评价