Robust Control for the Segway with Unknown Control Coefficient and Model Uncertainties.

Bong Park,Byung Kim

doi:10.3390/s16071000

Abstract

The Segway, which is a popular vehicle nowadays, is an uncertain nonlinear system and has an unknown time-varying control coefficient. Thus, we should consider the unknown time-varying control coefficient and model uncertainties to design the controller. Motivated by this observation, we propose a robust control for the Segway with unknown control coefficient and model uncertainties. To deal with the time-varying unknown control coefficient, we employ the Nussbaum gain technique. We introduce an auxiliary variable to solve the underactuated problem. Due to the prescribed performance control technique, the proposed controller does not require the adaptive technique, neural network, and fuzzy logic to compensate the uncertainties. Therefore, it can be simple. From the Lyapunov stability theory, we prove that all signals in the closed-loop system are bounded. Finally, we provide the simulation results to demonstrate the effectiveness of the proposed control scheme.

Highlights

The Segway is a vehicle extended from the inverted-pendulum system and balancing robot
For the stability of the proposed scheme, we prove that all error signals of the closed-loop control system are bounded using the Lyapunov stability theory
The proposed control scheme does not require the exact information of model parameters for the application and the simulation results show the robustness against these model uncertainties

Summary

Introduction

The Segway is a vehicle extended from the inverted-pendulum system and balancing robot. By using the prescribed performance function, it can adjust the transient and steady-state responses It does not require the adaptive technique, neural network, and fuzzy logic to compensate the uncertainties. The robust formation controller for nonlinear multi-agent systems was proposed in [19] All these works assume that the control coefficient is known or constant if it is unknown. Compared with previous methods for the Segway, the main contribution of this paper is as follows: (i) The proposed approach can provide the desired performance of the tracking error without knowing the time-varying control coefficient; (ii) adaptive technique, neural network, and fuzzy logic, which make the controller complex, are not required to compensate the uncertainties and the proposed scheme can be simple; (iii) by introducing an auxiliary variable, we can solve the underactuated problem.

Problem Formulation

Controller Design

Simulation Results

Conclusions