Open AccessNew robust bounded control for uncertain nonlinear system using mixed backstepping and lyapunov redesign
Author(s) -
Muhammad Nizam Kamarudin,
Sahazati Md. Rozali,
Tole Sutikno,
Abdul Rashid Husain
Publication year - 2019
Publication title -
international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.277
H-Index - 22
ISSN - 2088-8708
DOI - 10.11591/ijece.v9i2.pp1090-1099
Subject(s) - control theory (sociology) , lyapunov function , bounded function , backstepping , variable structure control , control lyapunov function , linear matrix inequality , robust control , robustness (evolution) , lyapunov redesign , lyapunov stability , adaptive control , mathematics , law , sliding mode control , controller (irrigation) , nonlinear system , computer science , mathematical optimization , control (management) , physics , artificial intelligence , mathematical analysis , chemistry , biochemistry , quantum mechanics , political science , gene , biology , agronomy
This paper presents a new robust bounded control law to stabilize uncertain nonlinear system with time varying disturbance. The design idea comes from the advantages of backstepping with Lyapunov redesign, which avoid the needs of fast switching of discontinuous control law offered by its counterpart - a variable structure control. We reduce the conservatism in the design process where the control law can be flexibly chosen from Lyapunov function, hence avoiding the use of convex optimization via linear matrix inequality (LMI) in which the feasibility is rather hard to be obtained. For this work, we design two type control algorithms namely normal control and bounded control. As such, our contribution is the introduction of a new bounded control law that can avoid excessive control energy, high magnitude chattering in control signal and small oscillation in stabilized states. Computation of total energy for both control laws confirmed that the bounded control law can stabilize with less enegry consumption. We also use Euler's approximation to compute average power for both control laws. The robustness of the proposed controller is achieved via saturation-like function in Lyapunov redesign, and hence guaranting asymptotic stability of the closed-loop system.