Adaptive Backstepping Control of a Class of Uncertain Nonlinear Systems With Unknown Backlash-Like Hysteresis

Abstract

In this note, we consider the same class of systems as in a previous paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the "disturbance-like" term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance.

Extended Backstepping Sliding Controller Design for Chattering Attenuation and Its Application for Servo Motor Control

“…By adding and subtracting the virtual control law φ 2 (e 1 , z 1 ) to (11) and defining an error variable as z 2 = e 3 − φ 2 (e 1 , z 1 ), (11) can then be represented as:…”

“…Some nonlinear functions can be estimated using neural networks with a backstepping design scheme. Other robust backstepping control approaches for specific nonlinearities, such as system time delays [9], mismatched uncertainties [10], backlash-like hysteresis [11] and input uncertainties [12], were also developed to make the resulting system insensitive to model uncertainties and external disturbances. Moreover, in recent studies [13][14][15][16], it has been demonstrated that the backstepping controller design concept can be applied for different nonlinear systems.…”

Tracking Control for a Piezoelectric Nanopositioner Using Estimated States and Feedforward Compensation of Hysteresis

“…where the control gain β 0 =b 0 K q , and we consider ∆ q h = b 0 q h , due to hysteresis, a bounded disturbance input to the system, as has been done in Su et al [2000] and Zhou et al [2004]. From (13) and (14) we see that the hysteretic behavior is bounded by q h ∞ = b a .…”

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

“…[19][20][21] However, the backstepping has trouble solving the 'explosion of complexity'. To solve this issue, by introducing a first-order filter at each recursive step of backstepping, the dynamic surface control is proposed to avoid the differentiation items on the virtual function.…”