An approximated scalar sign function approach to optimal anti-windup digital controller design for continuous-time nonlinear systems with input constraints

Wu, Jian; Shieh, Leang-San; Tsai, Jason Sheng‐Hong; Zhang, Yongpeng

doi:10.1080/00207720903144511

Cited by 3 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was shown that a certain order of truncation of the expansion can effectively approximate the absolutevalue function by a smooth rational function. The smooth nature of ASSF has been successfully utilised in designing an anti-windup controller (Wu, Shieh, Tsai, and Zhang 2010) where the ASSF is used to reformulate the system model as the input saturation is encountered. It leads to a systematic updating approach for linear quadratic regulator (LQR) weighting matrices such that control inputs are ultimately obtained within the desired limits.…”

Section: Introductionmentioning

confidence: 99%

Digital controller design for Bouc–Wen model with high-order hysteretic nonlinearities through approximated scalar sign function

Shieh

Zhang

et al. 2011

International Journal of Systems Science

Self Cite

View full text Add to dashboard Cite

In the models of piezoelectric actuator (PEA) systems, the hysteresis effects are often described by the concise Bouc-Wen models; however, these models are nonlinear and non-smooth because of the existence of terms which involve the absolute-value function. In particular, a challenging control problem is posed when, due to the properties of certain materials, such absolute-value terms are of high order. This control problem has been rarely studied. This article proposes the use of the approximated scalar sign function (ASSF), which is a numerically stable and differentiable nonlinear function, to represent the hysteresis function, with single-order or high-order absolute-value terms. This innovative step leads to a nonlinear but sufficiently smooth model. Then, a systematic digital design methodology is presented, which involves the following steps: (1) establish an optimal linear model based upon the resulting smooth model, (2) adopt a PI-based analogue controller and (3) apply the predictionbased digital redesign technique for digital implementation. A digital observer is also developed for state reconstruction, and to improve the input disturbance rejection. The positioning control of a PEA system with a high-order hysteretic Bouc-Wen model is implemented to demonstrate the effectiveness of the proposed ASSF based modelling and controller design approaches.

show abstract

Section: Introductionmentioning

confidence: 99%