TY - JOUR
T1 - An approximated scalar sign function approach to optimal anti-windup digital controller design for continuous-time nonlinear systems with input constraints
AU - Wu, Jian
AU - Shieh, Leang San
AU - Tsai, Jason S.H.
AU - Zhang, Yongpeng
N1 - Funding Information:
Yongpeng Zhang received his BS and MS from Xi’an University of Technology and Tianjin University, China, in 1994 and 1999, respectively. He received his PhD from the University of Houston in 2003. Currently, he is a Tenure-Track Assistant Professor in Engineering Technology at Prairie View A&M University. His research interests include control system, power electronics and motor drive, mechatronics and DSP solutions for industry applications. As the 3M non-tenured faculty award recipient, his research has been funded by the US Army Research Office, NSF and industry.
Funding Information:
This work was supported by the US Army Research Office under grant W911NF-06-1-0507, the National Science Foundation under grant NSF 0717860 and the National Science Council of Republic of China under contract NSC96-2221-E-006-292-MY3.
PY - 2010/6
Y1 - 2010/6
N2 - This article presents an approximated scalar sign function-based digital design methodology to develop an optimal anti-windup digital controller for analogue nonlinear systems with input constraints. The approximated scalar sign function, a mathematically smooth nonlinear function, is utilised to represent the constrained input functions, which are often expressed by mathematically non-smooth nonlinear functions. Then, an optimal linearisation technique is applied to the resulting nonlinear system (with smooth nonlinear input functions) for finding an optimal linear model, which has the exact dynamics of the original nonlinear system at the operating point of interest. This optimal linear model is used to design an optimal anti-windup LQR, and an iterative procedure is developed to systematically adjust the weighting matrices in the performance index as the actuator saturation occurs. Hence, the designed optimal anti-windup controller would lie within the desired saturation range. In addition, the designed optimal analogue controller is digitally implemented using the prediction-based digital redesign technique for the effective digital control of stable and unstable multivariable nonlinear systems with input constraints.
AB - This article presents an approximated scalar sign function-based digital design methodology to develop an optimal anti-windup digital controller for analogue nonlinear systems with input constraints. The approximated scalar sign function, a mathematically smooth nonlinear function, is utilised to represent the constrained input functions, which are often expressed by mathematically non-smooth nonlinear functions. Then, an optimal linearisation technique is applied to the resulting nonlinear system (with smooth nonlinear input functions) for finding an optimal linear model, which has the exact dynamics of the original nonlinear system at the operating point of interest. This optimal linear model is used to design an optimal anti-windup LQR, and an iterative procedure is developed to systematically adjust the weighting matrices in the performance index as the actuator saturation occurs. Hence, the designed optimal anti-windup controller would lie within the desired saturation range. In addition, the designed optimal analogue controller is digitally implemented using the prediction-based digital redesign technique for the effective digital control of stable and unstable multivariable nonlinear systems with input constraints.
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U2 - 10.1080/00207720903144511
DO - 10.1080/00207720903144511
M3 - Article
AN - SCOPUS:77952937141
SN - 0020-7721
VL - 41
SP - 657
EP - 671
JO - International Journal of Systems Science
JF - International Journal of Systems Science
IS - 6
ER -