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

Abstract

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.

Keywords:

• nonlinear systems
• scalar sign function
• digital control
• anti-windup control
• optimal linearisation model
• sampled-data systems

Acknowledgements

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.