The stability of nonlinear PID control with arbitrary partial-state knowledge

Author

Armstrong, B. ; Gutierrez, J.A. ; Joseph, R. ; Wade, B.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Wisconsin Univ., Milwaukee, WI, USA

Volume

4

fYear

2002

fDate

2002

Firstpage

3429

Abstract

Nonlinear proportional-integral-derivative (NPID) is realized by modulating the control gains of a conventional linear controller in response to system state or error. Performance benefits such as increased damping or reduced tracking error have been experimentally demonstrated. Previous results (2000) have established Lyapunov stability of NPID control for full-state knowledge and for special cases of partial-state knowledge; but the general problem of stability with arbitrary state knowledge remained unsolved. In the present work, design methods for NPID control are extended to the case of arbitrary partial-state knowledge. Given any combination of a stabilizable linear system and NPID control law, an upper bound on control effort can be determined for which global asymptotic stability is assured. The result is based on a Lyapunov stability proof and is applied to establish the stability of NPID control for the Sarcos dexterous manipulator.

Keywords

Lyapunov methods; asymptotic stability; dexterous manipulators; nonlinear systems; state-space methods; three-term control; Lyapunov stability; asymptotic stability; damping; dexterous manipulator; nonlinear PID control; partial state knowledge; state-space system; upper bound; Control systems; Damping; Design methodology; Error correction; Lyapunov method; Nonlinear control systems; Pi control; Proportional control; Stability; Three-term control;

fLanguage

English

Publisher

ieee

Conference_Titel

Robotics and Automation, 2002. Proceedings. ICRA '02. IEEE International Conference on

Print_ISBN

0-7803-7272-7

Type

conf

DOI

10.1109/ROBOT.2002.1014241

Filename

1014241