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The International Journal of Robotics Research
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Nonlinear PID Control with Partial State Knowledge: Damping without Derivatives

Brian Armstrong

Department of Electrical Engineering and Computer Science, and Center for Industrial Mathematics, UW-Milwaukee P.O. Box 784, Milwaukee, Wisconsin 53201, USA

Bruce A. Wade

Department of Mathematical Sciences and Center for Industrial Mathematics, UW-Milwaukee P.O. Box 413, Milwaukee, Wisconsin 53201, USA

Nonlinear PID (NPID) control is implemented by allowing the controller gains to vary as a function of system state. NPID control has been previously described and implemented, and recently a constructive Lyapunov stability proof has been given. The controllers arising with the constructive Lyapunov method will in general depend on knowledge of the full state vector. In the present work, NPID controllers that operate without knowledge of some state variables are demonstrated. A general but conservative design method is presented with an experimental demonstration. For a special case, complete necessary and sufficient conditions are established; for this case, simulation of a robotic force control application demonstrates well-damped control with no requirement for a force-rate signal. The extension to cases of partial state knowledge is important for NPID control, which is most practical when some state variables—particularly rate variables—are poorly known, confounding full-state feedback or other high-damping linear control designs. Extension of NPID control to MIMO systems and computed torque control is also shown.

Key Words: nonlinear control • nonlinear feedback • linear systems • robotic force control • Lyapunov stability • partial state feedback • MIMO systems • computed torque control

The International Journal of Robotics Research, Vol. 19, No. 8, 715-731 (2000)
DOI: 10.1177/02783640022067120
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B. S. R. Armstrong, J. A. Gutierrez, B. A. Wade, and R. Joseph
Stability of Phase-Based Gain Modulation with Designer-Chosen Switch Functions
The International Journal of Robotics Research, August 1, 2006; 25(8): 781 - 796.
[Abstract] [PDF]