Haptic Systems 530 655 Mohsen Mahvash Lecture 11

Haptic Systems 530 -655 Mohsen Mahvash Lecture 11 24/1/06 1

Stability of Haptic Systems Ø An overview of classic control Ø Control problems in haptic systems Ø Passivity theory Ø References 2

An overview of classic control systems Control tools Performance factors Minimum rise time Root locus Rise time Minimum overshoot Nyquist diagram Gain margin and Phase margin Stability Bode diagram Bandwidth Control objectives Steady state error 3

Haptic rendering systems Plan: Robot + Human user Controller: Virtual environment + Compensator Control objectives Control tools Performance factors Stability Analytical tool ? Transparency Passivity Theory Do not look at the control problem in haptic systems as a classic control problem 4

Haptic system for a virtual wall Operator: uncertain model Virtual wall : Nonlinear model Passivity theory Nonlinear control theory 5

Comparing a physical wall and a virtual wall Interaction with a physical wall Interaction with a virtual wall There is no oscillation There might be oscillation The wall does not generate energy The wall may generate energy The wall is passive The wall can be active 6

Passivity condition Interaction with a physical wall 7

Passive system properties Passivity and stability A passivie system is stable 8

Components of a haptic system 9

Passivity of a Virtual Wall 10

References: Jean-Jacques Slotine, Weiping Li , Applied Nonlinear Control Englewood Cliffs, N. J. : Prentice Hall, c 1991. Tomorrow Effects of time-discritization and position quantization on the stability of haptic systems 11