1 Haptic Systems Mohsen Mahvash Lecture 11 24/1/06

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

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

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

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

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

7 Passivity condition Interaction with a physical wall

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

9 Components of a haptic system

10 Passivity of a Virtual Wall

11 Tomorrow Effects of time-discritization and position quantization on the stability of haptic systems References: Jean-Jacques Slotine, Weiping Li, Applied Nonlinear Control Englewood Cliffs, N.J. : Prentice Hall, c1991.