The Real Stabilizability Radius of the Multi-Link Inverted Pendulum

1
The Real Stabilizability Radius of the
Multi-Link Inverted Pendulum

• Connections 2006
• ECE Graduate Symposium
• Presenter Simon Lam
• Supervisor Professor E. J. Davison
• Systems Control Group, ECE
• University of Toronto
• Date June 9, 2006

2
Introduction

• classic problem in control theory
• widely used as a benchmark for testing control
  algorithms

?
3
Properties of a v-link Inverted Pendulum

• ? Linearized Model
• ? System is stabilizable for any number of links
• ? Can design a controller to (locally) stabilize
  a pendulum with any number of links!

4
Gap

• Of course, in reality, we cant stabilize an
  inverted pendulum with too many links.
• Possible factors?
• Nonlinear effects (e.g. friction)
• Initial conditions
• Sensitivity to physical disturbances
• Conjecture
• ? real stabilizability radius is too small

5
Real Stabilizability Radius

• Given a stabilizable LTI system
• the real stabilizability radius measures the
  smallest
• such that the perturbed
  system
• is no longer stabilizable.

6
Real Stabilizability Radius of Pendulum
v rc,norm Sig. Fig.
1 1.00E00 1-2
2 1.11E-01 2-3
3 4.69E-02 3-4
4 2.46E-02 3-4
5 1.47E-02 3-4
6 9.56E-03 3-4
7 6.64E-03 4-5
7
Thank you!