1. Tip Position Control Using an Accelerometer & Machine Vision Aimee Beargie March 27, 2002

2. Problem Statement Develop an algorithm to control the tip position of a mechanism that is actuated at the base Sensors Encoder Accelerometer Machine Vision Kalman Filter Variable Structure Control

3. System Model m 1 = 8 kg m 2 = 2 kg k = 7928.3 N/m b = 1.258 Ns/m

4. System Model

5. Variable Structure Control (VSC) Switched feedback control method that drives a system trajectory to a specified surface in the state space. Design: Switching Surface,   plant dynamics Controller  Lyapunov analysis

6. VSC: Regular Form Useful in design of sliding surface

7. VSC: Designing  Dynamics of state feedback structure where State matrix = A 11 Input matrix = A 12 K =-

8. VSC: Sliding Surface Design Use LQR to find  K = [-64.4 18.7 -0.388]  2 = I  = [64.4 -18.7 0.388 1]X

9. VSC: Control Design Use Lyapunov stability theory Typical Lyapunov function for single input systems:

10. VSC: Control Design Obtain expressions for each gain:

11. Discrete System Model m = vision measurement sample time V: Input Covariance Matrix W: Output Covariance Matrix

12. Discrete Kalman Filter Initialized values: Covariance matrix, S(k) Initial estimate (usually zero) Algorithm to estimate states:

13. Simulation Results: Kalman Filter

14. Encoder gain Accel gain Vision gain

15. Formulation for Delayed Measurement M: output matrix for delayed meas. y  : meas. delayed for one time-step y d : progressively delayed meas.

16. Simulation Results: Delayed Meas

17. Encoder gain Accel gain Vision gain

18. Simulation Results

19. Future Work Simulation New system model Reduce tracking error Add delays to all measurements Saturation Implement on one-axis system