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

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

System Model m 1 = 8 kg m 2 = 2 kg k = N/m b = Ns/m

System Model

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

VSC: Regular Form Useful in design of sliding surface

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

VSC: Sliding Surface Design Use LQR to find  K = [ ]  2 = I  = [ ]X

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

VSC: Control Design Obtain expressions for each gain:

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

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

Simulation Results: Kalman Filter

Encoder gain Accel gain Vision gain

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

Simulation Results: Delayed Meas

Encoder gain Accel gain Vision gain

Simulation Results

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