Tip Position Control Using an Accelerometer

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Tip Position Control Usingan Accelerometer
Machine Vision

• Aimee Beargie
• March 27, 2002

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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

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System Model

• m1 8 kg
• m2 2 kg
• k 7928.3 N/m
• b 1.258 Ns/m

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System Model
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Variable Structure Control (VSC)

• Switched feedback control method that drives a
  system trajectory to a specified surface in the
  state space.
• Design
• Switching Surface, s plant dynamics
• Controller Lyapunov analysis

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VSC Regular Form

• Useful in design of sliding surface

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VSC Designing s

• Dynamics of state feedback structure where
• State matrix A11
• Input matrix A12
• K -

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VSC Sliding Surface Design

• Use LQR to find s
• K -64.4 18.7 -0.388
• s2 I
• s 64.4 -18.7 0.388 1X

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VSC Control Design

• Use Lyapunov stability theory
• Typical Lyapunov function for single input
  systems

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VSC Control Design

• Obtain expressions for each gain

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Discrete System Model
m vision measurement sample time
V Input Covariance Matrix W Output Covariance
Matrix
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Discrete Kalman Filter

• Initialized values
• Covariance matrix, S(k)
• Initial estimate (usually zero)
• Algorithm to estimate states

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Simulation Results Kalman Filter
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Simulation Results Kalman Filter
Encoder gain
Accel gain
Vision gain
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Formulation for Delayed Measurement

• M output matrix for delayed meas.
• yD meas. delayed for one time-step
• yd progressively delayed meas.

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Simulation Results Delayed Meas
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Simulation Results Delayed Meas
Encoder gain
Accel gain
Vision gain
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Simulation Results
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Future Work

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