Sliding Mode Control of a Non- Collocated Flexible System

builderanthologyAI and Robotics

Oct 19, 2013 (4 years and 22 days ago)

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Sliding Mode Control of a Non
-
Collocated Flexible System


Aimee Beargie

November 13, 2002


Committee

Dr. Wayne Book, Advisor

Dr. Nader Sadegh

Dr. Stephen Dickerson


Sponsor

CAMotion, Inc.


Problem Statement

Develop an algorithm to control the tip
position of a mechanism that is actuated at
the base (non
-
collocated problem)

Recently developed algorithms generally deal with
collocated problems

Sensors:
Encoder, Accelerometer, Machine Vision

State Feedback Control

Kalman Filter

Robust to parameter variations


Variable Structure Control Research

Model using Assumed Mode Method

Qian & Ma


Tracking Control

Chang & Chen


Force Control

Comparison to other Methods

Hisseine & Lohmann


Singular Perturbation

Chen & Zhai


Pole Placement

Robustness

Iordanou & Surgenor


using inverted pendulum

Combined with Other methods

Romano, Agrawal, & Bernelli
-
Zazzera


Input Shaping

Li, Samali, & Ha


Fuzzy Logic

System Model

System Model

Equations of Motion




Small Angle Approximation

System Model

System Model

System Parameters:



m
1

= 8 kg


m
2

= 2.55 kg


L = 0.526 m


r = 0.377 m


I = 0.4367 kg
-
m
2


k = 32,199 N
-
m


b = 9.8863 N
-
m
-
s

Variable Structure Control (VSC)

Also called Sliding Mode Control

Switched feedback control method that
drives a system trajectory to a specified
sliding surface

in the state space.

Two Part Design Process

Sliding Surface (
s)



desired dynamics

Controller


Lyapunov analysis


VSC: Sliding Surface Design

Regular Form






Dynamics of state feedback structure


VSC: Sliding Surface Design

Transformation to Regular Form

VSC: Control Design

Use Lyapunov stability theory

Positive Definite Lyapunov Function



Want Derivative to be Negative Definite for
Stability


VSC: Control Design

Control Structure




Resulting Equation


VSC: Generalizing Gain Calculation

Control System Overview

RASID: internal PID control @ 10kHz

Motor & Amp


System Dynamics


RASID


Control
Algorithm


Kalman Filter

Encoder Meas.

Accelerometer Meas.

Vision Meas.

Desired
Trajectory

Computer @ 1kHz

Outer Loop Simulation

Used LQR for Sliding Surface Design



Error used in Control Calculation

Outer Loop Simulation

Max error: 0.015mm

Inner Loop Simulation

Force converted into Position Signal

PD Equations



Discrete Position Calculation





Inner Loop Simulation

Max error: 0.02mm

Simulation using Estimated States

Developed by Mashner

Vision

Measurement Frequency of 30 Hz

Delay of 5 ms

Covariance

Accelerometer: std. deviation squared

Vision/Encoder:



Simulation using Estimated States

Max error: 0.2mm

Simulation: Penalty on x
tip

and v
base

Max error: 0.5mm

Robustness Simulation:
50% of m
tip

Max error: 0.3mm

Robustness Simulation: 110
% of m
tip

Max error: 0.5mm

Experimental Set
-
up

Experimental Results:
VSC w/ Kalman Filter

MSE = 1.3620e
-
6 m
2

Experimental Results: Robustness

Mean Squared Error

0%: 1.4170e
-
6 m
2

10%: 1.6309e
-
6 m
2

16%: 1.8068e
-
6 m
2


Experimental Results:

Comparison of Control Methods

Mean Squared Error

PD: 9.7750e
-
7 m
2

LQR: 1.8366e
-
5 m
2

VSC: 1.3620e
-
6 m
2

Conclusions

Developed method results in acceptable
tracking of tip position

Verified through simulations and experiments

Method generalized for LTI systems

Better performance than other control methods

Robust to parameter variations

Choice of Cost function critical

Verified experimentally for tip mass




Further Work

Desired Trajectory

Currently designed for rigid system

Possible use trajectory that is continuous in
fourth derivative

Adaptive Learning

Input Shaping

QUESTIONS