Machine Interaction in Mechatronic Systems

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14 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

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Nonlinear Control Techniques for Human
-
Machine Interaction in Mechatronic Systems

Masters Thesis Defense

Department of Electrical and Computer Engineering

Clemson University

Committee

Dr. Darren Dawson

Dr. Ian Walker

Dr. Adam Hoover

Apoorva Kapadia

Masters Thesis Defense

Control and Robotics

Presentation Outline


Nonlinear Controller for a Smart Exercise Machine


Introduction


Problem Motivation


Past Research


Model Development and Objectives


Exercise Machine Dynamics


Control Objectives


Primary Control Design with Force Sensor


Brent’s Method to Seek Extremum


Passivity


Control Design Without Force Sensor


Force Observer


Simulation and Experiment


Measurement of Human Alertness and Performance


The Pan
-
Tilt
-
Vergence Unit


Conclusion

Masters Thesis Defense

Control and Robotics

Motivation for a Smart Exercise Machine


Exercise Machines have become increasingly popular, but these are mainly
open
-
loop.


Recent research focuses on a closed
-
loop approach, incorporating feedback
from the user.


Two fundamental issues are addressed in its design:


Efficiency


Safety


Human muscle physiology research reveals that the force
-
position
-
velocity
relation is a Hill surface function.


Maximum output power occurs between maximum human force and
maximum machine velocity.


Our goal is to design an optimal exercise machine that enables the user to
put in maximum power in minimum time.

Masters Thesis Defense

Control and Robotics

Past Research


Traditional Exercise Machines either rely on manual adjustments of machine
parameters or automatic adjustments based on an open
-
loop approach.



Kazerooni et. al. (1993) focused on a closed
-
loop system approach. This
control design did not address the passivity or self
-
optimizing problem.



Shields et. al. (1997) designed an adaptive controller with only a braking
capability. Identification of exercise motions and torque output of the
resistance was utilized to deal with unknown human biomechanics.



P.Y. Li et. al. (1997) developed a passive controller based on the linear
force
-
velocity curve assumption. The reference trajectory generator required
a training phase for the algorithm to learn user specific parameters, to
compensate for uncertainties in the user’s biomechanics.

Masters Thesis Defense

Control and Robotics

Exercise Machine Dynamics


For simplicity, our Exercise Machine is modeled as a single DOF system. Its
dynamic model is where



Assumption 1 The user input is a function of machine velocity



Assumption 2 The user input is a continuous function



Assumption 3 User input is unidirectional, and satisfies the following




inequality:



Assumption 4 The desired trajectory is assumed to be designed such that


where desired velocity is


and assumed to be in the same direction as the user input.

Masters Thesis Defense

Control and Robotics

Control Objectives



Design a controller that forces the Machine to turn at an unknown velocity set
-
point that maximizes human power input to the Machine, given as




As optimal velocity set
-
point is unknown, controller must “hunt down” the
velocity as the Exercise Machine turns.



The controller must also satisfy a passivity condition to promote safe
operation.



To reduce cost, we use an observer instead of measuring input force.

Masters Thesis Defense

Control and Robotics

Primary Control Design with Force Sensor


To achieve the tracking control objective, we first introduce the velocity
tracking error as




Taking the time derivative, multiplying both sides by , we obtain the final
open
-
loop error system.



Since the human force and desired velocity are known, we propose the
following control law to achieve the stated control objectives



Substituting the control into the open
-
loop system, the closed
-
loop error
system is given as

Masters Thesis Defense

Control and Robotics

Brent’s Method to Seek Extremum


Brent’s Method uses an inverse parabolic interpolation algorithm,







Brent’s Method only requires that a maximum exist for user power input and
that the maximum is enclosed between two initial guesses, and .


Since the user power output is unknown, we measure user output in real
-
time.


The parabolic interpolation calculation is repeated until the difference
between the new upper and lower estimates is below some predefined
arbitrarily small threshold


The discontinuous output of the numerical calculation is passed through a set
of fourth order stable low pass filters to generate continuous, bounded signals,


Masters Thesis Defense

Control and Robotics

Passivity


Theorem 1



The controller ensures the Exercise Machine is passive with
respect to the user’s input by the following inequality






Proof
-

By substituting , the following expression can
be obtained





Since and with Assumption 3 and 4, the above equation can be
lower bounded as follows

Masters Thesis Defense

Control and Robotics

Control Design Without Force Sensor


First, the filter tracking error signal is designed as follows




Taking the time derivative, multiplying both sides by and substituting the
system dynamics, we obtain






Where



Closed loop dynamics can be determined as follows



Masters Thesis Defense

Control and Robotics

Stability Analysis


Lemma



Let be defined as follows





If then






Where are all positive constants



Define and


Masters Thesis Defense

Control and Robotics

Controller Design



can be upper bounded as indicated by the following inequality





Where



Based on the subsequent analysis, the following controller is designed










Or


Masters Thesis Defense

Control and Robotics

Design of Human Force Observer


To remove the requirement of a force sensor, we constructed the torque
observer as follows




After taking the time derivative of and multiplying the result by , the
following expression is obtained




After integrating both sides, we get




Since and

Masters Thesis Defense

Control and Robotics

Stability Analysis


Theorem 2


The Exercise Machine controller ensures all signals are bounded
under closed
-
loop operation and that provided the
control gains and are selected according to the sufficient conditions
above, and the control gain is selected sufficiently large with respect to the
initial condition of the system



Proof


We define the following non
-
negative function




After differentiation and substitution, the following expression is obtained

Masters Thesis Defense

Control and Robotics

Simulation Results


Simulation is presented to illustrate the performance of the controller based on
Brent’s Method



The system and human power equations are defined as





with hence, the optimum velocity is given by




For the simulation, the initial points of the system were set as



and the control gains were adjusted to

Masters Thesis Defense

Control and Robotics

Simulation Results

0
10
20
30
40
50
60
70
-2
0
2
4
6
8
10
Time (sec)
(rad/sec)
Desired Velocity

Velocity Error

0
10
20
30
40
50
60
70
0
1
2
3
4
5
6
7
8
9
10
11
Time (sec)
(rad/sec)
Masters Thesis Defense

Control and Robotics

Simulation Results

0
10
20
30
40
50
60
70
-10
-8
-6
-4
-2
0
2
Time (sec)
(N.m)
Human Input Observation Error

Motor Control Torque

0
10
20
30
40
50
60
70
-10
-8
-6
-4
-2
0
2
4
Time (sec)
(N.m)
Masters Thesis Defense

Control and Robotics

Experimental Setup
-

Hardware


The Exercise Machine testbed comprised of a handle connected to a rotating
assembly, mounted on the rotor of a switched reluctance motor, as shown
below.

Masters Thesis Defense

Control and Robotics

Experimental Setup
-

Program


The controller was implemented using Simulink
®

along with the dSpace
Windows Target in Real
-
Time Workshop. The control program is run through
the dSpace ControlDesk software, which also logs data and allows for online
parameter tuning.

Masters Thesis Defense

Control and Robotics

Experiment 1: Surrogate Function


For the first experiment, a surrogate function was used to test the ability of the
Exercise Machine to accurately maximize power expenditure.




Hence the system is maximized at


System Gains used were:





and the initial points were selected as



A 1.5 second time delay was utilized to allow the torque estimate to
converge to before Brent’s Method is invoked.

Masters Thesis Defense

Control and Robotics

Experiment 1: Velocity Plots

0
20
40
60
80
100
0
0.5
1
1.5
2
2.5
3
3.5
Time (sec)
(rad/sec)
Desired Velocity

Velocity Error

0
20
40
60
80
100
-1
-0.5
0
0.5
1
1.5
2
2.5
Time (sec)
(rad/sec)
Velocity Error
Masters Thesis Defense

Control and Robotics

Experiment 1: Force Plots

0
20
40
60
80
100
-2
0
2
4
6
8
10
Time (sec)
(N.m)
Human Force Observer

Motor Control Torque

0
20
40
60
80
100
-10
-8
-6
-4
-2
0
2
Time (sec)
(N.m)
Masters Thesis Defense

Control and Robotics

Experiment 2: Human Force Observation


In the second experiment, we removed to surrogate signal to allow the desired
trajectory to seek the maximum power expenditure of the user.



The gains for this experiment were found to be:





and initial points were selected as



A 1.5 second time delay was utilized to allow the torque estimate to
converge to before Brent’s Method is invoked.


Masters Thesis Defense

Control and Robotics

Experiment 2: Velocity and Error Plots

0
20
40
60
80
100
0
1
2
3
4
5
6
Time (sec)
(rad/sec)
Desired Velocity

Velocity Error

0
20
40
60
80
100
-1
-0.5
0
0.5
1
1.5
Time (sec)
(rad/sec)
Masters Thesis Defense

Control and Robotics

Experiment 2: Force Plots

0
20
40
60
80
100
-1
0
1
2
3
4
5
6
7
8
Time (sec)
(N.m)
Human Force Observer

Motor Control Torque

0
20
40
60
80
100
-8
-7
-6
-5
-4
-3
-2
-1
0
1
Time (sec)
(N.m)
Masters Thesis Defense

Control and Robotics

Other Work

Masters Thesis Defense

Control and Robotics

Measurement of Human Alertness and
Performance

Get EZ-IBI Input
Compute Pointer
Position
has the
pointer touched
the wall?
Sound to
Alert Use
r
Compute
Alertness
Performance
Analysis
Yes
No
Masters Thesis Defense

Control and Robotics

The Pan
-
Tilt
-
Vergence Unit

Bird Server
PC
Human
wearing VR
helmet
Position

Filter

Trajectory Generator

PD control

Head

Movement

Masters Thesis Defense

Control and Robotics

Conclusion


Presented a model for a Human Exercise Machine.



Presented a method to “hunt down” input
-
dependent desired velocity.



Presented a control algorithm that


Yields semi
-
global tracking


Maximizes human power output


Provides passivity



Explained the preliminary experimental set
-
up to measure human alertness
and performance.



Discussed the tracking of a VR helmet by a Pan
-
Tilt
-
Vergence Unit.

Masters Thesis Defense

Control and Robotics

Any Questions?