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
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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.
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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,
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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
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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
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10
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2
0
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Time (sec)
(rad/sec)
Desired Velocity
Velocity Error
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Time (sec)
(rad/sec)
Masters Thesis Defense
Control and Robotics
Simulation Results
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Time (sec)
(N.m)
Human Input Observation Error
Motor Control Torque
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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
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0.5
1
1.5
2
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3.5
Time (sec)
(rad/sec)
Desired Velocity
Velocity Error
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20
40
60
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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
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Time (sec)
(N.m)
Human Force Observer
Motor Control Torque
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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
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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 EZIBI 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
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