Motivating example
Autonomous Underwater Vehicle
speed control
Practical problem: design a control law so that the vehicle speed u
tracks a reference command
Tuesday, May 17, 2011
Motivating example
Autonomous Underwater Vehicle
speed control
Practical problem: design a control law so that the vehicle speed u
tracks a reference command
First step: modeling
External Thrust (generated by propeller)
-
Speed
Hydrodynamic Damping:
Linear + quadratic terms
Tuesday, May 17, 2011
-
Mass
-
Added mass
Motivating example
Newton Law
External
thrust force
;
- Sum of all external forces
Hydrodinamic
Damping
Inertial term
Added mass effect
Non Linear System
Tuesday, May 17, 2011
Nonlinear Control
Control Objectives
Reference r
(desired speed
profile)
External disturbances d
(currents, waves)
Controller K
Sensor
Sensor noise n
Tuesday, May 17, 2011
Nonlinear Control
Control Objectives
Reference r
(desired speed
profile)
External disturbances d
(currents, waves)
Controller K
Sensor
Sensor noise n
Design a controller K that stabilizes the plant
and such that r-u is small in spite of external disturbances
d, noise n, and plant parameter uncertainty (robust
stabilty and performance)
Tuesday, May 17, 2011
A Linear Approximation
Strategy: operate the AUV about selected
speed references
Equilibrium (trimming) condition
Study the system about the
equilibrium point
Tuesday, May 17, 2011
A Linear Approximation
Strategy: operate the AUV about selected
speed references
Equilibrium (trimming) condition
Study the system about the
equilibrium point
Tuesday, May 17, 2011
A Linear Approximation
;
appx.
Tuesday, May 17, 2011
A Linear Approximation
;
appx.
Taylor series expansion
Tuesday, May 17, 2011
A Linear Approximation
;
appx.
Taylor series expansion
Tuesday, May 17, 2011
A Linear Approximation
Tuesday, May 17, 2011
A Linear Approximation
LINEAR
SYSTEM
Dependence on trimming condition
Tuesday, May 17, 2011
A Linear Approximation
LINEAR
SYSTEM
Dependence on trimming condition
taking Laplace transforms (zero initial conditions)
Tuesday, May 17, 2011
A Linear Approximation
LINEAR
SYSTEM
Dependence on trimming condition
taking Laplace transforms (zero initial conditions)
Tuesday, May 17, 2011
Linear Controller Design
LINEAR
SYSTEM
Tuesday, May 17, 2011
Linear Controller Design
LINEAR
SYSTEM
Tuesday, May 17, 2011
Linear Controller Design
LINEAR
SYSTEM
Reference r
(about nominal
speed)
Linear Control
Law
Tuesday, May 17, 2011
External disturbances d
(currents, waves)
Controller K
Sensor
Sensor noise n