Oral Prelim
Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research
Control Methods for High-Speed Supercavitation Vehicles Preliminary Oral Exam Presentation
Research Direction LPV Modeling Simulation and Implementation
Summary
Bálint Vanek Department of Aerospace Engineering and Mechanics University of Minnesota
Advisor: Prof. Gary Balas 6th of September, 2006
Oral Prelim
Outline Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
1 Motivation
Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Summary
2 Future Research
Research Direction LPV Modeling Simulation and Implementation 3 Summary
Oral Prelim
Background Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
• M.S. in Mechanical Engineering, Budapest University of
Technology and Economics, 2003 • Thesis: Solution for Control Problems in Aircraft
Formation Flight, Advisor: Prof. József Bokor • Hungarian Champion in Swimming (1998-2002) • Ph.D student under Prof. Gary Balas since August
2004
Oral Prelim
Overview Motivation Supercavitation High-Speed Supercavitating Vehicle
Supercavitation
Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Vehicle
Fgrav v
Vehicle
x0
cavitator
Act.
fin
Bc
∫
Cs
ys
Control
_
Ac Fplane (Bimodal)
x
δ _
x (t-
Feedback Linearizing Controller (switching)
Linear system
Oral Prelim
Cavitation Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Cavitation happens when water is forced to move at extremely high speed, resulting in a pressure drop. If pressure drops below the water vapor pressure, it vaporizes forming small bubbles of water vapor. In propellers and pumps, cavitation causes noise, damage to components, vibrations, and a loss of efficiency. When the cavitation bubbles collapse, they create spots of high temperature and emit shock waves.
Oral Prelim
Supercavitation Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
• Gas ventilation can help
maintaining the cavity • Reduced skin friction drag • An order of magnitude
lower overall drag coefficient • Planing force can be used
to sustain the vehicle
• Transition to supercavitation
needs effort • Cavity bubble can be
destabilized with actuator • Control surfaces immersion
changes • Switched, delay dependent,
nonlinear planing forces
Oral Prelim
Research in Supercavitation Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
As a response to the Russian VA-111 supercavitating rocket ONR initiated a Supercavitation Program developing a small interceptor type anti torpedo missile. DARPA recently launched the Underwater Express program, which aims to develop a large 8 foot diameter 60 ton craft for paylod and crew. The interest in Supercavitation vehicle control is increasing. Linear control results: Kirschner et al. (2001), Goel (2002), Shao et al. (2003). A few nonlinear results are in early stage: Kirschner et al. (2003), Dzielski and Kurdila (2003), Lin et al. (2005), Vanek et al. (2005).
Oral Prelim
Vehicle Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Note: • fin immersion Lf • plane depth h • plane angle αp • plane contact
angle φ • cavity diameter
Rc • different fin
immersion • planing
depending on present and past states
Oral Prelim
Cavity Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Cavity dimensions are determined by: ∞ −pc • Cavitation number σ = p0.5ρV 2 • Froude number F = √V
gdn
• Ventillation coefficient CQ = • Cavitator drag coefficient • Cavitator radius
Cavity centerline is a function of: • Past trajectory of cavitator • Buoyancy
Q Vdn2
Oral Prelim
Research Goals Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Nonlinear Control Law Development for the High-Speed Supercavitation Vehicle (HSSV) • Develop a robust controller for the full 6-DOF nonlinear,
switching, delay dependent HSSV model • Establish stabilizeability and detectability criteria for the
system • Develop a systematic way to design control laws valid
for the full operating envelope • Control approach and controllability analysis should be
valid for a wider class of systems Requirements: • Guidance level tracking, with emphasis on drag
reduction • Single framework for control laws through the flight
envelope, including transition phase and planing
Oral Prelim
Challenges, Requirements Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives
The body is not fully wetted implies that the problem is fundamentally different from the control of torpedoes: • Transition from fully wetted to supercavitating operation requires the adaptation of control laws with speed
Previous Work
Future Research
• Slope discontinuous force curves depending on immersion require lookup tables
Research Direction LPV Modeling Simulation and Implementation
Summary
• Immersion to liquid shows time-delay effects • Inherently unstable vehicle behavior with cavitator, non-minimum phasedness with fins
Requirements: • Fins supporting the tail are required for the initial phase, but can be retractable during operation to provide only roll control, reducing drag
• Control laws should take into account the fins efficiency due to immersion
• Vehicle motion and wetted areas should be optimized for sensor performance and cavity shape
• Control laws should utilize the benefits of planing for agility
Oral Prelim
Previous Work Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Longitudinal dynamics models were analyzed, with the following properties: • Vehicle is close to straight and level flight with constant
speed, • Planing on the transom only, • Cavitator and fins force coefficient is constant, • Cavity wall disturbance is present, • Simplified dynamical planing model with memory effect.
Oral Prelim
Control Method Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives
Fgrav v
Vehicle
x0
cavitator
Act.
fin
Bc
∫
Cs
ys
_
Ac
x
δ
Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Fplane (Bimodal)
_
x (t-
Feedback Linearizing Controller (switching)
Linear system
Two loop structure with switching inner-loop, feedback linearizing controller, to eliminate nonlinearities and delay dependence introduced by planing • Control design synthesized in a multivariable canonic coordinate frame • Switching state dependent feedback • The system dynamics is the same regardless of the interior switching state • One linear outer loop controller can provide reference tracking
Oral Prelim
Controllability of Switched Systems
Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research
• Nilpotent system with identical linear dynamics in both
modes • The system is continuous on the switching hypersurface
Research Direction LPV Modeling Simulation and Implementation
Summary
• The relative degrees are equal in both modes
Controllability results obtained by the analysis of the zero dynamics on the switching hypersuface, using positive controls, with proper discretization to account for the delay effect.
Oral Prelim
Previous Results Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research
Publications on longitudinal plane vehicle control:
Research Direction LPV Modeling Simulation and Implementation
Summary
• Control design with simple outer loop control
Balas,Bokor,Vanek,Arndt (Springer, 2006) • Constrained Receding Horizon Control
Vanek,Balas,Bokor,Arndt (J. of Vibration and Control, 2006) • Controllability guaranties of the switched system
Vanek,Bokor,Balas (ACC, 2006) • Stability and tracking trade-off studies using one control
surface Vanek,Balas (ONR Workshop, 2006)
Oral Prelim
Motivation of Future Directions Motivation Supercavitation High-Speed Supercavitating Vehicle
The preceding results with several limiting assumptions has to be extended to a more comprehensive control law.
Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
• Control should be velocity dependent • Differen performance objectives apply to fins based on
immersion, to limit saturation and respect effectiveness • Variable fin detachment has to be included
Summary
• Planing avoidance should be also adapted by velocity
and available control authority These requirements with several parameter dependent coefficients, which can be measured online suggest the usage of Linear Parameter-Varying control methods. However, the dynamics depend on the switched planing force also. The problem can be resolved with a similar dynamic inversion control law, to obtain similar LPV systems on both sides of the switching surface.
Oral Prelim
Notable Properties
Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
The mathematical model of the vehicle is a combination of empirical and analytical results. The four force sources acting on the vehicle: • Gravity, acting on the center of mass • Cavitator force, with nonlinear trigonometric dependence and cross coupling on states and inputs • Forces on fins, nonlinear dependence on current and past states and inputs, provided in tabular form • Planing force, nonlinear dependence on vehicle current and past states and cavity dimensions
y(t-T)
High-Speed Supercavitating Vehicle
Pitch
Supercavitation
x,y(t-T)
Motivation
x(t-T) Port Fin root
Yaw Port Fin tip
Oral Prelim
Research Direction Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Overall objective: Nonlinear 6-DOF control of the High Speed Supercavitation Vehicle • The control philosophy developed earlier can be
extended to the parameter scheduled plants • Nonlinear delay dependent feedback to transform the
system into a Linear Parameter-Varying (LPV) model in all switched modes • LPV control of the switched LPV systems to guarantee
robust stability and tracking objectives • Stability and controllability analysis of nonlinear
systems using nonlinear feedback for LPV transformation
Oral Prelim
Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Motivation for the Feedback-LPV Inner-Loop • A similar system architecture developed earlier can be extended to the full vehicle model including stability and controllability properties • Nonlinearities associated with planing can be decoupled from the other system dynamics • The system in all switched modes can be treated in the same framework • The delay dependent behavior can be effectively handled by delay dependent feedback • Planing forces cause large disturbances which can be beneficial for steering but also destabilize the vehicle • The fins immersion and velocity dependence make a natural choice to derive a parameter dependent inner-loop system • The effects of planing can be suppressed based on the need of planing free or planing supported operation
Oral Prelim
Motivation for LPV control Motivation Supercavitation
• Requirements for velocity and fin immersion dependent
High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research
•
Research Direction LPV Modeling Simulation and Implementation
Summary
• • • • •
control laws can be handled by gain scheduled control methods LPV framework can incorporate switches between systems (since parameter rate could be infinite) Uncertain vehicle and cavity parameters require a robust controller synthesis tool Performance requirements can be set up based on parameter values in different frequency regions Admissible parameter space for the HSSV is well characterized Constrained control like MPC or set-theoretic methods are available for LPV systems The system dynamics after applying the nonlinear feedback is similar to a missile, which makes the method comparable with other methods
Oral Prelim
Quasi LPV Model Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction
x˙ 1 x˙ 2
B1 (x1 , ρ) A11 (x1 , ρ) A12 (x1 , ρ) x1 + δ = x2 B2 (x1 , ρ) A21 (x1 , ρ) A22 (x1 , ρ) (1)
LPV Modeling Simulation and Implementation
Summary
• ρ exogenous time-varying parameter vector • x1 subset of states, in LPV synthesis treated as
independent • Control input δ must enter affinely • Many nonlinear system can be described exactly in
LPV form • Techniques are available to treat systems nonlinear in
input
Oral Prelim
Motivation Supercavitation
Motivation for Stability and Controllability Analysis
High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
• The system is nonlinear,switched and delay dependent
providing a valuable reference for future control research • The nonlinear feedback and common LPV form could
simplify the controllability analysis of the system • Many results in switched and delay dependent systems
are available for linear case only • The connection between switched systems and LPV
systems is an emerging field of research • No results are available for the case when relative
degrees of the different switched systems are different, like when retracting the fins
Oral Prelim
Further Objectives Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
The cross coupling between the vehicle set-up and the control performance objectives need special attention during the design. There are several performance requirements besides position tracking: • Control design and simulation with water tunnel tests
have to identify the optimal control surfaces, to reduce drag and provide the best platform for sensors • The steering policy such as bank-to-turn has to be
decided • The onboard sensors will likely to be noisy hence the
control laws have to account for that • The question of using planing for steering is also under
debate Systems and control analysis could provide several guidelines for the optimal configuration.
Oral Prelim
Hardware in-the-loop Simulation Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
The proposed control methods can be evaluated on a "quarter" vehicle model at the high speed water tunnel at St. Antony Falls • Resulting forces and moments on cavitator and fins can be measured with force cells • The interaction between a dynamically actuated fin immersed into a dynamically changing cavity is not well understood • Different control scenarios can be evaluated in a close to real-world system
Oral Prelim
Accomplishments,Goals Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Accomplishments: • Control law design for the longitudinal dynamics model of the vehicle • Controllability test for a general class of nonlinear, switched, delay dependent systems • Reference tracking results with several variations of the main architecture Objective groups: • Develop a control design oriented 6-DOF model of the vehicle • Extend the current control design and controllability results to the refined model • Generalize the obtained control design and controllability results to a wider group of systems • Validate a simplified version of the control laws on the water tunnel testbed
Oral Prelim
References Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research
G.J. Balas, J. Bokor, B. Vanek and R.E.A. Arndt Control of Uncertain Systems: Modelling, Approximation and Design. Control of High-Speed Underwater Vehicles Springer-Verlag, 2006.
Research Direction LPV Modeling Simulation and Implementation
Summary
B. Vanek, J. Bokor, G.J. Balas and R.E.A. Arndt Longitudinal Motion Control of a High-Speed Supercavitation Vehicle Journal of Vibration and Control, 2006. B. Vanek, J. Bokor and G.J. Balas Theoretical aspects of High-Speed Supercavitation Vehicle Control American Control Conference, Minneapolis,2006. B. Vanek, J. Bokor and G.J. Balas High-Speed Supercavitation Vehicle Control AIAA Guidance,Navigation, and Control Conference,
Oral Prelim
Time for questions Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work
Future Research Research Direction LPV Modeling Simulation and Implementation
Summary
Thank You!
