Supercavitation Control Methods for High-Speed€¦ · Oral Prelim Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work Future Research Research

Oral Prelim

MotivationSupercavitation

High-SpeedSupercavitatingVehicle

Overall Objectives

Previous Work

FutureResearchResearch Direction

LPV Modeling

Simulation andImplementation

Summary

Control Methods for High-SpeedSupercavitation Vehicles

Preliminary Oral Exam Presentation

Bálint Vanek

Department of Aerospace Engineering and MechanicsUniversity of Minnesota

Advisor: Prof. Gary Balas6th of September, 2006

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Outline

1 MotivationSupercavitationHigh-Speed Supercavitating VehicleOverall ObjectivesPrevious Work

2 Future ResearchResearch DirectionLPV ModelingSimulation and Implementation

3 Summary

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Background

• M.S. in Mechanical Engineering, Budapest University ofTechnology and Economics, 2003

• Thesis: Solution for Control Problems in AircraftFormation Flight, Advisor: Prof. József Bokor

• Hungarian Champion in Swimming (1998-2002)• Ph.D student under Prof. Gary Balas since August

2004

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Overview

Supercavitation

Vehicle

Vehicle

fincavitator

Feedback Linearizing Controller

cB.Actv

gravF 0x

∫ sC

cA

planeF

δ

(Bimodal)

sy

(switching) Linear system

x (t-_

x_ Control

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Overall Objectives

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LPV Modeling


Summary

Cavitation

Cavitation happens when water isforced to move at extremely highspeed, resulting in a pressure drop.If pressure drops below the watervapor pressure, it vaporizesforming small bubbles of watervapor. In propellers and pumps,cavitation causes noise, damage tocomponents, vibrations, and a lossof efficiency. When the cavitationbubbles collapse, they create spotsof high temperature and emit shockwaves.

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Supercavitation

• Gas ventilation can helpmaintaining the cavity

• Reduced skin friction drag• An order of magnitude

lower overall dragcoefficient

• Planing force can be usedto sustain the vehicle

• Transition to supercavitationneeds effort

• Cavity bubble can bedestabilized with actuator

• Control surfaces immersionchanges

• Switched, delay dependent,nonlinear planing forces

Oral Prelim



Overall Objectives

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LPV Modeling


Summary

Research in Supercavitation

As a response to the Russian VA-111 supercavitating rocketONR initiated a Supercavitation Program developing a smallinterceptor type anti torpedo missile.DARPA recently launched the Underwater Expressprogram, which aims to develop a large 8 foot diameter 60ton 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 earlystage: Kirschner et al. (2003), Dzielski and Kurdila (2003),Lin et al. (2005), Vanek et al. (2005).

Oral Prelim



Overall Objectives

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LPV Modeling


Summary

Vehicle

Note:

• fin immersion Lf

• plane depth h• plane angle αp

• plane contactangle φ

• cavity diameterRc

• different finimmersion

• planingdepending onpresent and paststates

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Overall Objectives

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LPV Modeling


Summary

Cavity

Cavity dimensions are determined by:• Cavitation number σ = p∞−pc

0.5ρV 2

• Froude number F = V√gdn

• Ventillation coefficient CQ = QVd2

n

• Cavitator drag coefficient• Cavitator radius

Cavity centerline is a function of:• Past trajectory of cavitator• Buoyancy

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Research GoalsNonlinear Control Law Development for the High-SpeedSupercavitation 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 systemsRequirements:• Guidance level tracking, with emphasis on drag

reduction• Single framework for control laws through the flight

envelope, including transition phase and planing

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Overall Objectives

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LPV Modeling


Summary

Challenges, RequirementsThe body is not fully wetted implies that the problem isfundamentally different from the control of torpedoes:• Transition from fully wetted to supercavitating operation requires the

adaptation of control laws with speed

• Slope discontinuous force curves depending on immersion requirelookup tables

• Immersion to liquid shows time-delay effects

• Inherently unstable vehicle behavior with cavitator, non-minimumphasedness with fins

Requirements:• Fins supporting the tail are required for the initial phase, but can be

retractable during operation to provide only roll control, reducingdrag

• Control laws should take into account the fins efficiency due toimmersion

• Vehicle motion and wetted areas should be optimized for sensorperformance and cavity shape

• Control laws should utilize the benefits of planing for agility

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Previous Work

Longitudinal dynamics models were analyzed, with thefollowing 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



Overall Objectives

Previous Work


LPV Modeling


Summary

Control MethodVehicle

fincavitator

Feedback Linearizing Controller

cB.Actv

gravF 0x

∫ sC

cA

planeF

δ

(Bimodal)

sy

(switching) Linear system

x (t-_

x_

Two loop structure with switching inner-loop, feedbacklinearizing controller, to eliminate nonlinearities and delaydependence 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

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Overall Objectives

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LPV Modeling


Summary

Controllability of SwitchedSystems

• Nilpotent system with identical linear dynamics in bothmodes

• The system is continuous on the switching hypersurface• The relative degrees are equal in both modes

Controllability results obtained by the analysis of the zerodynamics on the switching hypersuface, using positivecontrols, with proper discretization to account for the delayeffect.

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LPV Modeling


Summary

Previous Results

Publications on longitudinalplane vehicle control:

• Control design with simple outer loop controlBalas,Bokor,Vanek,Arndt (Springer, 2006)

• Constrained Receding Horizon ControlVanek,Balas,Bokor,Arndt (J. of Vibration and Control,2006)

• Controllability guaranties of the switched systemVanek,Bokor,Balas (ACC, 2006)

• Stability and tracking trade-off studies using one controlsurface Vanek,Balas (ONR Workshop, 2006)

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Motivation of Future Directions

The preceding results with several limiting assumptions hasto be extended to a more comprehensive control law.• 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• Planing avoidance should be also adapted by velocity

and available control authorityThese requirements with several parameter dependentcoefficients, which can be measured online suggest the usage ofLinear Parameter-Varying control methods. However, thedynamics depend on the switched planing force also. Theproblem can be resolved with a similar dynamic inversion controllaw, to obtain similar LPV systems on both sides of the switchingsurface.

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Notable PropertiesThe mathematical model of the vehicle is a combination ofempirical and analytical results. The four force sourcesacting 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

Pitc

h

Yaw

x,y(

t-T)

PortFin tip

Port Fin root

y(t-T

)

x(t-T)

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Overall Objectives

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LPV Modeling


Summary

Research Direction

Overall objective: Nonlinear 6-DOF control of the HighSpeed Supercavitation Vehicle

• The control philosophy developed earlier can beextended to the parameter scheduled plants

• Nonlinear delay dependent feedback to transform thesystem into a Linear Parameter-Varying (LPV) model inall switched modes

• LPV control of the switched LPV systems to guaranteerobust stability and tracking objectives

• Stability and controllability analysis of nonlinearsystems using nonlinear feedback for LPVtransformation

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Motivation for theFeedback-LPV Inner-Loop

• A similar system architecture developed earlier can beextended to the full vehicle model including stability andcontrollability properties

• Nonlinearities associated with planing can be decoupledfrom the other system dynamics

• The system in all switched modes can be treated in thesame framework

• The delay dependent behavior can be effectively handled bydelay dependent feedback

• Planing forces cause large disturbances which can bebeneficial for steering but also destabilize the vehicle

• The fins immersion and velocity dependence make a naturalchoice to derive a parameter dependent inner-loop system

• The effects of planing can be suppressed based on the needof planing free or planing supported operation

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Motivation for LPV control• Requirements for velocity and fin immersion dependent

control laws can be handled by gain scheduled controlmethods

• LPV framework can incorporate switches betweensystems (since parameter rate could be infinite)

• Uncertain vehicle and cavity parameters require arobust controller synthesis tool

• Performance requirements can be set up based onparameter values in different frequency regions

• Admissible parameter space for the HSSV is wellcharacterized

• Constrained control like MPC or set-theoretic methodsare available for LPV systems

• The system dynamics after applying the nonlinearfeedback is similar to a missile, which makes themethod comparable with other methods

Oral Prelim



Overall Objectives

Previous Work


LPV Modeling


Summary

Quasi LPV Model

[x1x2

]=

[A11(x1, ρ) A12(x1, ρ)A21(x1, ρ) A22(x1, ρ)

] [x1x2

]+

[B1(x1, ρ)B2(x1, ρ)

]δ

(1)

• 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



Overall Objectives

Previous Work


LPV Modeling


Summary

Motivation for Stability andControllability Analysis

• The system is nonlinear,switched and delay dependentproviding a valuable reference for future controlresearch

• The nonlinear feedback and common LPV form couldsimplify the controllability analysis of the system

• Many results in switched and delay dependent systemsare available for linear case only

• The connection between switched systems and LPVsystems is an emerging field of research

• No results are available for the case when relativedegrees of the different switched systems are different,like when retracting the fins

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Overall Objectives

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LPV Modeling


Summary

Further ObjectivesThe cross coupling between the vehicle set-up and thecontrol performance objectives need special attentionduring the design. There are several performancerequirements besides position tracking:• Control design and simulation with water tunnel tests

have to identify the optimal control surfaces, to reducedrag and provide the best platform for sensors

• The steering policy such as bank-to-turn has to bedecided

• The onboard sensors will likely to be noisy hence thecontrol laws have to account for that

• The question of using planing for steering is also underdebate

Systems and control analysis could provide severalguidelines for the optimal configuration.

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Overall Objectives

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Summary

Hardware in-the-loop SimulationThe 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 wellunderstood

• Different control scenarios can be evaluated in a closeto real-world system

Oral Prelim



Overall Objectives

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LPV Modeling


Summary

Accomplishments,GoalsAccomplishments:• 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 architectureObjective 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

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Summary

ReferencesG.J. Balas, J. Bokor, B. Vanek and R.E.A. ArndtControl of Uncertain Systems: Modelling,Approximation and Design.Control of High-Speed Underwater VehiclesSpringer-Verlag, 2006.

B. Vanek, J. Bokor, G.J. Balas and R.E.A. ArndtLongitudinal Motion Control of a High-SpeedSupercavitation VehicleJournal of Vibration and Control, 2006.

B. Vanek, J. Bokor and G.J. BalasTheoretical aspects of High-Speed SupercavitationVehicle ControlAmerican Control Conference, Minneapolis,2006.

B. Vanek, J. Bokor and G.J. BalasHigh-Speed Supercavitation Vehicle ControlAIAA Guidance,Navigation, and Control Conference,Keystone,2006.

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Overall Objectives

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Summary

Time for questions

Thank You!

Documents

Supercavitation Control Methods for High-Speed€¦ · Oral Prelim Motivation Supercavitation High-Speed Supercavitating Vehicle Overall Objectives Previous Work Future Research Research