2. Feedbacks for Fluid Flows and Fusion Miroslav Krstic Department of Mechanical and Aerospace Engineering Feedbacks for Fluid Flows and Fusion

3. 1 MAE Control Program Control of Flows and Propulsion Systems: Tom Bewley Bob Bitmead Miroslav Krstic Control of Structures: Bob Skelton (macro-structures, e.g., satellite antennas) Raymond de Callafon (micro-structures, HDD positioning) Command and Control for Unmanned Aerial Vehicles: Bill McEneaney

4. 2 Bluff Body Flow Control Controlled Uncontrolled Ole Morten Aamo

5. 3 Mixing Control in Channels and PipesControlled Uncontrolled Control law: Pressure distribution Andras Balogh and Ole Morten Aamo

6. 4 Jet Flow Control Controller: Lawrence Yuan

7. 5 Particle mixing with control Controlled - heavy particles Controlled - light particlesUncontrolled Diffusive mixing

8. 6 Tailored Fuel Injection for Pulsed Detonation Engines (Aliseda, Ariyur, Lasheras, Krstic, and Williams) Laser measurement of water droplets sprayed into a glass tube time (PDE cycles) u (control) (desired equiv. ratio distribution) Multivariable PI controller Actuator valve array

9. COMBUSTION INSTABILITY CONTROL via Extremum Seeking EXTREMUM SEEKER Rayleigh criterion-based controllers, which use phase- shifted pressure measurements and fuel modulation, have emerged as prevalent The length of the phase needed varies with operating conditions. The tuning method must be non-model based. phase sin wt Pressure washout filter COMBUSTOR Phase-Shifting Controller Frequency/ amplitude observer fuel Problem Statement Tuning allows operation with minimum oscillations at lean conditions Reduced engine size, fuel consumption and NO x emissions Impact time ext. seeking suppresses oscillations Experimental Results (4MW combustor) with UTRC

10. AXIAL FLOW COMPRESSOR CONTROL by Extremum Seeking Problem Statement Active controls for rotating stall only reduce the stall oscillations but they do not bring them to zero nor do they maximize pressure rise. Extremum seeking to optimize compressor operating point. Caltech COMPRESSOR Air Injection Stall Controller Pressure rise washout filter sin wt EXTREMUM SEEKER bleed valve Smaller, lighter compressors; higher payload in aircraft Patent issued (August 2000) Impact H.-H. Wang time Pressure Rise Experimental Results Extremum seeking stabilizes the maximum pressure rise.

11. 9 Tokamak: Plasma electro-magnetically confined in a torus, to obtain nuclear fusion energy. Densities (~10 20 particles/m 3 ) and temperatures (~10 8 K) must be achieved. Reactivity rate, vs T, for D-T mixture Low Temperature – High Density Regime (economically attractive)  Reaction rate increases with temperature  Thermally Unstable Eugenio Schuster, coadvised w/ George Tynan Burn Instability Control in Tokamaks

12. 10 Burn Instability Open loop  desired equilibrium is unstable  MHD stability conditions are violated Active control is required for stabilization Our approach: Nonlinear Model-Based Control

13. 11 Model Total Density Electron Density Reactivity Rate Delay Confinement Time D- T Confinement Time Alpha Confinement Time Energy Confinement Time Impurity Confinement Time Alpha Particles Balance Equation D-T and Neutral Particles Balance Equations Impurity Particles Balance Equation Energy Balance Equation Impurity Density Fueling Rate Auxiliary Power Energy Neutral Density Deuterium-Tritium Density Alpha Density Impurity Injection

14. 12 Model ITER Scaling: Beta Limit Delay Scaling Constant Plasma Volume D-T Scaling Constant Elongation at  Alpha Scaling Constant Magnetic Field Minor Radius Major Radius Plasma Current Impurity Scaling Constant DT Reactivity: Radiation Losses: Bremsstrahlung (A b ) – Line (A l ) – Recombination (A r )

15. 13 Simulation Results—Region of Stability

16. 14 Control of Temperature and Density Profiles Goal: make the temperature and density converge to desired radial profiles. Burn Control MHD Instability Avoidance High-beta and High-confinement mode access Confinement Time Improvement Transport Reduction Why control kinetic profiles? Eugenio Schuster

17. 15 Model Density Balance Equation Energy Equation Boundary Conditions and Controls :

18. 16 Simulation Results Closed Loop: Energy Profile EvolutionClosed Loop: Density Profile Evolution

19. 17 Control of Tokamak Vertical Stability Objective: plasma shape control and vertical stability control Actuators: poloidal coils Eugenio Schuster, with Mike Walker and Dave Humphreys (General Atomics)

20. 18 Saturation Anti-Windup Design Experimental tests at GA this year DIII-D TOKAMAK GA design Loss of stability due to saturation!

21. 19 Control of Magnetohydrodynamic Flows For drag management in hypersonic flight (re-entry vehicles and SCRAMJET propulsion). For liquid metal blankets in fusion reactors. Control possible using purely electrical actuators and sensors (rather than MicroElectroMechanicalSystems). Eugenio Schuster

22. 20 MHD Governing Equations Navier-Stokes Equation Incompressibility Condition Magnetic Field Equation Faraday’s Law Ampere’s Law Ohm’s Law Magnetic Induction Equation

23. 21 Hartmann Flow Actuators and sensors on the wall.

24. 22 Control Approach Goal: minimize/maximize the cost functional Energy functional: Dissipation functional: Reynolds number Magnetic Re number Using the minimal amount of control energy

25. 23 Control Results (preliminary) Pressure or electric potential distribution V wall or j wall wall zoom out Velocity or current vectors Inspired by: