Inverse Simulation for Gas Turbine Engine Control through Differential Algebraic Inequality Formulation
-
Tarun Uppal
,
Soumyendu Raha
Abstract
Modern day gas turbines are prime movers in land, air and sea. They have stringent performance requirements to meet the complex mission objectives. Optimal control strategies can help them meet their performance objectives more efficiently. A novel inverse simulation method for optimal control and system analysis studies using Differential Algebraic Equality/Inequality (DAE/DAI) technique is brought out in this paper with a case study. The gas turbine model together with safety constraints and performance specifications is represented as a high index DAI/DAE system. The solution for this DAE/DAI system is obtained using a new numerical approach that is capable of handling both equality and inequality constraints on system dynamics. The algorithm involves direct numerical integration of a DAI formulation in a time stepping manner using Sequential Quadratic Programming (SQP) solver that detects and satisfy active constraints at each time step (mesh point). In this unique approach the model and the constraints are always solved together. The method ensures stable solution at each time step, local minimum at each iteration of simulation and provides a regularised basis to the solver. Compared to other existing computationally intensive techniques in usage, this approach is easy, ensures continuous constraint satisfaction and provides a viable option for Model Predictive Control (MPC) of gas turbine engines.
Symbols and notations
Damped natural frequency
Natural frequency
Alpha method tuning parameter-1
Alpha method tuning parameter-2
Damping ratio
Value of acceleration term at step
Value of acceleration term at
Time
Start time
Final time
Control vector
Value of control variables at
State vector
Initial start vector
Value of state variables at
Output vector
- A
Plant matrix
- B
Control matrix
- C
Output matrix
- D
Direct transmission matrix
- I/P
Input
- N1
Low pressure spool speed
- N2
High pressure spool speed
- NozArea
Exhaust nozzle area
- O/P
Output
- P1
Ambient pressure
- P2
Compressor inlet pressure
- P3
Compressor discharge pressure
- P5
Turbine pressure
- P6
Exhaust pressure
- P62
Mixer area pressure
- T1
Ambient temperature
- T6
Exhaust temperature
- Wf
Main combustor fuel rate
- Abbreviations
- DAE
Differential Algebraic Equation
- DAI
Differential Algebraic Inequality
- GTE
Gas Turbine Engine
- HPC
High Pressure Compressor
- HPT
High Pressure Turbine
- LPC
Low Pressure Compressor
- LPT
Low Pressure Turbine
- MIL-STD 5007E
Military Standard
- MPC
Model Predictive Control
- PID
Proportional Integral Derivative
- PLA
Pilot Level Angle
- ODE
Ordinary Differential Equation
- SFC
Specific Fuel Consumption
- SISO
Single Input Single Output
- SQP
Sequential Quadratic Programming
- VG
Variable Geometry
Acknowledgements
Authors are thankful to Director, Group Director and Divisional Head of flight mechanics and control engineering group of Aeronautical Development Establishment (ADE) for granting permission to publish this research work. Authors would also like to thank Shri.Sreenesh for helping with word processor for this manuscript.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorials
- Reasons for Triple-Funding of the Jet-Engine-Industry to Meet 2020–2040 6th-Gen-Challenge: Counter-Air Penetration, CAP
- Reasons for triple-funding of the jet-engine-industry to meet 2020-2040 6TH-Gen-Challenge: Counter-Air Penetration, CAP
- Original Research Articles
- Experimental Investigation of Reacting Flow Characteristics in a Dual-Mode Scramjet Combustor
- Experimental Investigation of Shape Transition Effects on Isolator Performance
- Effects of Inlet Parameters on Combustion Performance in Gas Turbine Combustor
- Gas Turbine Engine Gas-path Fault Diagnosis Based on Improved SBELM Architecture
- The Effects of Turbulent Burning Velocity Models in a Swirl-Stabilized Lean Premixed Combustor
- Inverse Simulation for Gas Turbine Engine Control through Differential Algebraic Inequality Formulation
- Aerodynamic Optimization of Turbine Based Combined Cycle Nozzle
- Nonlinear System Modeling based on System Equilibrium Manifold
- Numerical Study on Heat Transfer Enhancement of Swirl Chamber on Gas Turbine Blade
Articles in the same Issue
- Frontmatter
- Editorials
- Reasons for Triple-Funding of the Jet-Engine-Industry to Meet 2020–2040 6th-Gen-Challenge: Counter-Air Penetration, CAP
- Reasons for triple-funding of the jet-engine-industry to meet 2020-2040 6TH-Gen-Challenge: Counter-Air Penetration, CAP
- Original Research Articles
- Experimental Investigation of Reacting Flow Characteristics in a Dual-Mode Scramjet Combustor
- Experimental Investigation of Shape Transition Effects on Isolator Performance
- Effects of Inlet Parameters on Combustion Performance in Gas Turbine Combustor
- Gas Turbine Engine Gas-path Fault Diagnosis Based on Improved SBELM Architecture
- The Effects of Turbulent Burning Velocity Models in a Swirl-Stabilized Lean Premixed Combustor
- Inverse Simulation for Gas Turbine Engine Control through Differential Algebraic Inequality Formulation
- Aerodynamic Optimization of Turbine Based Combined Cycle Nozzle
- Nonlinear System Modeling based on System Equilibrium Manifold
- Numerical Study on Heat Transfer Enhancement of Swirl Chamber on Gas Turbine Blade
