Multivariable Design of Jet Engine using Quantitative Feedback Theory

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Multivariable Design of Jet Engine using
Quantitative Feedback Theory

• Mukesh D. Patil
• P.S.V.Nataraj

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Outline

• Introduction
• A 2 x 2 MIMO Design Problem
• Basic Concepts
• Design Method
• Controller Synthesis Procedure
• Gas Turbine Application
• Results
• Conclusion

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Introduction
LPC
Schematic Of A Twin Spool Gas Turbine Engine
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A 2 x 2 MIMO Design Problem
Controller Structure For 2 X 2 MIMO System
5
Basic Concepts
6
Design Method

• The MIMO design is carried out using Equivalent
  Disturbance Attenuation method based on QFT.
• Plant uncertainties are transferred into its
  equivalent disturbance sets.
• Thus, the design problem becomes the disturbance
  attenuation problem.
• The fundamental point is that if G is chosen so
  that the output ?T satisfies the system
  tolerances over the entire VT set, then the
  original MIMO specifications are satisfied

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Block Diagram of a Typical Jet Engine
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Controller Synthesis Procedure

• Translation of time domain specifications into
  frequency specifications.
• Translation of tracking specifications into its
  equivalent disturbance specifications.
• Bound generation for stability and disturbance.
• Loop-shaping and filter design.

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Gas Turbine Application Inner Loop
The plant set for inner fuel flow loop Input
Variable Fuel flow demand, Output variable
Nhdot
The plant set for inner variable geometry loop
Input Variable VG demand, Output variable VG
blade angle
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Gas Turbine Application Inner loop
(contd)

• Performance Specifications 
• The rise time of closed loop transfer function
  for inner speed control loop should lie between
  0.26 to 0.38 sec.
• The rise time of closed loop transfer function
  for inner variable geometry loop should lie
  between 0.1 to 0.2 sec.
•  The stability margins for both the loops are 6
  dB gain margin and 45 degrees phase margin.

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Results Inner loop

Loop-shaping of inner fuel flow loop
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Results Inner loop (contd)
Loop-shaping of inner variable geometry loop
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Results Inner loop (contd)
Inner fuel flow loop Controller g1(s)and
prefilter f1(s)
Inner variable geometry loop Controller g2(s)and
prefilter f2(s)
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Results Inner loop (contd)
Closed loop validation of inner fuel flow loop
for step change in fuel flow
Closed loop validation of inner variable geometry
loop for step change in VG demand
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Gas Turbine Application MIMO Outer LoopFuel
Flow LoopInput variable 1 Fuel flow, Output
variable 1LPC speedVariable Geometry
LoopInput variable 2 Variable geometry, Output
variable 2HPC speed

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Gas Turbine Application MIMO outer loop (contd)

• Performance Specifications 
• The rise time of closed loop transfer function
  for speed control (limiter) loop should lie
  between 0.7to 0.98 sec.
• The rise time of closed loop transfer function
  for variable geometry loop should lie between
  0.24 to 0.4 sec.
•  The stability margins for both the loops are 6
  dB gain margin and 45 degrees phase margin.
• The cross coupling effects are t12/t22 0.1,
• t21/t11 0.1

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Gas Turbine Application MIMO outer loop (contd)

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Results MIMO outer loop
Loopshaping of outer fuel flow loop
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Results MIMO outer loop (contd)
Loopshaping of outer variable geometry loop
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Results MIMO outer loop (contd) Fuel Flow
LoopInput variable 1 Fuel flow, Output
variable 1LPC speedVariable Geometry
LoopInput variable 2 Variable geometry, Output
variable 2HPC speed
Outer fuel flow loop Controller g11(s) and
prefilter f11(s)
Outer variable geometry loop Controller g22(s)
and prefilter f22(s)
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Results MIMO outer loop (contd)Fuel Flow
LoopInput variable 1 Fuel flow, Output
variable 1LPC speedVariable Geometry
LoopInput variable 2 Variable geometry, Output
variable 2HPC speed
Closed Loop Step Responses of outer fuel flow
loop and outer variable geometry loop
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Results SISO outer loop
Loopshaping of outer nozzle area loop for SISO
system
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Results SISO outer loop (contd)
Loopshaping of outer variable geometry loop for
SISO system
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Results SISO outer loop (contd)
Outer fuel flow loop Controller g11s(s) and
prefilter f11s(s)
Outer variable geometry loop Controller g22s(s)
and prefilter f22s(s)
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Results (contd) Fuel Flow LoopInput variable
1 Fuel flow, Output variable 1LPC
speedVariable Geometry LoopInput variable 2
Variable geometry, Output variable 2HPC speed
Comparision of SISO and MIMO system
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Results (contd)
Interaction of variables for SISO and MIMO system
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Gas Turbine Application Inner Loop
The plant set for inner fuel flow loop Input
Variable Fuel flow demand, Output variable
Nhdot
The plant set for inner nozzle area loop Input
Variable NA demand, Output variable NA blade
angle
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Gas Turbine Application Inner Loop

• Performance Specifications 
• The rise time of closed loop transfer function
  for inner speed control loop should lie between
  0.26 to 0.38 sec.
• The rise time of closed loop transfer function
  for inner nozzle area loop should lie between 0.1
  to 0.2 sec.
•  The stability margins for both the loops are 6
  dB gain margin and 45 degrees phase margin.

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Results Inner loop
Loopshaping of inner fuel flow loop
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Results Inner Loop (contd)
Loopshaping of inner nozzle area loop
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Results Inner Loop (contd)
Inner fuel flow loop Controller g1(s)and
prefilter f1(s)
Inner nozzle area loop Controller g2(s)and
prefilter f2(s)
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Results Inner Loop (contd)
Closed loop validation of inner fuel flow loop
for step change in fuel flow
Closed loop validation of inner nozzle area loop
for step change in NA demand
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Gas Turbine Application MIMO Outer LoopFuel
Flow LoopInput variable 1 Fuel flow, Output
variable 1LPC speedNozzle area LoopInput
variable 2 Nozzle area, Output variable
2Temperature
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Gas Turbine ApplicationMIMO outer loop (contd)

• Performance Specifications 
• The rise time of closed loop transfer function
  for outer speed control loop should lie between
  0.7to 0.98 sec.
• The rise time of closed loop transfer function
  for outer nozzle area loop should lie between 0.3
  to 0.5 sec.
•  The stability margins for both the loops are 6
  dB gain margin and 45 degrees phase margin.
• The cross coupling effects are t12/t22 0.1,
• t21/t11 0.1

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Gas Turbine Application MIMO outer loop (contd)

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Results MIMO outer loop
Loop-shaping of outer fuel flow loop for MIMO
system
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Results MIMO outer loop (contd)
Loop-shaping of outer nozzle area loop for MIMO
system
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Results (contd)Fuel Flow LoopInput variable
1 Fuel flow, Output variable 1LPC speedNozzle
area LoopInput variable 2 Nozzle area, Output
variable 2Temperature
Outer fuel flow loop Controller g11(s) and
prefilter f11(s)
Outer nozzle area loop Controller g22(s) and
prefilter f22(s)
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Results (contd) Fuel Flow LoopInput
variable 1 Fuel flow, Output variable 1LPC
speedNozzle area LoopInput variable 2 Nozzle
area, Output variable 2Temperature
Closed Loop Step Responses
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Results SISO outer Loop
Loop-shaping of outer fuel flow loop for SISO
system
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Results SISO outer loop (contd)
Loop-shaping of outer nozzle area loop for SISO
system
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Results SISO outer loop (contd)
Outer fuel flow loop Controller g11s(s) and
prefilter f11s(s)
Outer nozzle area loop Controller g22s(s) and
prefilter f22s(s)
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Results (contd) Fuel Flow LoopInput variable
1 Fuel flow, Output variable 1LPC speedNozzle
area LoopInput variable 2 Nozzle area, Output
variable 2Temperature
Comparision of SISO and MIMO system
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Results (contd)
Interaction of variables for SISO and MIMO system
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Conclusion

• The method is successfully applied to the gas
  turbine application.
• The closed loop responses of multivariable
  system are within the specified upper and lower
  bounds.
• The interaction of variables is within specified
  limits.

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Future Scope of work

• Design of 2 x 2 MIMO control system with
  different input-output pairing.
• Design of 3 x 3 MIMO control system considering
  additional control variable of afterburner fuel
  flow.

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• Thank You