Model Predictive Diesel Engine Control - LIRMM
Transcript of Model Predictive Diesel Engine Control - LIRMM
EECI19 M22: MPC for Diesel Engines
Components:
1. Compressor
2. Variable Geometry Turbine (VGT)
3. EGR Throttle
4. EGR Valve
5. Intake Manifold
6. Exhaust Manifold
7. Pre-Throttle Volume
8. Pre-Intercooler Volume
9. Combustion
10. EGR cooler
11. Intercooler
Diesel engine schematics
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High speed diesel engine
EECI19 M22: MPC for Diesel Engines
Diesel air path control
Tracking objectives:
โข Control intake manifold pressure and EGR rate (= EGR valve flow
/ Cylinder Flow) to specified set-points
โข Engine speed and fuel flow are measured disturbances
โข Fast response desired to reduce turbo-lag
Constraints:
โข Input constraints: EGR valve, EGR throttle, and VGT lift have limited
ranges
โข Output constraints are imposed on intake manifold pressure
overshoot, exhaust manifold pressure overshoot, turbocharger
speed, EGR rate, etc.
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EECI19 M22: MPC for Diesel Engines
Low complexity explicit LQ-MPC
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โข Nonlinear inversion to make plant to which MPC is applied โmore linearโ
โข Rate-based model at a single linearization point
โข Intermittent tightened constraint enforcement
โข Constraint re-modeling (e.g., constraint on turbocharger speed is remodeled as a constraint on intake manifold pressure)
โข Special MPC formulation:
โข Control horizon = 1
โข Prediction horizon = 1
โข LQ-based terminal cost
โข Longer constraint horizon, with intermittent enforcement
โข Low complexity gain scheduling
EECI19 M22: MPC for Diesel Engines
Combined EGR valve โ EGR throttle actuator
โข Two actuators are โgangedโ together to deliver EGR flow
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EECI19 M22: MPC for Diesel Engines
โข Define state and control increments and an augmented state:
โข The rate-based model has the following form,
ฮ๐ข๐ = ๐ข๐ โ ๐ข๐โ1ฮ๐ฅ๐ = ๐ฅ๐ โ ๐ฅ๐โ1๐๐ = ๐ฆ๐โ1 โ ๐๐โ1๐๐ = ฮ๐ฅ๐ ๐๐
๐ .
๐๐+1 = าง๐ด๐๐ + เดค๐ตฮ๐ข๐๐๐ = าง๐ถ๐๐
าง๐ด =๐ด 0๐ถ ๐ผ
, เดค๐ต =๐ต๐ท
, าง๐ถ = 0 ๐ผ .
Rate-based model
(assumes ๐๐ = ๐๐๐๐ ๐ก)
EECI19 M22: MPC for Diesel Engines
The MPC optimization problem then becomes,
min ๐๐๐๐๐๐ +
๐=1
๐โ1
๐๐๐๐๐๐ + ฮ๐ข๐
๐๐ ฮ๐ข๐
subject to:๐๐+1 = าง๐ด๐๐ + เดค๐ตฮ๐ข๐
๐๐ = าง๐ถ๐๐๐ข๐ = ๐ข๐โ1 + ฮ๐ข๐
๐๐ + ๐ โ ๐๐ ,๐ข๐ โ ๐๐ .
Rate-based MPC (contโd)
EECI19 M22: MPC for Diesel Engines
Linear model through system identification
โข A local 7th order linear model was obtained through system identification
โข Nominal operating condition chosen as 1600 rpm engine speed and 30 mm3/stroke fuel rate. Engine operates between 800 and 4000 rpm and 0 and 60 mm3/stroke
โข Model order reduction applied to obtain a 4th order linear model
๐ฅ๐+1 = ๐ด๐ฅ๐ + ๐ต๐ข๐,
๐ฆ๐ = ๐ถ๐ฅ๐ + ๐ท๐ข๐ .
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EECI19 M22: MPC for Diesel Engines
Computational complexity
Table: Comparison of MPC strategies. ๐๐ง denotes the number of zonespartitioning the engine operating range, ๐๐ฆ denotes the number of outputconstraints considered, ๐๐ denotes the number of constraints in the MPCoptimization problem (inputs and outputs with intermittent constraintenforcement), ฯ๐๐ is the total number of regions in the explicit solution, ROMand Time are estimated memory and computation time usage for explicitMPC on a ~150 MHz processor. The sampling/update period is 32 ms.
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EECI19 M22: MPC for Diesel Engines
minz
๐ฝ ๐ง, ๐ =
๐=0
๐
๐(๐ฅ๐ , ๐ข๐ , ๐ข๐โ1, ๐ , ๐)
๐ . ๐ก ๐ฅ๐+1 = ๐ ๐ฅ๐ , ๐ข๐ , ๐, ฮ๐๐ , ๐ = 0, โฆ ๐ โ 1,๐ ๐ฅ๐ , ๐ข๐ , ๐ โ ๐๐(๐, ๐ค๐) โค ๐ , ๐ = 0,โฆ๐ โ 1 ,
0 โค ๐๐๐ก๐๐
โค าง๐(๐), ๐ = 0โฆ๐ โ 1,
0 โค ๐๐ โค ๐๐ก๐๐ ๐ , ๐ = 0โฆ๐ โ 1,๐ โฅ 0
where
๐ = ๐พ ๐๐๐ก๐๐
โ าง๐ ๐2+ ๐ข๐ โ ๐ข๐โ1 ๐
2 + ๐ผ ๐๐ก๐๐ โ ๐๐ + ๐ฝ๐
Fuel trackingDampingEGR tracking
๐ง = ๐ข0๐ ๐ฅ1
๐ โฆ ๐ข๐โ1๐ ๐ฅ๐
๐ ๐
FAR slack penalty
Dynamics
Softened FAR constraint
EGR rate constraint
Fuel bounds
๐๐๐,๐๐ก๐๐
= าง๐๐๐(๐๐)
๐ข =๐๐ก๐๐
๐
๐ฅ = ๐๐๐ ๐๐๐ฅ ๐ค๐ ๐น1 ๐น2๐
MPC formulation
eMPC as an outer loop supervisor
Performance outputs:
๐ฆ๐ ๐ก =๐๐๐๐ฅ๐
Measured outputs:
๐ฆ๐ ๐ก =๐๐๐๐ค๐
Targets for inner loop:
๐ ๐ก =๐๐๐๐ก๐๐
๐๐ก๐๐
Actuators:
๐ค ๐ก =
๐ข๐กโ๐๐ข๐ฃ๐๐๐ข๐ฃ๐๐ก
๐ = ๐ธ๐บ๐ ๐ ๐๐ก๐ =๐ธ๐บ๐ ๐๐๐๐ค
๐ถ๐ฆ๐๐๐๐๐๐ ๐๐๐๐ค=๐ค๐๐๐
๐ค๐๐ฆ๐
๐ =๐ก๐๐๐๐ข๐ โ ๐๐๐๐๐๐ ๐ ๐๐๐๐
๐๐ข๐๐ ๐๐๐๐ค โ ๐๐๐ค๐๐ โ๐๐๐ก๐๐๐ ๐ฃ๐๐๐ข๐=
๐๐๐๐ค๐๐๐ฟ๐ป๐
๐ =๐๐ข๐๐ ๐๐๐๐ค
๐๐๐ ๐๐๐๐คโ
๐ด
๐น๐ ๐ก๐๐๐โ
=๐ค๐
๐ค๐
๐ด
๐น๐ ๐ก๐๐๐โ
๐๐ = ๐๐๐ฅ ๐๐๐๐๐๐๐ก๐๐๐ก๐๐๐๐๐๐ = ๐๐๐ก๐๐๐ ๐๐๐๐๐๐๐๐ ๐๐๐๐ ๐ ๐ข๐๐
Exogenous inputs:
๐ ๐ก =๐๐ก๐๐
๐๐Fuel per stroke:
๐(๐ก)eMPC control:
๐ข ๐ก =๐๐
EECI19 M22: MPC for Diesel Engines
eMPC Formulation
minz
๐ฝ ๐ง, ๐ =
๐=0
๐
๐(๐ฅ๐ , ๐ข๐ , ๐ข๐โ1, ๐)
๐ . ๐ก ๐ฅ๐+1 = ๐ ๐ฅ๐ , ๐ข๐ , ๐, ฮ๐๐ , ๐ = 0, โฆ ๐ โ 1,
๐ ๐ฅ๐ , ๐ข๐ , ๐ โค ๐lim ๐ , ๐ = 0,โฆ๐ โ 1 ,
ln(๐๐(๐ฅ๐ , ๐ข๐ , ๐)) โค ln(๐๐lim(๐)), ๐ = 0,โฆ๐ โ 1,
๐โ ๐ โค ๐๐ โค ๐+ ๐ , ๐ = 0โฆ๐ โ 1,๐โ ๐ โค ๐๐ โค ๐๐ก๐๐ ๐ , ๐ = 0โฆ๐ โ 1,
where
๐ = โ๐ฝ๐ ๐ฅ๐ , ๐ +ฮ๐ข๐ฮ๐๐ ๐
2
+ ๐ผ ๐๐ก๐๐ โ ๐๐
Dynamics
Emissions constraints
Target constraints
Fuel bounds
Fuel trackingDamping
Efficiency
๐ง = ๐ข0๐ ๐ฅ1
๐ โฆ ๐ข๐โ1๐ ๐ฅ๐
๐ ๐๐ข =
๐๐๐๐ก๐๐
๐๐ก๐๐
๐
๐ =๐๐๐๐ก๐๐
๐๐ก๐๐
EECI19 M22: MPC for Diesel Engines
๐ = 0 ๐ = 1 ๐ = 2 ๐ = 3 ๐ = 4 ๐ = 5
Non uniform horizon discretization
EECI19 M22: MPC for Diesel Engines
Numerical solution
โ Linearize dynamics and non-convex
constraints about the current measured state
and form the single-shooting OCP
โ Form quadratic programming sub-problem
about the solution at the previous time step
โ Solve QP and apply the resulting control to
the system
minฮ๐ง
1
2ฮ๐ง๐๐ป ฮ๐ง + ๐๐ฮ๐ง
๐ . ๐ก. ๐ดฮ๐ง โค ๐
๐ป = ๐ป๐ง2๐น ๐ง๐โ1, ๐๐ , ๐ = ๐ป๐ง๐น ๐ง๐โ1, ๐๐ ,
๐ด = ๐ป๐ง๐ ๐ง๐โ1, ๐๐ , ๐ = โ๐(๐ง๐โ1, ๐๐)
min๐ง
๐น(๐ง, ๐๐)
๐ . ๐ก. ๐ ๐ง, ๐๐ โค 0
๐ง๐ = ฮ๐ง + ๐ง๐โ1๐ข๐ = ๐ง 1: 3
1
2
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EECI19 M22: MPC for Diesel Engines
Simulation results
โข eMPC is stable over NEDC and WLTC cycles
โข Emissions are reduced compared to the benchmark during hard transients โ
WLTC
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EECI19 M22: MPC for Diesel Engines
Simulation results (contโd)โข NOx constraint violations are penalized, leading to soft constraint
enforcement and reducing NOx over the cycles
โข Fuel-air-ratio constraint is not always satisfied due to conflict with the
drivability constraint โ
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EECI19 M22: MPC for Diesel Engines
ReferencesHuang, M., Zaseck, K., Butts, K., and Kolmanovsky, I.V., โRate-based Model Predictive Controller for
diesel engine air path: Design and experimental evaluation,โ IEEE Transactions on Control Systems
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EECI19 M22: MPC for Diesel Engines
References (contโd)
Huang, M., Nakada, H., Butts, K., Kolmanovsky, I.V., โRobust rate-based Model Predictive Control of
diesel engine air path,โ Proceedings of 2014 American Control Conference, Portland, Oregon, pp. 1505-
1510, 2014.
Huang, M., Nakada, H., Polavarapu, S., Butts, K.R., and Kolmanovsky, I.V., โRate-based Model Predictive
Control of diesel engines,โ Proceedings of the 7th IFAC Symposium on Advances in Automotive Control,
September 4-7, 2013, Tokyo, Japan, pp. 177-182.
Huang, M., Nakada, H., Polavarapu, S., Choroszucha, R., Butts, K.R., and Kolmanovsky, I.V., โTowards
combining nonlinear and predictive control of diesel engines,โ Proceedings of 2013 American Control
Conference, Washington DC, pp. 2852-2859.