Nonlinear Model-Based Multivariable Control for Air & Charging System of Diesel Engine with Short and Long Route EGR Valves
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Abstract
The objective of this study is to investigate a nonlinear model-based multivariable (MIMO, Multi Input Multi Output) technique to decouple actuators interaction and to reduce the calibration effort, while increasing control performances, above all in transient conditions, and robustness with respect to model uncertainties and system parameter variations. The presented control technique is based on the development of a nonlinear dynamical physical model of the diesel air and charging system. Feedback Linearization control is then applied to decouple actuators’ interactions and compensate for nonlinearities. A new set of virtual inputs are defined inverting the system differential equations. Relation among the new virtual inputs and the outputs is purely linear and decoupled, meaning that each virtual input affects linearly only one output. Moreover, a linear control block is added to guarantee transient and steady state performances and closed loop robustness. The proposed control approach has been validated through small diesel engine dyno and vehicle activities. Transient test bench maneuvers show that the control is able to coordinate the actuators in order to fulfill the targets and to guarantee similar performances in different operating points. In addition the robustness to environmental changes has been demonstrated by vehicle tests at different ambient conditions.
Key words
Model-based Control Multivariable Air charge Feedback linearizationNomenclature
- βt
turbine pressure ratio (downstream/upstream) (-)
- βc
compressor pressure ratio (downstream/upstream) (-)
- uitv
intake throttle valve position (%)
- uegr_HP
high pressure EGR valve position (%)
- uegr_LP
low pressure EGR valve position (%)
- uvgt
turbine VGT position (%)
- pi
intake manifold pressure (kPa)
- px
exhaust manifold pressure (upstream turbine) (kPa)
- pc_us
upstream compressor pressure (kPa)
- pt_ds
downstream turbine pressure (kPa)
- pexh
downstream after-treatment pressure (kPa)
- pitv_us
upstream throttle pressure (kPa)
- Fi
residual gas fraction at intake manifold (%)
- Fx
residual gas fraction at exhaust manifold (%)
- Fc
compressor upstream residual gas fraction (%)
- Fe
residual gas fraction at engine outlet (%)
- Wegr_HP
high pressure EGR mass flow rate (g/s)
- Witv
throttle valve mass flow rate (g/s)
- Wegr_LP
low pressure EGR mass flow rate (g/s)
- Wc
compressor flow rate (g/s)
- Wair
air mass flow rate (g/s)
- Wf
fuel mass flow rate (g/s)
- Wt
turbine mass flow rate (g/s)
- We_in
engine-in mass flow rate (g/s)
- Wexh
mass flow rate that goes out the engine (g/s)
- Ne
engine speed (rpm)
- Nt
turbine speed (rpm)
- Pt
turbine power (W)
- Pt
compressor power (W)
- Ti
intake manifold temperature (K)
- Tx
exhaust manifold temperature (K)
- Tegr_LP
low pressure EGR gas temperature (K)
- Tc_us
upstream compressor gas temperature (K)
- Titv_us
upstream throttle gas temperature (K)
- Tt_ds
downstream turbine gas temperature (K)
- Vi
intake manifold volume (mm3)
- Vx
exhaust manifold volume (mm3)
- Vc_us
upstream compressor volume (mm3)
- Vt_us
downstream turbine volume (mm3)
- γ
ratio of specific heats (-)
- R
universal gas constant (m2/(K s2))
- cp
specific heat capacity at constant pressure (J/K)
- ηvo
volumetric efficiency (-)
- ηt
turbine efficiency (-)
- ηc
compressor efficiency (-)
- (A/F)s
stoichiometric air fuel ratio (-)
Subscripts
- EGR
exhaust gas recirculation
- VGT
variable geometry turbine
- ITV
Intake throttle valve
- LP
low pressure
- HP
high pressure
- ECU
engine control unit
- AT
after-treatment
- SISO
single input single output
- MIMO
multi input multi output
- PID
proportional integral derivative
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References
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