Model-Based Control for Automotive Cold Start Applications

J. Karl Hedrick Carlos Zavala

Pannag Sanketi

Mechanical Engineering Dept., University of California, Berkeley

2007 CHESS Winter Meeting

Coldstart Challenges

Low emission

- Suppressing emissions, especially HC

High quality

- Driveability : noise & vibration

- Robustness against environmental 　　 condition and disturbance

Less cost

- Calibration effort

- Design process, especially verification

- Computational load

- Sensors

0 25 50 75 1000

100

Spe

ed[k

m/h

]

Cum

ula

tive

HC

am

ount

Time[sec]

HC

Speed

Regulation limit

Coldstart in IC Engines-The problem

• The catalyst is not active below temperatures of around 300C- 400C

• Cold Combustion Chambers and poor vaporization in intake manifold

• Oxygen Sensor not active at cold temperatures

…more than 90% of Hydrocarbon (HC) emissions is produced during the Coldstart Cycle

Model Based Approach to Emissions Reduction during

Coldstart

• Utilizes formal description of the engine to derive efficient ways of control. – Physical Models. Intuitive representation.– Black box models. Non-physical parameters.– Gray models. Combination of the two above

• Motivation - improved control - efficient generation of software - software reusability

Model Based Strategy

ImplementationAnd

Testing

Engine Model Catalyst Model

Model Validation

Controller Design

Next designiteration

Control Oriented Modeling

• Simplicity in models is important

dx/dt= f(x,u)

Lumped Parameter Model (preferably low order ODE)Complex nonlinear system

Engine Subsystems

• Manifold Dynamics • Fuel Dynamics • Catalytic Converter

• Torque Gen• Raw HC• Exh Temp

Engine Subsystems Modeling

For control of air-fuel ratio, idle speed, models developed ~1980

• Combustion torque generation• Rotational dynamics and time delays• Actuator and sensor dynamics

• Air and fuel dynamics• Catalytic converter dynamics• Engine thermal dynamics

General Purpose Engine Modeling

Cold Start Engine Modeling

Fuel Dynamics Model

• Poor vaporization when air intake is cold

Puddle

AFR Estimation

using Fuel Dynamics

Use of fuel-dynamics model to predict AFR.

“Fuel Dynamics Model For Engine Coldstart”, Zavala, et.al, IMECE2006-15203, Nov. 2006

Catalytic Converter Model*

conversionefficiency map

cat. substratethermal

dynamics

O2 storagedynamics

internal convection:

* [Brandt, Wang, Grizzle, 1997]

external convection:

Qin=hinAin(Texh - Tcat )

Qout=houtAout(Tcat - Tamb )

Important Elements in a Catalyst Model

Heat transfer coefficients of the catalyst

Important Elements in a Catalyst Model

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

350

T cat (

C)

Time (s)

Typical Experimental Catalyst Temperature Profile

Plateau in the Tcat profile

–Due to evaporation of moisture

–Starting point can be detected (~470 C)

–For finding the end of plateau, various methods – adaptation, offline calculation of evaporation heat*

*[Sanketi, Zavala, Hedrick et al., AVEC ’06]

Experimental plots of Catalyst

Raw HC and Texh Modeling

• Simple, intuitive models

– Suitable for controller design

• Inputs chosen based on physics and experimental data

– AFR, Spark directly affect combustion

– Changes in RPM affect the combustion quality

• Sum of first order linear systems

– such behavior observed in exp

• Saturations, offsets on inputs exist

• Use of Least Squares to find parameters

Texh Modeling

Raw HC Modeling

Control Design

– Performance requirements

– Uncertainty

– Nonlinearities

– Actuator bandwidth

– Sensor noise

– Disturbances

Plant?yu

Once the plant is defined, the synthesis of a controller should considered :

Throttle angle

Lab Engine Interface

Texh sensor

AFR sensor

HC Analyzer

Tcat sensor

Catalyst model

Engine out HC estimation

Catalyst temperature estimation

Tailpipe HC estimation

Amount of Fuel

Spark Timing

AIR AIR

Variable Valve Timing

In cylinder pressure measurement

HC formation model

Air induction dynamics

Fuel induction dynamics

Thermal model

Two control approaches: mean value-hybrid

Plantmodel

ControlObjectives

ControllerDesign

Controller

Plantmodel

ControlObjectives

Hybrid ControllerDesign

Controller 1 … Controller n

Controller i

Controller kController j

…

Mean Value Hybrid

ControllerOperation Operation

Design Design

Mean Value MIMO Controller

Trying out different profiles

• Different HC desired and Tcat profiles

Desired Profiles

Model-Based Integration of Embedded Systems

• analysis of complex embedded systems

• software assurance through modeling in all phases of software development process

• Handling hybrid system analysis• Software timing analysis

The complexity of automotive systems demands the use of more sophisticated tools for control software verification:

Why hybrid models?

• Advantages

– It accounts for continuous dynamics and discrete events.

– It offers a more detailed description compared to mean-value models.

• Disadvantages

– No analytic solutions for stability analysis

– More complicated than mean-value models.

– Analysis tools still in development

Engine Model

• Mean Value models of Intake air flow and manifold air mass. (continuous dynamics).

• Air and fuel flowing into cylinder calculated for each combustion cycle.(Discrete quantities).

• Strokes of engine considered as discrete events using finite state machines (FSM:hybrid) .

• Torque and pollutants modeled for each combustion cycle. (continuous functions based on events: hybrid).

Controller Verification of Hybrid Systems

• Question of stability and evolution of the states

• Model simulations cannot cover all possible trajectories inside a set

• Reachability analysis

– Tells you how your state space will behave with time starting given a set of initial conditions and bounds on inputs

– Very useful in verifying the controller performance

Example Hybrid Controller

• Cumulative tailpipe HC function of both raw HC and catalyst efficiency

• Trade off exists between the two objectives

• A high level hybrid controller to exploit the trade-off

Control Hierarchy

The low level Texh and AFR controllers use spark timing and fuel injection rate as the inputs respectively

The Tcat and HC dynamic surface controllers use Texh and AFR respectively

The hybrid controller switches between the Tcat and HC dynamic surface controllers

Hybrid Controller Modes

Helps fast catalyst light-off

Helps keep the raw emissions low

Reachable sets

Test: starting from a safe set, remain in the set.

Set of Initial states

Forward Reachable Set

TargetSet

Backwards Reachable Set

Test: starting from an unsafe set, never touch the set of initial conditions

Backwards reachable set calculation

is the set of states for which, for all control actions, there exists a disturbance action which can drive the system to in at most

Say, the control u wants to keep the system away from target set of states whereas the disturbance d tries to drive the system to the target set G(0).

Now how to compute this set?

Turns out that it can be computed by solving a HJI PDERef. Tomlin et.al

TargetSet G(0)

Backwards Reachable Set G(t)

Reachability Analysis of Coldstart Controller*

Backwards Reachability

*[Sanketi, Zavala, Hedrick]- IJC, 2006

Conclusions

• Hybrid modeling helped to achieve a more detailed description of engine operation

• Hybrid control gave the chance to explore the tradeoff of hydrocarbon emissions level and catalyst light-off.

• Hybrid modeling is a useful tool for coldstart analysis.

Future of coldstart control

• Fewer experiments for model validation. • Closed-Loop control design• Easy adaptation to new engines.• Automated code generation. • Automated software validation and

verification.• Use of AFR and HC production sensors and/or

model based observers.