Model based control for automotive cold start applications
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J. Karl Hedrick Carlos Zavala Pannag Sanketi Mechanical Engineering Dept., University of California, Berkeley. Model-Based Control for Automotive Cold Start Applications. 2007 CHESS Winter Meeting. Regulation limit. HC. Cumulative HC amount. 100. Speed. Speed[km/h]. 0. 0. 25. 50.

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Model based control for automotive cold start applications

J. Karl Hedrick

Carlos Zavala

Pannag Sanketi

Mechanical Engineering Dept., University of California, Berkeley

Model-Based Control for Automotive Cold Start Applications

2007 CHESS Winter Meeting


Coldstart challenges

Regulation limit

HC

Cumulative HC

amount

100

Speed

Speed[km/h]

0

0

25

50

75

100

Time[sec]

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


Coldstart in ic engines the problem
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
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

Engine Model

Catalyst Model

Next design

iteration

Implementation

And

Testing

Model Validation

Controller Design

Model Based Strategy


Control oriented modeling
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
Engine Subsystems

  • Manifold Dynamics

  • Catalytic Converter

  • Fuel Dynamics

  • Torque Gen

  • Raw HC

  • Exh Temp


Engine subsystems modeling
Engine Subsystems Modeling

General Purpose Engine Modeling

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

  • Combustion torque generation

  • Rotational dynamics and time delays

  • Actuator and sensor dynamics

Cold Start Engine Modeling

  • Air and fuel dynamics

  • Catalytic converter dynamics

  • Engine thermal dynamics


Fuel dynamics model

Puddle

Fuel Dynamics Model

  • Poor vaporization when air intake is cold


Afr estimation using fuel dynamics
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
Catalytic Converter Model*

conversion

efficiency map

O2 storage

dynamics

cat. substrate

thermal

dynamics

Qin=hinAin(Texh -Tcat )

internal convection:

Qout=houtAout(Tcat -Tamb )

external convection:

* [Brandt, Wang, Grizzle, 1997]


Important elements in a catalyst model
Important Elements in a Catalyst Model

Heat transfer coefficients of the catalyst


Important elements in a catalyst model1

Typical Experimental Catalyst Temperature Profile

350

300

250

200

(C)

cat

T

150

100

50

0

0

10

20

30

40

50

60

70

80

90

100

Time (s)

Important Elements in a Catalyst Model

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]



Raw hc and t exh modeling
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


T exh modeling
Texh Modeling



Control design

y

u

?

Plant

Control Design

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

  • Performance requirements

  • Uncertainty

  • Nonlinearities

  • Actuator bandwidth

  • Sensor noise

  • Disturbances


Lab engine interface
Lab Engine Interface

Spark

Timing

Variable Valve

Timing

Throttle

angle

Amount

of Fuel

Sensors

Inputs

Texh sensor

AFR sensor

HC Analyzer

Tcat sensor

Catalyst model

AIR

AIR

Tailpipe HC estimation

Catalyst temperature estimation

Air induction dynamics

Performance

outputs

Engine out HC estimation

Fuel induction dynamics

Thermal model

HC formation model

In cylinder pressure measurement


Two control approaches mean value hybrid
Two control approaches: mean value-hybrid

MeanValue

Hybrid

Plant

model

Control

Objectives

Plant

model

Control

Objectives

Design

Hybrid Controller

Design

Design

Controller

Design

Controller 1

Controller n

Controller

Controller j

Controller k

Operation

Operation

Controller

Controller i



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

Model-Based Integration of Embedded Systems

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


Why hybrid models
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
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
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
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
Control Hierarchy

The hybrid controller switches between the Tcatand HC dynamic surface controllers

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

The Tcatand HC dynamic surface controllers use Texh and AFR respectively


Hybrid controller modes
Hybrid Controller Modes

Helps fast catalyst light-off

Helps keep the raw emissions low


Reachable sets
Reachable sets

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

Set of

Initial states

Target

Set

Backwards Reachable Set

Forward 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

Target

Set G(0)

Backwards

Reachable Set G(t)

Backwards reachable set calculation

Say, the controlu 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 PDE

Ref. Tomlin et.al


Reachability analysis of coldstart controller
Reachability Analysis of Coldstart Controller*

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

Backwards Reachability


Conclusions
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
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.


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