Estimator Design For Engine Speed Limiter
Professor: Riadh Habash
TA: Wei Yang
Presented By:Beshir, AbebaBeshir, AbebaKharrat, AmineKharrat, AmineHu, ZhiyuanHu, ZhiyuanSun,YuSun,YuHe, NanHe, Nan
Contents
• References
• Background
• Project Objective
• Kalman Observer & Design
• Experiment & Results
• Conclusion
References
• Engine Speed Limiter for Watercrafts– Philippe Micheau, R. Oddo and G. Lecours, from IEEE Transaction on Control Systems Technology
VOL 14, NO 3, May 2006.
• Engine Speed Control– Peter Wellstead and Mark Readman, control systems principles.co.uk
• An Observer-Based Controller Design Method for Improving Air/Fuel characteristics of Spark Ignition Engines
– By Seibum B. Choi and J. Karl Hedrick, IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 6, NO. 3, MAY 1998
• http://www-ccs.ucsd.edu/matlab/toolbox/control/kalman.html?cmdname=kalman
• http://auto.howstuffworks.com/engine1.htm• http://www.cs.unc.edu/~welch/kalman/
– Kalman Filter Tutorial
Background
• 3 cases: watercraft propeller:
Partially loaded (partially
submerged)
Unloaded (completely emerged)
Fully loaded (completely submerged)
Project Objective
• Design observer to estimate state variables:– Load Torque (Tload)
– Engine Speed (N)
Observer (State Estimation)
PlantObserver
(state estimator)
u(t) y(t) xhat(t)
u(t) = Teng y(t) = N, Tload
(2 outputs)
Xhat(t) = Nhat, Tloadhat(2 state variables)
System Modeling
eDisturbancRandomW
TorqueLoadT
TorqueEngineT
SpeedEngineN
inertiaengineisII
CWhere
WTTdt
dNC
T
Load
eng
TLoadeng
:
:
.:
:
,60
2: 1
1
System Modeling (cont’d)
loadedfully
unloaded
loadingtherepresentswhere
NfT
lyrespectivecylinderainfueland
airofamountthearemandmmm
AFRRatioFuelAiriswhere
NgT
Load
fafa
eng
:1
:0
:
)(
.
,66.14/
)(:
),(
System Modeling (cont’d)
• To estimate TLoad.
noiseprocessisw
noisetmeasuremenisv
TuCNfk
CG
k
CB
k
CA
T
Nx
Where
tvtCxty
tGwtButAxdt
tdx
functionspacestateandFromdt
dNf
dt
dN
dN
df
dt
dTNfT
WTTdt
dNC
englin
linlinLoad
LoadLoad
TLoadeng
],10
01[],
)(
0/1[
],/1
[],0
/10[],[
:
)()()(
)()()()(
:),2()1(
)2()()(
)1(
max
1
11
1
Kalman Filter
• Estimates the state of a system for measurements containing random errors (noise).
• Relatively recent development in filtering (1960)
Kalman Filter (Cont’d)
Circles -- vectors,
Squares -- matrices
Stars -- Gaussian noise with the associated covariance matrix at the lower right.
Fk -- state transition modelBk -- control-input modelwk -- the process noise
Kalman Filter (Cont’d)
Predict(k) Update(k)
K+1
Kalman Filter phases:
Experiment & Results
Input Data (Teng)
Experiment & Results (Cont’d)
Output Data (N, TLoad)
Conclusion
• Kalman filter provides good estimate of state variables in presence of noise/disturbance.
• Advantages:– Can achieve virtually any filtering effect– Forecasting characteristics using Least-Square
model– Reduce “False alarms” (filter disturbances)– optimal multivariable filter
Conclusion (Cont’d)
• Examples of application:– aerospace;
– marine navigation;
– nuclear power plant instrumentation;
– demographic modeling;
– manufacturing, and many others.
• Limitations/ Future improvements:– Speed: filter speed is limited by the system architecture
– Cost
Questions ?