Ijlal Haider, Habib-ur-Rehman Khalid, Umair Shafiq

An Initial Study of PID and Fuzzy PID Controller
Design for Non-Linear SI Engine Speed
and AFR Control
Performance Analysis Using MATLAB/Simulink
Ijlal Haider, Habib-ur-Rehman Khalid, Umair Shafiq Khan
Abstract
Introduction
This paper estimates the performance
of a Conventional PID versus Fuzzy
Logic based PID for the process of
controlling Non-Linear SI-Engine
Speed and AFR (Air to Fuel Ratio).
Dynamic SI Engine Model regarding
Speed and AFR is discussed, and
Fuzzy Logic PID control is shown to
have better performance over
Conventional PID control algorithm.
Design and Simulation Results are
shown using MATLAB/Simulink.
In this paper, a rule-base scheme for
gain-scheduling of PID controllers (Fuzzy
Logic PID) is implemented in conjunction
with fixed PID scheme, to control NonLinear Engine Speed and AFR model..
Engine Model
Constants and variables used in
the Modeling Process
Engine Model consists of three main
parts.
1). Intake manifold
Intake manifold dynamics are
described
using
equation
of
continuity for fluid flow.
ma = ma i − ma o
(1)
ma = MAX.TC.PRI − c1 .ƞv .ωe .ma (2)
2). Torque Production
Power and torque production
dynamics are described by differential
equation based on mechanics of
rotational motion.
T ind −TL =Je .ωe
cT .ma o .AFI.SI TL
ωe =
−
Je .ωe
Je
cT .c1 .ƞv .ma .AFI.SI TL
ωe =
−
Je
Je
3
(4)
(5)
3). Fuel injection
In Fuel injection dynamics port wall
wetting
phenomenon
is
also
modeled.
τ =0.05 + 2.25 ωe
mfi = 1 τ . mfc − mfi
6
ƞv
Je
cT
TL
AFI
SI
mf c
Volumetric efficiency
Engine Rotational inertia (kg 𝑚2 )
Torque constant (Nm/kg)
Load Torque (Nm)
Air to Fuel Ratio influence
Spark Ignition Influence
Mass flow of fuel at injector (kg/s)
mf i Mass flow of fuel into the cylinder (kg/s)
𝛽 Required Air to fuel Ratio
Fuzzy Membership Functions
For 𝑒 𝑡 and 𝑒(𝑡)
Simulation Method
Simulation was run for 30(sec) in
MATLAB/Simulink, with Fixed Step
size of 0.01(sec) and ode144
(extrapolation) solver. For Speed
controller performance test, speed
profile of 2 Hz sinusoidal of bias 900
(RPM) with amplitude of 100 was
chosen.
Simulation Results and
Conclusion
For comparison purposes Integral of
Absolute Magnitude of the Error
(IAE) for speed and standard
deviation of AFR from stoichiometric
ratio, 14.7, is computed.
2.50E+04
0.35
0.3
2.00E+04
0.25
1.50E+04
0.2
1.00E+04
0.15
0.1
5.00E+03
For 𝐾𝑝 and 𝐾𝑑
(7)
0.05
0.00E+00
0
PID for Speed Fuzzy PID for Fuzzy PID for
+ PI for AFR Speed + PI for Speed + Fuzzy
AFR
PI for AFR
Speed Controller's IAE
Oxygen sensor Model
Also known as 𝑂2 sensor is the only
feed- back used for controlling AFR.
y = sign mai − β. mfi
mai Air Flow into the manifold(kg/s)
mao Air Flow out of the manifold(kg/s)
MAX Maximum Air Flow in the intake manifold
(kg/s)
TC Throttle Characteristics, ranges from [0, 1],
Function of throttle plate angle.
PRI Pressure Ratio Influence
𝑐1 Engine constant, function of manifold and
cylinder volume
Cutaway View of Engine with
States
(8)
For 𝛼
AFR Controller's σ 14.7
Hence above results show that Fuzzy
PID and Fuzzy PI for Speed and AFR
Control respectively, gives optimum
results.