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.
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