MAE142_L18_ControlReview.pdf - Control System Design Review...

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Control System Design Review Cooling Fan Dynamics Parameter ID Open-Loop Control Closed-Loop Control Proportional Control Proportional + Integral Control Model Uncertainty MAE 142
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2 MAE 142 Fan Speed Control Design a control system that allows the user to set a desired cooling fan speed. duty cycle yellow wire tachometer blue wire 12V supply red wire ground black wire 12V wall supply pin 3 pin 9 5V GND GND A0 10K ohm resistor potentiometer (user input) cooling fan
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3 MAE 142 Fan Speed Dynamics Motor electronics neglecting armature inductance: R a = armature resistance i a = armature current V a = armature voltage ω= motor/fan speed T m = motor torque T p = propeller torque J = motor + fan inertia K b = back EMF coefficient K t = motor torque coefficient K p = propeller torque coefficient R a i a + K b ω= V a T m = K t i a Mechanical components include the motor and propeller (fan): J d ω dt = T m T p T p = K p ω Combine motor and propeller into one differential equation: J d ω dt + [ K t K b R a + K p ] ω= K t R a V a
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4 MAE 142 Fan Speed Transfer Function Assume the average armature voltage is proportional to the duty cycle input to the fan motor controller: Define new terms to simplify the equations of motion: The system time constant (tau) and the steady-state gain (kappa) are:
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