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3. Use the fourier series in the previous problem as the input to the undamped spring-mass model у+w2y = f(t) and assume that wメnn/L for any n. Find ONLY the particular solution yp(t). Plot the transfer function -you will notice that this is a bandpass amplifier. 2. Assume that our function above is used to open-loop heat a pot of coffee sitting on a coffee maker burner (open-loop means that no attempt is made to hold the coffee at a desired temperature - you just hardwire the numbers and live with the results - this is the situation with cheap coffee makers The coffee pot temperature satisfies dT/dt + kT- kToo(t) where the ambient temperature is a model for the external heat inputted to the coffee pot. Let's use Too (t) as Tif(t) where we use the f(t) we just found. This is a pulse-width modulation (PWM) way of holding temperature to a desired value - it is a cheap and easy solution to implement. Find ONLY the steady-state temperature Tp(t) under the assumption that the homogeneous solution has little impact on the coffee temperature given it was just made and the burner was on during that process Use the supplied Matlab code for the remainder of this problem. (Note you can check your answers above by referring to the Matlab code if you wish) Assume that Ti- 75°C, k-1/5 1/min. In our duty cycle the ambient tem- perature turns on/off twice during -L to L. First fix L and choose a to give a average desired temperature 60°C. Now vary L until the maximum variation of the coffee temperature from 60oC appears to be less than 5°C Now you have designed an open-loop coffee-maker PWM burner. Not bad!

Answer 1

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