Question

Find the fourier series for the 2L-periodic function f(t)-I,-L-t and f(t) -1,0sts as L a-L-0 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 kT(t) where the ambient temperature is a model for the external heat inputted to the coffee pot. Let's use T. (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 T1 = 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 average desired temperature 60°C. Now vary L until the maximum variation the coffee temperature from 60°C appears to be less than 5°C Now you have designed an open-loop coffee-maker PWM burner. Not bad Use the fourier series in the previous problem as the input to the undamped spring-mass model y + w217 #: ,f(t) and assume that w /L for any n. Find ONLY that this is a bandpass amplifier the particular solution y,(). Plot the transfer function you will notice

There are three questions all linked to one another (thus three parts to a problem) pictured. I am struggling with Fourier Series and how to evaluate them, help solving the problem is greatly appreciated.

Answer 1

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