Suppose that for the open loop toaster control you sketched in exercise 5, the variable that you really want to control is d (for darkness), where d is the energy absorbed by the toast, in units of joules. Assume the initial energy of the toast (in units of joules) is d = 0, and d_t+1 = dt + K × P × t, where P is the power in watts delivered by the heating coil at time t and K is the proportional gain relating d to P. (a) Fill in the toast block to correspond to this model. (b) If the line voltage is 115 V and the heater resistor is 13.2 ohms, and the darkness gain is 2.5, plot d in joules for 10. s.

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Current, A Power, W Color, J Plug, V +'p = L+"p 2.5. x P x t | = G x VIR P = 1?R Switch, G = 1 Heater Toast