let 0 = 0(t) [C] be the temperature of a graphics processing unit (GPU), a component of a computer. the computations performed by the GPU generate heat at a rate q=q(t) [J/s]. to prevent the temperature of the GPU from rising enough to damage its components, a fan is used to blow air, which is at temperature on = 0.(t) [C], across the GPU at a constant speed. owing to heat transfer from the (hotter) GPU to the (colder) air, the air cools the GPU. OK cool air 9315 fan GPU Figure 1: GPU cooling. two inputs: (1) the temperature of the air, 6.(t), and (2) the heat generated by the computations, q(t). both inputs affect one output: the tem- perature of the GPU, 0(t). a dynamic model for the output (t) in response to the two inputs q(t) and 0.(t) is: (1) de CE = 9(t) + UA[0.(t) (t)] dt here, C, U, and A are [constant] parameters. define deviation variables: . 0*(t) := 0,(t)- q*(t) := 9(t)-9 e*(t) := e(t)-7, with 7, 7., and q nominal steady state values of e(t), 0(t), and q(t), respectively. 4. (2 points) sketch the block diagram for this process (where two inputs affect a single output). write G,(s) and Ge(s) in the blocks and label the inputs and out- puts with o(s), Q*(s), and O*(s) (the Laplace transforms of the inputs and out- puts in deviation in form). 5. suppose a gamer starts playing Starcraft and, as a result, g(t) increases by Aq and stays there (a step input). i.e., q(t) 9 t 0. (2) (a) (1 point) (only one input "on") if the air temperature , remains unchanged at , what will be the new steady state value of the temperature of the GPU? i.e., write an expression for: lim 0(t). (b) (2 points) (both inputs "on") now, we wish to counteract the effect of the step increase in qon the GPU temperature by (also, deliberately) changing the air temperature e, by Ab,: . t0. write an expression for the A, that achieves the outcome that the steady state GPU temperature does not change in response to the step input in q(t). i.e., find Ae, so that: lim 0(t) = 0. t-00