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) = S t 0. (2) (a) (1 point) (only one input "on") if the air temperature 8, 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). t-00 = (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 0, by A,: s. t0. write an expression for the A8, 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 An, so that: lim e(t) = 7. 1-00 6. (4 points) now, suppose the air temperature is constant 0.(t) , Vt but the fan speed is variable, thereby changing the velocity v(t) [m/s] at which the air is blown across the GPU. 10 imput V mis cool air input 9 515 fan GPU output Figure 2: GPU cooling. two inputs: (1) the heat generated by the computations, 9(t), and (2) the velocity of the air blown across it, v(t), determined by the fan speed. both inputs affect one output: the temperature of the GPU, 0(t). a (nonlinear) dynamic model for the output 0(t) in response to the two inputs q(t) and v(t) accounts for the change in the heat transfer coefficient when v changes: C de dt = q(t) + (U6 + b[v(t)]?)A[0. 0(t)]. here, C, U., b, and A are [constant] parameters. let v, , and 7 be nominal steady state values of v(t), q(t), and e(t), respectively. write a linearized model about these nominal steady state values. your model should be written in terms of the deviation variables: v*(t) :=v(t) q* (t) := g(t) - *(t) == 0(t) 7