2. 16 points] Now consider a different system, +10x=u, where u is a control input that...

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2. 16 points] Now consider a different system, +10x=u, where u is a "control input" that we can choose to make a behave the way we want. (a) What u would you choose so that r eventually ends up at 10? (That is, limo r(t) = 10). (b) Will it tend towards this limiting value of 10 for every initial condition r(0)? Why? Would you call this stable or unstable behaviour? (c) Give a rough sketch of the solution with your choice of u (held constant) and initial condition 0. Show any working you need. 1(0) = 2. 16 points] Now consider a different system, +10x=u, where u is a "control input" that we can choose to make a behave the way we want. (a) What u would you choose so that r eventually ends up at 10? (That is, limo r(t) = 10). (b) Will it tend towards this limiting value of 10 for every initial condition r(0)? Why? Would you call this stable or unstable behaviour? (c) Give a rough sketch of the solution with your choice of u (held constant) and initial condition 0. Show any working you need. 1(0) =