Question 3 Consider an adaptive control system plant, k is the adaptive control gain, t is time and

Question 3 Consider an adaptive control system plant, k is the adaptive control gain, t is time and s is the Laplace variable time-varying parameter of the shown in Figure Q3, where a is a as У() r(t) G(s) a e(t) k s(s+1) Figure Q3 The gain k is adaptively adjusted so that the closed loop system has the transfer function of a desired model 1 M(s) +1 i.e. the plant output y(t) follows the model output ym(t) = M(s)r(t) 2 S де (a) Show that дк 1 (r-y) where e = y-y is the output error S dk (b) Show that the MIT adaptation law for k can be written in the form dt 1 – y) E -7 S

 

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