Consider the control system in Figure where v(t) is a sinusoidal disturbance, v(t)=sin(t). Compute the absolute...

 

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Consider the control system in Figure where v(t) is a sinusoidal disturbance, v(t)=sin(t). Compute the absolute value of the sensitivity function at w = 1 rad/s as a function of K. How must K be selected if the amplitude of y(t) shall be less than the amplitude of v(t) at this frequency w = 1 rad/s? (Hint: Recall that the sensitivity function can be interpreted as a measure of disturbance rejection.) 1 K 8(8+1) Figure 3: The closed-loop system in Problem 3 Consider the control system in Figure where v(t) is a sinusoidal disturbance, v(t)=sin(t). Compute the absolute value of the sensitivity function at w = 1 rad/s as a function of K. How must K be selected if the amplitude of y(t) shall be less than the amplitude of v(t) at this frequency w = 1 rad/s? (Hint: Recall that the sensitivity function can be interpreted as a measure of disturbance rejection.) 1 K 8(8+1) Figure 3: The closed-loop system in Problem 3