a. It is known that the output of the derivative action of a PID controller might inherit high frequencies if there is a noise in the measured system output(ym(t)=y(t)+m)asm=asin(wt)(wis relatively big). Present a solution (limitation) to the derivative action of the PID controller in presence of measurement noise(n)and mathematically show that the output of derivative action is limited to a fixed value. b. A system has the transfer function: \[ G(s)=\frac{-\mathbf{Y} s+1}{s^{2}+2 \mathbf{X} s+\mathbf{X}} \] Will the unit step response of the system exhibit undershoot or overshoot? Explain your answer in terms of the locations of the poles and zeros of the transfer function. The coefficientsXandYare defined as follows: \[ \begin{array}{l} X=a+1 \\ Y=b+1 \end{array} \] Herebis the last digit andais the penultimate (i.e. second last) digit of your student id (E.g.0400205ab)

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