Consider the forced mass-spring-damper (MSD) system: mir 1 M F K www The transfer function for this system is X(s) Gp(s) = Ms²+Bs+K F(s) Suppose that this forced MSD system is "enhanced" (as discussed in previous lectures for the PID controller): Force Amplifier Plant (MSD System) Position sensor Vin(s) [Volts] F(s) X(s) X₁(s) [Volts] K₁ Gp(s) G,(s) The following values are known: Newton 1) Force Amplifier (K₁ = 1 Volt 2) MSD System (M=1 kg, B=0.1 3) Position sensor (G,(s) 500 S+500 and K-1 m/sec' ZIE Part a) Sketch completely the Bode plots of the transfer function of the OVERALL system: (16 points) X₁(s) 1 G(s) Vin(s) K₁ Gp(s) G₁(s) = 500 + (0.1)s+1s+500 You must provide some explanation for these Bode plots (i.e. do not just sloppily draw them without written explanation). Phase (degrees) Magnitude (dB) -50 -100 -150 -200 50 0 -50 -100 -150 Bode plots for G(s) - Question (Part a) -200 -250 2 10 101 10° 10' 10² Frequency (rad/sec) D 10³ 10' 10³ -250 -300 102 101 10° 10' 10² 10³ 10 105 Frequency (rad/sec) Part b) Now consider the following transfer function: (7 points) -500 H(s)- + (0.1)s+1' +500 Note that this "H(s)" is equal to (-1)*G(s) from "Part a." This system could represent the same system as from "Part a," but with the reverse polarity of the position sensor output voltage. Describe how the Bode plots (magnitude, phase) for this "H(s)" would compare with the Bode plots for "G(s)" from "Part a." Note that you do NOT need to draw/sketch Bode plots for this part, but you need to explain your answer clearly (perhaps with "some" calculations?). HINT: You can view this new transfer function as H(s)= 500 + (0.1)s+1 +500)(-1).