1 G (s): s(s + 2)(s+7) 1. Sketch an approximate bode plot by hand a. Verify using Matlab >> bode(num,den) 2. Sketch an approximate polar plot by hand a. Verify using Matlab >>nyquist(num,den) b. Scale the axes to match your hand plots 3. Find the limits of K using the Nyqusit stability criterion. Compare with the Ker value from previous HWs. 4. Find the gain margin (GM) and phase margin (PM) for the system >>margins(num,den) 5. Now design a PID controller using the frequency response methods to obtain a. Mp% <20% b. tp <0.3 sec Design using Phase Margin ⚫Convenient for higher order systems C Draw Bode plots ⚫Find PM from a desired ea ⚫ Find w at PM ⚫ Change gain K to force mag curve to go through 0dB (so robust) at this frequency, w (thereby changing bandwidth to include this w to be robust, i.e. Mag=1 or 0db) 6. You can use PIDtool to validate your analysis.