Bode Plot Construction G(s) = 5* (s+1) / (10s+1)(100s+1) 1. Construct each Element plot 2. Graphical Summation: Complete plot. Note beginning and final values K = 5 Slope = -1 Slope = -2 Slope = -1
Phase Plot Construction G(s) = 5* (s+1) / (10s+1)(100s+1) 2. Graphical Summation of phase angles. Note beginning and final phase values. Here: = 0 at = 0, and = -90 final angle K = 5 Initial Phase is zero to 0.001, follows the first Phase up to 0.01 - 90 deg./decade 0 deg./decade +45 deg./decade Final phase: Constant - 90 deg
Bode Lag Design 1. All other design should be complete. Gain K and phase margin are fixed 2. Select Lag zero such that the phase margin does not drop further. (Slow) 3. Steady State Gain should now be about 10 times larger than without Lag.
Lead Design Example (a) P-control for phase margin of 45 degrees. Controller gain K = 0.95
(b) Lead-control for phase margin of 45 degrees. Lead zero and pole in RED. Initial design: Lead is too slow Lead is too slow. Lead Zero should be near the phase margin. Here: Place Lead zero around 3 rad/s.
(b) Lead-control for phase margin of 45 degrees. Lead zero and pole in RED. Improved design: Lead zero at 3, pole at 30 rad/s Lead zero at 3. Lead pole at 30. New gain crossover at 5 rad/s Final step: adjust gain K such that |F| = 0 dB at cr. Result: The controller gain is now K = 3.4 (4 times better than P- control)
Bode Lead and Lag Design: General placement rules