EE128 Feedback Control Lecture 12 10 5 2006 Outline The Root Locus Design Method chapter 5 Problems from previous lecture Design using dynamic compensation 5 5 Design using lead compensation Design using lag compensation Design using notch compensation Problem 5 4 Problem 5 5 Problem 5 6 Problem 5 7 Problem 5 8 Problem 5 12 Design using dynamic compensation Lead compensation output leads the input i e positive phase shift Approximates the function of PD control Speeds up response by lowering rise time and decreasing transient overshoot Lag compensation output lags the input i e negative phase shift Approximates the function of PI control Improves steady state accuracy of the system Notch compensation cancels a particular frequency Achieves stability for systems with lightly damped flexible modes s z D s K s p z p lead compensation z p lag compensation Design using dynamic compensation P and PD compensation 1 s s 1 D s K D s K s 2 G s Lead Compensation 5 5 1 s 2 D s K p 10 p 20 s p Design using dynamic compensation Design using lead compensation Example 5 10 Find a compensation for G s 1 s s 1 Mp 20 and tr 0 25s D s K s 2 s 10 Design using dynamic compensation Example 5 11 Pole required at r0 3 5 j 3 5 3 which corresponds to n 7 0 5 Mp 20 and tr 0 26s Lead pole not 20 Design a lead compensation to meet these specifications L s s 5 4 s s 20 s 1 Design using dynamic compensation Lag compensation s z D s K z p s p Notch compensation s 2 2 0 s 02 Dnotch s s 0 2 Problem 5 27
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