Root Locus Design Concepts 1 Control System Including a Delay 2 First-Order Time Lag Plus Dead Time 3 Root Locus without Delay (T = 0; Gp(S) = 1/S); H(S) = 1 4 Root Locus with Delay (T = 1; K varies) • >> n=[-1 2] ;d=[1 2 0]; • >> r=rlocus(n,d); • >> plot(r,'-'); • >>v=[-3 10 -3 3]; >>axis(v); • >>axis('square') • >> grid 5 Root Locus with Delay (K = 2; 1/T varies) 6 Conclusion • As a system is driven at larger gains (faster response), the value of the delay must be smaller for stability. 7 System to be Compensated 8 Proportional Compensated R-L [Gc(S)Gp(S) = K/(S + 2)2 9 Step Response for T(S) = K/(S2 + 2S + K + 1) and K = 1 10 Integral-Compensated Root Locus 11 Step Response with K = 1 12 Proportional–Plus-Derivative compensated R-L 13 Step Response for T(S) = K(S + 2)/[S2 + (2 + K)S + 2K] and K = 1 14 Light-Source Tracking System 15 Block Diagram 16 Root Locus 17 Typical Responses to Step 18 Block Diagram with Position and Rate Feedback 19 Signal Flow Graph 20 Unit Step Response with K = 250; K’ = 0.08 21