Ligure 5-1 Ki 150A PID Vc 150C 150H 150Y PID 0000 Km 1 Kp 1+STM SN 150C 150D 150x +150F V W K2 Kt 150B 150x Vo Ko Ov 150K power DC Motor Position Control with Cascade PID + Velocity Feedback Compensation This amplifier has the following transfer function: 1 Gc(S) = K[1 + T + S Ta] (5-1) where the proportional gain K and the integral and derivative time constants Ti and Td can be varied over specified ranges by means of three calibrated knobs on the unit. [The gain K can be varied from 0.11 to 11 in two decade ranges. The Integral Time Constant Ti can be set from 0.11 to 11 seconds (in two decade ranges) and the Derivative Time Constant Td can be set from 2 milliseconds to 220 milliseconds in two ranges. Also, the Integral and Derivative functions can be independently switched on or off as required.] Now consider the system with the PID unit in the forward path, but with the tachometer feedback removed (with the PID module parameters K, T, and T set, K=0, this will correspond to cascade PID compensation). Using G = GCGp = KKM[1 + Ti + sTa] S SN(1 + STM) the CLTF is given by T = K G 1 + GH and H = Ko Ki T = = may be found, assuming 1 by: Ko 1-T 1 T Ta (5-2) The equivalent unit-feedback transfer function Gufsc Gufsc(s) KKOKTa[s + s N(1 + STM)