By N C Jagan
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Additional resources for Control systems
V[t] Fig. 13 (a) Force - Voltage analogous circuit for mechanical system of Fig. 12. Mechanical quantities are shown in parenthesis Force - current analogous circuit can also be developed for the given mechanical system. It is given in Fig. 13 (b). Note that since the mass is represented by a capacitance and voltage is analogous to velocity, one end of the capacitor must always be grounded so that its velocity is always referred with respect to the earth. Transfer function XI(s) F(s) =-- Taking Laplace transform of eqns.
78) l+GH From eqns. 78) it is clear that the sensitivity of over all transfer function for a small variation in forward path transfer function is reduced by a factor (1 + GH) in a closed loop system compared to the open loop system. 2. Sensitivity of closed loop transfer function T( s) with respect to variation in feedback transfer function H(s), SJ ST G OTH =-oH·T G T(s) = - l+GH ST G -- H(1 + GH) G G G (1 + GH)2 GH ..... 79) l+GH From eqn. 79) it is clear that for large values of GH, the sensitivity approaches unity.
Y X-----1~ W X~y = w--u}l -------I Fig. 28 Moving a summing point to left of the block For the two systems to be equivalent the input and output of the system should be the same. For the left hand side system, we have, y = G [x] + W For the system on right side also, y = G [x + ~ [W]] = G [x] + w Rule 3: A summing point can be moved from left side of the block to right side of the block as shown in Fig. 29. t y x + y=G(x+w) =G[x]+G[w] Y = G[x] + G[w] Fig. 29 Moving a summer to the right side of the block Rule 4: A Pick off point can be moved from the right side of the block to left side of the block as shown in Fig.