By N C Jagan
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Additional info for Control systems
Consider two gears shown in Fig. 15. The first gear, to which torque T 1 is applied, is known as the primary gear and has N 1 teeth on it. The second gear, which is coupled to this gear and is driving a load, is known as the secondary gear and has N2 teeth on it. Fig. 15 Geartrain The relationships between primary and secondary quantities are bas~d on the following principles. 1. The number of teeth on the gear is proportional to the radius of the gear r\ N\ -=- ..... 31) 2. The linear distance traversed along the surface of each gear is same.
SL. Cs. 2 LCs R2 R[ Rz 47 Mathematical Modelling of Physical Systems (b) Its signal flow graph (a) The network Fig. L3 sL = - - (- R2 cs) Rl = R2 R . 13 Find the transfer function for the block diagram of Fig. 40. Solution: The block diagram and its signal flow graph are reproduced in Fig. 44 (a) and (b). - - t 1--'---' C(s) Fig. -<>--+--0 C(s) Fig. 44 (b) Signal flow graph of block diagram in Fig. 44 (a) Step 1 : Forward path gains PI=G I G 2 G 3 Step 2: Loop gain LI =-GIH I L2 =-G I G 2 H 2 L3 =-G2 G 3 H3 Two or more non touching loops are not present hence Pmr = 0 for r = 2, 3, .....
1. Forward paths MI = gl2 g23 g34 g4S gS6 g67 M2 = gl2 g23 g36 g67 M3 = gl2 g23 g34 g46 2. Loops LI = g23 h32 ~ = g23 g34 h42 L3 = ~s hS4 L4 = gS6 h6s Ls = g46 h6s hS4 L6 = g23 g36 h6s hS4 h42 C(s) Control Systems 46 3. Two non touching loops Out of the six loops there are 3 combinations of two non touching loops. Their gain products are: P12= LI L3 = g23 g4S h32 hS4 P22 = LI L4 = g23 gS6 h32 h6s P32 = LI Ls = g23 g46 h32 h6s hS4 4. Three non touching loops There is no combinations of 3 non touching loops or 4 nontouching loops etc.