Urban Planning Development

Control systems by N C Jagan

By N C Jagan

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Consider the network shown in Fig. 38. + R2 Vo(s) output Fig. 38 A network for constructing a signal flow graph Identifying the currents and voltages in the branches as shown in Fig. 38; we have Vis) = [Il(s) - I2(s)] sL I2(s) = [V 2(s) - Vo(s)]Cs Vo(s) = 12(s) R2 44 Control Systems The variables 11(s), 12(s), V 1(s), V2(s) and Vo(s) are represented by nodes and these nodes are interconnected with branches to satisfy the relationships between them. The resulting signal flow graph is shown in Fig.

54) dh where v ~ volume of the liquid tank in m 3. Hence the capacitance ofa tank is given by its area of cross section at a given liquid surface. Gas systems consisting of pressure vessels, connecting pipes, valves etc. may be analysed by using the fundamental law of flow of compressible gases. Again, we have to consider two types of flow: turbulent and laminar flow. , we have 0)=KAY~2g (pl -P2)Y where 0) K ~ flow rate, kg/sec ~ flow constant ..... 55) A ~ area of restriction, m 2 y ~ gas density, kg/m3 p ~ pressure in kg/m2 Turbulent gas flow resistance is therefore given by R= ~ dw sec/m2 .....

48. output feedback signal Fig. 48 A feedback system Let us now consider the effects of feedback on the performance of the system. 1 Effect on system dynamics The system dynamics can be changed without actually altering the system parameters. This can be illustrated with a simple example of a first order system. Consider the system shown in Fig. 49. ,--.... C(s) '-------0 Fig. 49 A first order system When the switch is open, the system is an open loop system and the open loop transfer function is given by T(s) = C(s) = ~ R(s) s+a The impUlse response of the system is given by h(t) The time constant 't .....

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