Download Control systems by N C Jagan PDF

By N C Jagan

ISBN-10: 144166176X

ISBN-13: 9781441661760

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P_l~______~I~rl________P~2 resistance R Capacitance C Fig. 19 Gas resistance and capacitance The capacitance parameter for pressure vessels is defined as dv C =-dp ..... 57) 31 Mathematical Modelling 0/ Physical Systems v -+ weight of gas in vessel, kg p -+ pressure kg/m2 The flow rate and the gas pressure are related by the continuity law : where dp =0) dt Where OJ is the flow rate in kg/sec. C- ..... 58) Let us now consider some thennal and fluid systems and obtain their transfer functions. 6 Find the transfer function C(s) of the thennal system shown in Fig.

26 Transfer function of the closed loop system (Note : If the feedback signal is added to the reference input the feedback is said to be positive feedback. On the other hand if the feedback signal is subtracted from the reference input, the feedback is said to be negative feedback). For the most common case of negative feedback, C(s) R(s) G(s) 1 + G(s) R(s) ..... 64) The block diagram of a complex system can be constructed by finding the transfer functions of simple subsystems. The overall transfer function can be found by reducing the block diagram, using block diagram reduction techniques, discussed in the next section.

Fig. 39 Signal flow graph for the network in Fig. 38 Now, consider the block diagram given in Fig. 40. - - ( I--'--~ C(s) Fig. 40 Block diagram of a system The relationship between the various variables indicated on the diagrams are : X 1(s) = R(s) - H 1(s) ~(s) - His) Xis) X2(s) = G 1(s) X 1(s) - H3(S) C(s) X3(s) = Gis) X2(s) C(s) = G3(s) X2(s) Signal flow graph can be easily constructed for this block diagram, as shown in Fig. 41. -H3 R(s) C(s) Fig. 41 Signal flow graph for the system in Fig.

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