Control systems by N C Jagan

By N C Jagan

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49), is given by : C=WCp = 7t0 2 L - 4 - pCp where, Cp is the specific heat of copper and p is the density of copper. From eqn. 43), we have, q = HA (u - c) and from eqn. 48), dc C - =q dt Combining these two equations, dc I C - = - (u-c) dt R 32 Control Systems C dc +~=~ dt R R dc RC - +c=u dt where RC = T is the time constant of the system. 7 Obtain the transfer function C(s) for the system shown in Fig. 21. c is the displacement of the U(s) piston with mass M. u, pressure ~ f- M, mass B,damping Gas ~:Area Fig.

50 Poles of open loop and closed loop systems and their responses Thus without altering the system parameter 'a' the system time constant can be adjusted to a desired value by using an external amplifier with a suitable gain. c. 74. This gain can be compensidated by having additional gain outside the loop. 2 Effect due to parameter variations The output of an open loop system is affected by any variations in the parameter values. However, in a closed loop system, the variations in system parameters do not change the output significantly.

Although block diagram representation of a system is a simple way of describing a system, it is rather cumbusome to use block diagram algebra and obtain its overall transfer function. A signal flow graph describes how a signal gets modified as it travels from input to output and the overall transfer function can be obtained very easily by using Mason's gain formula. Let us now see how a system can be represented by a signal flow graph. Before we describe a system using a signal flow graph, let us define certain terms.

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