20.08.2015   Fast Reactor Safety. (Nuclear science. and technology)

2.5.4 Nonlinearities

All the foregoing text has referred to linear stability analysis and any system with nonlinearities would have to be linearized before being treated in this way. [Witness Eq. (2.28), which linearizes the дк P term of Eq. (2.25).] However, many systems are significantly nonlinear.

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Подпись: Figure 2.37a and b illustrates (a) the nonlinear behavior of a system composed of a force acting on a spring and its linearized representation, and (b) a system that saturates for a high enough input, which can clearly be linearized only for small changes or for high input values. There are nonlinear stability criteria, but Liapunov’s theorem states that linear analysis is valid for small disturbances even in nonlinear systems. The simulation technique is a nonlinear method if the simulation includes the nonlinear terms. The ideal initial assessment would include a simulation technique in conjunction with other methods to check on their validity before delving further into nonlinear methods of analysis and their corresponding criteria for stability (8, 9).

Fig. 2.37. (a) Nonlinear system: spring displacement for a given force, (b) Nonlinear system: saturated system behavior.