. . . Determination of Dynamic Performance Characteristics of Higher Order Systems . . Theory   System dynamics is an important area of study in widespread engineering applications such as vibrations, electric circuits, and control systems. Dynamic performance characteristics of a system describe how the system responds to a varying input. The most useful mathematical model for representing system behavior is the ordinary linear differential equation with constant coefficients. Accordingly, the relationship between system input x(t) and system output y(t) may be written in the following form.     where a and b are constants dependent on system physical parameters.   The corresponding transfer function of the system is   where s is the Laplace operator.   Fig. 1 shows a block diagram of the system with input x(t) and output y(t).       1.  Test Inputs   The following test inputs are normally used for testing the dynamics of a system. For characterizing system in time domain, the test inputs used are impulse, step, and ramp. A swept frequency sine wave is used to characterize system in frequency domain.   1.1 Impulse Input The unit impulse function is defined as for and is zero elsewhere. The Laplace transform of unit impulse is given by                                                                                                                                 Unit impulse input  Unit impulse response    1.2 Step Input The unit step function is defined as The Laplace transform of unit impulse is given by                                                                                Unit step input  Unit step response     1.3  Ramp Input The unit ramp function is defined as   The Laplace transform of unit ramp is given by                                                                     Unit ramp input   Unit ramp response     1.4 Sine Wave Input   The unit sine wave function x(t) is defined as A swept-frequency sine wave input is used to characterize system in frequency domain and the frequency response is obtained. The frequency response consists of two plots: Gain versus frequency and phase versus frequency.           Frequency response  , where  .                                                                                                                                                                                                                                                                                                                                                                                 Cite this Simulator:iitg.vlab.co.in,. (2012). Determination of Dynamic Performance Characteristics of Higher Order Systems. Retrieved 22 April 2018, from iitg.vlab.co.in/?sub=61&brch=174&sim=1361&cnt=1 ..... ..... .....