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International Journal of Engineering Research and Development e-ISSN: 2278-067X, p-ISSN : 2278-800X, www.ijerd.com
Volume 5, Issue 2 (December 2012), PP. 44-46

System Identification-Different Techniques
Ramesh Kr1, Chitranjan Kr2, Ruchita3
1

National Institute of Technology Patna, 2PSCET Vaishali, 3RIET Jaipur

Abstract:- Engineering applications require description of the dynamic behavior of the system. Though a no. of applications are known in the field of system identification, three techniques are considered for the identification of linear system. Different techniques are frequency chirp, coherence function and pseudoinverse. In chirp method, wideband excitation such as frequency chirp is used. Frequency response is obtained as the DFT of the output of the system for time-domain input. Inverse method uses SVD function to find pseudoinverse. Coherence function has been used to identify the system using MATL AB function tfestimate. The performances of the methods are demonstrated by means of experimental investigation. Keywords:- System Identification, SUT, Pseudoinverse, Coherence, Frequency chirp.

I.
INTRODUCTION
System identification[1] is a powerful tool in engineering. Its various methods in the frequency and in the time domain have extensively discussed in CISM courses [2]. It deals with the problem of identifying a model describing some physical system by measuring the response of the system. This is don e by designing the input signal, which is applied to the system [3], whereas output is taken as impulse response of system. Input signal is used for excitation. In this paper identification has been achieved by basic approaches as variable frequency signa l (chirp), coherence function and pseudo inverse.

II.

SYSTEM IDENTIFICATION

A suitable system is considered for the application at hand. Then a special input signal is designed such that the system captures the behavior of the system to be modeled. Then an i dentification experiment is carried out in which Input and output signals are measured. An identification method is selected to estimate the parameters that describe the system from the collected input and output measurements. Finally, the validity of the obtained system is evaluated. An important step in system identification is the determination of the type of system to be used. This decision is based on knowledge of t he system under consideration, and on the properties of the system. The methods are presented here below :A. Chirp method Dirac impulse can be used to excite the SUT and output will be impulse response function denoted as h() . The Dirac impulse (‘delta function’) is not truly a function at all, but a ‘unit mass’ abstraction [ 4, p. 5]: The Dirac impulse (‘delta function’) having infinite amplitude at the point at which its argument is zero, is infinitely narrow and has unity integral over time. In the discrete-time case, we can attempt to approximate this function by an input that changes amplitude entirely within one sampling period, i.e., by a Kronecker delta appropriately scaled in amplitude. In practice, however, this approximation is unlikely ever to be entirely satisfactory. Hence, other wideband input excitations (e.g., band limited white noise, frequency chirp) are sometimes used.

To avoid such difficulties, assuming a causal system, the impulse response function of the SUT can be recovered from the (sampled) output signal {y(n)} for a (sampled) input signal {x(n)} of any general form by the following recursive equation, obtained directly from the convolution-sum:

n 1

h( n) 

y ( n)   h( k ) x ( n  k )
k 1

x (0)

(1)

However, round-off errors accumulate with larger time indices, making this approach impractical for slowly decaying (i.e., infinite) impulse response functions.
B. Inverse fitering
The transformed-domain approach determines the SUT impulse response function by inverse filtering the output signal by the input signal as H(z)...
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