BASIC OF INSRUMENTAION PROCESS & CONTROL -:Guided by:- Proff. Piyush Modi Dept. of Chemical Engg. Pacific School of Engg. Surat.

Prepared by.. SR.NONAMEENROLLMENT NO. 1TAPRE MUKESH RANA KARAN TARSARIYA JAYDEEP PALAVWALA HARDIK KALSARIYA BHAUTIK SHAIKH UVESH

Content:  Introduction.  Bode plots for 1st order system.  rules.  Example.

introduction:  The frequency response characteristic of a system is represented by the bode diagram.  The bode diagram is known in the honour of H.W bode and it is a convenient way for analysis of the frequency response of linear control system.  The bode diagram consist of pair of following graphs. 1. the variation of the logarithmic of the amplitude ratio with radian frequency. 2. the variation of phase angle with radian frequency.

Bode plots for 1st order system:  If first order is given sinusoidal change in the input variable. Or X (t) =A sin wt Where, A is the input amplitude of variation and w is the radian frequency. Substituting for s=jw in the transfer function of the first order system,

Becomes,

 Thus transfer function has been converted into complex number/ The real part of complex number And the imaginary part of complex number

 G(jw)=m-jn Considering a complex plan,

Therefore the modulus or absolute value or magnitude of G(jw) is OA which is the amplitude ratio=AR=OA Or The distance of point A in the complex plane from the origine is amplitude ratio or AR=OA. Therefore,

 The angle made by joining point ‘A’ with the origin is with the real axis or the argument of G(jw) is the phase angle. Therefore,

So, the amplitude ratio and the phase angle for a first order system given as, And phase angle, The variation of the amplitude ratio versus radian frequency can be obtained by the following method: For the low frequency, or so, log AR = 0 and AR = 1 For the high frequency or here, or log AR = - log

The high frequency asymptote is line with slope -1 and passing through the point AR=1 and =1  The point of intersection of low frequency asymptote and high frequency asymptote is known as corner frequency. Which is, For the variation in phase angle with frequency, o -90o θ

Bode plots:

Rules: 1. The overall AR is obtained by adding the individual ARs. 1. The overall phase lag is obtained by addition of individual phase angle. 1. The presence of a constant in the overall transfer function shifts the entire AR curve vertically by a constant amount and has no effect on the phase angle.