1 / 13

2.0 STABILITY AND FREQUENCY RESPONSE

2.0 STABILITY AND FREQUENCY RESPONSE. SUB TOPIC. Know stability analysis of system (Bode Plot Method) Describe Bode Plot Identify the standard factors G(j ω ) H(j ω ) Sketch Bode plot according to response Explain frequency response specifications

tahlia
Download Presentation

2.0 STABILITY AND FREQUENCY RESPONSE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 2.0 STABILITY AND FREQUENCY RESPONSE

  2. SUB TOPIC • Know stability analysis of system (Bode Plot Method) • Describe Bode Plot • Identify the standard factors G(jω) H(jω) • Sketch Bode plot according to response • Explain frequency response specifications • Determine the gain margin (G.M) and phase margin (P.M) • Analyze the stability of Bode diagram

  3. INTRODUCTION • Stability is an important aspect in the design of a system. The most popular method for determining the stability is Bode plot sketches. • Bode sketch is to determine the stability of a response to a process control loop. • Bode sketch can be obtained by using the asymptotic approximation (which is a straight line drawing).

  4. DEFINITION OF BODE PLOT • Bode Plot is :- Magnitude in dB and phase angle in degrees are the magnitudes and phase angles of G(jw)H(jw) plotted against log w (rad/s) • The basic objective of control system design is to meet the performance specifications. These specifications are the constraints or limitation put on the mathematical functions describing the system characteristics.

  5. INTRODUCTION TO BODE PLOT • So, in general Bode plot consists of two plots which are :- 1) Magnitude expressed in logarithmic values of frequency called Magnitude Plot. 2) Phase angle in degrees against logarithmic values of frequency called Phase angle Plot

  6. INTRODUCTION TO BODE PLOT • Basic of any frequency response is to plot magnitude and phase angle against input frequency ‘ω’(rad/s) • Such plot are called Logarithmic plots which allows us to show wide range of variations in magnitude on a single paper. • Plots are made on semilog graph paper. Frequency is plotted on the horizontal log scale while amplitude and phase angle are plotted on the linear vertical scale.

  7. INTRODUCTION TO BODE PLOT

  8. INTRODUCTION TO BODE PLOT Magnitude Plot - The magnitude expressed in its logarithmic values by finding out the value 20 log |G| , which has a unit as decibel denoted by dB. - For Bode plot : |G (jω)| = 20 log10 |G|(jω) dB = 20 log10ω dB - Such decibels values are to be plotted against log (ω) Phase angle Plot - Phase angle in degrees against logarithmic values of frequency called Phase angle Plot

  9. IMPORTANT TERMS IN THE SKETCH BODE Gain Margin (GM) • Defined as the margin in gain allowable by which gain can be increased till system reaches on the verge of instability. • Is the amplitude/magnitude, |G| vertical line, on frequency phase angle -180°. • Gain Margin value is taken at the intersection of angle -180° on phase line and is projected to cross the gain line Gain Margin = 0 – ( ____ ) dB Get the value from the graph Bode

  10. IMPORTANT TERMS IN THE SKETCH BODE Phase Margin (PM) • The amount of additional phase lag which can be introduced in the system till system reaches on the verge of instability. • Phase Margin value is taken at the intersection of 0 dB on gain (magnitude) line and is projected to cross the phase line Phase Margin = 180° + ( ____ °) Get the value from the graph Bode

  11. The stability of Bode diagram • Stability of a system can be obtained through : • based on the values of Gain Margin (GM) and Phase Margin (PM) : If the values of GM and PM are positives, the system is stable, meanwhile If the values of GM or PM are negatives, the system is unstable

  12. ADVANTAGES OF BODE PLOTS • It shows both low and high frequency characteristic s of transfer function on a single diagram. • The plots can be easily constructed using some valid approximations. • Relative stability of system can be studied by calculating GM and PM from the Bode Plot.

  13. Asymptote Approximation method • This method is replaced s = jω in the open loop transfer function G(s)H(s) and calculate G(jω) H(jω) for variations of ω

More Related