matlab gain margin and phase margin

Gain Margin. When I analyze stability using frequency response by observing the bode plot in Matlab, I found the magnitude in the gain margin plot below the 0db line for all frequencies (see bode attached). The smaller the stability margins, the more fragile stability is. [Gm,Pm,Wcg,Wcp] = MARGIN(SYS) computes the gain margin Gm, the phase margin Pm, and the associated frequencies Wcg and Wcp, for the SISO open-loop model SYS (continuous or discrete). The gain margin Gm is defined as 1/G where G is the gain at the -180 phase crossing. Notes on Frequency Methods: Gain Margin Phase Margin, Delays, and the Nyquist Map Dr. Daniel S. Stutts Missouri University of Science and Technology May 3, 19991 1 Introduction to Frequency Methods Using frequency methods, it is possible to determine a great deal of information from the open-loop transfer function. MATLAB : margin MARGIN Gain and phase margins and crossover frequencies. Similarly, the gain margin measures what relative gain variation is needed at the gain crossover frequency to lose stability. Disk margins provide a stronger guarantee of stability than the classical gain and phase margins. The gain margin Gm is defined as 1/G where G is the gain at the -180 phase crossing. These terms are defined below. In other words, the gain margin is if is the gain at the -180° phase frequency. Determine the gain margin and the phase margin for a system that gave the following open-loop experimental frequency response data: at frequency 0.005 Hz a gain of 1.00 and phase −120°, at 0.010 Hz a gain of 0.45 and phase −180°. The phase margin measures how much phase variation is needed at the gain crossover frequency to lose stability. The gain margin is the factor by which the gain must be multiplied at the phase crossover to have the value 1. If no output arguments are given, both gain and phase margin are plotted on a bode diagram. Understanding gain margins and phase margins is crucial to understanding Bode plots. Similarly, the phase margin is the difference between the phase of the response and -180° when the loop gain is 1.0. Gm is the amount of gain variance required to make the loop gain unity at the frequency Wcg where the phase angle is –180° (modulo 360°). cm, or classical gain and phase margins, is an N-by-1 structure corresponding to loop-at-a-time gain and phase margins for each channel.L is an LTI model. Together, these two numbers give an estimate of the "safety margin" for closed-loop stability. Together, these two numbers give an estimate of the "safety margin" for closed-loop stability. For example, if the phase can vary by 30 degrees then the gain can only vary by about 8.4 dB (red mark). The gain margin is the amount of gain increase required to make the loop gain unity at the frequency where the phase angle is -180°. For example, if the gain margin plot in Control System Tuner indicates a 10 dB margin at a particular frequency, then trace the contour starting at (Gain,Phase) = (10,0) to see how a given amount of phase variation reduces the allowable gain variation at that frequency. Together, these two numbers give an estimate of the "safety margin" for closed-loop stability. [Gm,Pm,Wcg,Wcp] = MARGIN(SYS) computes the gain margin Gm, the phase margin Pm, and the associated frequencies Wcg and Wcp, for the SISO open-loop model SYS (continuous or discrete). The smaller the stability margins, the more fragile stability is. Otherwise, the margins and their corresponding frequencies are computed and returned.