The Bode diagram approach is the most commonly used method for the analysis and synthesis of
Nichol's chart is a plot of
The initial slope of Bode plot for a transfer function having no poles at origin is
With no-pole at origin, initial slope will be OdB/decade.
For n-pole at origin, initial slope will be -20 ndB/decade.
The gain margin of a control system having the loop transfer function G(s)H(s) =
Gain crossover frequency is the frequency at which the gain of G(jω) is
For a control system having gain margin of -10 dB, the magnitude of GH(s) for 180° phase shift is
If the Nyquist plot of the loop transfer function G(s)H(s) of a closed-loop system does not encloses the (-1, j0) point in the G(s)H(s) plane, the gain margin of the system will be
Since the critical point (-1 + j0 ) is not enclosed, therefore m agnitude of OLTF, will be less than unity.
Therefore, G.M. = 20 log will be positive and the system will be stable.
A system with phase margin close to zero or gain margin close to unity is
If the transfer function of a first-order system in then the time constant of this system will be
Hence, time constant = T= 5 seconds
The polar plot of
Given system is of type-1 and order-2, therefore its polar plot will be as shown below.
Hence, the polar plot will neither cross the real axis nor the imaginary axis.