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Dr Sai Academy Lectures and Tutorials
FREQUENCY RESPONSE METHODS (BODE DIAGRAMS)
When a linear system is subjected to a sinusoidal input, its ultimate response (after a long time) is also a sustained sinusoidal wave. This characteristic constitutes the basis of frequency response analysis.
With frequency response analysis we are interested primarily in determining how the features of the output sinusoidal wave (amplitude, phase shift) change with the frequency of the input sinusoid.
A frequency response analysis characteristic is a useful tool for designing feedback controllers. It helps the designer:
1. To study the stability characteristics of a closed loop system, using Bode or Nyquist diagrams of the open-loop transfer function.
2. To select the most appropriate values for the adjustable parameters of a controller.
The Bode Stability Criterion
The Bode stability criterion indicates how we can establish a rational method for tuning the feedback controllers in order to avoid unstable behavior by the closed-loop response method.
Consider the Bode plots for open-loop transfer function of a feedback system (Figure). The two important features of these plots are:
The crossover frequency, ωco where φ = -180 deg
The point where AR= 1

A control system is unstable if the open-loop frequency response exhibits an AR exceeding unity at the frequency for which the phase lag is 180deg. This frequency is called the crossover frequency. The rule is called the Bode stability criterion.