Bode Plots Construction

The Bode plot is an essential tool in control system analysis, mapping the frequency response of a system through a magnitude plot and a phase plot, both against a logarithmic frequency axis. To construct a Bode plot, consider the transfer function H(ω):

It has constant gain, zeros, and poles. After normalizing the transfer function is written as:

Each term in this normalized function affects the Bode plot distinctly. The term 10jω has a constant gain of 10 and zero at origin jω. Each simple pole term (1+jω/ω_i) introduces a breakpoint or corner frequency ω_i. The zero's positive slope is evident from the origin, while the poles' negative slopes commence at their corner frequencies, ω=2 and ω=10 respectively.

Once the individual contribution of each term is identified, the overall Bode plot can be constructed. This involves superposing the slopes and phase changes of each factor. At low frequencies, the magnitude plot starts at 20 dB (since 20log₁₀(10) =20) and maintains a flat response up to the first corner frequency. The phase plot starts at 90° due to the zero at the origin and begins its descent before the first corner frequency.

The magnitude plot's slope will change at each corner frequency, decreasing by 20 dB/decade at ω=2 and again at ω=10. Correspondingly, the phase plot will bend downwards, approaching -90° at a frequency much higher than ω=10.

Finally, the asymptotic Bode plot, which consists of these straight lines, can be adjusted to approximate the actual frequency response more closely. This involves adding a smooth curve intersecting the asymptotic plot at each corner frequency, typically resulting in a slight overshoot near the corner frequencies, known as peaking.