S4-3.4 Frequency Response Analysis

Work through these

• Frequency-domain specifications

  Frequency-domain specifications describe a system by how it treats sinusoids of each frequency, in terms like resonant peak and bandwidth. They matter because, unlike pole locations, they can be measured on real hardware.

• Bode plot construction

  A Bode plot draws gain and phase against frequency on logarithmic axes, which turns products into sums and makes sketching by hand practical. It is the working engineer's first instrument for a reason.

• Principle of argument; Nyquist plot and stability criterion

  The Nyquist plot maps the whole frequency response into one curve, and the principle of argument turns encirclements of a point into a stability verdict. It handles cases where simpler tests are silent.

• Gain and phase margins from Bode and Nyquist diagrams

  Gain margin and phase margin say how much extra gain or delay a system tolerates before it becomes unstable. They are the safety margins of control design and the numbers a review will ask you for.

• Lead and lag compensators: what each achieves

  A lead compensator adds phase where the system needs it, buying speed and stability; a lag compensator raises low-frequency gain, buying steady-state accuracy. Diagnosing which problem you have is the design skill.

• Lab: obtain a Bode plot in simulation and read off the margins

  Obtain a Bode plot in simulation and read the two margins off it. Doing it by hand once makes the automatic readouts in software meaningful rather than magical.