Defined by natural frequency and damping ratio.
G(s)=ω_n²/(s²+2ζω_n s+ω_n²): ζ<1 oscillatory, ζ=1 critically damped, ζ>1 overdamped. Overshoot M_p=e^{-πζ/√(1-ζ²)}; peak time π/ω_d; settling time 4/(ζω_n). Pole locations map directly to time-response features.
ζ=0.5 gives about 16% overshoot.
Second-order responses describe systems with two energy stores, and their damping ratio controls overshoot and oscillation.
Defined by natural frequency and damping ratio.
Second-order responses describe systems with two energy stores, and their damping ratio controls overshoot and oscillation.
The natural frequency sets the speed of the response and the damping ratio sets how much it overshoots and oscillates.
Values around 0.7 are often used because they give a good balance of speed and overshoot.
Typical applications include predicting the overshoot of a robot joint with a given damping ratio, choosing damping for a suspension to limit bounce and designing a sensor mount that must not ring after a shock.
Study "First-order system response" first (topic 47 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Damped natural frequency ω_d. Pole angle cosθ=ζ. Dominant pole approximation.
ζ=0.5 gives about 16% overshoot.
The next topic is "Time-domain specifications", which builds directly on this one.
It is classed as Intermediate in Signals, Control & Comms (topic 48 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.
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