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MEC524 — Chapter 4
Root Locus & Performance
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Evaluating System Performance

Performance metrics define how well a system tracks its reference. Key specs include settling time, overshoot, rise time, and steady-state error.

◆ Diagram
Time-Domain Performance Specificationsty(t)1.0+1%−1%tᵣMptₚtₛSettling Time (1%)eₛₛtᵣ = Rise time (10→90%)tₚ = Peak timetₛ = Settling timeSteady-state error: eₛₛ = lim(s→0) s·E(s) (Final Value Theorem)
◆ Key Points
01.Settling Time (ts): 2% criterion ts ≈ 4/(ζωn), or 1% criterion ts ≈ 4.6/(ζωn)
02.Peak Overshoot (Mp): Mp = exp(−πζ/√(1−ζ²)) × 100%
03.Rise Time (tr): time from 10% to 90% of final value (overdamped) or 0% to 100% (underdamped)
04.Steady-State Error (e_ss): use Final Value Theorem — lim(s→0) sE(s)
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Ch 3: Mathematical Modeling Ch 5: Frequency Response