Engineering Hub/Control Systems & Automation/Control Systems Stability Analysis & Root Locus Lab

Control Systems & AutomationDiscipline: Control Systems Engineering (EEE2005)

Control Systems Stability Analysis & Root Locus Lab

Interactive laboratory exploring system stability criteria (BIBO and asymptotic), the Routh-Hurwitz array builder with special cases (first-column zero and row of zeros / auxiliary polynomials), Evans root locus construction rules with dynamic gain exploration, and allowable s-plane pole placement regions.

Instrument State:Live Analytical DSP Engine

EEE2005 • CONTROL SYSTEMS UNIT 3Presidency Core

Stability Analysis & Root Locus Techniques Laboratory

Open-Loop Plant Selection1 + K G(s)H(s) = 0

Canonical Configurations

Loop Gain (K)20

K=0 (Open-Loop)K_crit = 48K=120

Stability Status

BIBO Stable (All Poles in LHP)

Gain Margin: 2.40× headroom

COMPLEX s-PLANE EVANS ROOT LOCUS [K = 20]Centroid σ_a = -2 • Asymptotes = 60°, 180°, 300°

Critical Gain (K_crit)

jω crossing boundary

Oscillation Freq (ω_osc)

2.83 rad/s

Marginal frequency

Centroid (σ_a)

-2

(Σp - Σz) / (P - Z)

Dominant Pole (Current)

-0.54 ± j1.75

At loop gain K = 20

Technical Instrument Specifications

Routh Array EngineLive array computation, sign changes, marginal gain Kcrit, and oscillation frequency ωosc

Evans RulesReal-axis segments, asymptote centroid σa, departure angles φd, and breakaway points dK/ds = 0

Root Locus TracerInteractive gain slider K from 0 to 150+ with animated closed-loop pole migration

Design Boundss-Plane allowable regions mapped from damping ζ, settling time ts, and peak overshoot %Mp

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