Control System Stability Analyzer
Control System Stability Analyzer determines the stability of a linear system by analyzing the poles of its transfer function \( G(s) = \frac{N(s)}{D(s)} \). Enter the coefficients of the numerator and denominator polynomials.
Stability Analysis
A system is stable if all poles (roots of the denominator polynomial \( D(s) = 0 \)) have negative real parts. The Routh-Hurwitz criterion is used to determine stability without computing roots explicitly.
Transfer Function:
\[ G(s) = \frac{N(s)}{D(s)} = \frac{b_2 s^2 + b_1 s + b_0}{s^3 + a s^2 + b s + c} \]Routh-Hurwitz Criterion: For a polynomial \( D(s) = s^n + a_{n-1} s^{n-1} + \dots + a_0 \), construct the Routh array. The system is stable if all elements in the first column of the Routh array are positive.
Pole Locations: Poles in the left half-plane (Re(s) < 0) indicate stability, on the imaginary axis (Re(s) = 0) indicate marginal stability, and in the right half-plane (Re(s) > 0) indicate instability.