class 4 .1.pptx root locus and bode plot for control systems
- 1. Stability A system is stable if any bounded input produces a bounded output for all bounded initial conditions.
- 3. • Characteristic Equation • Consider an nth -order system whose the characteristic equation (which is also the denominator of the transfer function) is • Routh Hurwitz Criterion • Determining whether the system is stable or unstable from a characteristic equation in polynomial form without actually solving for the roots Routh‘s stability criterion is useful for determining the ranges of coefficients of polynomials for stability, especially when the coefficients are in symbolic (non numerical) form.
- 4. • Statement of Routh stability criterion • The necessary and sufficient condition for stability is that all of the element in the first column of the Routh array be positive. If this condition is not met the system is unstable and the number of sign changes in the elements of the first column of the Routh array corresponds to the number of roots of the characteristic equation in the right half of the s-plane
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