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A stable system is one for which the output response is bounded for all bounded inputs..
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All real poles are –ve.. For imaginary poles all real parts are –ve..
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+ 2öü)nS + S2. The general form of the characteristic equation of a 2nd order system.
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52 —öOn — O —1. abstract. — öü.)n + On —1. . Both roots are real and negative.
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Both roots are equal, real and negative. abstract.
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Roots are complex conjugates with negative real parts.
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Both roots are complex with no real parts. System is unstable.
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Of the above cases, the underdamped response occurs most frequently in control systems. Hence a number of terms are used to describe the underdamped response quantitatively..
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Decay ratio. T he ratio of the sizes of successive peaks and is given by C/A in Figure above ..
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T he time required for the response to come within 5 percent of its ultimate value and remain there..
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Substituting each S in the equation above by j we obtain.
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I —j2ö + 2ö. + 26 + 26 26. Ø = tan¯l 26 = —tan-.