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Unformatted text preview: input at ∞ . • The time constant, , is the time required for the output to reach 63.2% of the steady‐state value: 1 0.632 63.2% • After three time constants (i.e.; state: 1
0.950
• After four time constants (i.e.; state: 1 0.981 3 ), the output is within 5% of steady‐ 95% 4 ), the output is within 2% of steady‐ 98% • After 4.6 time constants (i.e.; state: 4.6 ), the output is within 1% of steady‐ 1
0.990 99% • Although a first‐order system theoretically never reaches steady‐state, the rule of thumb is that steady‐state conditions have been achieved after five time constants have elapsed. . EXAMPLES: • At ∞, the output, , therefore the steady‐state gain, 1. This can also be determined by replacing the capacitor with an open circuit at ∞ . • The time constant, . • For a step‐input, the current flowing around the loop is the i...
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 Winter '14
 DrKrouglicof
 Mechatronics, Laplace, Meter

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