lecture 18

# lecture 18 - Transient and steady-state response analysis...

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1 Transient and steady-state response analysis Transient response: Relation between Characteristic-Equation Roots and Transient Response

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2 Roots on the positive real axis inside the unit circle of the z -plane give rise to responses that decay exponentially with an increase of kT. The roots closer to the unit circle will decay slower. When the root is at z=1, the response has a constant amplitude. Roots outside the unit circle correspond to unstable systems, and the responses will increase with kT. Example 1: Analyse transient response
3 When the sampling period is small, the output responses of the discrete-data and the continuous-data systems are very similar. The maximum value of y ( kT ) is 1.0731, or a 7.31 percent maximum overshoot, as against the 4.3 percent maximum overshoot for the continuous- data system. When 01 . 0 = T s, The maximum value of y ( kT ) is 1.3712, but the true maximum overshoot is considerably higher than that. Thus, the larger sampling period only makes the system less stable, but the sampled output no longer gives an accurate measure of the true output.

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lecture 18 - Transient and steady-state response analysis...

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