數位控制（三）.

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Presentation transcript:

數位控制（三）

z transform z transformation transforms linear difference equation into algebraic in s. Laplace transformation transforms linear time-invariant differential equation into algebraic in z. G H x y + -

In time domain x(t) H(t) y(t) In s domain x(s) + y(s) G(s) - H(s)

The z transform method allows Conventional analysis and design techniques Root-locus Frequency response analysis (convert z to w) Z transformed characteristic equation allows Simple stability test

Elementary Functions Unit-step Unit-ramp Polynomial Exponential Sinusoidal Table of z transforms (Ogata p-29)

Important properties Multiplication by a constant Linearity of z transform Multiplication by ak Shifting theorem Complex translation theorem Initial value theorem Final value theorem

Poles and Zeros in the z plane

Exercise 1 Ogata B-2-1 B-2-2