MATLAB CONTROL SYSTEM TOOLBOX 9 Specifikace stáhnout pdf (Strana 96)

100

101

3 Operations on LTI Models

3-22

---------

(z+0.5)^2

Sampling time: 0.1

First-Order Hold

First-order hold (FOH) differs from ZOH by the underlying hold mechanism.

To turn the input samples into acontinuous input , FOH uses linear

interpolation between samples.

This method is generally more accurate than ZOH for systems driven by

smooth inputs. Due to causality constraints, this option is only available for

c2d conversions, and not d2c conversions.

Note This FOH method differs from standard causal FOH and is more

appropriately called triangle approximation (see [2], p. 151). It is also known

as ramp-invariant approximation because it is distortion-free for ramp inputs.

Tustin Approximation

The Tustin or bilinear approximation uses the approximation

to relate s-domain and z-domain transfer functions. In

c2d conversions, the

discretization of a continuous transfer function is derived by

Similarly, the

d2c conversion relies on the inverse correspondence

[]

()

[]

tkT

–

------------------

uk 1+

[]

–

()

,+= kT

tk1+

()

≤≤

1 sT

⁄

1 sT

⁄

–

--------------------------

≈

()

'()

,where= s

------

z 1–

z 1+

------------

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