c2dOptions

Create option set for continuous- to discrete-time conversions

Syntax

opts = c2dOptions opts = c2dOptions('OptionName', OptionValue)

Description

opts = c2dOptions returns the default options for c2d.

opts = c2dOptions('OptionName', OptionValue) accepts one or more comma-separated name/value pairs that specify options for the c2d command. Specify OptionName inside single quotes.

Input Arguments

Name-Value Pair Arguments

'Method'

Discretization method, specified as one of the following values:

`'zoh'`	Zero-order hold, where `c2d` assumes the control inputs are piecewise constant over the sample time `Ts`.
`'foh'`	Triangle approximation (modified first-order hold), where `c2d` assumes the control inputs are piecewise linear over the sample time `Ts`. (See [1], p. 228.)
`'impulse'`	Impulse-invariant discretization.
`'tustin'`	Bilinear (Tustin) approximation. By default, `c2d` discretizes with no prewarp and rounds any fractional time delays to the nearest multiple of the sample time. To include prewarp, use the `PrewarpFrequency` option. To approximate fractional time delays, use the`FractDelayApproxOrder` option.
`'matched'`	Zero-pole matching method. (See [1], p. 224.) By default, `c2d` rounds any fractional time delays to the nearest multiple of the sample time. To approximate fractional time delays, use the `FractDelayApproxOrder` option.
`'least-squares'`	Least-squares method. Minimize the error between the frequency responses of the continuous-time and discrete-time systems up to the Nyquist frequency.

For information about the algorithms for each conversion method, see Continuous-Discrete Conversion Methods.

Default: 'zoh'

'PrewarpFrequency'

Prewarp frequency for 'tustin' method, specified in rad/TimeUnit, where TimeUnit is the time units, specified in the TimeUnit property, of the discretized system. Takes positive scalar values. A value of 0 corresponds to the standard 'tustin' method without prewarp.

Default: 0

'FractDelayApproxOrder'

Maximum order of the Thiran filter used to approximate fractional delays in the 'tustin' and 'matched' methods. Takes integer values. A value of 0 means that c2d rounds fractional delays to the nearest integer multiple of the sample time.

Default: 0

Examples

collapse all

Discretize Two Models Using Tustin Discretization Method

Open Live Script

Generate two random continuous-time state-space models.

sys1 = rss(3,2,2);
sys2 = rss(4,4,1);

Create an option set for c2d to use the Tustin discretization method and 3.4 rad/s prewarp frequency.

opt = c2dOptions('Method','tustin','PrewarpFrequency',3.4);

Discretize the models, sys1 and sys2, using the same option set, but different sample times.

dsys1 = c2d(sys1,0.1,opt);
dsys2 = c2d(sys2,0.2,opt);

References

[1] Franklin, G.F., Powell, D.J., and Workman, M.L., Digital Control of Dynamic Systems (3rd Edition), Prentice Hall, 1997.

Documentation