samhld (Mu Analysis and Synthesis Toolbox)

Create a sample-hold approximation of a continuous system

Syntax

discout = samhld(sys,T)

Description

samhld applies a sample-hold to the input of the continuous-time systems sys, and samples the output, to produce a discrete-time system, discout. The sampling time is the same at the input and output, and is specified by T.

Examples

Construct the system sys via the nd2sys command and verify that all of its poles are in the closed left-half plane. Perform a sample hold of the system for a 200 Hz sample rate. All the poles for the discretized system, discout, are within the unit disk.

sys = nd2sys([1 2 4 5],[2 7 9 2]); 
spoles(sys)
-1.6114 + 1.0049i
-1.6114 - 1.0049i
-0.2773
discout = samhld (sys ,1 / 2 0 0)
seesys (discout, '%8 .4f ')

0.9826    -0.0223   -0.0050  |  0.0050
o.0050     0.9999   -0.0000  |  0.0000
0.0000     0.0050    1.0000  |  0.0000
-----------------------------|---------
-0.7500    -0.2500   2.0000  |  0.5000

spoles(discout)

0.9920 + 0.0050i
0.9920 - 0.0050i
0.9986

Algorithm

Suppose that the continuous-time system has state-space representation

If u(t) is held constant over the interval [kT,(k + 1)T], then over that interval, the state evolution is governed by the differential equation

which captures the behavior of the continuous-time system, over one sample period, while the input u(t) is held constant.

Let

. Define

. Then W appears as

Define A_disc := W₁₁, and B_disc := W₁₂, and define the discretized system as