Simulink Control Design 

This example shows how to specify the rate conversion method for the linearization of a multirate model. The choice of rate conversion methodology can affect the resulting linearized model. This example illustrates the extraction of a discrete linear time invariant model using two different rate conversion methods.
In the Simulink model scdmrate.mdl there are three different sample rates specified in five blocks. These blocks are
sysC  a continuous linear block,
Integrator  a continuous integrator,
sysTs1  a block that has a sample time of 0.01 seconds,
sysTs2  a block that has a sample time of 0.025 seconds, and
ZeroOrder Hold  a block that samples the incoming signal at 0.01 seconds.
Open the Simulink model.
scdmrate
In this example, you linearize the model between the output of the block sysTs1 and the block ZeroOrder Hold. Additionally, you add a loop opening at the block ZeroOrder Hold to extract the plant model for the system.
model = 'scdmrate'; io(1) = linio('scdmrate/sysTs1',1,'input'); io(2) = linio('scdmrate/ZeroOrder Hold',1,'openoutput');
Using these linearization points the linearization effectively results in the linearization of the model scdmrate_ol.
scdmrate_ol
When linearizing a model that contains both continuous and discrete signals, the software first converts the continuous signals to discrete signals, using a rate conversion method. The default rate conversion method is zeroorder hold. To view or change the rate conversion method, use the RateConversionMethod property in the linearizeOptions function. The following command shows that RateConversionMethod is set to the default setting, zoh:
opt = linearizeOptions
Options for LINEARIZE: LinearizationAlgorithm : blockbyblock SampleTime (1 Auto Detect) : 1 UseFullBlockNameLabels (on/off): off UseBusSignalLabels (on/off): off Options for 'blockbyblock' algorithm BlockReduction (on/off) : on IgnoreDiscreteStates (on/off) : off RateConversionMethod (zoh/tustin/prewarp/ : zoh upsampling_zoh/ upsampling_tustin/ upsampling_prewarp PreWarpFreq : 10 UseExactDelayModel (on/off) : off AreParamsTunable (true/false) : true Options for 'numericalpert' algorithm NumericalPertRel : 1.000000e05 NumericalXPert : [] NumericalUPert : []
The following command performs a linearization using the zeroorder hold method. Because the linearization includes the ZeroOrder Hold block, the sample time of the linearization is 0.01.
sys_zoh = linearize(model,io,opt);
The following commands change the rate conversion method to the Tustin (Bilinear transformation) method and then linearize using this method. The sample time of this linearized model is also 0.01.
opt.RateConversionMethod = 'tustin';
sys_tust = linearize(model,io,opt);
It is also possible to create a continuoustime linearized model by specifying the sample time as 0 in the options object. The rate conversion method still creates a discretetime linearized model but then converts the discretetime model to a continuoustime model.
opt.SampleTime = 0; sys_c = linearize(model,io,opt);
The Bode plots for the three linearizations show the effects of the two rate conversion methods. In this example, the Tustin rate conversion method gives the most accurate representation of the phase response of the continuous system and the zeroorder hold gives the best match to the magnitude response.
p = bodeoptions('cstprefs'); p.YLimMode = {'manual'}; p.YLim = {[100 0];[180 30]}; p.Grid = 'on'; bodeplot(sys_c,sys_zoh,sys_tust,p); h = legend('sys_c','sys_zoh','sys_tust','Location','SouthWest'); set(h,'Interpreter','none')