Simulink Control Design™ - MathWorks

Step 1: Linearizing the Blocks in the Model

The first step of the linearization is to linearize each block in the model. The linearization

of the Saturation and Zero-Order Hold blocks is 1. The LTI blocks are already linear and

therefore remain the same. The new model with linearized blocks is shown below.

scdmratestep1

Step 2: Rate Conversions

Because the blocks in the model contain different sample rates, it is not possible to create

a single-rate linearized model for the system without first using rate conversion functions

to convert the various sample rates to a representative single rate. The rate conversion

functions use an iterative method. The iterations begin with a least common multiple of

the sample times in the model. In this example the sample times are 0, 0.01, and 0.025

seconds which yields a least common multiple of 0.05. The rate conversion functions then

take the combination of blocks with the fastest sample rate and resample them at the next

fastest sample rate. In this example the first iteration converts the combination of the

linearized continuous time blocks, sysC and integrator to a sample time of 0.01 using

a zero order hold continuous to discrete conversion.

sysC_Ts1 = c2d(sysC*Integrator,0.01);

The blocks sysC and Integrator are now replaced by sysC_Ts1.

scdmratestep2

2 Linearization