System - HLDS Block

Contents

Description

The block System models controlled distributed parameter system as lumped-input / distributed-output systems.

Through the Dialog distributed step responses of modelled system are provided into the block System.

Then, in the block parameters of distributed parameter model by methodology presented in further parts of this HELP are adjusted.

In the control loop the block System assignes to supplied lumped input variables, distributed output model quantities. See DPS Examples and DPS Wizard.

In the control loop, LDS block is connected with block of zero-order hold units, H, and these blocks give the block of controlled system: HLDS.

where:

The determinition of distributed parameter responses to input step changes is based on:

HLDS based on analytical models

Step change of i-th input quantity, $U_{i}$, acts on string of blocks with transfer functions: $\{SA_{i}(s)\}_{i}$, $\{SG_{i}(s)\}_{i}$, $\{T_{i}(x)\}_{i}$ and $S(x,\xi,s)$.

Then, the distributed transfer function between i-th input variable and distributed output variable, is given in the form:

$$S_{i}\left ( x,s \right ) = SA_{i}\left ( s \right )SG_{i}\left ( s
\right )\int_{x_{1}}^{x_{2}}S\left ( x,\xi ,s \right )T_{i}\left ( \xi
\right )d\xi $$

For discrete points of the interval $<0,L>:0=x_{1},...,x_{j},...,x_{m}=L$ on the output of LDS transfer functions are given:

$$S_{i}\left ( x_{j},s \right ) = \frac{num_{i}\left ( x_{j},s \right
)}{den_{i}\left ( x_{j},s \right )}$$

Then for chosen sampling period, T, at k varied, given computational points, $\{x_{j}\}_{j}$, j = 1...m, for input step quantities, $\{U_{i}\}$, i = 1...n, discrete distributed step responses, $\{Y_{i}(x_{j},kT)\}_{j,i}$, are obtained - see MONOGRAPHY: Chapter 9.1., which are used as $\{Y_{i}(j,kT)\}_{j,i}$, when instead of coordinates of computational points, $\{x_{j}\}_{j}$, only serial numbers of these points are considered, $\{j\}_{j}$. Finally these responses are given through Dialog into the block HLDS for determination of distributed parameter model parameters.