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:
- LDS - lumped-input / distributed output system
- H - block of zero-order hold units
- U(x) - lumped input quantity
- Y(x,t) - distributed output quantity
The determinition of distributed parameter responses to input step changes is based on:
- analytical models
- numerical models
- experimental identification of dynamics charakteristics
HLDS based on analytical models
- actuating members of lumped input variables
- generators of distributed input variables
- shaping units in space domain
- distributed-input / distributed-output system on the interval [0,L]
- lumped input quantities
- distributed output quantity
Step change of i-th input quantity, , acts on string of blocks with transfer functions:
,
,
and
.
Then, the distributed transfer function between i-th input variable and distributed output variable, is given in the form:
For discrete points of the interval on the output of LDS transfer functions are given:
Then for chosen sampling period, T, at k varied, given computational points, , j = 1...m, for input step quantities,
, i = 1...n, discrete distributed step responses,
, are obtained - see MONOGRAPHY: Chapter 9.1., which are used as
, when instead of coordinates of computational points,
, only serial numbers of these points are considered,
. Finally these responses are given through Dialog into the block HLDS for determination of distributed parameter model parameters.