Analytical aperiodics of the 1st order

| Vectorized | C |
in the palette on the schematic
The block implements an analytic-discrete mathematical model of the aperiodic link of the 1st order, the continuous mathematical model of the dynamics of which is described by a linear ordinary differential equation (ODE) of the form:

where ui(t) is the i-th element of the input signal to the block, Ti is an element of the time constant vector, ki is an element of the gain vector, yi(t) is an element of the output signal from the block. Mandatory requirement Ti≠0
The block algorithm implements the calculation of the output signal at discrete moments of time (at each step of integration, including the bad steps) according to the following ratio:

where yi is the value of the signal at the input and output of the block at the j-th step of integration, xj+1 is the value of the signal at the input of the block at the (j+1)-th step of integration, ∆tj+1 is the current step of integration.

Inputs

  • input - input signal.

Outputs

  • output - output converted signal.

Properties

  • Gain coefficients – vector of coefficients ki, by which the input value is multiplied;
  • Time constants – vector of time constants Ti in seconds;
  • Initial conditions – vector of initial values yi(0) of the block output quantity;
  • Auxiliary inputs – indicates the presence of additional inputs of the block;
  • The initial conditions are taken from – the source pointer of the initial conditions of the block.
If the "Sign of input translation" option is selected in the 4th dialog line, then the block has a new additional input port designed to input a logical control signal to the block, where 0 corresponds to the conversion of the input signal according to the basic algorithm (refer to the formula), and 1 corresponds to the instantaneous transmission of the input signal to the output of the block (without conversion). If the "Time constants via ports" option is selected in the 4th dialog line, then the unit has a new additional input port (second or third) designed to enter the unit values of the unit time constant. This, for example, allows you to dynamically change the time constants of the link during the simulation process. If the option from the "Block parameters" is selected in the 5th dialog line, the initial condition is taken from the 3rd dialog line. If option from the "Input” is selected (default value) in the 5th dialog line, the initial condition is taken from the 1st input port at the zero calculation step ("at the start").

Parameters

None