Integrator control block with (positive) time constant T and non-windup variable limits on output

Authors: Mathilde Bongrain

Diagram

integrator diagram

Syntax:

function name: invlim
input variable : \(x_i\)
output variable: \(x_j\)
variable \(x_{min}\)
variable \(x_{max}\)

Internal states : none

Discrete variable : \(z \in \{-1,1\}\)

Equations

\[\left\{ \begin{array}{lll} T \dot{x_j} = x_i & if & z=0 \\ 0= x_j - x_{min} & if & z=-1 \\ 0 = x_j - x_{max} & if & z=1 \end{array} \right.\]

Discrete transitions

if z = 0 then
    if xj > xmax then
        z ← 1
    else if xj < xmin then
        z ← −1
    end if
else if z = 1 then
    if xi < 0 then
        z ← 0
    end if
else if z = −1 then
    if xi > 0 then
        z ← 0
    end if
end if

Initialisation of discrete variables

if xj > xmax then
    z ← 1
else if xj < xmin then
    z ← −1
else
    z ← 0
end if

N.B. A zero value for \(T\) is not allowed. If too small a value is specified for \(T\), the solver may encounter a singularity and the simulation may not proceed.

Evaluate