Limiter control block with constant bounds

Diagram

limiter diagram

Syntax:

function name: lim
input variable : \(x_i\)
output variable: \(x_j\)
data name, parameter name or math expression for \(x_{min}\)
data name, parameter name or math expression for \(x_{max}\)

Internal states : none

Discrete variable : \(z \in \{-1,0, 1\}\)

Equations

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

Discrete transitions

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

Evaluate