Deadband control block

Diagram

deadbandDiagram

Deadband control block diagram

detailedDeadbandDiagram

Detailed deadband diagram

Syntax:

• function name: db
• input variable : \(x_i\)
• output variable: \(x_j\)
• data name, parameter name or math expression for \(\delta_1\)
• data name, parameter name or math expression for \(s_1\)
• data name, parameter name or math expression for \(a_1\)
• data name, parameter name or math expression for \(\delta_2\)
• data name, parameter name or math expression for \(s_2\)
• data name, parameter name or math expression for \(a_2\)

Internal states : none

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

Equations

\[ 0 = \left\{ \begin{array}{lll} x_j & if & z=0 \\ x_j - s_2 - a_2(x_i - \delta_2) & if & z=1 \\ x_j - s_1 - a_1(x_i - \delta_1) & if & z=-1 \end{array} \right. \]

Discrete transitions

if z ∈ {0, 1} then
    if xi < δ1 then
        z ← −1
    end if
else if z ∈ {−1, 0} then
    if xi > δ2 then
        z ← 1
    end if
else if z ∈ {−1, 1} then
    if δ1 < xi < δ2 then
        z ← 0
    end if
end if

Initialization of discrete variables

if xi > δ2 then
    z ← 1
else if xi < δ1 then
    z ← −1
else
    z ← 0
end if

N.B.

The data must obey \(\delta_1 < \delta_2\), \(a_1 \geq 0\) and \(a_2 \geq 0\) (see for instance the diagram above). A particular case is \(s_1 = s_2 = 0\) and \(a_1 = a_2 = 1\) (but all values are allowed for these four parameters).