Timer control block

Authors: Mathilde Bongrain

Timer with varying delay. The latter is a piecewise linear function of the monitored variable If \(x_i\) is smaller than a threshold \(v_1\), the output \(x_j\) is equal to zero. Otherwise, \(x_j\) changes from zero to one at time \(t* + \tau(x_i)\) where t* is the time at which the input \(x_i\) became larger than \(v_1\) and the delay \(\tau (x_i)\) varies with \(x_i\) according to a piecewise linear characteristic involving \(n\) points (see diagram below).

Diagram

Syntax:

• function name: timer
• input variable : \(x_i\)
• output variable: \(x_j\)
• data name, parameter name or math expression for \(v_l\) where \(l \in \{0,1, ..., n\}\)
• data name, parameter name or math expression for \(T_l\)

Internal states : \(x_1\)

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

Equations

Discrete transitions

if z = −1 then
    if xi ≥ v1 then
        z ← 0
    end if
else
    if xi < v1 then
    z ← −1
    end if
end if

if z = 0 then
    if x1 ≥ $$\tau (xi)$$ then
        z ← 1
    end if
end if

Initialization of internal states

x1 ← 0

Initialisation of the discrete variables

z ← -1

The \(v_i\) values must be increasing, but two consecutive values may be equal, i.e. \(v_1 \leq v_2 \leq v_3 \leq . . . \leq v_{n−1} \leq v_n\). The piecewise linear characteristic is typically used to approximate an inverse-time characteristic, in which case the \(T\) values are decreasing, i.e. \(T_1 \geq T_2 \geq T_3 \geq . . . \geq T_{n−1} \geq T_n\).
Nevertheless, non decreasing values are also allowed. If the initial value of \(x_i\) is larger than \(v_1\), \(x_j\) will change to one after the time \(\tau(x_i)\), unless \(x_i\) decreases below \(v_1\) before the delay \(\tau\) is elapsed.