Proportional integral (PI) controller with non-windup limit on the integral term

Authors: Mathilde Bongrain

Diagram

Syntax:

• function name: pictllim
• input variable : $x_k$
• output variable: $x_j$
• data name, parameter name or math expression for $K_I$
• data name, parameter name or math expression for $K_p$
• data name, parameter name or math expression for $x_i^{min}$
• data name, parameter name or math expression for $x_i^{max}$

Internal states : variable $x_i$

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

Equations

Discrete transitions

if z = 0 then
    if xi > xmaxi then
        z ← 1
    else if xi < xmini then
        z ← −1
    end if
else if z = 1 then
    if Ki*xk < 0 then
        z ← 0
    end if
else if z = −1 then
    if Ki*xk > 0 then
        z ← 0
    end if
end if

Initialization of internal state variables and discrete variables

if Ki*xk > 0 then
    z ← 1
    xi ← xmaxi
else if Ki*xk < 0 then
    z ← −1
    xi ← xmini
else
    z ← 0
    xi ← xj
end if