Proportional integral (PI) controller with non-windup limit on the integral term
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
\[\left\{ \begin{array}{lll} \dot{x_i} = K_i x_k & if & z=0 \\ 0= x_i - x_i^{min} & if & z=-1 \\ 0 = x_i - x_i^{max} & if & z=1 \end{array} \right.\] \[0 = K_p x_k + x_i - x_j\]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