PIDE – PID controller with defined static error

Block SymbolLicensing group: ADVANCED

Function Description
The PIDE block is a basis for creating a modified PI(D) controller which differs from the standard PI(D) controller (the PIDU block) by having a finite static gain (in fact, the value $𝜀$ which causes the saturation of the output is entered). In the simplest case it can work autonomously and provide the standard functionality of the modified PID controller with two degrees of freedom in the automatic ( $MAN = off$ ) or manual mode ( $MAN = on$ ).

If in automatic mode and if the saturation limits are not active, the controller implements a linear control law given by

U (s) = \pm K [b W (s) - Y (s) + \frac{1}{T_{i} s + β} E (s) + \frac{T_{d} s}{\frac{T_{d} s}{N} + 1} (c W (s) - Y (s))] + Z (s),

where

β = \frac{K 𝜀}{1 - K 𝜀}

and $U (s)$ is the Laplace transform of the manipulated variable mv, $W (s)$ is the Laplace transform of the setpoint sp, $Y (s)$ is the Laplace transform of the process variable pv, $E (s)$ is the Laplace transform of the deviation error, $Z (s)$ is the Laplace transform of the feedforward control variable dv and $K$ , $T_{i}$ , $T_{d}$ , $N$ , $𝜀$ $(= b_{p} ∕ 100)$ , $b$ and $c$ are the controller parameters. The sign of the right hand side depends on the parameter RACT. The range of the manipulated variable mv (position controller output) is limited by parameters hilim, lolim.

By connecting the output mv to the input tv and choosing the tt parameter appropriately, we achieve the desired behaviour of the controller when reaching the saturation values of mv. This eliminates the undesirable integral windup effect while ensuring smooth switching (bumpless transfer) between automatic and manual modes.

In the manual mode ( $MAN = on$ ), the input hv is copied to the output mv unless saturated. In this mode the inner controller state tracks the signal connected to the tv input so the successive switching to the automatic mode is bumpless. But the tracking is not precise for $𝜀 > 0$ .

This block propagates the signal quality. More information can be found in the 1.4 section.

Input

dv	Feedforward control variable	Double (F64)
sp	Setpoint variable	Double (F64)
pv	Process variable	Double (F64)
tv	Tracking variable	Double (F64)
hv	Manual value	Double (F64)
MAN	Manual or automatic mode	Bool
	off .. Automatic mode on ... Manual mode

Parameter

irtype	Controller type (control law) $⊙$ 6	Long (I32)
	1 .... D 2 .... I 3 .... ID 4 .... P 5 .... PD 6 .... PI 7 .... PID
RACT	Reverse action flag	Bool
	off .. Higher mv -> higher pv on ... Higher mv -> lower pv
k	Controller gain $↓$ 0.0 $⊙$ 1.0	Double (F64)
ti	Integral time constant $↓$ 0.0 $⊙$ 4.0	Double (F64)
td	Derivative time constant $↓$ 0.0 $⊙$ 1.0	Double (F64)
nd	Derivative filtering parameter $↓$ 0.0 $⊙$ 10.0	Double (F64)
b	Setpoint weighting - proportional part $↓$ 0.0 $⊙$ 1.0	Double (F64)
c	Setpoint weighting - derivative part $↓$ 0.0	Double (F64)
tt	Tracking time constant $↓$ 0.0 $⊙$ 1.0	Double (F64)
bp	Static error coefficient	Double (F64)
hilim	Upper limit of the controller output $⊙$ 1.0	Double (F64)
lolim	Lower limit of the controller output $⊙$ -1.0	Double (F64)

Output

mv	Manipulated variable (controller output)	Double (F64)
de	Deviation error	Double (F64)
SAT	Saturation flag	Bool
	off .. The controller implements a linear control law on ... The controller output is saturated

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