### SAT – Saturation with variable limits

Block SymbolLicensing group: STANDARD

Function Description
The SAT block copies the input u to the output y if the input signal satisfies $\mathtt{\text{lolim}}\le \mathtt{\text{u}}$ and $\mathtt{\text{u}}\le \mathtt{\text{hilim}}$, where lolim and hilim are state variables of the block. If $\mathtt{\text{u}}<\mathtt{\text{lolim}}$ ($\mathtt{\text{u}}>\mathtt{\text{hilim}}$), then $\mathtt{\text{y}}=\mathtt{\text{lolim}}$ ($\mathtt{\text{y}}=\mathtt{\text{hilim}}$). The upper and lower limits are either constants ($\mathtt{\text{HLD}}=\mathtt{\text{on}}$) defined by parameters hilim0 and lolim0 respectively or input-driven variables ($\mathtt{\text{HLD}}=\mathtt{\text{off}}$, hi and lo inputs). The maximal rate at which the active limits may vary is given by time constants tp (positive slope) and tn (negative slope). These rates are active even if the saturation limits are changed manually ($\mathtt{\text{HLD}}=\mathtt{\text{on}}$) using the hilim0 and lolim0 parameters. To allow immediate changes of the saturation limits, set $\mathtt{\text{tp}}=0$ and $\mathtt{\text{tn}}=0$. The HL and LL outputs indicate the upper and lower saturation respectively.

If necessary, the hilim0 and lolim0 parameters are used as initial values for the input-driven saturation limits.

Inputs

 u Analog input of the block double hi Upper limit of the output signal (for the case $\mathtt{\text{HLD}}=\mathtt{\text{off}}$) double lo Lower limit of the output signal (for the case $\mathtt{\text{HLD}}=\mathtt{\text{off}}$) double

Outputs

 y Analog output of the block double HL Upper limit saturation indicator bool LL Lower limit saturation indicator bool

Parameters

 tp Time constant defining the maximal positive slope of active limit changes  $\odot$1.0 double tn Time constant defining the maximum negative slope of active limit changes  $\odot$1.0 double hilim0 Upper limit of the output (valid for $\mathtt{\text{HLD}}=\mathtt{\text{on}}$)  $\odot$1.0 double lolim0 Lower limit of the output (valid for $\mathtt{\text{HLD}}=\mathtt{\text{on}}$)  $\odot$-1.0 double HLD Fixed saturation limits  $\odot$on bool off .. Variable limits on ... Fixed limits

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