Control Rules

• Object (a category of object)

• Id (the object's ID label)

• Attribute (an attribute or property of the object)

• Relation (a relational operator (=, <>, <, ≤, >, >=)) 

• Value (an attribute value)

• For Pumps, it is a multiplier applied to the flow computed from the pump curve 

• For Orifices, it is the fractional amount that the orifice is fully open (orifice control is accomplished by lowering or raising a horizontal gate from the top of the orifice) 

• For Weirs, it is the fractional amount of the original freeboard that exists (i.e., weir control is accomplished by moving the crest height up or down) 

• For Outlets, it is a multiplier applied to the flow computed from the outlet's rating curve 

$m(t) = k_p \left[e(t) + \frac{1}{T_i} \int e(T) \, dT + T_d \frac{de(t)}{dt} \right]$ Where, $m(t)$ = controller output; $k_p$=Proportional coefficient (gain); $T_i$=Integral time (minutes); $T_d$ = Derivatinve time (minutes); $e(t)$ = Error (difference between set point and observed variable value); t= Time.

The controller output $m(t)$ has the same meaning as a link setting used in a rule's Action Clause while $dt$ is the current flow routing time step in minutes. Because link settings are relative values (with respect to either a pump's standard operating curve or to the full opening height of an orifice or weir), the error $e(t)$used by the controller is also a relative value. It is defined as the difference between the control variable set point $x^*$and its value at timet,$x(t)$, normalized to the set point value:

$e(t) = \frac{x^* - x(t)}{x^*}$ Note that for direct action control, where an increase in the link setting causes an increase in the controlled variable, the sign of $k_p$ must be positive. For reverse action control, where the controlled variable decreases as the link setting increases, the sign of $k_p$ must be negative. The user must recognize whether the control is direct or reverse action and use the proper sign on $k_d$ accordingly. For example, adjusting an orifice opening to maintain a desired downstream flow or downstream water level is direct action. Adjusting it to maintain an upstream water level is reverse action. Controlling a pump to maintain a fixed wet well water level would be reverse action while using it to maintain a fixed downstream flow is direct action.