SWMM - Regras de Controle - Controlador PID

A PID (Proportional-Integral-Derivative) Controller is a generic closed-loop control scheme that attempts to maintain a desired setpoint on some process variable by calculating and applying a corrective action that adjusts the process accordingly. In the context of a hydraulic transport system, a PID controller can be used to adjust the opening in a closed orifice to maintain a target flow rate in a specific conduit or to adjust a variable speed pump to maintain a desired depth in a unit. of storage. The classic PID controller has the form:

Where:

m(t) - controller output
Kp - proportional coefficient (gain)
ti - full time (minutes)
Td - derived time (minutes)
e(t) - error (difference between the set point and the observed variable value)
t - time

The performance of a PID controller is determined by the values assigned to the Kp, Ti and Td coefficients.

The controller output m(t) has the same meaning as a link configuration used in the action clause of a rule, while dt is the current flow's routing time step in minutes. Since the link settings are relative values (relative to the standard operating curve of a pump or the total 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 setpoint of the control variable x* and its value at time t, x(t), normalized to the setpoint value:

e(t) = (x* - x(t)) / x*

Note that for direct action control, where an increase in link adjustment causes an increase in the controlled variable, the sign of Kp must be positive. For reverse action control, where the controlled variable decreases as the link adjustment increases, the sign of Kp must be negative. The user must recognize whether the control is direct or reverse action and use the appropriate sign in Kp accordingly. For example, adjusting the opening of an orifice to maintain a desired downstream flow or downstream water level is a direct action. Adjusting it to maintain an upstream water level is a reverse action. Controlling a pump to maintain a fixed wet well water level would be a reverse action, while using it to maintain a fixed flow downstream is a direct action.