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Rockwell Automation Publication 2080-UM002N-EN-E - November 2022
Appendix E PID Function Blocks
PID Application Example
The illustration above shows a basic water level control system, to maintain a preset water
level in the tank. A solenoid valve is used to control incoming water, filling the tank at a preset
rate. Similarly, outflowing water is controlled at a measurable rate.
IPID Autotuning for First and Second Order Systems
Autotune of IPID can only work on first and second order systems.
A first order system can be described by a single independent energy storage element.
Examples of first order systems are the cooling of a fluid tank, the flow of fluid from a tank, a
motor with constant torque driving a disk flywheel or an electric RC lead network. The energy
storage element for these systems are heat energy, potential energy, rotational kinetic energy
and capacitive storage energy, respectively.
This may be written in a standard form such as f(t) =
dy/dt + y(t), where
is the system time
constant, f is the forcing function and y is the system state variable.
In the cooling of a fluid tank example, it can be modeled by the thermal capacitance C of the
fluid and thermal resistance R of the walls of the tank. The system time constant will be RC,
the forcing function will be the ambient temperature and the system state variable will be the
fluid temperature.
A second order system can be described by two independent energy storage elements that
exchange stored energy. Examples of second order systems are a motor driving a disk
flywheel with the motor coupled to the flywheel via a shaft with torsional stiffness or an
electric circuit composed of a current source driving a series LR (inductor and resistor) with a
shunt C (capacitor). The energy storage elements for these systems are the rotational kinetic
energy and torsion spring energy for the former and the inductive and capacitive storage
energy for the latter. Motor drive systems and heating systems can be typically modeled by the
LR and C electric circuit.
Water In
Water Level
Tank
Water Out