Chapter 20 Proportional Integral Derivative (PID) instruction
570 Rockwell Automation Publication 2080-RM001D-EN-E - February 2015
Auto-tune in first and second order systems
Auto-tune can be used in first order system, which uses a single element, or in a
second order system, which uses two independent elements.
Auto-tune a first order system
A first order system uses a single independent energy storage element. Examples
include:
• Cooling of a fluid tank, with heat energy as the storage unit.
• Flow of fluid from a tank, with potential energy as the storage unit.
• A motor with constant torque driving a disk flywheel, with rotational
kinetic energy as the storage unit.
• An electric RC lead network, with capacitive storage energy as the storage
unit.
In a first order system, the function may be written in a standard form such as f(t)
= τ dy/dt + y(t)
Where:
Variable Description Example: Cooling of a fluid tank using heat energy as the storage element
t System time constant Is equal to RC
Where
R = Thermal resistance of the walls of the tank
C = Thermal capacitance of the fluid
f Forcing function Is the Ambient temperature
y System state variable Is the Fluid temperature
Auto-tune in a second order system
A second order system uses two independent energy storage elements that
exchange stored energy. Examples include:
• A motor driving a disk flywheel with the motor coupled to the flywheel via a
shaft with torsional stiffness; Rotational kinetic energy and torsion spring
energy are the storage units.
• An electric circuit composed of a current source driving a series LR
(inductor and resistor) with a shunt C (capacitor); Inductive energy and
capacitive energy are the storage units.
Motor driven systems and heating systems can typically be modeled by the LR and
the C electric circuit.
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