Auto-tune in first and second order systems
Use auto-tune in a first order system, which uses a single element, or in a second order system, which uses two independent elements.
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 might be written in a standard form such as f(t) = t 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
|
f | Forcing function | Is the Ambient temperature |
y | System state variable | Is the Fluid temperature |
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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