Control Engineering › Oscillating Systems 2

Summary

PT2 behaviour is described by the characteristic parameters k_P,PT2, ω₀ and D. The general transfer function is

\[ H_{\mathrm{PT2}} = \frac{k_{P,\mathrm{PT2}}}{\frac{1}{\omega_0^2} s^2 + \frac{2D}{\omega_0} s + 1} \]

Depending on the damping D, the behaviour is categorised as follows:

D = 0: continuous undamped oscillation

0 < D < 1: decaying oscillation

D = 1: critical damping

D > 1: non-oscillating system

The parameter ω₀ is (approximately, for small damping) the angular frequency at which the system oscillates. It is determined from the period T, which can be read from the step response of a system capable of oscillation. The following applies:

\[ \omega_0 = \frac{2\pi}{T_0} \]

Non-oscillating PT2 systems and PT1 systems behave similarly in terms of their step response. The step response of a system with PT2 behaviour begins with a horizontal tangent (S-shaped rise). With PT1 behaviour, the step response begins with a kink in the curve upwards. This is how you distinguish these two behaviours graphically, even if the PT2 system does not overshoot.

Non-oscillating or non-overshooting PT2 behaviour is usually characterised by the parameters t_u and t_g according to the inflection tangent method.

Further information

Wikipedia (German)