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The transfer functions of the symmetrical optimum exhibit similar tendencies.
As the gain increases, the rise time decreases. An excessively large Kp results in more
pronounced hunting, as does an excessively small Tn. If the reset time is too large, this
results in a degree of settling, if the Kp is correctly set. If the Kp is too small or too large, the
overshoot increases and if Tn is too small, pronounced oscillations whose frequency grows
with the gain occur for every Kp.
Moreover, at the symmetrical optimum, the phase offset from critical positive feedback is
smaller than for the absolute value optimum. While the absolute value optimized control loop
can become more and more stable by reducing the gain, this is only possible for the
symmetrically optimized loop by increasing the reset time at the same time as having correct
gain.
Equivalent time constant of the optimized control loop
A controlled system often contains not just two but more time constants and integrals. This
sometimes results in impermissibly slow settling.
For example, a drive not only has the speed control as a main controlled variable but also the
armature current as an auxiliary variable.
In this case, the current control is therefore subordinate to the speed controller. For the
higher-level control loop, the lower-level control must therefore be considered part of the
controlled system. To be able to represent the frequency response of the higher-level loop as
simply as possible, it is useful to use a first-order function for the lower-level loop.
For a lower-level controller optimized according to the absolute value optimum, the
equivalent time constant t
eBO
= 2 applies.
For a lower-level control loop optimized according to the symmetrical optimum, the following
applies:
Equivalent time constant is t
eSO
= 4
Adjustment according to the symmetrical optimum
2 Kp; 0.5 Tn
2 Kp; Tn
2 Kp; 2 Tn
Kp; 0.5 Tn
Kp; Tn
optimum
Kp; 2 Tn
0.5 Kp; 0.5 Tn
0.5 Kp; Tn
0.5 Kp; 2 Tn
