Multiple zeta function

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. The Ziegler–Nichols tuning method is a heuristic method of tuning a PID controller. It was developed by John G. Ziegler and Nathaniel B. Nichols. It is performed by setting the I (integral) and D (derivative) gains to zero. The "P" (proportional) gain, $K_p$ is then increased (from zero) until it reaches the ultimate gain $K_u$, at which the output of the control loop oscillates with a constant amplitude. $K_u$ and the oscillation period $T_u$ are used to set the P, I, and D gains depending on the type of controller used:

Ziegler–Nichols method
Control Type	$K_p$	$K_i$	$K_d$
P	$0.5K_u$	-	-
PI	$0.45K_u$	$K_p/T_u/1.2$	-
PD	$0.8K_u$	-	$K_p{T}_u/8$
classic PID	$0.60K_u$	$2K_p/T_u$	$K_p{T}_u/8$
Pessen Integral Rule	$0.7K_u$	$2.5K_p/T_u$	$0.15K_p{T}_u$
some overshoot	$0.33K_u$	$2K_p/T_u$	$K_p{T}_u/3$
no overshoot	$0.2K_u$	$2K_p/T_u$	$K_p{T}_u/3$

Evaluation

Z–N tuning creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications.

• "The Ziegler-Nichols tuning rule is meant to give PID loops best disturbance rejection

Z–N yields an aggressive gain and overshoot – some applications wish to instead minimize or eliminate overshoot, and for these Z–N is inappropriate.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

• Template:Cite web

External links

• http://controls.engin.umich.edu/wiki/index.php/PIDTuningClassical#Ziegler-Nichols_Method

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