Ziegler–Nichols method

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Main article: PID controller

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[1]
Control Type K_p K_i K_d
P 0.5 K_u - -
PI 0.45 K_u 1.2 K_p/T_u -
PD 0.8 K_u - K_p T_u/8
classic PID[2] 0.60 K_u 2K_p/T_u K_p T_u/8
Pessen Integral Rule[2] 0.7 K_u 0.4K_p/T_u 0.15K_p T_u
some overshoot[2] 0.33 K_u 2K_p/T_u K_pT_u/3
no overshoot[2] 0.2 K_u 2K_p/T_u K_pT_u/3

Evaluation[edit]

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.[2]

Z–N yields an aggressive gain and overshoot[2] – some applications wish to instead minimize or eliminate overshoot, and for these Z–N is inappropriate.

References[edit]

  1. ^ Ziegler, J.G and Nichols, N. B. (1942). Optimum settings for automatic controllers. Transactions of the ASME 64. pp. 759–768. 
  2. ^ a b c d e f Ziegler-Nichols Tuning Rules for PID, Microstar Laboratories

External links[edit]