# Ziegler–Nichols method

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

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

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