Hello,
Basically Ziegler and Nichols tuning rules are as follows. Integrating and derivative components of the control are disabled and the proportional gain is increased until the loop is brought to self-exciting oscillations. Frequency of the oscillations and the value of the proportional gain are recorded. They are called ultimate frequency Fu and ultimate gain Ku. After that ultimate period is calculated as an inverse of ultimate frequency: Tu=1/Fu and the gains of the PID control are calculated in accordance with the following rules: For P-controller: Kp=0.5Ku; for PI-controller; Kp=0.4Ku, Ti=0.8Tu; for PID-controller Kp=0.6Ku, Ti=0.5Tu, Td=0.12Tu.
The experiment of bringing the system into self-excited oscillations provides one point of the Nyquist plot of the process. This is the point of
intersection of the Nyquist plot with the real axis. After that the controller gains are chosen so that stability of about 6db of gain margin (this is an exact value in case of P-control, and approximate value in most cases of PI or PID-control) would be insured. This method was developed in the forties. Now more sophisticated methods are available.
Regards,
Dr. Igor Boiko
Consulting in Control is available
(including modeling, simulations and control design) [email protected]
Tel: 1-403-294-2745
Ziegler and Nichols worked for Taylor Instrument Companies in the days when controllers were typically pneumatic. Be careful of the units. The numbers were arrived at using experience, some maths and a lot of testing. Their paper was published by the American Society of Mechanical Engineers in 1942. I'm sure you could get a copy somewhere if you are interested.
Optimum Settings for Automatic Controlers. J. G. Ziegler and N. B. Nichols. Trans. ASME, 64, 759-768 (Nov. 1942)
A copy is also available in the textbook Automatic Control - Classical Linear Theory. Ed: George J Thaler. Pub: Dowden, Hutchinson and Ross, Inc. It also has some other interesting old papers by people like Bode and Nyquist and an 1868 mathematical analysis by J. C. Maxwell of the governors of Watt, Jenkins, Thompson
and Foucault.
If you are having trouble tuning then you could do a search for automatic controller tuning. There are a number of methods used. Any method is only part of the exercise. First step is to determine and define the tuning strategy. Second is to tune according to one of the methods (or experience) and third to fine tune the settings to achieve the defined stategy using a combination of response testing, experience and trial and error.
There's more to it than that from what I've found in my searching.
There are open loop and closed loop tuning procedures. What Dr.Boiko is describing if the closed loop procedure. As well, the multipliers (0.4, 0.8, etc.) are different for different forms of the PID equation used (standard ISA, Fischer, etc.). This means you need to know what form of the PID equation your loop controller is using.
