Ultimate Gain Tuning of Control Loops

When only P and / (proportional and integral) actions are used in a controller, the recommended P (proportional gain) is a fraction of the ultimate gain, 0.45 UG. Some controllers use proportional band, which is 100 divided by the proportional gain. 

The value of / (integral action) is set by % (integral time constant) in minutes in some controllers, or the reciprocal, /% as reset rate in repeats/minute, in other controllers. Ziegler and Nichols recommended the value for integral time constant to be set as a fraction of the ultimate peak-to-peak time period, Tj = 0.83 UTP, in units such as minutes. The controller action from the proportional gain times error will 

Robbins recommended using a proportional gain of 0.3 UG for minimum variability in the process response. The recommended integral time constant is 1.0 times UTP for good response to load change and 2.0 times UTP for minimum lAE (integral of absolute error) in response to a step change in setpoint. 

One good feature of the Ziegler-Nichols closed-loop method is that it can be learned more quickly than starting with trial and error alone. There is a procedure to be followed, and the pattern of sustained cycling is easy to recognize. The Ziegler-Nichols method is often completely acceptable for tuning control loops that respond quickly, for example, liquid flow rate control loops that respond with an ultimate peak-to-peak time period (UTP) of 5 to 15 s. 

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