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Article:Ziegler-Nichols closed -Loop MethodFinn HaugenTechTeach17. July 20101 IntroductionZiegler and Nichols published in 1942 a paper [1] where they described twomethods for tuning the parameters of P-, PI- and PID controllers. Thesetwo methods are theZiegler-Nichols closed loop method1, and theZiegler-Nichols open loop method2. The present article describes theclosed-loop method , while the open-loop method is described in anotherarticle (available at ).Ziegler and Nichols [1] used the following definition of acceptable stabilityas a basis for their contoller tuning rules: The ratio of the amplitudes ofsubsequent peaks in the same direction (due to a step change of thedisturbance or a step change of the setpoint in the control loop) isapproximately 1/4, see Figure 1:A2A1=14(1)However, there is no guaranty that the actual amplitude ratio of a givencontrol system becomes 1/4 after tuning with one of the Ziegler andNichols methods , but it should not be very different from 1 that the Ziegler-Nichols closed loop method can be applied only toprocesses having a time delay or having dynamics of order higher than are a few examples of process transfer function models for which themethod cannotbe used:H(s) =Ks(integrator)(2)H(s) =KTs+1(first order system)(3)H(s) =K(s 0)2+2 s 0+1(second order system)(4)1Also denoted theUltimate gain theProcess reaction curve method1yyrA1A2ttvFigure 1.

Process Sensor v y Measured y ySP e u PID u 0 Auto Manual Controller T p Figure2: TheZiegler-Nichols’closedloopmethodisexecutedonanestablished controlsystem. 3.

  Loops, Methods, Closed, Closed loop method