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Ziegler-Nichols

Ziegler-Nichols method

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Principle of the method

The Ziegler-Nichols method allows the parameters of the regulator controlling the PROCESS process to be adjusted.

By simulating the loop in the figure above for various models, Ziegler and Nichols (ZN) searched for the parameters of the PI, PD, PID regulators minimizing the J criterion, during an index variation of the setpoint, the system being in steady state at time t=0.

The method used is called «Pumping limit»

The process being looped by a proportional action regulator only, the critical gain Kcr is increased until sustained oscillations appear (pumping phenomenon).

Method activation

The method is activated by selecting « Ziegler-Nichols » from the main menu bar of HydroStab:

By default, HydroStab runs the Ziegler-Nichols search method in automatic mode.

It is possible to perform this search in manual mode. To do this:

  • Enter the command Auto_ZN=%f in the Scilab console
  • In this case, the operator must modify the gain Kcr at each iteration
  • Initialization of the algorithm

    The ZN model parameters are initialized, by default, with the values Ti=1.e+4 s, Td=0 s, and Kd=10. These values inhibit the Integral action and the derivative action.

    The critical gain Kcr is initialized with the inverse of the optimization coefficient, applied to the current Kp value: : Kcr=Kp/0.6

    The other constants Ts, Tw, k, Gain, aut, Ta, r2, ty are identical to those corresponding to the simulation of the transfer function in progress in HydroStab.

    Setting the critical gain Kcr

    When the procedure is launched, an initial simulation is carried out with the input parameters specified above.

    A digital oscilloscope can be used to monitor the step response of the process, looped back by its PID corrector.

    The period of the oscillations is automatically calculated by HydroStab, considering the average of the recorded time intervals:

    Manual adjustment

    Validation of calculations

    When the pumping limit is reached, the calculation rule for the PID corrector parameters is then applied:

    Activation in automatic mode

    Under these conditions, HydroStab automatically searches for the value of the gain Kcr by a series of iterations with variable steps, to determine a precise value of the gain to 1/1000 IIth.

    Comparison of the Module Margin and Ziegler-Nichols Methods

    The margin gain goes from de 6 dB (FT1 : Module Margin) to 3.45 dB (FT2 : Ziegler-Nichols)


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