PID  CONTROLLER LABORATORY

If you are controlling temperature, pressure, flow or concentration, you can only suppose that your process has a monotone step response. You don't know anything about the mathematical model (e.g. the process order or transfer function parameters). Thus, you need to obtain some experimental data (see below). After that, you can use the Java applet 'PID Control Laboratory' which offers the model set approach based on experimental data described below and a priori information about the transfer function form. You needn't to know anything about process order, time constants, etc. In frequency domain, the applet shows you the area created by all processes from the model set which satisfy your experimental data. This method is very reliable because all typical process models in the arbitrary order lag/deadtime form are included in the class of a priori admissible processes.

One sample of frequency response

Relay identification experiment is one of the two most common industrial experiments. However, one usually makes two mistakes: The phase shift of the measured sample is -180' and only the nominal model is taken into account for computing controller parameters. These are the reasons why the heuristic methods and the autotuning algorithms of compact controllers often fail. In PID Control Laboratory you can do the following:

• You can arbitrary sample amplitude and phase shift - it can be shown that for PID -135' is optimal if the process gain is not known.
• The applet shows you uncertainty at any frequency produced by all monotone processes of arbitrary order. Therefore, you can make a robust design for complete band of processes (see the right picture).
  
  

Moments of the impulse response

Moments of the impulse response can be obtained from the rectangle pulse experiment which is the second most common in industrial practice. The three characteristic numbers have a meaning of static gain, rais time, and a normalized dead time. By three parameters, one can scale the process in gain, in time and define the shape of step response from processes close to first order to processes close to pure dead time (see the picture below). These three parameters are enough for description of wide range of monotone industrial processes.

You can specify these three numbers in PID Control Laboratory and you'll get the uncertainty in frequency domain. Then you can make a robust design for a complete band of processes

Combination of experimental data

If you have data from more identification experiments you can combine them and compute intersection of uncertainty at each frequency in PID Control Laboratory. The most useful combination is one sample of the frequency response and a static gain of the process.