Non-parametric tuning of PID Controllers: Evolution of ideas

Non-parametric tuning was introduces by J. Ziegler and N. Nichols with the step test and continuous cycling tests and the respective tuning rules. Whereas the step test based tuning had some feature of parametric tuning, the continuous cycling test based tuning was purely non-parametric. The latter test involves bringing the system under proportional control into a sustained oscillation and measuring the frequency of these oscillations and fixing the gain value, that are called the ultimate frequency and ultimate gain. The test was intended for manual tuning of PID controllers. It is relatively hard to automate, and it is not used in auto-tuners. Another test, called relay feedback test (RFT), was proposed by K. Astrom and T. Hagglund to excite self-oscillations through the inclusion of a nonlinear element (relay) in the control loop. This test is easier to automate, and it found applications in industrial auto-tuners. In both these tests ultimate frequency coincides with the phase cross-over frequency of the process/plant. Yet, both the original continuous cycling test and the RFT suffer from such a drawback as the change of the phase cross-over frequency after PID controller introduction. A new test, the modified relay feedback test (MRFT), which can ensure that the test oscillations are excited at he frequency that becomes the phase cross-over frequency after introduction of a controller in the loop, was recently introduced. This property is attained through coordinated test and tuning, which is considered in the book chapter. Moreover, the tuning rules are optimized for a selected class of processes, which offers the paradigm of optimal non-parametric tuning.