Application of second-order sliding-mode control algorithms in continuous cycling tests for PID tuning

Continuous cycling tests are widely used in the practice of PID controller tuning. The first continuous cycling test was proposed by J. Ziegler and N. Nichols. It is known as a part of the Ziegler-Nichols closed-loop tuning method. The other part is the tuning rules. This 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 tests ultimate frequency coincides with the phase cross-over frequency of the process/plant. Both tests mentioned above suffer from such a drawback as the change of the phase crossover frequency after PID controller introduction. A new class of continuous cycling tests that are based on second-order sliding mode control algorithms and free from the noted drawback is considered in this paper.