An improved relay auto tuning of PID controllers for unstable FOPTD systems

Using a single symmetric relay feedback test, a method is proposed to identify all the three parameters of a first order plus time delay (FOPTD) unstable model. It is found by simulation that, the relay autotune method gives −23% error in the calculation of ku, when D/τ = 0.6. In the present work, a method is proposed, by incorporating the higher order harmonics to explain the error in the ku calculation. A method is proposed to estimate all the parameters of an unstable FOPTD system. Two simulation results are given on unstable first and second order plus time delay transfer function models. The estimated model parameters of the unstable FOPTD model are compared with the methods of Majhi, S. & Atherton, D.P. [(2000). Online tuning of controllers for an unstable FOPTD process. IEE Proceedings Control Theory Applications, 147(4), 421–427] and the Thyagarajan, T., & Yu, C.C. [(2003). Improved autotuning using the shape factor from relay feedback, Industrial engineering Chemistry Research, 42, 4425–4440] PID controllers are designed for the identified model and for the actual system. The proposed method gives performance close to that of the actual system. For a second order plus time delay system, the latter two methods fail to identify the FOPTD model. Simulation results are also given for a nonlinear bioreactor system. The PID controller designed on the model identified by the proposed method gives a performance close to that of the controller designed on the locally linearized model.