AN IMPROVED RELAY AUTO TUNING OF PID CONTROLLERS FOR CRITICALLY DAMPED SOPTD SYSTEMS

Abstract

Using a single-symmetric relay feedback test, a method is proposed to identify all three parameters of a stable second-order plus time delay (SOPTD) model with equal time constants [k_p exp(-Ds)/(τs + 1)²]. The conventional analysis of the relay auto-tune method gives 27% error in the calculation of k_u, for a large D/τ. In the present work, a method is proposed to improve the accuracy in the k_u calculation by incorporating higher order harmonics. Three simulation examples are given for SOPTD and higher order time delay transfer function models. The estimated model parameters of the SOPTD model are compared with those of the Li et al. (1991) method and those of the Thyagarajan and Yu (2003) method. The open-loop performance of the identified model is compared with that of the actual system. The proposed method gives performance close to that of the actual system. Simulation results are also given for a nonlinear bioreactor system. The closed-loop performance of the model identified by the proposed method is close to that of the actual system.

Keywords:

• Auto tuning
• Critically damped system
• Identification
• Soptd model
• Symmetric relay
• Transfer function

Notes

% Error in k_u = (k_{u principle harmonics} - k_{u exact})/k_{u exact}.

Model used for simulation: G(s) = exp(−10 s)/(s + 1)².

A locally linearized model.

PID controller settings by Equations (56) and (57).

For simulation example: G(s) = 0.125 exp(−s)/(s + 1)³.