Relay Feedback Autotuning – A Polynomial Design Approach

Abstract

A method of autotuning using an asymmetric relay with hysteresis feedback test is proposed and developed. Then, three parameters for aperiodic first or second order transfer functions can be obtained. After the identification relay experiment, controller parameters are computed through linear diophantine equation in the ring of proper and stable rational functions. This algebraic approach for a traditional 1-DOF feedback structure generates a class of PI or PID controllers. The pole placement principle in the methodology brings a scalar positive "tuning knob" for additional controller tuning. A Matlab-Simulink program implementation was developed for simulation and verification of the studied approach. Two illustrative examples support simplicity and efficiency of the proposed methodology.

Relay Feedback Autotuning – Implementation and Simulation

“…The estimation of first and second order transfer function parameters is performed from asymmetric limit cycle data, see [7], [8], [18], [19], [20] . The control synthesis is carried out through the solution of a linear diophantine equation according to [16], [17] in the ring of proper and stable rational functions RPS. This approach defines a scalar tuning parameter which can be adjusted by various strategies ( [4], [18], [20], [22]).…”

“…The formulas for the calculation of estimated parameters (1) are generally known and can be found e.g. [7], [8], [16], [17], various details for relay parameter identification are adopted from [23], [24].…”

“…the ring of stable and proper rational function RPS (e.g. [17], [20]), the ring of stable and proper meromorphic functions RMS, see [8], [19], [21].…”

A Class of PID Controllers Tuned in Fractional Representation

“…The traditional engineering design approach of PID like controllers was performed either in the frequency domain or in polynomial representation, see e. g. Åström and Hägglund, (1995). Nevertheless, the fractional approach developed in (Vidyasagar, 1985;Kučera, 1993) and analyzed in (Prokop and Corriou, 1997;Prokop et al, 2005Prokop et al, , 2010) enables a deeper insight into control tuning and a more elegant expression of all suitable controllers.…”

“…where K is a process gain and T u is the ultimate period obtained from the Ziegler-Nichols experiment. However, the fulfillment of (23) by unique value of m>0 is impossible, see Prokop, et al (2010). The exact fulfillment of both relations in (23) could be obtained in the case of distinct poles at the right side of (16).…”