Enhanced relay autotuning of unstable series cascade systems

A widely used controller tuning method is relay autotuning. Approximate values for ultimate gain (Ku) and critical frequency (ωu) are achieved by this tuning procedure. Astrom and Hagglund have proposed a method of estimating Ku and ωu, which considers only fundamental harmonics, neglecting higher order harmonics, hence resulting in erroneous ultimate gain Ku values. In this paper, the effect of higher order harmonic analysis for simultaneous relay autotuning of open loop unstable series cascade systems is studied. Simultaneous relay autotuning for conventional P/PI cascade control configuration is designed for comparison with the proposed method, which utilizes corrected ultimate controller gain values. Three simulation examples are studied in this paper. The two controllers for the two methods are designed using Ziegler–Nichols tuning rules. The proposed method gives significant improvement in both the servo and regulatory responses for the three examples. Robustness studies using complimentary sensitivity function is carried out and robustness is ensured.