Abstract
ABSTRACT A robust control and stability analysis of a tuned mass damper attached to benchmark the model of mass-spring-damper system via different Kharitonov-related approaches, including the post-Kharitonov Edge Theorem, is presented in this paper. The control of uncertain parameters of the given system is demonstrated via robust Proportional-Integral-Derivative (PID) system tuning techniques in MATLAB. Usually, the Kharitonov theorem is sufficient to check the stability analysis of a controlled interval system. A detailed stability analysis of the given system by forming the Kharitonov rectangular parameter boxes and testing the positivity of Hurwitz determinants of the enclosed segments connecting opposite corners of the box is explained here. Stability checking is validated by the analysis based on the Hurwitz matrices of two Kharitonov polynomials. The multi-linear affine system model in the overall system plant is controlled and analysed via Edge theorem.
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