Algebraic Methods in Autotuning Design: Theory and Design

  • Roman ProkopEmail author
  • Jiří Korbel
  • Libor Pekař
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 348)


The contribution presents a set of single input – output (SISO) principles for the design and tuning of continuous-time controllers for the utilization in autotuning schemes. The emphasis of the design is laid to SISO systems with time delays. Models with up to three parameters can estimated by means of a single relay experiment. Then a stable low order transfer function with a time delay term is identified. Two algebraic control syntheses then are presented in this paper. The first one is based on the ring of proper and stable rational functions R PS. The second one utilizes a special ring R MS, a set of RQ-meromorphic functions. In both cases, controller parameters are derived through a general solution of a linear Diophantine equation in the appropriate ring. The generalization for a two degree of freedom (2DOF) control structure is outlined. A final controller can be tuned by a scalar real parameter m>0. The presented philosophy covers a generalization of PID controllers and the Smith-like control structure. The analytical simple rule is derived for aperiodic control response in the R PS case.


Algebraic control design Diophantine equation Relay experiment Autotuning Pole-placement problem Smith predictor 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of applied informaticsTomas Bata University in ZlínZlínCzech Republic

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