Fractional Transformation-Based Intelligent H-Infinity Controller of a Direct Current Servo Motor

Muhammad Zia Ur Rahman, Víctor Leiva, Carlos Martin-Barreiro, Imran Mahmood, Muhammad Usman, Mohsin Rizwan

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Direct current (DC) servo motors are central to many complex systems, such as electrical, electro-mechanical, and electro-hydraulic frameworks. In practice, these systems can have nonlinear characteristics and parameter variations. Accurate model representation and position tracking of DC motors are the main issues in many real systems, such as twin rotors, aircraft, airships, and robot manipulators. The precise position tracking of these systems has already been achieved using conventional H-infinity (H (Formula presented.)) controllers. However, the order and structure become more intricate when employing complex weights to shape the closed-loop system, which limits the current proposals. To overcome the above-mentioned limitations, in this article, we provide a precise angular position tracking of a DC servo motor utilizing an intelligent, robust linear controller based on a fixed-structure linear fractional transformation. The conventional H (Formula presented.) controllers are based on the minimization of an unstructured linear fractional transformation objective function that leads to a complex design of these controllers. The main advantage of the proposed intelligent H (Formula presented.) synthesis is the fixed and simple structure that increases its practical implementation. The methodology is formulated in the MATLAB software for the robust design of the proposed synthesis based on an intelligent fixed-structure H (Formula presented.) optimization. Simulation results are compared with conventional H (Formula presented.) and proportional-integral-derivative controllers. The results are also validated experimentally.

Original languageEnglish
Article number29
JournalFractal and Fractional
Issue number1
StatePublished - Jan 2023


  • H controller
  • fixed-structured controllers
  • linear fractional transformation
  • mayfly optimization
  • non-smooth H optimization
  • proportional derivative integral controller


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