Control System Loop-Shaping as a Mathematical Optimization Problem: An Ensemble of Models

Baraa Mohandes, Igor Boiko, Youssef Abdel-Magid

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper proposes an extension to the established loop-shaping method, where the loop-shaping method is modeled mathematically and solved as a mathematical optimization program. In this process, a novel cost function is proposed and employed as the objective of optimization in the controller tuning problem. This cost function evaluates different characteristics of the system in the frequency domain, such as the stability margins and the operability bandwidth. These characteristics reflect the quality of load disturbance rejection, set-point tracking, and operability bandwidth of the control system. Consequently, the proposed technique circumvents running a time-domain simulation completely. More importantly, the proposed technique can be used with any controller structure. The generic cost function can be customized to fit any control objective and application. This is conducted in the second half of this paper, with the aim of obtaining a system with near-optimum time-domain performance with respect to the integral of time times absolute error (ITAE) criterion. At the same time, the control system obtained with the customized cost function has better operability bandwidth than that of a system optimized in the time-domain for the ITAE criterion. The proposed optimization model is analyzed for two plant models: first order and second order plus dead-time (FOPDT), (SOPDT), respectively.

Original languageBritish English
Article number9151959
Pages (from-to)137185-137197
Number of pages13
JournalIEEE Access
StatePublished - 2020


  • crossover frequency
  • dead time processes
  • error magnitude
  • Frequency domain optimization
  • ITAE
  • Nyquist plot
  • operability bandwidth
  • stability margins


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