Modeling Linear Systems for Pulsewidth-Modulated Control

Bernard Friedland

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10 Scopus citations


An approximate linear model is developed for a linear process in which the control signal can assume only two values, Umax and and which is controlled by varying the fraction δn of a sampling cycle of duration T that the control is at Umax. The dynamic equations are of the form [formulla omitted] where wn is related to the average state xn over one cycle, and rn = δn − δs where δs is the steady-state value of δn required to maintain a desired average state xd. The system error e(nT) at sampling intervals is related to these variables by an equation of the form e(nT) = M1wn + M2δ5 + M3b, where b is a bias vector. These relations may be used to design a linear control system by well-known techniques for discrete-time systems. The method is illustrated by the design of a third-order process which could represent a temperature control problem. Simulation results are given for a design that includes a Kalman filter for estimating the inaccessible states.

Original languageEnglish (US)
Pages (from-to)739-746
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - Oct 1976
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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