Modeling Linear Systems for Pulsewidth-Modulated Control

Bernard Friedland

doi:10.1109/TAC.1976.1101367

Modeling Linear Systems for Pulsewidth-Modulated Control

Bernard Friedland

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10 Scopus citations

Abstract

An approximate linear model is developed for a linear process in which the control signal can assume only two values, U_max and and which is controlled by varying the fraction δ_n of a sampling cycle of duration T that the control is at U_max. The dynamic equations are of the form [formulla omitted] where w_n is related to the average state x_n over one cycle, and r_n = δ_n − δ_s where δ_s is the steady-state value of δ_n required to maintain a desired average state x_d. The system error e(nT) at sampling intervals is related to these variables by an equation of the form e(nT) = M₁w_n + 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 language	English (US)
Pages (from-to)	739-746
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	21
Issue number	5
DOIs	https://doi.org/10.1109/TAC.1976.1101367
State	Published - Oct 1976
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.1976.1101367

Cite this

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title = "Modeling Linear Systems for Pulsewidth-Modulated Control",

abstract = "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.",

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year = "1976",

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AU - Friedland, Bernard

PY - 1976/10

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N2 - 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.

AB - 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.

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Modeling Linear Systems for Pulsewidth-Modulated Control

Abstract

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