## 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) = M_{1}w_{n} + M_{2}δ_{5} + M_{3}b, 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) |
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Pages (from-to) | 739-746 |

Number of pages | 8 |

Journal | IEEE Transactions on Automatic Control |

Volume | 21 |

Issue number | 5 |

DOIs | |

State | Published - Oct 1976 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

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