# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Flervariabla system

(1969) In MSc Theses
Department of Automatic Control
Abstract
In this report multi-input systems are treated by considering the input vector consist of two elements, its magnitude which is a scalar, and a unit vector representing the direction of the control vector (i.e. the ratio between the control signals) in the linear space formed by the control vectors (III:1). <br><br> A formalism for representing multi-variable systems in matrix-form, where the magnitude of the control vector is considered being the one and only input, while the unit vector representing the direction is treated as a parameter of the system itself (III:2). Using this formalism the system is analyzed by methods for single-input systems and after an investigation of the controllability (III:3) and the observability (III:4)... (More)
In this report multi-input systems are treated by considering the input vector consist of two elements, its magnitude which is a scalar, and a unit vector representing the direction of the control vector (i.e. the ratio between the control signals) in the linear space formed by the control vectors (III:1). <br><br> A formalism for representing multi-variable systems in matrix-form, where the magnitude of the control vector is considered being the one and only input, while the unit vector representing the direction is treated as a parameter of the system itself (III:2). Using this formalism the system is analyzed by methods for single-input systems and after an investigation of the controllability (III:3) and the observability (III:4) transfer functions are constructed from the single-input of the formal system to the output signals (III:5). They will provide a profound insight to the poles and zeroes of multi-input systems. <br><br> There will be shown that the poles of the closed-loop system are variables of the magnitude of the input vector only (IV:2). After having fixed the control function for the magnitude of the input vector, i.e. the poles are fixed, the direction of the input vector can be used to create other desirable properties of the system (IV:3). Two cases are considered, a constant or a variable direction of the input vector. Minimum-phase-characters and minimum-energy-control are discussed. Simulation of an example is presented. <br><br> Finally the pole assignment problem is treated (IV:4) and it is shown that if the control-law is bound to be a linear feedback from the state-vector the direction of the control vector must necessarily be a constant. (Less)
author
supervisor
organization
year
type
H3 - Professional qualifications (4 Years - )
subject
publication/series
MSc Theses
report number
TFRT-5067
ISSN
0346-5500
language
Swedish
id
8850836
2016-03-29 16:55:47
date last changed
2016-03-29 16:55:47
```@misc{8850836,
abstract     = {In this report multi-input systems are treated by considering the input vector consist of two elements, its magnitude which is a scalar, and a unit vector representing the direction of the control vector (i.e. the ratio between the control signals) in the linear space formed by the control vectors (III:1). <br><br> A formalism for representing multi-variable systems in matrix-form, where the magnitude of the control vector is considered being the one and only input, while the unit vector representing the direction is treated as a parameter of the system itself (III:2). Using this formalism the system is analyzed by methods for single-input systems and after an investigation of the controllability (III:3) and the observability (III:4) transfer functions are constructed from the single-input of the formal system to the output signals (III:5). They will provide a profound insight to the poles and zeroes of multi-input systems. <br><br> There will be shown that the poles of the closed-loop system are variables of the magnitude of the input vector only (IV:2). After having fixed the control function for the magnitude of the input vector, i.e. the poles are fixed, the direction of the input vector can be used to create other desirable properties of the system (IV:3). Two cases are considered, a constant or a variable direction of the input vector. Minimum-phase-characters and minimum-energy-control are discussed. Simulation of an example is presented. <br><br> Finally the pole assignment problem is treated (IV:4) and it is shown that if the control-law is bound to be a linear feedback from the state-vector the direction of the control vector must necessarily be a constant.},
author       = {Fick, Göran},
issn         = {0346-5500},
language     = {swe},
note         = {Student Paper},
series       = {MSc Theses},
title        = {Flervariabla system},
year         = {1969},
}

```