Universal Method of Static Output Feedback Pole Placement for Fourth-Order Linear Time-Invariant Systems with Two Inputs and Two Outputs

A universal analytical method of static output feedback pole placement (for constructing controllers by output) for fourth-order linear time-invariant systems with two control inputs and two observable outputs is proposed, which does not depend on the relations between the controllability and observ...

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Vydáno v:Journal of computer & systems sciences international Ročník 64; číslo 2; s. 153 - 168
Hlavní autoři: Zubov, N. E., Lapin, A. V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.04.2025
Springer Nature B.V
Témata:
Closed loops
Control
Control in Deterministic Systems
Control systems
Controllability
Controllers
Decomposition
Determinants
Engineering
Feedback control
Mechatronics
Observability (systems)
Output feedback
Pole placement
Polynomials
Robotics
Time invariant systems
modal output control
observability index
trace of matrix
controllability index
complete modal controllability by output
static output feedback pole placement
one-sided matrix equation
fourth-order control system
ISSN:1064-2307, 1555-6530
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Shrnutí:A universal analytical method of static output feedback pole placement (for constructing controllers by output) for fourth-order linear time-invariant systems with two control inputs and two observable outputs is proposed, which does not depend on the relations between the controllability and observability indices. The method does not require decomposing or reducing the system and may be applied to any fourth-order systems modally controllable by static output feedback, including systems irreducible to control (observation) with a single input (output). The method is based on linear matrix dependence of the characteristic polynomial of a closed-loop control system on the coefficients and determinant of a matrix of controller by output. The proposed approach gives the necessary and sufficient condition for static output feedback pole placement—it allows defining all possible matrices of controllers by output and the conditions of their existence. A new algebraic criterion of complete modal controllability by output is formulated and proved. Examples of applying the approach to controlling the aviation and space systems based on linearized models both in numerical and symbolic form are given.
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ISSN:1064-2307
1555-6530
DOI:10.1134/S1064230725700121