Synthesis of asymptotically stable linear time-invariant closed-loop systems incorporating multivariable 3-term controllers

1969 ◽  
Vol 5 (22) ◽  
pp. 557 ◽  
Author(s):  
B. Porter
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Asymptotically Stable ◽  
Linear Time Invariant ◽  
Closed Loop Systems ◽  
Time Invariant ◽  
Stable Linear

scholarly journals Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 300
Author(s):  
Marcin Bąkała ◽  
Piotr Duch ◽  
J. A. Tenreiro Machado ◽  
Piotr Ostalczyk ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Closed Loop ◽  
Linear Time ◽  
Classical Model ◽  
Linear Difference Equation ◽  
Discrete Models ◽  
Measured Velocity ◽  
Linear Time Invariant ◽  
Wheel Drive ◽  
Time Invariant

This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate. A classical model described by the second-order linear difference equation is used as the reference. According to the sum of the squared error criterion (SSE), we compare a two-parameter integer order model with four-parameter non-commensurate and three-parameter commensurate FO descriptions. The computer simulation results are compared with the measured velocity of a real autonomous platform powered by a closed-loop electric individual-wheel drive.

scholarly journals Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 915
Author(s):  
Robert Vrabel
Keyword(s):  
Linear Systems ◽  
Linear Time ◽  
Upper Bounds ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Lower And Upper Bounds ◽  
Linear Time Invariant ◽  
Vector Norm ◽  
Linear Time Invariant Systems ◽  
Stable Linear

Based on the eigenvalue idea and the time-varying weighted vector norm in the state space R n we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones.

Proportional–integral–derivative controller family for pole placement

2016 ◽  
Vol 231 (20) ◽  
pp. 3791-3797 ◽  
Author(s):  
Chimpalthradi R Ashokkumar ◽  
George WP York ◽  
Scott F Gruber
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Proportional Integral Derivative ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral ◽  
Linear Time Invariant ◽  
Generalized Eigenvalue ◽  
Square Systems ◽  
Time Invariant

In this paper, linear time-invariant square systems are considered. A procedure to design infinitely many proportional–integral–derivative controllers, all of them assigning closed-loop poles (or closed-loop eigenvalues), at desired locations fixed in the open left half plane of the complex plane is presented. The formulation accommodates partial pole placement features. The state-space realization of the linear system incorporated with a proportional–integral–derivative controller boils down to the generalized eigenvalue problem. The generalized eigenvalue-eigenvector constraint is transformed into a system of underdetermined linear homogenous set of equations whose unknowns include proportional–integral–derivative parameters. Hence, the proportional–integral–derivative solution sets are infinitely many for the chosen closed-loop eigenvalues in the eigenvalue-eigenvector constraint. The solution set is also useful to reduce the tracking errors and improve the performance. Three examples are illustrated.

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