Closed loop experiment design for linear time invariant dynamical systems via LMIs

Automatica ◽  
2008 ◽  
Vol 44 (3) ◽  
pp. 623-636 ◽  
Author(s):  
Håkan Hjalmarsson ◽  
Henrik Jansson
Keyword(s):  
Dynamical Systems ◽  
Closed Loop ◽  
Linear Time ◽  
Experiment Design ◽  
Linear Time Invariant ◽  
Time Invariant

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 Complete Controllability of Impulsive Fractional Linear Time-Invariant Systems with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xian-Feng Zhou ◽  
Song Liu ◽  
Wei Jiang
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Linear Time ◽  
Complete Controllability ◽  
Linear Time Invariant ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Some flaws on impulsive fractional differential equations (systems) have been found. This paper is concerned with the complete controllability of impulsive fractional linear time-invariant dynamical systems with delay. The criteria on the controllability of the system, which is sufficient and necessary, are established by constructing suitable control inputs. Two examples are provided to illustrate the obtained results.

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.

scholarly journals Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

2011 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Paknosh Karimaghaee ◽  
Navid Noroozi
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Linear Time ◽  
Order Reduction ◽  
Bilinear Transformation ◽  
Reduced Order ◽  
Linear Time Invariant ◽  
The Stability ◽  
Controllability And Observability ◽  
Time Invariant

Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear TransformationThis paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed ins-plane. Then, bilinear transformation is applied to map the closed loop system toz-plane. Next, new closed loop controllability and observability grammians are calculated inz-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.

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