Eigenvalue assignment in linear time-invariant closed-loop systems incorporating multi-variable three-term controllers†

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.

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Low-order multi-rate linear time-invariant decentralized trackers using the new observer-based sub-optimal method for unknown sampled-data nonlinear time-delay system with closed-loop decoupling

Optimal Control Applications and Methods ◽

10.1002/oca.955 ◽

2010 ◽

Vol 32 (4) ◽

pp. 433-475 ◽

Cited By ~ 8

Author(s):

N. T. Hu ◽

J. S. H. Tsai ◽

S. M. Guo ◽

L. S. Shieh ◽

Y. Chen

Keyword(s):

Time Delay ◽

Closed Loop ◽

Linear Time ◽

Delay System ◽

Sampled Data ◽

Time Delay System ◽

Optimal Method ◽

Linear Time Invariant ◽

Time Invariant ◽

Low Order

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Proportional–integral–derivative controller family for pole placement

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406216651893 ◽

2016 ◽

Vol 231 (20) ◽

pp. 3791-3797 ◽

Cited By ~ 1

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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Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

Journal of Electrical Engineering ◽

10.2478/v10187-011-0007-1 ◽

2011 ◽

Vol 62 (1) ◽

pp. 44-48 ◽

Cited By ~ 2

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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