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Technical Brief

Parametric Approach for Eigenstructure Assignment in Descriptor Second-Order Systems via Velocity-Plus-Acceleration Feedback

[+] Author and Article Information
Taha H. S. Abdelaziz

Department of Industrial Engineering,
Faculty of Engineering,
Northern Border University, Arar, KSA;
Department of Mechanical Engineering,
Faculty of Engineering,
Helwan University, 1 Sherif Street,
Helwan 11792, Cairo, Egypt
e-mail: tahahelmy@helwan.edu.eg

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 8, 2013; final manuscript received February 9, 2014; published online April 28, 2014. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 136(4), 044505 (Apr 28, 2014) (8 pages) Paper No: DS-13-1263; doi: 10.1115/1.4026876 History: Received July 08, 2013; Revised February 09, 2014

In this article, the problem of eigenstructure in descriptor matrix second-order linear systems using combined velocity and acceleration feedbacks is considered. This is promising for better applicability in many practical applications where the velocity and acceleration signals are easier to obtain than the proportional and velocity ones. First, the necessary and sufficient conditions which ensure solvability are derived. Then the parametric expressions of gain controller and eigenvector matrix are formulated. The proposed approach can offer all the degrees of freedom and has great potential in practical applications. The solution is general and can be applied when mass matrices that can be either singular or nonsingular. In this framework, infinite eigenvalues for descriptor systems are relocated by finite ones.

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System's response for the simulation example

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