Robust partial quadratic eigenvalue assignment with time delay using the receptance and the system matrices

2016 ◽  
Vol 384 ◽  
pp. 1-14 ◽  
Author(s):  
Zheng-Jian Bai ◽  
Jin-Ku Yang ◽  
Biswa Nath Datta
Keyword(s):  
Time Delay ◽  
Quadratic Eigenvalue ◽  
Eigenvalue Assignment

Eigenvalue Assignment for Control of Time-Delay Systems Via the Generalized Runge–Kutta Method

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
JinBo Niu ◽  
Ye Ding ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Time Delay ◽  
Optimization Techniques ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Kutta Method ◽  
Feedback Controllers ◽  
Runge Kutta Method ◽  
Linear Delay ◽  
Runge Kutta ◽  
Eigenvalue Assignment

This paper presents an eigenvalue assignment method for the time-delay systems with feedback controllers. A new form of Runge–Kutta algorithm, generalized from the classical fourth-order Runge–Kutta method, is utilized to stabilize the linear delay differential equation (DDE) with a single delay. Pole placement of the DDEs is achieved by assigning the eigenvalue with maximal modulus of the Floquet transition matrix obtained via the generalized Runge–Kutta method (GRKM). The stabilization of the DDEs with feedback controllers is studied from the viewpoint of optimization, i.e., the DDEs are controlled through optimizing the feedback gain matrices with proper optimization techniques. Several numerical cases are provided to illustrate the feasibility of the proposed method for control of linear time-invariant delayed systems as well as periodic-coefficient ones. The proposed method is verified with high computational accuracy and efficiency through comparing with other methods such as the Lambert W function and the semidiscretization method (SDM).

An Approach to Partial Quadratic Eigenvalue Assignment of Damped Vibration Systems Using Static Output Feedback

2018 ◽  
Vol 18 (01) ◽  
pp. 1850012 ◽  
Author(s):  
Jiafan Zhang ◽  
Yongxin Yuan ◽  
Hao Liu
Keyword(s):  
Output Feedback ◽  
Second Order ◽  
Order System ◽  
Feedback Gain ◽  
Static Output Feedback ◽  
Homogeneous Matrix ◽  
Quadratic Eigenvalue ◽  
Static Output ◽  
Damped Vibration Systems ◽  
Eigenvalue Assignment

This paper addresses the problem of the partial eigenvalue assignment for second-order damped vibration systems by static output feedback. The presented method uses the combined acceleration, velocity and displacement output feedback and works directly on second-order system models without the knowledge of the unassigned eigenpairs. It allows the input and output matrices to be prescribed beforehand in a simple form. The real-valued spectral decomposition of the symmetric quadratic pencil is adopted to derive a homogeneous matrix equation of output feedback gain matrices that assure the no spillover eigenvalue assignment. The method is validated by some illustrative numerical examples.

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