Matrix Second-order Linear Systems Research Articles

Robust Solution for Second-Order Systems Using Displacement–Acceleration Feedback

This paper addresses the robust and minimum norm controller design for matrix second-order linear systems by means of combined displacement and acceleration feedback. First, the necessary conditions that ensure solvability are presented. Then, the parametric expressions of gain controller and eigenvector matrix are formulated on the basis of a set of free parameters. The proposed solution simultaneously makes the resulting closed-loop system numerically robust and obtains gain controllers with minimum norms. Also, the solution is general and can be applied when mass matrices are either singular or nonsingular. This is promising for better applicability in many practical applications. Finally, two examples are provided to illustrate the effectiveness of the proposed control strategy.

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

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.

Robust pole placement for second‐order linear systems using velocity‐plus‐acceleration feedback

This paper considers the robust pole assignment problem using combined velocity and acceleration feedbacks for matrix second-order linear systems. The necessary and sufficient conditions which ensure solvability are derived. Based on recently developed parametric solution to the eigenstructure assignment problem by velocity-plus-acceleration feedback, a new technique is described to perform robust pole placement for second-order systems. The available degrees-of-freedom offered by the velocity-plus-acceleration feedback in selecting the associated eigenvectors are utilised to improve robustness of the closed-loop system. The main advantage of the described approach is that the problem is tackled in the second-order form without transformation into the first-order form. Finally, several examples are introduced to demonstrate the effectiveness of the proposed approach.

Hilbert-Schmidt-Hankel norm model reduction for matrix second-order linear systems

This paper considers the optimal model reduction problem of matrix second-order linear systems in the sense of Hilbert-Schmidt-Hankel norm, with the reduced order systems preserving the structure of the original systems. The expressions of the error function and its gradient are derived. Two numerical examples are given to illustrate the presented model reduction technique.

Observer design for matrix second order linear systems with uncertain disturbance input-a parametric approach

A simple parametric approach to design a full-order observer for matrix second-order linear systems with uncertain disturbance input in the matrixsecond-order framework is proposed. The basic idea is to minimize the H 2 norm of the transfer function from disturbance to estimation error using the design degrees of freedom provided by a parametric approach in the observer design. Besides the design parameters, the eigenvalues of the closed-loop system are also optimized within desired regions on the left-half of the complex plane. Using the proposed approach, additional specifications can be easily achieved. A spring-mass system is using to show the effect of the proposed approaches.

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parameteric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.

Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

Abstract A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H 2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.