Eigenstructure assignment for second-order systems using velocity-plus-acceleration feedback

2012 ◽  
Vol 20 (4) ◽  
pp. 465-482 ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Second Order ◽  
Eigenstructure Assignment ◽  
Acceleration Feedback ◽  
Second Order Systems

Eigenstructure Assignment by Displacement–Acceleration Feedback for Second-Order Systems

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Dynamic Response ◽  
Necessary Conditions ◽  
Second Order ◽  
New Technique ◽  
Eigenstructure Assignment ◽  
Mass Matrices ◽  
Acceleration Feedback ◽  
Simulation Results ◽  
A New Technique ◽  
Second Order Systems

Abstract This paper presents a new technique for controlling the dynamic response of second-order systems by means of combined displacement and acceleration feedback. The necessary conditions that guarantee the solvability for the problem are formulated. Parametric expressions for the displacement–acceleration gains and the eigenvector matrix are derived. The solution can be applied for the systems with nonsingular or singular mass matrices. Based on the simulation results, we can conclude that the proposed technique is effective.

scholarly journals Finite-Time Trajectory Tracking of Second-Order Systems Using Acceleration Feedback Only

Automation ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 266-277
Author(s):  
Romain Delpoux ◽  
Thierry Floquet ◽  
Hebertt Sira-Ramírez
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Algebraic Approach ◽  
Second Order ◽  
Asymptotic State ◽  
Control Input ◽  
Positioning Systems ◽  
Acceleration Feedback ◽  
On Line ◽  
Second Order Systems

In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems such as positioning systems and force-position controllers in robotic systems and aerospace applications. Based on an algebraic approach, an on-line algebraic estimator is developed in order to estimate in finite time the unmeasured position and velocity variables. The obtained expressions depend solely on iterated integrals of the measured acceleration output and of the control input. The approach is shown to be robust to noisy measurements and it has the advantage to provide on-line finite-time (or non-asymptotic) state estimations. Based on these estimations, a quasi-homogeneous second-order sliding mode tracking control law including estimated position error integrals is designed illustrating the possibilities of finite-time acceleration feedback via algebraic state estimation.

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

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Degrees Of Freedom ◽  
Sufficient Conditions ◽  
Second Order ◽  
Descriptor Systems ◽  
Practical Applications ◽  
Mass Matrices ◽  
Acceleration Feedback ◽  
Descriptor Matrix ◽  
Second Order Systems ◽  
Necessary And Sufficient

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.

scholarly journals ℋ∞ Control Tunning to Guarantee the Output Performance of LTI Second-Order Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 4611-4616
Author(s):  
Ramón I. Verdés ◽  
Luis T. Aguilar ◽  
Yury Orlov
Keyword(s):  
Second Order ◽  
Output Performance ◽  
Second Order Systems

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

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