Controllability and Observability of Linear Matrix-Second-Order Systems

1980 ◽  
Vol 47 (2) ◽  
pp. 415-420 ◽  
Author(s):  
P. C. Hughes ◽  
R. E. Skelton
Keyword(s):  
Positive Definite ◽  
Second Order ◽  
Special Structure ◽  
Linear Matrix ◽  
Sensors And Actuators ◽  
Modal Behavior ◽  
Second Order Systems ◽  
Controllability And Observability ◽  
Output Equation

This paper studies the controllability and observability of the system Mq¨ + Gq˙ + Kq = Bu, where M is symmetric and positive-definite, G is skew-symmetric and K is symmetric. In all cases, the output equation is y = Pq + Rq˙. This special structure is exploited to derive relatively simple controllability and observability conditions which are shown to provide important insights on the modal behavior of the system and to furnish information on the number and positioning of sensors and actuators.

Modal Cost Analysis for Linear Matrix-Second-Order Systems

1980 ◽  
Vol 102 (3) ◽  
pp. 151-158 ◽  
Author(s):  
R. E. Skelton ◽  
P. C. Hughes
Keyword(s):  
Cost Analysis ◽  
Attitude Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Performance Criterion ◽  
Second Order ◽  
Linear Matrix ◽  
Early Model ◽  
Second Order Systems ◽  
Mode Truncation

Reduced models and reduced controllers for systems governed by matrix-second-order differential equations are obtained by retaining those modes which make the largest contributions to quadratic control objectives. Such contributions, expressed in terms of modal data, are called “modal costs” and when used as mode truncation criteria, allow the statement of the specific control objectives to influence the early model reduction from very high order models which are available, for example, from finite element methods. The relative importance of damping, frequency and eigenvector in the mode truncation decisions are made explicit for each of these control objectives: attitude control, vibration suppression and figure control. The paper also shows that using Modal Cost Analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop modal coordinates which are most critical to the quadratic control performance criterion. In this way, the modes which should be controlled (and hence the modes which must be observable by choice of measurements), are deduced from truncations of the optimal controller.

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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