Advances in Helicopter Vibration Control Methods Time-Periodic Reduced Order Modeling and H2/H-Infinity Controller Design

2012 ◽  
Author(s):  
Fatma Ulker ◽  
Fred Nitzsche
Keyword(s):  
Vibration Control ◽  
Controller Design ◽  
Reduced Order Modeling ◽  
Control Methods ◽  
H Infinity ◽  
Reduced Order ◽  
Time Periodic ◽  
Helicopter Vibration

Solving Vibration Control Problems Using Reduced Order Models for Flexible Structures: A Genetic Algorithm Approach

1997 ◽  
Author(s):  
Sourav Kundu ◽  
Kentaro Kamagata ◽  
Shigeru Sugino ◽  
Takeshi Minowa ◽  
Kazuto Seto
Keyword(s):  
Genetic Algorithm ◽  
Vibration Control ◽  
Controller Design ◽  
Fitness Function ◽  
Flexible Structures ◽  
Design Solution ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Fitness Value ◽  
Genetic Algorithm Approach

Abstract A Genetic Algorithm (GA) based approach for solution of optimal control design of flexible structures is presented in this paper. The method for modeling flexible structures with distributed parameters as reduced-order models with lumped parameters, which has been developed previously, is employed. Due to some restrictions on controller design it is necessary to make a reduced-order model of the structure. Once the model is established the design of flexible structures is considered as a feedback search procedure where a new solution is assigned some fitness value for the GA and the algorithm iterates till some satisfactory design solution is achieved. We propose a pole assignment method to determine the evaluation (fitness) function to be used by the GA to find optimal damping ratios in passive elements. This paper demonstrates the first results of a genetic algorithm approach to solution of the vibration control problem for practical control applications to flexible tower-like structures.

Reduced Order Controller Design for Nonlinear Systems With Periodic Coefficients

2009 ◽  
Author(s):  
Amit P. Gabale ◽  
Subhash C. Sinha
Keyword(s):  
Controller Design ◽  
Linear Part ◽  
Eigenvalue Decomposition ◽  
Order System ◽  
Time Varying ◽  
Periodic Coefficients ◽  
Reduced Order ◽  
Periodic Linear ◽  
Time Invariant ◽  
Time Periodic

This study provides a methodology for reduced order controller design for nonlinear dynamic systems with time-periodic coefficients. System equations are represented by quasi-linear differential equations in state space, containing a time-periodic linear part and nonlinear monomials of states with periodic coefficients. The Lyapunov-Floquet (L-F) transformation is used to transform the time-varying linear part of the system into a time-invariant form. Eigenvalue decomposition of the time-invariant linear part can then be used to identify the dominant/ non-dominant dynamics of the system. The non-dominant states of the system are expressed as a nonlinear, time-periodic, manifold relationship in terms of the dominant states. As a result, the original large system can be expressed as a lower order system represented only by the dominant states. A reducibility condition is derived to provide conditions under which a nonlinear order reduction is possible. Then a proper coordinate transformation and state feedback can be found under which the reduced order system is transformed into a linear, time-periodic, closed-loop system. This permits the design of a time-varying feedback controller in linear space to guarantee the stability of the system. The proposed methodology is illustrated by designing a reduced order controller for a 4-dof, inverted pendulum subjected to a periodic follower force. Treatment for the time-invariant case is also included as a subset of the problem.

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