Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges

This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type frequency-dependent balanced truncation} to copy with the cases that only a single dominating point of the operating frequency interval is pre-known, the other is \emph{interval-type frequency-dependent balanced truncation} to deal with the cases that both of the upper and lower bound of frequency interval are known \emph{a priori}. SF-type error bound and interval-type error bound are derived for the first time to estimate the desired approximation error over pre-specified frequency interval. We show that the new methods generally lead to good in-band approximation performance, at the same time, provide accurate error bounds under certain conditions. Examples are included for illustration.Comment: prepared to submit for International Journal of Contro

Optimal Linear Parameter-Varying Control Design for a Pressurized Water Reactors

The applicability of employing parameter-dependent control to a nuclear pressurized water reactor is investigated. The synthesis techque produces a controller which achieves specified performance against the worst-case time variation of a measurable parameter which enters the plant in a linear fractional manner. The plant can thus have widely varying dynamics over the operating range. The results indicate this control technique is comparable to linear control when small operating ranges are considered

Reduced-Order Reference Models for Adaptive Control of Space Structures

In addition to serving as a brief overview of aspects relevant to reduced-order modeling (in particular balanced-state and modal techniques) as applied to structural finite element models, this work produced tools for visualizing the relationship between the modes of a model and the states of its balanced representation. Specifically, error contour and mean error plots were developed that provide a designer with frequency response information absent from a typical analysis of a balanced model via its Hankel singular values. The plots were then used to analyze the controllability and observability aspects of finite element models of an illustrative system from a modal perspective -- this aided in the identification of computational artifacts in the models and helped predict points at which to halt the truncation of balanced states. Balanced reduced-order reference models of the illustrative system were implemented as part of a direct adaptive control algorithm to observe the effectiveness of the models. It was learned that the truncation point selected by observing the mean error plot produced the most satisfactory results overall -- the model closely approximated the dominant modes of the system and eliminated the computational artifacts. The problem of improving the performance of the system was also considered. The truncated balanced model was recast in modal form so that its damping could be increased, and the settling time decreased by about eighty percent

Linear Parameter-Varying Versus Linear Time-Invariant Reduced-Order Controller Design for Turboprop Aircraft Dynamics

The  applicability  of  parameter-varying  reduced-order  controllers  to aircraft  models  is  proposed.  A  generalization  of  the  balanced  singular perturbation method of the linear time-invariant (LTI) system was used to reduce the order of  the  linear parameter-varying (LPV) system. Based on the reducedorder model, a  low-order  LPV  controller  was  designed  using  the H∞ synthesis technique.  The  performance  of  the  reduced-order  controller  was  examined  by applying  it  to  the  lateral-directional  control  of  a  20th-order  aircraft  model. Furthermore, the time responses of the closed-loop system with  several reducedorder LPV controllers and  a  reduced-order LTI controller  were  compared.  The simulation results  show that an  ,  8th -order LPV controller can maintain stability and  provide  the  same  level  of  closed-loop  system  performance  as  a  full-order LPV  controller.  This  was  not  the  case  with  the  reduced-order  LTI  controller, which  cannot  maintain  stability  and  performance  for  all  allowable  parameter trajectories