Sparsity Invariance for Convex Design of Distributed Controllers

Abstract In this paper the issue of string stability for acceleration-controlled vehicles interconnected in a chain is studied. String stability is concerned with having bounded displacements between vehicles in such a way that displacements should not grow unboundedly with respect to the perturbation. Different definitions can be given to string stability: one that relates to the amplification of a local disturbance acting on one vehicle towards the whole vehicle chain, more strict definition that is related to the boundedness of vector norm of displacements with respect to the bounded vector norm of disturbance inputs acting on all vehicles; and, most practical definition that considers the boundedness of signal norm of each individual displacement with respect to the bounded signal norm of disturbance inputs acting on all vehicles, independently from the number of vehicles. It has been proven that these definitions are all impossible to be achieved using any linear homogeneous unidirectional distributed controllers with constant spacing policy. This paper proposes linear heterogeneous controllers where each vehicle behaves differently from others in a vehicle chain. We prove that three different definitions of string stability can be attained using the proposed heterogenous controller. We propose sufficient conditions to guarantee string stability and boundedness of acceleration of each vehicle. Finally, simulation results are given to illustrate the effectiveness of proposed heterogenous control synthesis.

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Distributed and Centralized H∞ Control of Large Segmented Telescopes

Volume 8: Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2010-39187 ◽

2010 ◽

Cited By ~ 2

Author(s):

Baris Ulutas ◽

Afzal Suleman ◽

Edward J. Park

Keyword(s):

Next Generation ◽

Vast Number ◽

Primary Mirror ◽

Performance Requirements ◽

Distributed Controller ◽

Nodal Model ◽

Distributed Controllers ◽

Simulation Results ◽

Imaging Performance ◽

Large Primary

Next generation telescopes are to employ segmented mirrors to realize extremely large primary mirror surfaces. Most of the current ground-based telescopes has monolithic mirrors with radius upto 8 metres. Due to limitations segmentation is preferred for larger size mirrors. Segmentation of mirrors brings a challenging task of controlling the vast number of individual units. In this paper, the H∞ control of the primary mirror of the next generation telescopes are investigated. Both spatially-invariant distributed and centralized controllers are designed for simplified dynamic model of a 37 segment test unit. Firstly, the 37 segment system is modelled by adopting a nodal model. Secondly, an analytic calculation of a H∞ controller is presented. A centralized H∞ controller is, then, designed and simulated in MatLab-Simulink environment. Next, the simulation results are presented and the performance of the controller is evaluated. Thirdly, spatially-invariant distributed controller synthesis is described and a spatially-invariant distributed controller is designed for 37 segment system by controller truncation. The spatially-invariant distributed controller is simulated for the 37 segment system. The simulation results of the controller is presented and compared with the results from centralized scheme. It is shown that both centralized and spatially-invariant distributed controllers satisfy the imaging performance requirements.

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