Optimal design of complex passive-damping systems for vibration control of large structures: An energy-to-peak approach

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/510236 Open AccessWe present a new design strategy that makes it possible to synthesize decentralized output-feedback controllers by solving two successive optimization problems with linear matrix inequality (LMI) constraints. In the initial LMI optimization problem, two auxiliary elements are computed: a standard state-feedback controller, which can be taken as a reference in the performance assessment, and a matrix that facilitates a proper definition of the main LMI optimization problem. Next, by solving the second optimization problem, the output-feedback controller is obtained. The proposed strategy extends recent results in static output-feedback control and can be applied to design complex passive-damping systems for vibrational control of large structures. More precisely, by taking advantages of the existing link between fully decentralized velocity-feedback controllers and passive linear dampers, advanced active feedback control strategies can be used to design complex passive-damping systems, which combine the simplicity and robustness of passive control systems with the efficiency of active feedback control. To demonstrate the effectiveness of the proposed approach, a passive-damping system for the seismic protection of a five-story building is designed with excellent results

Hardware and control co-design enabled by a state-space formulation of cascaded, interconnected PID controlled systems

In recent years, more and more attention has been paid to the simultaneous optimization of hardware and control to achieve an optimal design of complex and interacting systems. To efficiently carry out this co-design optimization, there is a need for flexible methods to apply the variable hardware and control co-design aspects while also allowing a faster system response calculation compared to traditional methods. These time savings in the response calculations are of significant importance when using iterative optimization algorithms that typically require a large number of simulations to arrive at a solution. That is why this paper proposes a general methodology to create a closed-loop state-space model consisting of an open-loop process with an observer and extensive control loop structures. These structures comprise a combination of cascaded decentralized and distributed controllers, synchronizing controllers, and feedforward controllers while taking into account reference trajectories and input disturbances. It is shown that with the proposed methodology, response calculations for a motion application are much faster compared to traditional graphical programming tools that enable to apply flexible control architecture features. This shows that the presented methodology permits the efficient co-design optimization of hardware en control aspects

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADMM). We first apply a classical parameterization technique to restrict the optimal decentralized control into a convex problem that inherits the sparsity pattern of the original problem. The parameterization relies on a notion of strongly decentralized stabilization, and sufficient conditions are discussed to guarantee this notion. Then, chordal decomposition allows us to decompose the convex restriction into a problem with partially coupled constraints, and the framework of ADMM enables us to solve the decomposed problem in a distributed fashion. Consequently, the subsystems only need to share their model data with their direct neighbours, not needing a central computation. Numerical experiments demonstrate the effectiveness of the proposed method.Comment: 11 pages, 8 figures. Accepted for publication in the IEEE Transactions on Control of Network System

Algorithms for output feedback, multiple-model, and decentralized control problems

The optimal stochastic output feedback, multiple-model, and decentralized control problems with dynamic compensation are formulated and discussed. Algorithms for each problem are presented, and their relationship to a basic output feedback algorithm is discussed. An aircraft control design problem is posed as a combined decentralized, multiple-model, output feedback problem. A control design is obtained using the combined algorithm. An analysis of the design is presented