Josep Rubió-Massegú

Technical communique: Static output-feedback control under information structure constraints

An important challenge in the static output-feedback control context is to provide an isolated gain matrix possessing a zero-nonzero structure, mainly in problems presenting information structure constraints. Although some previous works have contributed some relevant results to this issue, a fully satisfactory solution has not yet been achieved up to now. In this note, by using a Linear Matrix Inequality approach and based on previous results given in the literature, we present an efficient methodology which permits us to obtain an isolated static output-feedback gain matrix having, simultaneously, a zero-nonzero structure imposed a priori.

Feasibility issues in static output-feedback controller design with application to structural vibration control

Abstract Recent results in output-feedback controller design make possible an efficient computation of static output-feedback controllers by solving a single-step LMI optimization problem. This new design strategy is based on a simple transformation of variables, and it has been applied in the field of vibration control of large structures with positive results. There are, however, some feasibility problems that can compromise the effectiveness and applicability of the new approach. In this paper, we present some relevant properties of the variable transformations that allow devising an effective procedure to deal with these feasibility issues. The proposed procedure is applied in designing a static velocity-feedback H ∞ controller for the seismic protection of a five-story building with excellent results.

Discrete-time static output-feedback semi-decentralized H ∞ controller design: An application to structural vibration control

In this work, we present a new and effective method to design discrete-time static output-feedback H∞ controllers. This new method, based on a Linear Matrix Inequality (LMI) formulation, introduces a suitable transformation of the LMI variables that allows to obtain an explicit expression for the output-feedback gain matrix. Moreover, for problems involving a set of subsystems with information exchange constraints, a convenient structure on the LMI variables can be imposed in order to design semi-decentralized controllers, where the corresponding output-feedback gain matrix has a prescribed zero-nonzero structure. To illustrate the proposed methodology, discrete-time static velocity-feedback H∞ controllers to mitigate the seismic response of a five-story building are designed. In particular, two different designs are presented: (i) a centralized controller that requires all the inter-story velocities to compute the control actions, and (ii) a semi-decentralized controller that can operate using only the inter-story velocities of neighboring floors.

Static output-feedback control for vehicle suspensions: a single-step linear matrix inequality approach

In this paper, a new strategy to design static output-feedback controllers for a class of vehicle suspension systems is presented. A theoretical background on recent advances in output-feedback control is first provided, which makes possible an effective synthesis of static output-feedback controllers by solving a single linear matrix inequality optimization problem. Next, a simplified model of a quarter-car suspension system is proposed, taking the ride comfort, suspension stroke, road holding ability, and control effort as the main performance criteria in the vehicle suspension design. The new approach is then used to design a static output-feedback controller that only uses the suspension deflection and the sprung mass velocity as feedback information. Numerical simulations indicate that, despite the restricted feedback information, this static output-feedback controller exhibits an excellent behavior in terms of both frequency and time responses, when compared with the corresponding state-feedback controller.

Sequential design of multioverlapping controllers for structural vibration control of tall buildings under seismic excitation

In this article, a computationally effective strategy to obtain multioverlapping controllers via the inclusion principle is applied to design a state-feedback multioverlapping linear-quadratic regulator controller for a 20-story building. The proposed semidecentralized controller only requires state information of neighboring stories to compute the corresponding control actions. This particular information exchange configuration allows introducing a dramatic reduction in the transmission range required for a wireless implementation of the communications system. More specifically, just a one-story transmission range is required by the proposed multioverlapping controller, while a full-building transmission range would be necessary in a classical centralized design. From a computational point of view, the presented design strategy only involves the actual computation of a reduced set of low-dimension controllers. The numerical simulations indicate that despite the simplified low-dimension design and the severe information exchange constraints, the proposed semidecentralized multioverlapping controller achieves a surprisingly high level of seismic attenuation when compared with the centralized linear-quadratic regulator controller.

Passive-damping design for vibration control of large structures

In this work, a systematic strategy to design passive damping systems for structural vibration control is presented. The proposed design methodology is based on the equivalence between decentralized static velocity-feedback controllers and passive damping systems. By using recent developments in static output-feedback control, the design of passive-damping systems can be formulated as a single optimization problem with Linear Matrix Inequality constraints. Moreover, this optimization problem can be efficiently solved with standard numerical tools, even for large dimension systems. Due to its computational effectiveness, the proposed methodology can be applied to the design of passive damping systems for large structures. To illustrate the main ideas and methods, a passive damping system is designed for the seismic protection of a five-story building with excellent results.

On the enveloping method and the existence of global Lyapunov functions

An interpretation of Culls enveloping method used to determine global asymptotic stability of one dimensional population models is given. This is done by relating the enveloping property with the existence of a global Lyapunov function. Following this spirit we revisit a result of Liz.

Global periodicity and openness of the set of solutions for discrete dynamical systems

In this paper, we find additional conditions to be satisfied by a globally periodic discrete dynamical system, so that its good set (the set of initial conditions providing well-defined solutions) is an open set of ℝ k or ℂ k . We will pay especial attention to the rational case and several examples will be given.

On the existence of solutions for difference equations

The problem of existence of solutions for difference equations is discussed here. Especially, we give sufficient conditions in order to obtain that the solution of an equation is well defined for almost every initial condition (except initial conditions in a set of Lebesgue measure zero). The obtained results will be generalized to discrete dynamical systems and several examples will be given.

Advanced design of integrated vibration control systems for adjacent buildings under seismic excitations

In vibration control of adjacent buildings under seismic excitations, a twofold objective has to be considered: (i) to mitigate the vibrational response of the individual structures and (ii) to provide a suitable protection against interbuilding impacts (pounding). An interesting strategy to deal with this complex control problem consists in considering an integrated control system, which combines interbuilding actuation devices with local control systems implemented in the individual buildings. In this paper, an effective computational strategy to design this kind of integrated control systems is presented. The proposed design methodology is based on a linear matrix inequality formulation, allows including active and passive actuation devices, and makes it possible to deal with important information constraints associated to the problem. The main ideas are illustrated by means of a twobuilding systemequipped with three actuation devices: two interstory actuation devices implemented at the ground level of the buildings, plus an interbuilding actuation device installed at the top level of the lowest building. For this control setup, two different integrated controllers are designed. A proper set of numerical simulations is conducted to assess the performance of the proposed controllers with positive results.