Francisco Palacios-Quiñonero

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.

Sequential design of multi-overlapping controllers for longitudinal multi-overlapping systems

In this paper a strategy to design multi-overlapping controllers for systems with longitudinal multi-overlapping structure is presented. The design process uses the Inclusion Principle to carry out a multi-step expansion that allows the decentralized design of a sequence of expanded local controllers. These expanded local controllers are subsequently contracted to produce a multi-overlapping controller that can be implemented in the original system. To illustrate the proposed methodology, the response of a four-story building under a seismic excitation is considered.

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.

Order regularity of two-node Birkhoff interpolation with lacunary polynomials

In this short work we study the existence and uniqueness of solution for some Birkhoff interpolation problems with lacunary polynomials. First we solve the one-node problem; next we solve the two-node problem in the restricted case where one of the nodes is null.

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.

Improved Switching Strategy for Selective Harmonic Elimination in DC-AC Signal Generation via Pulse-Width Modulation

We present an advanced design methodology for pulse-width-modulated (PWM) DC-AC signal generation. Using design methods based on the Walsh transform, AC sinusoidal signals can be approximated by suitable PWM signals. For different AC amplitudes, the switching instants of the PWM signals can be efficiently computed by using appropriate systems of explicit linear equations. However, the equation systems provided by conventional implementations of this approach are typically only valid for a restricted interval of AC amplitudes and, in general, a supervised implementation of several equation systems is necessary to cover the full AC amplitude range. Additionally, obtaining suitable equation systems for designs with a large number of switching instants requires solving a complex optimization problem. In defining the constitutive pulses of a PWM signal, a suitable partition of the time interval is used as a reference system. In the new methodology, pulses are chosen to be symmetric with respect to the partition points, and the switching times are specified by means of switching ratios with respect to the endpoint subintervals. This approach leads to particularly simple Walsh series representations, introduces a remarkable computational simplification, and achieves excellent results in reducing the harmonic distortion.

Active-passive control strategy for adjacent buildings

In this paper, a control strategy to mitigate the vibrational response of adjacent buildings under seismic excitation is presented. The proposed strategy combines inter building passive actuators with active actuators placed in the building stories. The main ideas are presented by means of a simplified two-building model; however, a semi-decentralized overlapping approach via the inclusion principle has been used to impose a proper information exchange structure suitable for wireless control of large buildings. Numerical simulations have been carried out to assess the performance of the proposed methodology with promising results. The overall control system exhibits some degree of fault-tolerance since only partial degradation of the control performance results from partial failures of the control system.