Overlapping guaranteed cost control for uncertain continuous-time delayed systems

Overlapping guaranteed cost control design problem is solved for a class of linear continuous-time uncertain systems with state as well as control delays. Unknown arbitrarily time-varying uncertainties with known bounds are considered. A point delay is supposed. Conditions preserving closed-loop systems expansion-contraction relations including the identical bounds of performance indices are proved. A linear matrix inequality (LMI) delay independent procedure is used for control design in the expanded space. The results are specialized on the overlapping decentralized control design. A numerical illustrative example is supplied.Peer ReviewedPostprint (published version

Controllability-observability of expanded composite systems

The relation between original and expanded systems within the Inclusion Principle from the point of view of controllability–observability of both subsystems and composite systems is studied. It is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable–observable. Two practically important large classes of complementary matrices are identified to offer results computationally attractive. First, the existence of complementary matrices ensuring controllability–observability of decoupled subsystems is proved. Then, using this result, the same property is proved for the composite expanded system.Peer ReviewedPostprint (published version

Assessment of errors in the transmission of the orientation and cartographic system from the surface to an underground mine

An accurate transmission of the orientation between surface and underground workings, by means of vertical shafts, is a major challenge in the mining industry, especially for deep mines. We assessed the accuracy of this operation in a case study using the two-shaft plumbing and gyroscopic methods in order to compare and analyse the planimetric displacement of the baseline due to different sources of error in each method. The advantages and disadvantages of both methods are discussed. Some disadvantages in each method have been reduced thanks to technological progress, especially in the two-shaft plumbing method. The different sources of error that affect the measurements are analysed in detail with the aim of compensating them and achieving the required precision for an underground infrastructure. Mine ventilation has been identified as one of the most important sources of error in the plumbing method due to intake and return air flow producing a significant displacement of the verticality of the plumbs in the shafts. In this regard, we describe some measures to reduce the influence of ventilation and give details of a compensation method.Peer ReviewedPostprint (published version

Hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems

In this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.Peer ReviewedPostprint (published version

A design procedure for overlapped guaranteed cost controllers

© 2008 the authors. This work has been accepted to IFAC for publication under a Creative Commons Licence CC-BY-NC-NDIn this paper a quadratic guaranteed cost control problem for a class of linear continuous-time state-delay systems with norm-bounded uncertainties is considered. We will suppose that the systems are composed by two overlapped subsystems but the results can be easily extended to any number of subsystems. The main objective is to design overlapping guaranteed cost controllers with tridiagonal gain matrices for these kind of systems by using a linear matrix inequality (LMI) approach. With this idea in mind, we present a design strategy to reduce the computational burden and to increase the feasibility in the LMI problem. In this context, the use of so-called complementary matrices play an important role. A simple example to illustrate the advantages achieved by using the proposed method is supplied.Peer ReviewedPostprint (published version

Integrated design of hybrid interstory-interbuilding multi-actuation schemes for vibration control of adjacent buildings under seismic excitations

The design of vibration control systems for the seismic protection of closely adjacent buildings is a complex and challenging problem. In this paper, we consider distributed multi-actuation schemes that combine interbuilding linking elements and interstory actuation devices. Using an advanced static output-feedback H∞ approach, active and passive vibration control systems are designed for a multi-story two-building structure equipped with a selected set of linked and unlinked actuation schemes. To validate the effectiveness of the obtained controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations is conducted using the full scale North–South El Centro 1940 seismic record as ground acceleration disturbance. The observed results indicate that using combined interstory-interbuilding multi-actuation schemes is an effective means of mitigating the vibrational response of the individual buildings and, simultaneously, reducing the risk of interbuilding pounding. These results also point out that passive control systems with high-performance characteristics can be designed using damping elements.Peer ReviewedPostprint (published version

Decentralized control with information structure constraints

In this paper, some problems related to the design of decentralized controllers are considered. Due to information structure constraints on the systems, we are interested in determine when a gain-matrix corresponding to a control law can be designed having a required structure. To discuss this issue, we consider some generic classes of systems with different control strategies: optimal overlapping control, guaranteed cost control and H∞ control. For each one of them, two scenarios are supposed: state feedback and output feedback controllers. In this line, some new contributions are offered.Postprint (published version

Complete kinematic analysis of the Stewart-Gough platform by unit quaternions

In this paper, a complete analysis of Stewart–Gough platform kinematics by unit quaternions is proposed. Even when unit quaternions have been implemented in different applications (including a kinematic analysis of the Stewart platform mechanism), the research regarding the application of this approach is limited only to the analysis of some issues related to the kinematic properties of this parallel mechanism. For this reason, a complete analysis of the Stewart–Gough platform is shown. The derivation of the inverse and forward kinematics of the Stewart platform using unit quaternions shows that they are suitable to represent the orientation of the upper platform due to their simplicity, equivalence, and compact representation as compared to rotation matrices. Then, the leg velocities are derived to compute these values under different conditionsPeer ReviewedPostprint (published version

Computational effectiveness of LMI design strategies for vibration control of large structures

Distributed control systems for vibration control of large structures involve a large number of actuation devices and sensors that work coordinately to produce the desired control actions. Design strategies based on linear matrix inequality (LMI) formulations allow obtaining controllers for these complex control problems, which are characterized by large dimensionality, high computational cost and severe information constraints. In this paper, we conduct a comparative study of the computational effectiveness of three different LMI-based controller design strategies: H-infinity, energy-to-peak and energy-to-componentwise-peak. The H-infinity approach is a well-known design methodology and has been widely used in the literature. The energy-to-peak approach is a particular case of generalized H2 design that is gaining a growing relevance in structural vibration control. Finally, the energy-to-componentwise-peak approach is a less common case of generalized H2 design that produces promising results among the three considered approaches. These controller design strategies are applied to synthesize active state-feedback controllers for the seismic protection of a five-story building and a twenty-story building both equipped with complete systems of interstory actuation devices. To evaluate the computational effectiveness of the proposed LMI design methodologies, the corresponding computation times are compared and a suitable set of numerical simulations is carried out to assess the performance of the obtained controllers. As positive results, two main facts can be highlighted: the computational effectiveness of the energy-to-peak control design strategy and the particularly well-balanced behavior exhibited by the energy-to-componentwise-peak controllers. On the negative side, it has to be mentioned the computational inefficiency of the considered LMI design methodologies to properly deal with very-large-scale control problems.Peer ReviewedPostprint (published version

Distributed passive actuation schemes for seismic protection of multibuilding systems

In this paper, we investigate the design of distributed damping systems (DDSs) for the overall seismic protection of multiple adjacent buildings. The considered DDSs contain interstory dampers implemented inside the buildings and also interbuilding damping links. The design objectives include mitigating the buildings seismic response by reducing the interstory-drift and story-acceleration peak-values and producing small interbuilding approachings to decrease the risk of interbuilding collisions. Designing high-performance DDS configurations requires determining convenient damper positions and computing proper values for the damper parameters. That allocation-tuning optimization problem can pose serious computational difficulties for large-scale multibuilding systems. The design methodology proposed in this work—(i) is based on an effective matrix formulation of the damped multibuilding system; (ii) follows an H8 approach to define an objective function with fast-evaluation characteristics; (iii) exploits the computational advantages of the current state-of-the-art genetic algorithm solvers, including the usage of hybrid discrete-continuous optimization and parallel computing; and (iv) allows setting actuation schemes of particular interest such as full-linked configurations or nonactuated buildings. To illustrate the main features of the presented methodology, we consider a system of five adjacent multistory buildings and design three full-linked DDS configurations with a different number of actuated buildings. The obtained results confirm the flexibility and effectiveness of the proposed design approach and demonstrate the high-performance characteristics of the devised DDS configurations.Peer ReviewedPostprint (published version