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In this paper, a computationally effective strategy to obtain multioverlapping controllers via the Inclusion Principle is applied to design discrete-time state-feedback multioverlapping LQR controllers for seismic protection of tall buildings. To compute the corresponding control actions, the proposed semidecentralized controllers only require state information from neighboring stories. This particular configuration of information exchange allows introducing a dramatic reduction in the transmission range required for a wireless implementation of the communication system. To investigate the behavior of the proposed semidecentralized multioverlapping controllers, a proper simulation model has been designed. This model includes semiactive actuation devices with limited force capacity, control sampling times consistent with the communication latency, time-delayed state information, and communication failures. The performance of the proposed multioverlapping controllers has been assessed through numerical simulations of the seismic response of a 20-story building with positive results.

Over the last decades, problems of ever increasing complexity have been considered in the field of Structural Vibration Control (SVC). Current SVC systems for seismic protection of tall buildings can involve a large number of sensors and actuation devices and a wide and sophisticated communication network [

In this context, the design of semidecentralized controllers using multioverlapping decompositions based on the

The main contribution of the present paper is to present a large-scale application of the IP to the design of semidecentralized controllers for SVC, paying special attention to some aspects of practical relevance. More specifically, the computational strategy proposed in [

The organization of the paper is as follows: In Section

Let us consider the

Building lumped-mass model.

Actuation scheme.

Now, we take the state vector

To design a discrete-time centralized state-feedback LQR controller for the

To design a multioverlapping controller that is able to compute the control actions

Decomposition in two-story overlapping subsystems.

The expansion-contraction procedure associated to the design of multioverlapping controllers for large buildings is only outlined in this section. For clarity and simplicity, a detailed account of this procedure has not been included in the paper. However, a complete presentation of this background material together with some practical applications to SVC of small buildings can be found in [

The expanded block-diagonal system (

It should be noted that the control gain matrix

For clarity and simplicity, the controllers presented in this section have been computed following an LQR approach. However, it has to be highlighted that other control strategies are also possible. For example, an application of the IP to the design of semidecentralized static output-feedback controllers for SVC can be found in [

One of the main objectives of the present work is to gain a meaningful insight into the behavior of semidecentralized multioverlapping controllers through numerical simulations. To this end, the simulation models have to include some relevant factors such as sampling rates, realistic implementation of the control actions, time-delayed state information, and communication latency and failures. Trying to achieve a proper balance between simplicity and accuracy, we have considered a simulation framework formed by three different models: (i)

The basic building model is:

The centralized control model is:

In the multioverlapping control model, we consider the actuation-communication system schematically depicted in Figure

The local control action

The local controller unit

The state information of neighboring stories obtained through the wireless communication unit

For a given time interval

If

Through the time interval

The control action computed at the sampling time

Actuation-communication system for the multioverlapping control model.

Time intervals for state information gathering and control action holding.

The multioverlapping control model can now be obtained by completing (

In this section, the behavior of discrete-time multioverlapping LQR controllers is investigated through numerical simulations of the seismic response of a 20-story building. The parameter values for this particular building are collected in Table

Particular parameter values for the 20-story building.

Story | ||||||
---|---|---|---|---|---|---|

1–5 | 6–11 | 12–14 | 15–17 | 18-19 | 20 | |

Mass (×10^{6} Kg) |
1.10 | 1.10 | 1.10 | 1.10 | 1.10 | 1.10 |

Stiffness (×10^{6} N/m) |
8.62 | 5.54 | 4.54 | 2.91 | 2.56 | 1.72 |

Number of actuation devices | 4 | 2 | 2 | 1 | 1 | 1 |

Max. actuation force (×10^{6} N) |
4.8 | 2.4 | 2.4 | 1.2 | 1.2 | 1.2 |

Natural damping | 5% |

For this 20-story building, three different discrete-time LQR controllers are designed: a centralized controller

In the numerical simulations, the maximum absolute interstory drifts have been computed for different control configurations. The basic building model given in (

Full scale Kobe 1995 North-South seismic record.

In Figure

Maximum absolute interstory drifts for the 1995 Kobe North-South seismic record. Simulations with maximum state delay.

Controller sampling time 40 ms

Controller sampling time 20 ms

Maximum absolute interstory drifts for maximum and minimum state delays (controller sampling time 40 ms).

The graphics in Figure

Finally, the graphics in Figure

It is worth to be mentioned that the behavior of the ideal discrete-time centralized controller

The proposed semidecentralized controllers can operate using only state information from neighboring stories. This fact makes it possible for them to successfully collect the required state information in a relatively small time interval. As a side effect, state delays are also small and have no significant impact on the controller performance.

Force saturation is an important issue in SVC. For large seismic excitations, the required control actions frequently exceed the force capacity of the actuation devices. Consequently, force actuation constraints should be considered when studying the controllers behavior. All the numerical simulations of the controlled responses presented in this paper have been conducted using the force saturation values displayed in Table

In this paper, a computationally effective strategy has been used to design discrete-time state-feedback multioverlapping LQR controllers for seismic protection of tall buildings. This strategy, based on a sequential application of the Inclusion Principle, produces a block-tridiagonal control gain matrix that allows computing the corresponding control actions using only state information from neighboring stories. Due to this particular information exchange configuration of the multioverlapping controllers, the transmission range and the control sampling frequency in wireless implementations of the communication system can be dramatically improved. To investigate the behavior of the proposed semidecentralized multioverlapping controllers, a proper simulation model has been designed, which allows including semiactive actuation devices with limited force capacity, control sampling times consistent with the communication latency, time-delayed state information, and communication failures. To assess the performance of the proposed multioverlapping controllers, numerical simulations of the seismic response for a 20-story building model have been conducted with positive results.

For clarity and simplicity, the controllers presented in this paper have been designed following an LQR approach. In future works, further research effort should be addressed at exploring the effectiveness of the proposed control design strategy in more complex scenarios, which can involve issues of practical interest such as structural information constraints [

This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through the Grant DPI2011-25567-C02 and by the Norwegian Center of Offshore Wind Energy (NORCOWE) under Grant 193821/S60 from the Research Council of Norway (RCN).