Vibration control system and vibration control method

Abstract

To provide a vibration control system and a vibration control method that can utilize the system to its maximum performance limit without restricting the input level of the target disturbance and taking into account the constraints of the system.SOLUTION: The vibration control system has an active mass damper installed at the top of a building, a building response measurement unit that measures the building response when an external force acts on the building, a modal response estimation unit that estimates a modal response from the building response measured by the building response measurement unit, and a model predictive control unit that controls the active mass damper to reduce the acceleration of the building using an evaluation function of the following equation (1) that sets weights independently for each modal response according to the modal response estimated by the modal response estimation unit. [Equation 1]SELECTED DRAWING: None

Description

[Technical field]

[0001] The present invention relates to a vibration damping system and a vibration damping method. [Background technology]

[0002] An AMD (Active Mass Damper) is an active vibration control device consisting of a movable mass and an actuator that is installed on high-rise buildings, tower-like structures, bridges, etc., for the purpose of improving habitability during strong winds and small to medium earthquakes. Compared to a passive TMD (Tuned Mass Damper), an AMD has high vibration control performance even though its mass ratio to the main structure is small, and it can control multiple modes with a single device. By installing and controlling an AMD on the roof of a building, it is possible to achieve even higher vibration control performance. The vibration control performance of AMD is determined by two factors: the specifications of the vibration control device, such as the mass ratio and stroke of the moving part relative to the building, and the control law that determines how the AMD is moved. Since AMDs are installed on the rooftop of buildings, there are limitations to the mass and stroke that can be achieved. For this reason, efficient control that makes the most of the limited device specifications is important in order to improve vibration control performance.

[0003] However, because conventional AMD control laws do not clearly take into account the mechanical constraints of the device, they are designed to restrict the input level to be controlled in order to maintain stable operation, and are primarily designed to target wind disturbances and aftershocks during earthquakes. For small to medium-sized earthquakes that exceed a certain input level, to large earthquakes, the output is suppressed to prevent the stroke from being exceeded, allowing conservative operation (variable gain control), or the device itself is stopped or made passive and operated as a TMD. For this reason, the current situation is that the vibration control performance of AMD is not actively utilized in earthquakes.

[0004] To address these issues with AMD operation during earthquakes, we have developed a control method using model predictive control (MPC) as a control law that can utilize the equipment to its performance limits without restricting the input level of the target disturbance, while taking into account the equipment constraints. By applying model predictive control, AMD can be actively operated even during earthquakes, reducing building response to frequent small and medium-sized earthquakes and improving habitability and safety. In addition, stable control that makes the most of the equipment's performance is possible even during large earthquakes, making it possible to realize an AMD vibration control system that is highly useful against earthquakes, which can achieve the maximum effect within the performance range without shutting down the equipment.

[0005] The main AMD control methods include LQR, H∞ control, pole placement (modal control), and MPC. When dealing with shaking caused by earthquakes, it is important that the control law can also control the response of higher modes of the building. However, with time-domain control methods such as LQR, the control input is determined taking into account only the magnitude of the response, so the first mode, which has a large response, becomes dominant as the control target, making it difficult to reduce the response of second- and third-order modes. In contrast, with frequency-domain control methods such as H∞ control and pole placement (modal control), it is possible to arbitrarily set and control the target mode and frequency band, making them suitable for vibration control of buildings. However, the above conventional methods cannot take into account the constraints of device performance, and therefore it is necessary to reduce the output in response to disturbances that exceed a certain input level. For example, there is the variable gain control disclosed in Patent Document 1. In contrast, in recent years, with the development of computers, complex processing and smarter control in real time have become possible, and as a control method that can take constraints into account, for example, model predictive control disclosed in Patent Document 2 is widely used in the fields of autonomous driving and robotics. Model predictive control is a method that can derive the optimal control output within the range of determined constraints by predicting the future response of the controlled object at each time using a mathematical model of the building. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] JP 2007-239942 A [Patent Document 2] JP 2023-009484 A Summary of the Invention [Problem to be solved by the invention]

[0007] However, these methods, like LQR, are time domain control methods, and cannot control any mode or frequency band, so they are not suitable for vibration control of buildings. For these reasons, in high-rise and super-high-rise buildings, the acceleration response can be large during an earthquake due to the influence of higher modes in addition to the first mode, but it is difficult to actively control the building during an earthquake while taking into account the multiple modes of the building.

[0008] Therefore, an object of the present invention is to provide a vibration control system and a vibration control method that can be utilized to the maximum performance limit while taking into account the constraints of the device without restricting the input level of the target disturbance. [Means for solving the problem]

[0009] In order to achieve the above-mentioned objective, the vibration control system of the present invention comprises an active mass damper provided at the top of a building, a building response measurement unit that measures a building response when an external force acts on the building, a modal response estimation unit that estimates a modal response from the building response measured by the building response measurement unit, and a model predictive control unit that controls the active mass damper so as to reduce the acceleration of the building using an evaluation function of the following equation (1) that sets weights independently for each modal response in accordance with the modal response estimated by the modal response estimation unit.

[0010]

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[0011] In order to achieve the above-mentioned objective, the vibration control method of the present invention provides an active mass damper at the top of a building, measures the building response when an external force acts on the building, estimates a modal response from the measured building response, and controls the active mass damper to reduce the acceleration of the building using an evaluation function of the following equation (1) that sets weights independently for each modal response according to the estimated modal response.

[0012]

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[0013] In this invention, the active mass damper is controlled to reduce the building acceleration according to the modal response estimated from the measured building response. This enables active and stable control up to the performance limit of the device even during an earthquake, taking into consideration multiple modes, including not only the first mode of the building but also higher modes that have a large effect on the acceleration response in high-rise and super-high-rise buildings. By controlling the system while taking into account multiple modes without restricting the level of disturbance to be controlled, it is possible to reduce not only wind disturbances and aftershocks caused by earthquakes, which are dominated by the first mode, but also the acceleration response that increases due to the influence of higher modes in the main motion of small to medium-sized earthquakes and large earthquakes. Since the weights for each mode can be set independently in the evaluation function, it is possible to reduce the response of a targeted mode according to the control objective. In other words, the weights for each mode can be set independently according to the control objective while taking into account the constraints of the active mass damper. By using a model predictive control unit to predict the response (stroke and speed) of the active mass damper and take into account the constraints of the device, it is possible to utilize the performance limits of the device (stroke, thrust, speed) without restricting the target disturbance level from small to large input levels. This expands the operating range of the active mass damper and improves the vibration control effect against frequent small to medium-sized earthquakes as well as large earthquakes. Since the constraints of the active mass damper can be clearly taken into account, there is no need to estimate an excessive safety factor for the device's limit performance, and active and stable control that effectively utilizes the device's performance limits is possible. Effect of the Invention

[0014] According to the vibration control system and vibration control method of the present invention, it is possible to utilize the performance limit of the device while taking into account the limitations of the device, without restricting the input level of the target disturbance. [Brief description of the drawings]

[0015] [Figure 1] 1 shows a building provided with a vibration control system according to an embodiment of the present invention; [Diagram 2] FIG. 2 is a diagram illustrating an image of response prediction in model predictive control. [Diagram 3] FIG. 2 is a diagram showing a building model to be controlled. [Figure 4] FIG. 2 is a diagram showing a two-mass model of an i-th mode to be controlled. [Diagram 5] 1 is a graph showing the relationship between acceleration and maximum response value in a shaking table experiment, and a graph showing the relationship between displacement and maximum response value. [Figure 6] 13 is a graph showing the time history waveform of acceleration on the sixth floor. [Figure 7] 1 is a graph showing the time history waveform of AMD behavior. [Figure 8] 13 is a graph showing an estimated modal response used for control. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] Hereinafter, a vibration control system and a vibration control method according to an embodiment of the present invention will be described with reference to FIGS. As shown in Fig. 1, the vibration control system 1 according to this embodiment is installed in a building 2 such as a high-rise building or an ultra-high-rise building, where the acceleration response may become large due to the influence of higher modes in addition to the primary mode during an earthquake. Note that the vibration control system 1 can also be applied to mid-story seismically isolated buildings in which the seismic isolation layer is fixed by a semi-active or active locking device to counter wind vibration.

[0017] The vibration control system 1 includes an active mass damper 3 (hereinafter referred to as AMD 3), a building response measurement unit 4, a modal response estimation unit 5, and a model prediction control unit 6. The AMD 3 is provided at the top of a building 2. The building response measurement unit 4 measures the building response of the building 2 when an external force acts on the building 2. The modal response estimation unit 5 estimates a modal response from the building response measured by the building response measurement unit 4. The model prediction control unit 6 controls the AMD 3 so as to reduce the acceleration of the building 2 in accordance with the modal response estimated by the modal response estimation unit 5.

[0018] In the vibration control method of this embodiment, an AMD 3 is provided at the top of a building 2, and when an external force acts on the building 2, the building response is measured by a building response measurement unit 4, a modal response is estimated from the building response measured by the building response measurement unit 4 by a modal response estimation unit 5, and the AMD 3 is controlled by a model prediction control unit 6 so as to reduce the acceleration of the building 2 in accordance with the modal response estimated by the modal response estimation unit 5.

[0019] In the vibration control system 1 and the vibration control method according to the present embodiment, model predictive control is applied that can utilize the performance limit (stroke, thrust, speed) without restricting the input level of the target disturbance, while considering the constraints of AMD3. In this case, by estimating the modal response from the building response and feeding it back to the control, it becomes possible to independently suppress each mode while considering the constraints of AMD3. As a result, when vibrations of higher modes occur in addition to the first mode, it becomes possible to actively and stably suppress the vibrations by AMD3. When the building response is directly fed back to a general model predictive control, the first mode with a large response becomes dominant, and it is difficult to obtain the effect of reducing the response of the higher mode. In this embodiment, by using the response separated into each mode estimated based on the building response for the model predictive control, it is possible to consider multiple modes while considering the constraint conditions.

[0020] The measuring equipment employed as the building response measurement unit 4 and the method of estimating the modal response by the modal response estimation unit 5 may be set appropriately. For example, an acceleration sensor may be used as the building response measurement unit 4 to measure the building response, and a Kalmantan filter may be used to estimate the modal response in the modal response estimation unit 5. The modal shape of the building 2 required when estimating the modal response by the modal response estimation unit 5 may be set by a method in which the modal shape is known based on design values ​​or observation data, or by a method in which the modal shape is identified sequentially.

[0021] The model predictive control unit 6 predicts the future response of the controlled object at each time using a mathematical model of the building 2, thereby deriving the optimal control input within the range of determined constraints. This allows for active and stable control that effectively utilizes the performance limits of the AMD3, taking into account the constraints of the AMD3 stroke, speed command value, and thrust. Figure 2 shows an image of response prediction by the model predictive control unit 6.

[0022] A mathematical model of the building 2 used for response prediction is derived. The model is an n-mass system building 2 with AMD 3 installed on the top as shown in Figure 3. X in the figure gis the earthquake input. The equation of motion for this model is expressed by the following equation (1) if the external force term is ignored.

[0023]

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[0024] If the known mode shape obtained from design or observation data is i, the state equation for the i-th mode is expressed by the following equation (2). Furthermore, the model of each mode can be expressed as a two-mass system as shown in Figure 4. In this two-mass system model, each mode is independent, and it can be seen that when focusing on a certain mode, it can be expressed only by the response of that mode and the response of AMD3. β in the figure i is the excitation coefficient of the i-th mode.

[0025]

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[0026] If the modes to be controlled are the first mode to the nth mode, the discrete state equations and state quantities handled by the model predictive control unit 6 are expressed by the following equation (3).

[0027]

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[0028] Next, the evaluation function in the model predictive control is shown in the following equation (4).

[0029]

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[0030] The evaluation function is composed of a quadratic form of the predicted state quantity (modal response of the building 2 and the response of the AMD3) and the control input, and Q and R are weight matrices for each. The selection of the state quantity (for example, the displacement and velocity of each mode) and the weight matrix are design parameters and are set arbitrarily according to the control purpose. At each time, the optimal control input is derived by solving the above evaluation function using the modal response estimated based on the building response and the response of the AMD3. In the vibration control system 1 according to this embodiment, the state quantity given to the model predictive control unit 6 is composed of the response separated into each mode and the response of the AMD3 as shown in the above formula (3). Therefore, it is possible to set independent weights for each mode (each vibration frequency), and it is also possible to consider the stroke of the AMD3 and the constraint conditions of the control input.

[0031] The results of a shaking table experiment using the control law formulated above, with a six-story test specimen with a single-axis actuator mounted on top as AMD3, are shown below. Figure 5 shows the maximum response value when the JMA Kobe wave was input. Figure 6 shows the time history of the acceleration at the sixth layer. Three cases are shown: when AMD3 is not controlled (uncontrolled), when the first and second modes are controlled (first + second), and when only the first mode is controlled (first). As shown in Figures 5 and 6, when only the first mode is considered (first), the effect of reducing the acceleration response is small, whereas when the second mode is considered in addition to the first mode (first + second), the acceleration response can be reduced compared to when not controlled.

[0032] Figure 7 shows the time history waveforms of the displacement, speed, and control input of the AMD behavior. As shown in Figure 7, even when multiple modes are controlled, it can be seen that the stroke (displacement), speed, and control input of the AMD3 can be controlled within the range of constraints. The dotted lines in Figure 7 show the respective constraints. The actual estimated modal responses used for control in the case where the first and second modes are the control targets are shown in Figure 8. As shown in Figure 8, it can be seen that the response of each mode can be well estimated based on the building response.

[0033] Next, the operation and effect of the vibration control system and vibration control method according to the present embodiment will be described. In the vibration control system 1 according to this embodiment, the model prediction control unit 6 controls the AMD 3 to reduce the acceleration of the building in accordance with the modal response estimated by the modal response estimation unit 5 from the building response measured by the building response measurement unit 4. This enables active and stable control up to the performance limit (stroke, thrust, speed) of the device even during an earthquake, taking into consideration multiple modes including not only the first mode of the building 2 but also higher modes that have a large effect on the acceleration response in high-rise and super-high-rise buildings 2. By controlling the system while taking into account multiple modes without restricting the level of disturbance to be controlled, it is possible to reduce not only wind disturbances and aftershocks caused by earthquakes, which are dominated by the first mode, but also the acceleration response that increases due to the influence of higher modes in the main motion of small to medium-sized earthquakes and large earthquakes. Since the weights for each mode can be set independently in the evaluation function, it is possible to reduce the response of a targeted mode according to the control objective. In other words, the weights for each mode can be set independently according to the control objective while taking into account the constraints of the active mass damper.

[0034] The model predictive control unit 6 predicts the response (stroke and speed) of the AMD3 and takes into account the constraints of the device, making it possible to utilize the performance limits of the device without limiting the target disturbance level from small to large input levels. This expands the operating range of the AMD3 and improves the vibration control effect against frequent small to medium earthquakes and large earthquakes. Since the constraints of AMD3 can be clearly taken into account, there is no need to estimate an excessive safety margin for the equipment's limit performance, enabling active and stable control that effectively utilizes the equipment's performance limits.

[0035] Although the embodiment of the vibration control system and vibration control method according to the present invention has been described above, the present invention is not limited to the above embodiment and can be modified as appropriate without departing from the spirit of the present invention. For example, in the above embodiment, the vibration control system and the vibration control method are adopted in a building 2 such as a high-rise building or an ultra-high-rise building, but they may also be adopted in mid-rise buildings, tower-like structures, bridges, etc.

[0036] The Sustainable Development Goals (SDGs) are among the 17 international goals adopted at the United Nations Summit in September 2015. The vibration control system and vibration control method according to this embodiment can contribute to achieving the 17 SDGs goals, for example, goal 11: "Sustainable cities and communities." [Explanation of symbols]

[0037] 1. Vibration Control System 2. Building 3. AMD 4. Building response measurement section 5 Modal response estimation section 6 Model predictive control section

Claims

1. An active mass damper installed at the top of the building; a building response measurement unit that measures a building response when an external force acts on the building; a modal response estimation unit that estimates a modal response from the building response measured by the building response measurement unit; a model predictive control unit that controls the active mass damper so as to reduce the acceleration of the building by using an evaluation function of the following equation (1) that sets a weight independently for each mode response in accordance with the modal response estimated by the modal response estimation unit. [0010]

2. An active mass damper is installed at the top of the building. measuring a building response when an external force acts on the building; Estimating modal responses from the measured building responses; A vibration control method for controlling the active mass damper so as to reduce the acceleration of the building using an evaluation function of the following equation (1), which sets weights independently for each mode response according to the estimated mode response. [0025]

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