Optimal structure control for earthquake resistance

2021 ◽  
pp. 1-7
Author(s):  
Xianyang Yang ◽  
James D. Lee
Keyword(s):  
Optimal Control ◽  
Structural Control ◽  
Algorithm Design ◽  
Computer Software ◽  
Earthquake Resistance ◽  
Control Law ◽  
State Variables ◽  
Optimal Control Strategy ◽  
Earthquake Excitation ◽  
History Of

This work developed the optimal and active control algorithms applicable to structural control for earthquake resistance. [Lewis, F. L., Vrabie, D. and Syrmos, V. L. [2012] Optimal Control (John Wiley & Sons)] developed a rigorous and comprehensive procedure for the derivation of an optimal control strategy based on the calculus of variation. This work is an application of Lewis’ formulation to the control of a structure for earthquake resistance. We developed a computer software which can be used to generate a dynamic model to simulate a planar structure and to construct the control law. This model also includes the tendon driven actuators, sensors and true history of earthquake excitation. The control law has two parts: (I) the feedback control which depends on the estimate state variables (Kalman filter) and (II) the record of the realistic earthquake excitation. The optimal control problem eventually leads to a two-point boundary value problem whose solution hinges on the knowledge of the entire history of the earthquake excitation. We employ true records of earthquake excitation as input. This approach enables one to solve the Riccati equations rigorously. Then, from the simulation results, one may study the relations between the control algorithm design and the characteristics (frequency, amplitude and duration) of earthquake excitation.

When Is a Linear Control System Optimal?

1964 ◽  
Vol 86 (1) ◽  
pp. 51-60 ◽  
Author(s):  
R. E. Kalman
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Control Variable ◽  
Point Of View ◽  
Complete Analysis ◽  
Control Law ◽  
Quadratic Loss ◽  
Mathematical Form ◽  
State Variables

The purpose of this paper is to formulate, study, and (in certain cases) resolve the Inverse Problem of Optimal Control Theory, which is the following: Given a control law, find all performance indices for which this control law is optimal. Under the assumptions of (a) linear constant plant, (b) linear constant control law, (c) measurable state variables, (d) quadratic loss functions with constant coefficients, (e) single control variable, we give a complete analysis of this problem and obtain various explicit conditions for the optimality of a given control law. An interesting feature of the analysis is the central role of frequency-domain concepts, which have been ignored in optimal control theory until very recently. The discussion is presented in rigorous mathematical form. The central conclusion is the following (Theorem 6): A stable control law is optimal if and only if the absolute value of the corresponding return difference is at least equal to one at all frequencies. This provides a beautifully simple connecting link between modern control theory and the classical point of view which regards feedback as a means of reducing component variations.

scholarly journals Optimal Performance of Variable Stiffness Devices for Structural Control

2006 ◽  
Vol 129 (2) ◽  
pp. 171-177 ◽  
Author(s):  
John Leavitt ◽  
Faryar Jabbari ◽  
James E. Bobrow
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Structural Control ◽  
Vibration Suppression ◽  
Variable Stiffness ◽  
Experimental Results ◽  
Control Law ◽  
Structural Vibrations

This paper addresses control of structural vibrations using semi-active actuators that are capable of manipulating stiffness and∕or producing variable stiffness. Usually vibration suppression is achieved using damping devices rather than stiffness ones. However, stiffness devices can produce large forces and have significant advantages for shock isolation purposes. In this work we use a passivity approach to establish the requirements for the control law for a structure equipped with semi-active stiffness devices. We also solve an optimal control problem that demonstrates that our passive, resetting feedback control law approximates the optimal control. Simulation and experimental results are presented in support of the proposed approach.

scholarly journals Receding Horizon Control of Cooling Systems for Large-Size Uninterruptible Power Supply Based on a Metal-Air Battery System

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1611 ◽  
Author(s):  
Bonhyun Gu ◽  
Heeyun Lee ◽  
Changbeom Kang ◽  
Donghwan Sung ◽  
Sanghoon Lee ◽  
...  
Keyword(s):  
Optimal Control ◽  
Power Supply ◽  
Large Scale ◽  
Control Variable ◽  
Receding Horizon Control ◽  
State Variables ◽  
Optimal Control Strategy ◽  
Uninterruptible Power Supply ◽  
Air Battery ◽  
Uninterruptible Power

As application of electric energy have expanded, the uninterruptible power supply (UPS) concept has attracted considerable attention, and new UPS technologies have been developed. Despite the extensive research on the batteries for UPS, conventional batteries are still being used in large-scale UPS systems. However, lead-acid batteries, which are currently widely adopted in UPS, require frequent maintenance and are relatively expensive as compared with some other kinds of batteries, like metal-air batteries. In previous work, we designed a novel metal-air battery, with low cost and easy maintenance for large-scale UPS applications. An extensive analysis was performed to apply our metal-air battery to the hybrid UPS model. In this study, we focus on including an optimal control system for high battery performance. We developed an algorithm based on receding horizon control (RHC) for each fan of the cooling system. The algorithm reflects the operation properties of the metal-air battery so that it can supply power for a long time. We solved RHC by applying dynamic programming (DP) for a corresponding time. Different variables, such as current density, oxygen concentration, and temperature, were considered for the application of DP. Additionally, a 1.5-dimensional DP, which is used for solving the RHC, was developed using the state variables with high sensitivity and considering the battery characteristics. Because there is no other control variable during operation, only one control variable, the fan flow, was used, and the state variables were divided by section rather than a point. Thus, we not only developed a sub-optimal control strategy for the UPS but also found that fan control can improve the performance of metal-air batteries. The sub-optimal control strategy showed stable and 6–10% of improvement in UPS operating time based on the simulation.

Optimal Control for Response Reduction of Single Hinged Articulated Tower Using MR-Damper

2019 ◽  
Author(s):  
Kushal Solomon ◽  
Deepak Kumar
Keyword(s):  
Optimal Control ◽  
Structural Control ◽  
Mr Damper ◽  
Linear Quadratic Regulator ◽  
Wave Loads ◽  
Linear Quadratic ◽  
Offshore Structure ◽  
Damping Force ◽  
Optimal Control Strategy ◽  
Sea Bed

Abstract Articulated tower is a compliant offshore structure deployed in deep waters for oil and gas exploration. The base of the tower is connected to the sea bed through universal joint, which allows the tower to rotate about horizontal axis (pitch). Articulated towers attain stability due to large buoyancy forces acting on it. Under extreme wave loads, the response of ALP can exceed the design limit causing discomfort to the occupants and create unfavourable working conditions. Structural control systems can be implemented in order to reduce the response of ALP, thereby protecting the structure from damages and to increase its life span. In this paper, a semi-active optimal control strategy using Magneto-Rheological damper is adopted to reduce the responses of ALP. Bouc-Wen model is used to describe the force generated by MR-Damper. For achieving the optimal performance of the control system, the applied voltage is varied according to the measured feedback at any moment to change the damping force using linear quadratic regulator technique. Several parametric studies have been conducted and the performance of the controller is evaluated. It is observed that the response of ALP is reduced considerably by using MR-damper as a semi-active control device. However, the capacity of the damper required for achieving the desired control is huge.

scholarly journals Effects of Isoperimetric Constraint for Reducing HSV-2 Infection Using Optimal Control Strategy

2021 ◽  
pp. 62-68
Author(s):  
Samiha Islam Tanni ◽  
Jakia Sultana ◽  
Shamima Islam ◽  
Farzana Afroz ◽  
Md Robiul Islam
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Vaccination Schedule ◽  
State Variables ◽  
Optimal Control Strategy ◽  
Sexually Transmitted ◽  
Isoperimetric Constraint ◽  
Fourth Order Method ◽  
The Cost

Optimal control is helpful for testing and comparing different vaccination strategies of a certain disease. Genital herpes is one of the most prevalent sexually-transmitted diseases globally. In this paper, we have proposed an optimal control problem applied to HSV-2 model after introducing the constraint and state variables. Optimal control problem is formulated based on ordinary differential equation and isoperimetric constraint in the vaccine supply is also included. Mathematical analysis such as the characterization of optimal control using Pontryagin’s maximum principle is studied. Generally optimal control theory is used for finding the optimal way for implementing the strategies, minimizing the number of infectious and latent individuals and keeping the cost of implementation as low as possible. Here the optimality system is derived and solved numerically using a Runge-Kutta fourth order method and this is an iterative method. Using numerical simulation we observe that how the optimal vaccination schedule is altered by imposing isoperimetric constraint. Finally, on applying the isoperimetric constraint on the optimal control problem of HSV-2 epidemic model, we observe that optimal vaccination schedule with isoperimetric constraint indicates successful short-term control of the disease. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 62-68

scholarly journals Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Q. F. Lü ◽  
X. F. Wang ◽  
K. Lu ◽  
R. H. Huan
Keyword(s):  
Optimal Control ◽  
Hamiltonian System ◽  
Control Strategy ◽  
Random Vibration ◽  
Vibration Reduction ◽  
Integrable Hamiltonian System ◽  
Control Law ◽  
Nonlinear Structures ◽  
Optimal Control Strategy ◽  
Inertial Actuator

An optimal control strategy for the random vibration reduction of nonlinear structures using piezoelectric stack inertial actuator is proposed. First, the dynamic model of the nonlinear structure considering the dynamics of a piezoelectric stack inertial actuator is established, and the motion equation of the coupled system is described by a quasi-non-integrable-Hamiltonian system. Then, using the stochastic averaging method, this quasi-non-integrable-Hamiltonian system is reduced to a one-dimensional averaged system for total energy. The optimal control law is determined by establishing and solving the dynamic programming equation. The proposed control law is analytical and can be fully executed by a piezoelectric stack inertial actuator. The responses of optimally controlled and uncontrolled systems are obtained by solving the Fokker–Planck–Kolmogorov (FPK) equation to evaluate the control effectiveness of the proposed strategy. Numerical results show that our proposed control strategy is effective for random vibration reduction of the nonlinear structures using piezoelectric stack inertial actuator, and the theoretical method is verified by comparing with the simulation results.

Flocking of Multi-Agent Systems Using a Unified Optimal Control Approach

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Jianan Wang ◽  
Ming Xin
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Distributed Feedback ◽  
Control Law ◽  
Multi Agent Systems ◽  
Optimal Control Strategy ◽  
Control Approach ◽  
Control Framework ◽  
Multi Agent ◽  
Optimal Control Approach

In this paper, the multi-agent flocking problem is investigated in a unified optimal control framework. The flocking characteristics, such as velocity alignment, navigation, cohesion, and collision/obstacle avoidance, are accomplished by formulating them into respective cost function terms. The resultant nonquadratic cost function poses a challenging optimal control problem. A novel inverse optimal control strategy is adopted to derive an analytical optimal control law. The optimality and asymptotic stability are proved and the distributed feedback control law only requires local information to achieve the flocking behaviors. Various simulation scenarios are used to demonstrate the effectiveness of the optimal flocking algorithm.

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