Algebra Students Build Stock/Flow Models to Study Non-linear, Dynamic Feedback System Problems

2020 ◽  
pp. 505-514
Author(s):  
Diana M. Fisher
Keyword(s):  
Feedback System ◽  
Dynamic Feedback ◽  
Flow Models ◽  
Algebra Students ◽  
Linear Dynamic ◽  
Non Linear ◽  
Stock Flow

scholarly journals A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders

2019 ◽  
Vol 52 (7-8) ◽  
pp. 913-921 ◽  
Author(s):  
Paweł Skruch ◽  
Marek Długosz
Keyword(s):  
Differential Equations ◽  
Linear Systems ◽  
Differential Algebraic Equations ◽  
Feedback Controller ◽  
Dynamic Feedback ◽  
Algebraic Equations ◽  
Linear Dynamic ◽  
Wide Range ◽  
Non Linear ◽  
Non Linear Systems

The paper presents a design scheme of the linear dynamic feedback controller for some non-linear systems. These systems are mathematically described by matrix non-linear differential equations of the first and second orders. A first-order form of the studied systems includes some types of differential-algebraic equations. The stability property of the non-linear systems with the linear controller is assured by an appropriate definition of the system output, and the linear dynamic compensator is an important part of the feedback control system. The order of the dynamic part is equal to the size of the system input and is independent of the size of the system state vector. The asymptotic stability in the Lyapunov sense is analysed and proved by the use of Lyapunov functionals and LaSalle’s invariance principle. Stabilisation in a wide range of controller parameters improves the system’s robustness.

scholarly journals Non-linear dynamic joint selection strategy for Hinge controlled masonry arches

2020 ◽  
Author(s):  
Gabriel Stockdale ◽  
Vasilis Sarhosis ◽  
Gabriele Milani
Keyword(s):  
Selection Strategy ◽  
Masonry Arches ◽  
Linear Dynamic ◽  
Non Linear

scholarly journals Seismic Strengthening Effects of Full-Size Reinforced Concrete Frame Retrofitted with Novel Concrete-Filled Tube Modular Frame by Pseudo-Dynamic Testing

2021 ◽  
Vol 11 (11) ◽  
pp. 4898
Author(s):  
Jin-Seon Kim ◽  
Ju-Seong Jung ◽  
Dong-Keun Jung ◽  
Eui-Yong Kim ◽  
Kang-Seok Lee
Keyword(s):  
Dynamic Analysis ◽  
Shear Failure ◽  
Dynamic Testing ◽  
Seismic Intensity ◽  
Seismic Retrofitting ◽  
Restoring Force ◽  
Rc Structures ◽  
Linear Dynamic ◽  
Non Linear ◽  
Force Characteristics

The present study proposes a new seismic retrofitting method using a concrete-filled tube modular frame (CFT-MF) system, a novel technique to overcome and improve the limitations of existing seismic strengthening methods. This CFT-MF seismic retrofitting method makes the most of the advantages of both concrete and steel pipes, thereby significantly improving constructability and increasing integration between the existing structure and the reinforcement joints. This method falls into the category of typical seismic retrofitting methods that focus on increasing strength, in which the required amount of seismic reinforcement can be easily estimated. Therefore, the method provides an easy solution to improving the strength of existing reinforced concrete (RC) structures with non-seismic details that are prone to shear failure. In the present study, a full-size two-story test frame modeled from existing domestic RC structures with non-seismic details was subjected to pseudo-dynamic testing. As a result, the effect of the CFT-MF system, when applied to existing RC structures, was examined and verified, especially as to its seismic retrofitting performance, i.e., restoring force characteristics, stiffness reinforcement, and seismic response control. In addition, based on the pseudo-dynamic testing results, a restoring force characteristics model was proposed to implement non-linear dynamic analysis of a structure retrofitted with the CFT-MF system (i.e., the test frame). Finally, based on the proposed restoring force characteristics, non-linear dynamic analysis was conducted, and the results were compared with those obtained by the pseudo-dynamic tests. The results showed that the RC frame (building) with no retrofitting measures applied underwent shear failure at a seismic intensity of 200 cm/s2, the threshold applied in seismic design in Korea. In contrast, in the frame (building) retrofitted with the CFT-MF system, only minor earthquake damage was observed, and even when the maximum seismic intensity (300 cm/s2) that may occur in Korean was applied, small-scale damage was observed. These results confirmed the validity of the seismic retrofitting method based on the CFT-MF system developed in the present study. The non-linear dynamic analysis and the pseudo-dynamic test showed similar results, with an average deviation of 10% or less in seismic response load and displacement.

Sign in / Sign up

Export Citation Format

Share Document