Stability and chaos of the duopoly model of Kopel: A study based on symbolic computations

Since Kopel's duopoly model was proposed about three decades ago, there are almost no analytical results on the equilibria and their stability in the asymmetric case. The first objective of our study is to fill this gap. This paper analyzes the asymmetric duopoly model of Kopel analytically by using several tools based on symbolic computations. We discuss the possibility of the existence of multiple positive equilibria and establish necessary and sufficient conditions for a given number of positive equilibria to exist. The possible positions of the equilibria in Kopel's model are also explored. Furthermore, if the duopolists adopt the best response reactions or homogeneous adaptive expectations, we establish rigorous conditions for the existence of distinct numbers of positive equilibria for the first time. The occurrence of chaos in Kopel's model seems to be supported by observations through numerical simulations, which, however, is challenging to prove rigorously. The second objective is to prove the existence of snapback repellers in Kopel's map, which implies the existence of chaos in the sense of Li-Yorke according to Marotto's theorem.Comment: arXiv admin note: substantial text overlap with arXiv:2301.1262

Cathode Pressure Control of Air Supply System for PEMFC

This paper proposes a backstepping method controller for the polymer electrolyte membrane fuel cell (PEMFC)air supply system. The control objective is adjusting the cathode pressure to its reference value quickly, in order to solve the problem of excessive extreme pressure difference between anode and cathode in practice. Considering model uncertainty and some disturbances, we design an extend state observer (ESO) to estimate disturbances. Next, a backstepping method is proposed to adjust control law. Finally, the experiment results demonstrate the effectiveness and robustness of the control strategy

Real-Time FPGA/CPU-Based Simulation of a Full-Electric Vehicle Integrated with a High-Fidelity Electric Drive Model

Real-time simulations refer to the simulations of a physical system where model equations for one time-step are solved within the same time period as in reality. An FPGA/CPU-based real-time simulation platform is presented in this paper, with a full-electric vehicle model implemented in a central processing unit (CPU) board and an electric drive model implemented in a field programmable gate arrays (FPGA) board. It has been a challenge to interface two models solved with two different processors. In this paper, one open-loop and three closed-loop interfaces are proposed. Real-time simulation results show that the best method is to transmit electric machine speed from the vehicle model to the electric derive model, with feedback electric machine torque calculated in FPGA. In addition, a virtual vehicle testing tool (CarMaker) is used when building the vehicle model, achieving more accurate modeling of vehicle subsystems. The presented platform can be used to verify advanced vehicle control functions during hardware-in-the-loop (HIL) testing. Vehicle anti-slip control is used as an example here. Finally, experiments were performed by connecting the real-time platform with a back-to-back electric machine test bench. Results of torque, rotor speed, and d&q axis currents are all in good agreement between simulations and experiments

An adaptive power split strategy with a load disturbance compensator for fuel cell/supercapacitor powertrains

Electric vehicles powered by fuel cell and supercapacitor hybrid power sources are of great interest. However, the power allocation between each power source is challenging and the DC bus voltage fluctuation is relatively significant in cascaded PI control schemes. This paper develops a power control strategy with an adjustable cut-off frequency, using an artificial potential field, to adaptively split the load current between the fuel cell and the supercapacitor under various load conditions. The adaptive cut-off frequency is calculated by cutting the load frequency spectrum with an allocation ratio that changes with the supercapacitor state of charge. Therefore, the relatively lower frequency portion of the load current is provided by the fuel cell and the supercapacitor handles the higher frequency portion. To enhance the control performance of the DC bus voltage regulation against the load disturbance, a load disturbance compensator is introduced to suppress the DC bus voltage fluctuation when the load variation occurs, which is implemented by a feed-forward controller that can compensate the load current variation in advance. The effectiveness of the proposed strategy is validated by extensive experiments

電池とスーパーキャパシタを用いた電気自動車用ハイブリッドエネルギー貯蔵システムの研究

学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 堀 洋一, 東京大学教授 大崎 博之, 東京大学教授 古関 隆章, 東京大学准教授 藤本 博志, 東京大学准教授 馬場 旬平University of Tokyo(東京大学