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MICROELECTRONIC IMPLEMENTATIONS OF FRACTIONAL ORDER INTEGRO-DIFFERENTIAL OPERATORS

机译:分数阶积分微分算子的微电子实现

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摘要

For practical applications, the fractional order integral and differential operators require to be approximated as stable, causal, minimum-phase integer order systems, which usually leads, in both continuous and discrete domains, to high order transfer functions. Assuming that an approximation of good quality is available for the fractional operator, efficient implementations, in both cost and speed, are required. The fast development of the microelectronics gives us the opportunity of using cheap, accurate, programmable and fast devices for implementing reconfigurable analog and digital circuits. Among these devices, Field Programmable Gate Arrays (FPGAs), Switched Capacitors Circuits (SCCs), and Field Programmable Analog Arrays (FPAAs) are used in this paper for the implementation of a fractional order integrator, previously approximated by the recursive Oustaloup's method. The fundamentals of the devices, as well as the design procedures are given, and the implementations are compared considering their simulated frequency responses, the design efforts, and other important issues.
机译:对于实际应用,分数阶积分和微分算子需要近似为稳定的,因果的,最小相位整数阶系统,通常在连续和离散域中都导致高阶传递函数。假设小数运算符可以提供高质量的近似值,则需要在成本和速度上都有效的实现。微电子学的快速发展为我们提供了使用廉价,准确,可编程和快速的设备来实现可重构模拟和数字电路的机会。在这些器件中,本文使用现场可编程门阵列(FPGA),开关电容器电路(SCC)和现场可编程模拟阵列(FPAA)来实现分数阶积分器,该积分器以前通过递归Oustaloup方法近似。给出了设备的基本原理以及设计过程,并考虑了它们的模拟频率响应,设计工作和其他重要问题,对实现进行了比较。

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