A recursive net-grid-type analog fractance circuit for any order fractional calculus (original) (raw)

Realization of fractional-order proportional-integral-derivative controller using fractance circuit

This paper concerned with the realization of fractional-order proportional-integral-derivative (FOPID) by electronic circuit utilizing the syntheses of a fractance circuit that can be connected on operational amplifier (OPAMP) either in the input or the output feedback of OPAMP circuit. Where the fractional-order derivative (FD) and fractional-order integral (FI) have been approximated to integer order rational transfer function depending on Carlson method. The continued fractional expansion (CFE) and partial fraction expansion have been performed on the FI and FD approximated transfer function to synthesize the fractance circuit. The analog electronic circuit has been simulated using circuit wizard to realize the FD, FI, and FOPID circuits. The time domain response has been tested with sine wave input. The Bode plot for both real FD and FI with that the approximated one has been drawn.

REALIZATION OF FRACTIONAL ORDER DIFFERENTIATOR BY ANALOGUE ELECTRONIC CIRCUIT

The aim of this paper is to realize fractional order derivative (FD) with electronic circuit utilizing the syntheses of a fractance circuit. The realization has been done via synthesis of two type of fractances as passive RC circuits connected in operational amplifier. The continuous fractional expansion (CFE) and partial fraction expansion (PE) have been utilized on the (FD) transfer function which has been approximated to integer order rational transfer function depending on Carlson, Caurer and Foster method through special Matlab instructions. As case of study FD raised to order 0.9 has been implemented with electronic realization. The analogue electronic circuit has been simulated using Circuit Wizard to realize the derivative function. The time, frequency domain response has been tested for both real fractional order derivative and the approximated one KEYWORD: Fractional order derivative (FD) , Nintegerv.2.3Fractional control toolbox , Partial fraction expansion (PE) , Continuous fractional expansion (CFE),fractance.

Realization of Fractance Device using Continued Fraction Expansion Method

The realization of fractional-order circuits is an emerging area of research for people working in the areas of control systems, signal processing and other related fields. In this paper, an attempt is made to realize fractance devices. The continued fraction expansion formula is used to calculate the fractance device's rational approximation. For the simulation in the experimentation, the third-order approximation for fractional order, α =-1/2,-1/3,-1/4 is used. For the aim of mathematical simulation, the MATLAB platform was used. The proposed rational approximation is used to create a circuit. The TINA programme is used to simulate circuits. It has been discovered that the simulation and theoretical conclusions are in agreement.

Studies on fractional order differentiators and integrators: A survey

Studies on analysis, design and applications of analog and digital differentiators and integrators of fractional order is the main objective of this paper. Time and frequency domain analysis, different ways of realization of fractance device is presented. Active and passive realization of fractance device of order 1 2 using continued fraction expansion is carried out. Later, time and frequency domain analysis of fractance based circuits is considered. The variations of rise time, peak time, settling time, time constant, percent overshoot with respect to fractional order a is presented. Digital differentiators and integrators of fractional order can be obtained by using direct and indirect discretization techniques. The s to z transforms used for this purpose are revisited. In this paper by using indirect discretization technique fractional order differentiators and integrators of order 1 2 and 1 4 are designed. These digital differentiators and integrators are implemented in real time using TMS320C6713 DSP processor and tested using National instruments education laboratory virtual instrumentation system (NIELVIS). The designed fractional order differentiators have been used for the detection of QRS sequences as well as the occurrence of Sino Atrial Rhythms in an ECG signal and also for the detection of edges in an image. The obtained results are in comparison with the conventional techniques.

Fractional-Order Differentiators and Integrators with Reduced Circuit Complexity

2018 IEEE International Symposium on Circuits and Systems (ISCAS), 2018

Fractional-order differentiation and integration stages are essential building blocks for performing signal processing using fractional-order calculus. One important characteristic of fractional-order differentiators/integrators is the circuit complexity of the integer-order topologies required for approximating such stages. The already introduced schemes suffer from this obstacle, making the derived structures power demanding. A simple structure, constructed from 21 MOS transistors and 3 dc current sources, which is capable of approximating fractional-order differentiators and integrators is presented in this paper. Other attractive benefits of the proposed scheme are the electronic tuning capability as well as the capability for implementation in monolithic form. The evaluation of its behavior is performed using Cadence and the Design Kit provided by the Austrian Mikro Systems (AMS) 0.35p.m CMOS process.

Capacitorless Fractional-Order Circuits

2018

Studies on analysis and design of digital fractional order differentiators and integrators is the main objective of this paper. In order to design a digital fractional order differentiator or integrator, one needs to obtain a transfer function in the digital domain. Commonly used techniques of obtaining a digital transfer function from a continuous-time domain transfer function are direct discretization and indirect discretization. In this paper second method is followed. That approach is tested for differentiators and integrators of order ½ and ¼. The results were compared with the ideal characteristic.

Design and application examples of CMOS fractional-order differentiators and integrators

Microelectronics Journal, 2018

Reduced complexity CMOS fractional-order differentiator and integrator building blocks are introduced in this work, based on 2 nd-order integer-order transfer function approximations. These blocks are then used for implementing fractional-order filters as well as a Leaky-Integrate-and-Fire Mihalas-Niebur neuron model. Cascading 1 st and 2 nd-order blocks to obtain 5 th-order integer-order transfer functions, improved bandwidth of approximation accuracy is achieved. Furthermore, the realization of floating fractional-order capacitor and inductor emulators is demonstrated.

Implementation of fractional order integrator/differentiator on field programmable gate array

Alexandria Engineering Journal, 2016

Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractional calculus i.e. fractional integrator and derivative, using Gru¨nwald-Letnikov definition, on field programmable gate array (FPGA) in LabVIEW environment. The simulation and hardware implementation results for fractional order integrator and derivative of sinusoid and square waveform signals for some selected fractional orders have been presented. A close agreement between the simulated and the experimental results demonstrated the suitability of FPGA device in fractional order control and signal processing applications. LabVIEW being one of the finest tools for measurement and control, and signal processing applications the fractional order operator implementation is expected to further enhance the capability of the tool to cater to the needs of advanced experimental research employing fractional order operators.

Improving the Hardware Complexity by Exploiting the Reduced Dynamics-Based Fractional Order Systems

IEEE Access, 2017

Fractional calculus is finding increased usage in the modeling and control of nonlinear systems with the enhanced robustness. However, from the implementation perspectives, the simultaneous modeling of the systems and the design of controllers with fractional-order operators can bring additional advantages. In this paper, a fractional order model of a nonlinear system along with its controller design and its implementation on a field programmable gate array (FPGA) is undertaken as a case study. Overall, three variants of the controllers are designed, including classical sliding mode controller, fractional controller for an integer model of the plant, and a fractional controller for a fractional model of the plant (FCFP). A high-level synthesis approach is used to map all the variants of the controllers on FPGA. The integro-differential fractional operators are realized with infinite impulse response filters architecturally implemented as cascaded secondorder sections to withstand quantization effects introduced by fixed-point computations necessary for FPGA implementations. The experimental results demonstrate that the fractional order sliding mode controllerbased on fractional order plant (FCFP) exhibits reduced dynamics in sense of fractional integration and differentials. It is further verified that the FCFP is as robust as the classical sliding mode with comparable performance and computational resources.