Siddhartha Sen

Realization of a Constant Phase Element and Its Performance Study in a Differentiator Circuit

A simple method for fabricating a constant phase element (CPE) has been discussed. Dependence of the phase angle on several physical parameters have also been elaborated. Finally, a fractional-order differentiator circuit has been constructed using the CPE, and its performance has been compared with the simulated results

Experimental studies on realization of fractional inductors and fractional-order bandpass filters

This paper presents the hardware realization and performance study of fractional inductors of order 0<α<2. The fractional inductors used in this work have been realized with the help of general impedance converter circuit and fractional capacitors. Impedance characterization of fractional inductors with different exponents has been carried out experimentally. Also a generalized approach to design a fractional-order bandpass filter is discussed in this work. The fractional-order bandpass filter consists of a series combination of a resistor, a fractional inductor of order 1<α<2, and a fractional capacitor of order 0<β<1. The performance of fractional-order bandpass filters has been studied and compared with corresponding integer-order filters through both experimentation and simulation. Copyright

A Design Example of a Fractional-Order Kerwin–Huelsman–Newcomb Biquad Filter with Two Fractional Capacitors of Different Order

Design, realization and performance studies of continuous-time fractional order Kerwin–Huelsman–Newcomb (KHN) biquad filters have been presented. The filters are constructed using two fractional order capacitors (FC) of orders α and β (0<α, β≤1). The frequency responses of the filters, obtained experimentally have been compared with simulated results using MATLAB/SIMULINK and also with PSpice (Cadence PSD 14.2), where the fractional order capacitor is approximated by a domino ladder circuit. It has been observed that fractional order filters can give better performance in certain aspects compared to integer order filters. The effects of the exponents (α and β) on bandwidth and stability of the realized filter have been examined. Sensitivity analysis of the realized fractional order filter has also been carried out to investigate the deviation of the performance due to the parameter variation.

Fractional optimal control problems: a pseudo-state-space approach

A scheme for optimal control problem formulation and solution of a fractional order system using pseudo-state-space formulation is presented in this paper. A pseudo-state-space representation for a particular type of fractional dynamical equation is proposed. The dynamic constraint is in the form of a fractional differential equation that includes integer derivatives in addition to the fractional derivatives. The order of the fractional derivatives is taken as less than one and fractional derivatives are defined in terms of Riemann-Liouville. The performance index considered is a function of both the state and the control variables. Using the proposed pseudo-state-space model a new formulation of a class of fractional optimal control problem is developed. A direct numerical technique based on Grünwald-Letnikov approximation is used to solve the resulting equations. A numerical example of a fractional order spring-mass-viscodamper system is considered to illustrate the methodology and technique.

Practical Realization of Tunable Fractional Order Parallel Resonator and Fractional Order Filters

This paper introduces a tunable fractional order parallel resonator (FOPR) whose resonating frequency can be tuned by the coefficient of a fractional order (FO) element (fractor). At the same time, its Q-factor can be set very high (theoretically infinite) by varying its resistor. Using this FOPR circuit, two simple FO filters (FO bandpass and FO notch) are also developed. The paper includes detail sensitivity analyses of these circuits for various circuit parameters and describes how different design parameters of proposed FOPR and FO filters are chosen accordingly. Proposed FOPR and FO filters are simulated in MATLAB and realized in hardware. The hardware circuits are tested practically, and detail experimental results are provided. It is found that the experimental data are in good agreement with the simulation data. In hardware, the realized FOPR has achieved a Q-factor up to 360, and the realized FO notch filter has Q > 10 when its attenuation is more than 30 dB. Different practical aspects of filter tuning are also described in detail.

Design and performance study of phase-locked loop using fractional-order loop filter

The present work reports the realization of an analog fractional-order phase-locked loop FPLL using a fractional capacitor. The expressions for bandwidth, capture range, and lock range of the FPLL have been derived analytically and then compared with the experimental observations using LM565 IC. It has been observed that bandwidth and capture range can be extended by using FPLL. It has also been found that FPLL can provide faster response and lower phase error at the time of switching compared to its integer-order counterpart. Copyright

Fractional Optimal Control Problems With Specified Final Time

A constrained dynamic optimization problem of a fractional order system with fixed final time has been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The dynamic constraint is described by a fractional differential equation of order less than 1, and the fractional derivative is defined in terms of Riemann-Liouville. The performance index includes the terminal cost function in addition to the integral cost function. A general transversility condition in addition to the optimal conditions has been obtained using the Hamiltonian approach. Both the specified and unspecified final state cases have been considered. A numerical technique using the Grunwald-Letnikov definition is used to solve the resulting equations obtained from the formulation. Numerical examples are provided to show the effectiveness of the formulation and solution scheme. It has been observed that the numerical solutions approach the analytical solutions as the order of the fractional derivatives approach 1.

Free final time fractional optimal control problems

Abstract A formulation and solution scheme of free final time fractional optimal control problems is presented in this paper. The dynamic constraint is described by a fractional differential equation. Performance index considered is a function of both the state and control variables. The necessary conditions of optimality and the transversality condition are obtained using Lagrange multiplier technique. A numerical technique similar to Shooting method is used for solving the optimal conditions. Numerical example is provided to show the effectiveness of the formulation and numerical solution scheme. It is interesting to note that the final time changes with the interchange of the boundary conditions, which does not occur in classical optimal control problems.

Disturbance Rejection and Control Allocation of Over-Actuated systems H

This paper presents the development and application of two approaches to control allocation for an over-actuated system. These approaches considered the effect of disturbance acting on the system through an Hinfin controller designed using LMIs. The approach minimizes weighted norm of control input to distribute control effort and also takes into account of actuator saturation. The design 2 has an adaptive weight updating algorithm, while determining the weighted-pseudo inverse allocation, avoids the control input saturation for all attainable control demands. The proposed design and algorithms are demonstrated with an eight actuator model of a satellite launch vehicle.

Reconfigurable Direct Allocation for Multiple Actuator Failures

Flight control systems are often equipped with reconfigurable control allocation schemes to redistribute control commands in the event of actuator failures. In this brief, a reconfiguration scheme is proposed and is based on the direct allocation method. An iterative algorithm is developed and uses the same lookup tables prepared offline for normal operations, thereby saving a considerable amount of computation time and process memory. To elucidate the effectiveness of the method, the proposed allocation algorithm is applied to a satellite launch vehicle model. Simulation results show satisfactory performance of the method in the presence of multiple actuator failures.