Identification and tuning fractional order proportional integral controllers for time delayed systems with a fractional pole

First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the model with a single fractional pole replacing the integer order pole, which is believed to better characterize the reaction curve. In this paper, using time delayed system model with a fractional pole as the starting point, fractional order controllers design for this class of fractional order systems is investigated. Integer order PID and fractional order PI and [PI] controllers are designed and compared for these class of systems. The simulation comparison between PID controller and fractional order PI and [PI] controllers show the advantages of the properly designed fractional order controllers. Experimental results on a heat flow platform are presented to validate the proposed design method in this paper.     

Experimental study of fractional order proportional derivative controller synthesis for fractional order systems

In recent years, studies on real systems have revealed inherent fractional order dynamic behavior, and fractional order systems have attracted more and more attentions. It is intuitively true that these fractional order models require the corresponding fractional order controllers to achieve desired performance. In this paper, an experimental study of the fractional order proportional and derivative (FO-PD) controller systematic design is presented, to validate the control performance for the fractional order systems with generalized fractional capacitor membrane model. The performance of the designed FO-PD controller is compared with both the integer order and fractional order controllers which are designed based on the approximate integer order system. This comparison results are presented both in the simulation and the hardware-in-the-loop experiment.     

Control of a novel chaotic fractional order system using a state feedback technique

We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the Routh–Hurwitz and the Matignon stability criteria, we analyze the novel chaotic fractional order system and propose a control methodology that is better than the nonlinear counterparts available in the literature, in the sense of simplicity of implementation and analysis. A scalar control input that excites only one of the states is proposed, and sufficient conditions for the controller gain to stabilize the unstable equilibrium points derived. Numerical simulations confirm the theoretical analysis.     

Two-stage adaptive estimation of irrational linear systems

In the present paper, an adaptive parameter estimation algorithm applicable to linear systems with transfer functions of arbitrary structure is proposed. The approach can be applied to a wide class of linear processes, including non-linearly parameterized ones. The proposed method is applicable to fractional-order systems, distributed-parameter and delayed systems, and other classes of systems described by irrational transfer functions. In the first stage of the proposed procedure, values of the transfer function at specific frequencies are pinpointed by means of the Recursive Least Square algorithm with forgetting factor. In the second stage, the unknown parameters are found by numerically inverting complex non-linear relations linking them to the quantities estimated in the first stage. The inversion is performed by means of an iterative, gradient-based scheme. The method is illustrated by several detailedly explained numerical examples.     

Design of adjustable fractional order differentiator using expansion of ideal frequency response

In this paper, the design and implementation structures of adjustable fractional order differentiator (AFOD) are presented. First, the series expansion of ideal frequency response is used to transform the design of AFOD into the designs of log differentiators with various orders. Then, conventional FIR filter design method is applied to design log differentiators. The proposed method is flexible because the AFOD can be designed by considering the trade-off among the storage requirement of filter coefficients, implementation complexity and delay of filter. Finally, several numerical examples are shown to illustrate the effectiveness of the proposed design approach.     

Higher order spectral estimation for random fields

This paper is concerned with the nonparametric estimation of the higher order cumulant spectra of vector-valued stationary random fields onZ ^d by smoothing the periodograms, whereZ is the space of integers and the dimensiond1. We derive the asymptotic cumulant properties of the spectral estimates, and consider an application to multidimensional nonlinear systems identification. Numerical examples with simulated data are provided.     

On the fractional signals and systems

A look into fractional calculus and its applications from the signal processing point of view is done in this paper. A coherent approach to the fractional derivative is presented, leading to notions that are not only compatible with the classic but also constitute a true generalization. This means that the classic are recovered when the fractional domain is left. This happens in particular with the impulse response and transfer function. An interesting feature of the systems is the causality that the fractional derivative imposes. The main properties of the derivatives and their representations are presented. A brief and general study of the fractional linear systems is done, by showing how to compute the impulse, step and frequency responses, how to test the stability and how to insert the initial conditions. The practical realization problem is focussed and it is shown how to perform the input-ouput computations. Some biomedical applications are described.     

Fractional order modeling and control for permanent magnet synchronous motor velocity servo system

This paper presents the application of fractional order system on modeling the permanent magnet synchronous motor (PMSM) velocity servo system. The traditional integer order model of the PMSM velocity system is extended to fractional order one in this work. In order to identify the parameters of the proposed fractional order model, an integer order approximation of the fractional order operator is applied and a state-space structure is presented for using the output-error identification algorithm. In real-time PMSM velocity servo plant, the fractional order model is identified according to some experimental tests using the presented algorithm. Two proportional integral (PI) controllers are designed for velocity servo using a simple scheme according to the identified fractional order model and the traditional integer order one, respectively. The experimental test performance using these two designed PI controllers is compared to demonstrate the advantage of the proposed fractional order model of the PMSM velocity system.     

Analytical design of fractional order PID controllers based on the fractional set-point weighted structure: Case study in twin rotor helicopter

In this paper, an analytical method for tuning the parameters of the set-point weighted fractional order PID (SWFOPID) controller is proposed. The studied control scheme is the filtered fractional set-point weighted (FFSW) structure. Also to achieve a desired closed-loop performance, a fractional order pre-filter is employed. The proposed method is applicable to stable plants describable by a simple three-parameter fractional order model. Such a model can be considered as the fractional order counterpart of a first order transfer function without time delay. Finally, the proposed method is implemented on a laboratory scale CE 150 helicopter platform and the results are compared with those of applying a filtered fractional order PI (FFOPI) controller in a similar structure. The practical results show the effectiveness of the proposed method.     

Stability preservation analysis in direct discretization of fractional order transfer functions

In this paper, a class of the direct methods for discretization of fractional order transfer functions is studied in the sense of stability preservation. The stability boundary curve is exactly determined for these discretization methods. Having this boundary helps us to recognize whether the original system and its discretized model are the same in the sense of stability. Finally, some illustrative examples are presented to evaluate achievements of the paper.     

Improved parameter estimation by noise compensation in the time-scale domain

It was shown recently that parameter estimation can be performed directly in the time-scale domain by isolating regions wherein the prediction error can be attributed to the error of individual dynamic model parameters [1]. Based on these single-parameter equations of the prediction error, individual model parameters error can be estimated for iterative parameter estimation. An added benefit of this parameter estimation method, besides its unique convergence characteristics, is the added capacity for direct noise compensation in the time-scale domain. This paper explores this benefit by introducing a noise compensation method that estimates the distortion by noise of the prediction error in the time-scale domain and incorporates that as a confidence factor to bias the estimation of individual parameters error. This method is shown to improve the precision of the estimated parameters when the confidence factors accurately represent the noise distortion of the prediction error.     

基于分数低阶矩的非整数时间延迟估计方法

依据信号的噪声特性和分数低阶矩理论,提出一种基于最小平均p范数的非整数时间延迟估计方法(称为LMPFTDE算法)。该算法是对直接估计非整数采样间隔的时间延迟估计算法(ETDGE)的广义化,运用最小分散系数准则,通过使误差的p阶矩最小得到非整数时间延迟估计值。理论分析和计算机仿真结果都表明该方法不仅可以在高斯噪声环境下工作,而且在脉冲噪声下也具有良好的健壮性。     

DMBT系统中利用FWT快速实现信道估计

根据PN码的结构特性,针对DMB-T系统多载波模式,本文提出了一种新的理论上与滑窗相关法等价的信道估计方法,利用FWT(快速沃尔什变换)实现快速多径捕获.通过干扰抵消进一步消除了径间干扰.该方法具有很强的抗多径效应和抗强窄带干扰的能力,将运算复杂度从传统滑动互相关法的N~2降低到(N+1)log_2(N+1).     

分数低阶循环统计量及其在脉冲噪声环境下时延估计中的应用

本文以α稳定分布作为噪声模型,研究了非高斯噪声对传统的二阶循环统计量的影响,提出了分数低阶循环统计量的概念,研究并证明了其性质。在此基础上提出基于分数低阶循环统计量的新的时延估计方法—RCCC(Robust Corre- lated Cyclic Covariation)。计算机模拟表明,这种算法是一种在高斯和α稳定分布噪声条件下具有良好韧性的时延估计方法。     

Analytical impulse response of a fractional second order filter and its impulse response invariant discretization

In this paper, we derive the impulse response of a fractional second order filter of the form (s²+as+b)^−γ, where a,b?0 and γ>0. The asymptotic properties of the impulse responses are obtained. Moreover, based on the derived analytical impulse response, we show how to perform the discretization of the above fractional second order filter. Finally, a number of illustrated examples in time and frequency domains are provided as proofs of concepts.     

高阶累积量在谱估计中的应用

本文提出了两种利用高阶累积量估计MA参数的新算法。当信号可以看作一个非高斯白噪声通过一个线性时不变系统的输出时,新算法运算简单、估计准确。本文还通过模拟实验分析了两种算法的性能。     

分数阶超混沌系统的动力学分析及同步

对一个新的超混沌系统通过分数阶线性系统稳定性理论分析得出其分数阶形式,并利用matlab仿真得出该系统的混沌吸引子图像.接着对该分数阶系统的同阶数和不同阶数两种形式进行异结构的同步分析,设计自适应同步控制器,实现该系统的异结构同步,数值仿真的结果表明设计控制器很好的实现了驱动系统和响应系统的同步.