Evaluation of fractional order of the discrete integrator. Part II

This is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

Fractional-order value identification of the discrete integrator from a noised signal. part I

In the paper we investigate the fractional-order evaluation of the fractional-order discrete integration element. We assume that the input and output signals are known. The main problem is to calculate fractional-order value. From a theoretical point of view there is no mathematical problem of the solution. One should solve linear algebraic equation or find roots of a polynomial in a variable ν. The problem arises when the measured output signal contains a noise. Then, the solution is unsettled because the polynomial roots are very sensitive to coefficients variability. In the paper we propose a method of evaluating of the discrete integrator fractional-order. The investigations are supported by numerical examples.

Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

Optimal Preview Control for Discrete-Time Systems in Multirate Output Sampling

This paper studies the disturbance preview optimal control problem for discrete-time systems with multirate output sampling. By constructing the error system and using the discrete lifting technique, we reduce the multirate preview control problem to a single-rate one for a formal augmented system. Then, applying preview control theory, the optimal preview control law of the augmented error system is obtained. Meanwhile, we introduce a discrete integrator to eliminate the static error. Then we study a method to design a controller with preview action for the original system. And the existence conditions of the controller are also discussed in detail. Finally, numerical simulation is included to illustrate the effectiveness of the proposed method.

A Novel DCGA Optimization Technique for Guaranteed BIBO-Stable Frequency-Response Masking Digital Filters Incorporating Bilinear Lossless Discrete-integrator IIR Interpolation Sub-Filters

This work is concerned with the development of a novel diversity-controlled (DC) genetic algorithm (GA) for the design and rapid optimization of frequency-response masking (FRM) digital filters incorporating bilinear lossless discrete-integrator (LDI) IIR interpolation sub-filters. The selection of FRM approach is inspired by the fact it lends itself to the design of practical sharp-transition band digital filters in terms of gradual-transition band FIR interpolation sub-filters. The proposed DCGA optimization is carried out over the canonical-signed-digit (CSD) multiplier coefficient space, resulting in FRM digital filters which are capable of direct implementation in digital hardware. A novel CSD look-up table (LUT) scheme is developed so that in every stage of DCGA optimization, the IIR interpolation sub-filters constituent in the intermediate and final FRM digital filters are guaranteed to be automatically BIBO stable. The proposed DCGA optimization permits simultaneous optimization of the magnitude-frequency as well of the group-delay frequency response of the desired FRM digital filters. An example is given to illustrate the application of the resulting DCGA optimization to the design of a lowpass FRM digital filter incorporating a fifth-order bilinear-LDI interpolation subfilter.

Reduction the effects of opamp finite gain and offset voltage in LDI termination with a minus one half delay of SC ladder filters

In this paper a combined approach for reducing the effects of op amp imperfections (finite gain A and offset voltage VOS) in first-order SC cell, realizing LDI (loss less discrete integrator) termination with a minus one half delay is presented. First, the conventional integrator is replaced with gain- and offset-compensated (GOC) integrator. Next, the gain errors m(?) and the phase errors ?(?) are further reduced by using the precise op amp gain approach in the GOC structure. The variation of the dc gain A from its nominal value A0 is taken into account.