A Suite of Interactive Programs for Teaching Computer Control

The theory and design of linear adaptive filters based on FIR filter structures is well developed and widely applied in practice. However, the same is not true for more general classes of adaptive systems such as linear infinite impulse response adaptive filters (MR) and nonlinear adaptive systems. This situation results because both linear IIR structures and nonlinear structures tend to produce multi-modal error surfaces for which stochastic gradient optimization strategies may fail to reach the global minimum. After briefly discussing the state of the art in linear adaptive filtering, the attention of this paper is turned to MR and nonlinear adaptive systems for potential use in echo cancellation, channel equalization, acoustic channel modeling, nonlinear prediction, and nonlinear system identification. Structured stochastic optimization algorithms that are effective on multimodal error surfaces are then introduced, with particular attention to the particle swarm optimization (PSO) technique. The PSO algorithm is demonstrated on some representative IIR and nonlinear filter structures, and both performance and computational complexity are analyzed for these types of nonlinear systems.

Structure for FIR and IIR Filters

This paper describes a laboratory facility capable of simulating time-varying radio multipath channel responses in real time under computer control. Four independent fading channels are available that can be used for single-polarization nondiversity, combined in pairs for single-polarization dual diversity, or cross-coupled to simulate the two outputs of a dual-polarization nondiversity channel. Each channel contains a controllable variable network capable of producing a narrowband intermediate frequency response that resembles the “three-path” function of Rummler. A wide range of models can be accommodated by altering the computer-stored sequences used to control each variable channel network. The only assumption implicit in the choice of model is that the channel response can be fitted to the generic function over bandwidths up to 40 MHz. The channel responses are controlled by either entering fixed parameters from a keyboard, or by reading time-varying parameters stored in disk memory. This description includes the architecture, hardware design, software implementation, and performance of the simulation facility.

Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Time Delay Autonomous Systems

A new approach to solving discrete Lyapunov matrix algebraic equations is based on methods for spectral decomposition of their solutions. Assuming that all eigenvalues of the matrices on the left-hand side of the equation lie inside the unit disk, it is shown that the matrix of the solution to the equation can be calculated as a finite sum of matrix bilinear quadratic forms made up by products of Faddeev matrices obtained by decomposing the resolvents of the matrices of the Lyapunov equation. For a linear autonomous stochastic discrete dynamic system, analytical expressions are obtained for the decomposition of the asymptotic variance matrix of system’s states.

The method introduced here determines explicitly whether a given system has only eigenvalues with negative real parts, without determining these eigenvalues, but rather by determining the eigenvalues of a related symmetric matrix which are always real and hence easy to calculate. The new method is similarly applied to linear autonomous discrete systems where all the eigenvalues of the system matrix are required to be positioned within the unit circle in the z-plane.

Anti-control of chaos of two-degrees-of-freedom loudspeaker system and chaos synchronization of different order systems

A bank of circuit design solutions for active RC filters of the second order is considered - alow-pass filter, a high-pass filter and band-pass filters, in which independent tuning of the mainparameters - the pole frequency, the quality factor of the pole and the transmission coefficient isprovided. From these positions, the requirements for three special transfer functions of a multipolefrequency-setting RC circuit, which contains two resistors and two capacitors, are formulated.By choosing the coefficients of the numerator of the first transfer function, the type of the requiredfilter (LPF, HPF, BPF) is implemented. The coefficients of the second transfer function are chosenso that they affect only the frequency of the pole. It should be noted that, depending on the set ofcoefficients of the transfer function numerator polynomial, the developed circuits have the propertyof lowering the pole frequency or increasing the pole frequency. In this case, the choice of parametersof the third transfer function provides the necessary attenuation of the pole. Using theThe introduction describes a generalized architecture of second-order active RC filters, whichallows implementing an algorithm for step-by-step tuning of the main parameters and can be usedas the basis for the synthesis of many other modifications of active RC filters. For correct independentadjustment, the following sequence must be observed: the frequency of the pole, the secondstage is the adjustment of the quality factor of the pole, and the third stage is the scalingfactor. The stages of synthesis of this class of active RC filters are considered, the coefficients ofthe transfer functions of the presented circuits of 12 band-pass filters, a high-pass filter and a lowpassfilter, confirmed by 14 patents of the Russian Federation, are given.

Frequency responses are frequently referred to in the stability analysis of fractional order control systems. Frequency response-based methods have been introduced in the literature to reduce complex fractional order systems. However, the magnitude and phase response improvement is not handled by these techniques. The optimization methods are utilized to improve the approximation of fractional order filters in the desired frequency range. The article discusses the ideal Fractional-Order Butterworth Filter (FOBF) configuration by utilizing integer-order rational approximations to achieve a precise magnitude and phase response. Additionally, this study utilizes optimal FOBF magnitude and phase characteristics to minimize errors and expands the approximation bandwidth to cover multiple decades in both pass and stop bands. Optimized fractional order Butterworth filter designs have been implemented in biomedical signal processing, audio engineering, telecommunications, and control systems, enhancing performance in noise reduction and signal fidelity across these applications. It is essential to precisely determine these transfer functions regarding frequency and time responses. Therefore, there is room for further enhancements in these approximation methods to reduce errors and enhance the accuracy of real-world implementations. In pursuit of this goal, the study introduced a powerful metaheuristic optimization technique called Enhanced Colliding Bodies Optimization (ECBO), which not only showcases better precision in modelling but also exhibits a higher level of stability when compared to existing methods. This process guides all entities towards an optimal solution in each successive round, boosting the likelihood of finding a superior solution and thoroughly examining the full range of potential solutions. This technique better fits the BF filter function to a fractional-order continuous filter. The digital integrator is optimized in the frequency domain using the Coyote Optimization Algorithm (COA) because of its effectiveness, ease of use, and strength in tackling various complex optimization challenges. This optimizes the magnitude and phase reaction of the low-pass BF filter depending on the Minimum Square Error (MSE). Expanding the scope of the ECBO’s search range allows the enhanced filter to closely replicate the frequency behaviour of fractional order continuous filter functions.

Starting with the established concepts of multi-dimensional network resonance, practical-bounded-input-bounded-output (BIBO) stability of multi-dimensional discrete systems, and the integer order approximation of fractional order filters, a new method for the realization of integer-order approximations of 2-D fractional-order systems having frequency-planar beam shaped passbands is proposed. The method results in 2-D infinite impulse response (IIR) filters having nonseparable denominators in their transfer-functions while having guaranteed practical-BIBO stability for zero initial conditions in the corresponding discrete system. The resulting integer-order filters are shown to approximate 2-D fractional order frequency-planar beam shapes in both magnitude and phase leading to a new theoretical tool for use in the emerging area of multi-dimensional fractional-order circuits and systems. Although examples are provided for frequency-planar filters in two dimensions, the proposed methods are equally applicable to other types of transfer-functions having prototypes based on resistively-terminated passive networks defined over any integer number of dimensions.

The problem of constructing optimum observers (filters) of different dynamic orders is considered for stochastic control objects in discrete time. Analytical expressions are obtained for the transfer functions of filters,which allow us to calculate the quadratic optimality criterion. With an example of a fourth-order system, the constructed filters are compared by the mean-square observation error in the steady state.

: Fixed configuration filter theory provides a methodology for designing filters of reduced complexity which will provide suboptimal performance in general, and optimal performance under certain conditions. In this report we derived fixed configuration reduced order filters for continuous and discrete time systems, with and without state dependent noise. (Author)

Several recent publications have developed the concept of adaptive fault tolerance (AFT) by demonstrating how adaptive filter architectures and adaptive algorithms can be designed to continue operating effectively in the presence of certain classes of hardware failures. Previous studies limited the use of AFT to one-dimensional FIR filter structures. This paper further develops the concept of AFT for one-dimensional IIR filter structures, demonstrating that indeed AFT can be extended to these more general classes of linear systems.

This paper presents evaluation and comparison of different SC FIR filter structures with the point of view of a chip area for 3 μm, 2 μm, 0.8 μn CMOS technologies. To realize the considered structures, three types of building blocks are necessary, namely: memory elements (which store a signal sample aver one or more clock periods), multipliers (which realize multiplication of signal samples by a constant coefficient), and summers (which add two or more processed signal samples). Each of these basic building blocks comprieses elements of only three types: operating amplifiers (OA’ s), switches (S’ s) and unit or coefficient capacitors (UC’s or CC’s, respectively). To estimate the entire chip area for the considered FIR structures, it is necessary to determine the numbers of particular elements as functions of the filter order N .

The authors present an algorithm for order formulation of linear time invariant discrete systems using a new version of evolutionary computing technique namely, modified particle swarm optimization (MPSO). In the modified PSO, the movement of a particle is governed by three behaviors namely, inertia, cognitive and social. The cognitive behavior helps the particle to remember its previous visited best position. This paper proposes to split the cognitive behavior into two sections. This modification helps the model order formulation with minimum integral squared error. The results are shown in the form of unit step and unit impulse time response curves and compared with Genetic algorithm and general PSO based optimization techniques. The proposed method is illustrated through numerical example from literature.