Parameter identification of linear multi-delay systems via a hybrid of block-pulse functions and Taylor’s polynomials

In this paper, an efficient and effective procedure is successfully developed for parameter identification of linear time-invariant multi-delay systems. The proposed framework is based on a hybrid of block-pulse functions and Taylor’s polynomials. Two upper error bounds corresponding to hybrid functions are established. The excellent properties of these functions together with the associated operational matrices of integration and delay are utilised to transform the original problem into a system of linear algebraic equations. The least squares method is then implemented for estimation of the unknown parameters. Several numerical experiments are investigated to demonstrate the usefulness and effectiveness of the proposed procedure. Easy implementation, simple operations and accurate solutions are the main features of the suggested approximation scheme.     

Sensitivity analysis in. multilinear systems†

The primary objective of this study is to examine tho sensitivity properties of a multilinear plant embedded in a feedback structure. As a prelude tho existing linear theory ia summarized and extended. Tho bilinear case is then treatod in detail. Extrapolation to the multilinear ease has been carried out by Porter and DeSantis (1974 a). New results includo the following : (i) the use of causality structure as a component of sensitivity analysis in closed-loop linear and non-linear systems, (ii) the establishment of terminal equivalence conditions for multilinear plants and multilinear compensators, (iii) the development of a sensitivity operator in the multilinear setting including existence conditions, (iv) extensions of linear results to largo parameter perturbations.     

Sensitivity analysis of coupled structural–acoustic systems subjected to stochastic excitation

A development for computing the acoustic pressure spectral density and its sensitivity of coupled structural–acoustic systems subjected to stochastic excitation is presented. Previous work in the area of structural–acoustic response considered systems subject to deterministic excitations. The response computation depends on the excitation; therefore, new methods are developed to account for stochastic excitation. The structural–acoustic response is calculated using finite element methods and stochastic analysis techniques. An accurate and highly efficient algorithm series for structural stationary random response analysis, pseudo excitation method (PEM) is used. Numerical examples are given to demonstrate the effectiveness of the methods and the program.     

Gain-scheduled H ∞ filtering of parameter-varying discrete-time systems via parameter-dependent Lyapunov functions

This paper is concerned with the problem of gain-scheduled H _∞ filter design for a class of parameter-varying discrete-time systems. A new LMI-based design approach is proposed by using parameter-dependent Lyapunov functions. Recommended by Editorial Board member Huanshui Zhang under the direction of Editor Jae Weon Choi. This work was supported in part by the National Natural Science Foundation of P. R. China under Grants 60874058, by 973 program No 2009CB320600, but also the National Natural Science Foundation of Province of Zhejiang under Grants Y107056, and in part by a Research Grant from the Australian Research Council. Shaosheng Zhou received the B.S. degree in Applied Mathematics and the M.Sc. and Ph.D. degrees in Electrical Engineering, in January 1992, July 1996 and October 2001, from Qufu Normal University and Southeast University. His research interests include nonlinear control and stochastic systems. Baoyong Zhang received the B.S. and M.Sc. degrees in Applied Mathematics, in July 2003 and July 2006, all from Qufu Normal University. His research interests include and nonlinear systems, robust control and filtering. Wei Xing Zheng received the B.Sc. degree in Applied Mathematics and the M.Sc. and Ph.D. degrees in Electrical Engineering, in January 1982, July 1984 and February 1989, respectively, all from the Southeast University, Nanjing, China. His research interests include signal processing and system identification.     

Sensitivity design of optimal linear systems†

A measure of sensitivity is introduced into the performance index of the optimal linear system. The sensitivity vector is adjoined to the system state vector and the overall system is optimized. A procedure for selecting the weighting matrix elements is given. Finally a design procedure for obtaining approximately optimal feedback controllers with bounds on sensitivity is given. The methods are illustrated with a first-order example.     

Real and complex-exponential describing functions for transient analysis of non-linear control systems†

A real exponential describing function as an analysis tool for studying the transient response of a class of non-linear feedback systems was developed by Bickart (1966). In this paper describing functions are developed for similar analysis more suitable to higher-order non-linear feedback systems. The two classes of describing functions developed are identified as real exponential or complex exponential.

Here, signals in ?₂ ( ? ∞, t] a space of the space of square integrable signals defined on (?∞, t ], are approximated by the sum of n signals in ?₂ ^{1, m} (?∞, t)one-dimensional sub-spaccs of ?₂ ( ? ∞, t] having the mth function from the set of reversed time orthogonalized real or eponential functions as a basis. A system mapping ?₂ ^{1, m}(?∞, t] into itself is associated with a system mapping ?₂ ^{1, m}(?∞, t] into itself; the latter system is characterized by a gain—real or exponential describing function. These multiple one-dimensional system mappings give rise to approximation components of the response whoso addition will represent a better approximation to the actual response than each component by itself. The contraction-mapping fixed point theorem is also used to determine conditions for the existence of a solution prior to the use of the exponential describing functions for obtaining on approximate response.     

Sensitivity functions for multi-input linear time-invariant systems—II. Minimal-order models†

In Part I, the authors utilized frequency domain techniques to obtain low-order sensitivity models M of m-input, linear, constant, nth-order dynamic systems. The purpose of this paper is to develop a constructive approach for determining the minimal order (ρ) of M. For single-input systems it is demonstrated that ρ = n and for normal systems ρ = inn. For general systems, tight upper and lower bounds on ρ are provided. These bounds are stated in terms of the system structural properties. Procedures for synthesizing the minimal-order sensitivity models are mentioned. Examples motivate and illustrate both the key ideas and applications of the results.     

Sensitivity analysis and optimization of vehicle–bridge systems based on combined PEM–PIM strategy

This paper presents a new optimization method for coupled vehicle–bridge systems subjected to uneven road surface excitation. The vehicle system is simplified as a multiple rigid-body model and the single-span bridge is modeled as a simply supported Bernoulli–Euler beam. The pseudo-excitation method transforms the random surface roughness into the superposition of a series of deterministic pseudo-harmonic excitations, which enables convenient and accurate computation of first and second order sensitivity information. The precise integration method is used to compute the vertical random vibrations for both the vehicle and the bridge. The sensitivities are used to find the optimal solution, with vehicle ride comfort taken as the objective function. Optimization efficiency and computational accuracy are demonstrated numerically.     

Sensitivity of optimal control systems with bang-bang control†

The effects of small parameter variations on the performance index of optimal control systems with initial and final target manifolds, free end time, and bang-bang control are analysed in this paper. A new approach to the sensitivity equation is presented. This approach takes into account the pulse-shaped variation produced by the parameter change on the bang-bang control. An expression, that relates the variations of the performance index, the trajoctory, the final time, and the parameter, is derived. This expression extends to the class of optimal systems with bang-bang control, a result previously obtained by Courtin and Rootenberg (1971).     

Sensitivity in the decoupling of non-linear control systems†

The problem of decoupling the inputs and outputs of non-linear control systems is considered for the situation where the system parameters are subject to variations or disturbances. The exact decoupling is obtained by an adaptive state feedback controller which requires full knowledge of the instantaneous values of the system parameters. By utilizing the parameter sensitivity concept an approximate adaptive decoupling controller is synthesized in the present paper which is shown to decouple the system to first (or higher) order in the variations of the system parameters from their known nominal values. The sensitivity equations which generate the state sensitivity function required for the synthesis are derived. The results of the paper actually provide the tools for reducing the system sensitivity to parameter variations when the final goal is the improvement of decoupling.     

Proof of the circle criterion for state space systems via quadratic Lyapunov functions — Part 2

In Part 1 of this paper a detailed analysis of the stability of a closed-loop system containing a single nonlinearity was made. The analysis is repeated here, but with stronger assumptions on the nonlinearity. The class of Total Derivative matrices is introduced and the role played by this class in generating quadratic Lyapunov functions for certain dynamical systems is considered. A new approach for deriving stability criteria is presented which is equivalent to the path integral method of Brockett.     

Sensitivity of performance of control systems to unintentional coupling signals†

The problem of undesired inherent coupling signals in control systems is quite well known and their effects on performance of the system have been observed. In this paper, some attempt has been made to throw some more light on the effect of the coupling signals on control systems. The sensitivity of performance of the control system due to the coupling signals has been calculated in the same way as the sensitivity of performance of control systems due to parameter variations of the system. Two methods of calculation of the sensitivity function using an analog computer are described with special reference to a particular example of a control system. In both cases, the approximations are pointed out and the limitations of the methods are discussed.     

A new recurslve method for the analysis of linear time invariant dynamic systems via double-term triangular functions （DTTF） in state space environment

This paper presents a new recursive method for system analysis via double-term triangular functions (DTTF) in state space environment. The proposed method uses orthogonal triangular function sets and proves to be more accurate as compared to single term Walsh series (STWS) method with respect to mean integral square error (MISE). This has been established theoretically and comparison of error with respect to MISE is presented for clarity. A numerical example is treated to establish the proposed method. Relevant curves for the solutions of states of the dynamic system are also presented with plots of percentage error for DTTF-based analysis.     

Adaptive λ-tracking for locomotion systems

This paper deals with the (adaptive) control of mechanical systems, which are inspired by biological ideas. We introduce a certain type of mathematical models of worm-like locomotion systems and present some theoretical control investigations.Only discrete straight worms will be considered in this paper: chains of point masses moving along a straight line. We introduce locomotion systems in the form of a straight chain of $k=3$ interconnected point masses, where we focus on interaction which emerges from a surface texture as asymmetric Coulomb friction. We consider two different types of drives: (i) The point masses are under the action of external forces, which can be regarded as external force control inputs. (ii) We deal with massless linear springs of fixed stiffnesses and controllable original spring lengths, which can be regarded as internal control inputs.The locomotion systems with these two types of drive mechanisms are described by mathematical models, which fall into the category of nonlinearly perturbed, multi-input, multi-output systems (MIMO-systems), where the outputs of the system are, for instance, the positions of the point masses or the displacements of the point masses.The goal is to simply control these systems in order to track given reference trajectories to achieve movement of the system. Because one cannot expect to have complete information about a sophisticated mechanical or biological system, but instead only structural properties are known, we deal with uncertain systems. Therefore, the method of adaptive control is chosen in this paper. Since we deal with nonlinearly perturbed MIMO-systems, we focus on the adaptive $\lambda$-tracking control objective to achieve our goal. This means tracking of a given reference signal for any pre-specified accuracy $\lambda >0$. The objective is not to obtain information about the characteristics of the system or about system parameters, but simply to control the unknown system. This control objective allows us to design simple adaptive controllers, which achieve $\lambda$-tracking.Numerical simulations of tracking different reference signals, for an arbitrary choice of the system parameters, will demonstrate and illustrate, that the introduced, simple adaptive controller works successfully and effectively.     

Construction of high order balanced multiscaling functions via PTST

1 Introduction In recent years, multiscaling functions and multiwavelets have been studied exten- sively (see refs. [1―17]). An important motivation for the study of multiwavelets is the design of orthogonal linear-phase finite-impusely response transform systems. However, there exist important differences between multiwavelets and uni-wavelet bases and these differences become apparent when one implements the discrete multiwavelets transform. Indeed, in the processing of discrete-time signal…     

Sensitivity analysis of shock wave Burgers’ equation via a novel algorithm based on scale-3 Haar wavelets

In this paper, a novel technique is being formulated for the numerical solutions of Shock wave Burgers' equations for planar and non-planar geometry. It is well known that Burgers' equation is sensitive to the perturbations in the diffusion term. Thus we use robustness of wavelets generated by dilation and translation of Haar wavelets on third scale to capture the sensitivity information. The present approach is an improved form of the scale-2 Haar wavelet method. The scheme is based on the forward finite difference scheme for time integration, scale-3 Haar wavelets for space integration and the nonlinearity has been tackled via quasilinearzation technique. Through scale-3 Haar wavelet analysis once the wavelet coefficient is calculated then we can compute the solutions at near the perturbation point. The computation cost of the present scheme is negligible. The proposed method is tested on six test problems to check its computational efficiency where the convergence analysis of scale-3 Haar wavelet method is the proof of our computational arguments.     

Sensitivity analysis of pulse-frequency-modulated control using a linearized model†

The paper discusses the sensitivity of pulse-frequency modulated (PFM) control systems with respect to changes in the plant and controller parameters. The investigations of the sensitivity behaviour of non-linear PFM control systems are carried out using a linearized approach for the PFM controller, as proposed by Frank and Dillmann. The goal of this paper is to study the effectiveness of this method as applied to the investigation of an unstable plant. The sensitivity functions of the PFM system and the corresponding continuous equivalent systems are evaluated by considering parameter changes in the actual plant. The limitations of this method are pointed out.     

Sensitivity analysis of distributed parameter elements in high-speed circuit networks

This paper presents an analysis method, based on MacCormack＇s technique, for the evaluation of the time domain sensitivity of distributed parameter elements in high-speed circuit networks. Sensitivities can be calculated from electrical and physical parameters of the distributed parameter elements. The proposed method is a direct numerical method of time-space discretization and does not require complicated mathematical deductive process. Therefore, it is very convenient to program this method. It can be applied to sensitivity analysis of general transmission lines in linear or nonlinear circuit networks. The proposed method is second-order-accurate. Numerical experiment is presented to demonstrate its accuracy and efficiency.     

Reachability analysis of switched linear discrete singular systems

This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.     

Computer generation of sensitivity functions for sampled-data control systems†

Methods have been presented previously (Suryanarayanan and Soudack 1970) for the generation of sensitivity functions for general non-linear sampled-data systems. In this paper, it is shown that economy of simulator components (for hybrid computer generation) or of computational time (for digital computer generation) is achieved for simultaneously generating a number of sensitivity functions in a class of linear sampled-data control systems. Extensive use of signal flow graph algebra is made for this purpose and comprehensive examples are presented.