Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2002"
TL;DR: The quasilinearization method is used to replace the nonlinear optimal control problem with a sequence of constrained linear-quadratic optimal control problems, then each of the state variables is approximated by a finite length Chebyshev series with unknown parameters.
Abstract: In this paper, a numerical method to solve nonlinear optimal control problems with terminal state constraints, control inequality constraints and simple bounds on the state variables, is presented. The method converts the optimal control problem into a sequence of quadratic programming problems. To this end, the quasilinearization method is used to replace the nonlinear optimal control problem with a sequence of constrained linear-quadratic optimal control problems, then each of the state variables is approximated by a finite length Chebyshev series with unknown parameters. The method gives the information of the quadratic programming problem explicitly (The Hessian, the gradient of the cost function and the Jacobian of the constraints). To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.
90 citations
TL;DR: The proposed approach is based on nonlinear disturbance decoupling techniques and nonlinear observers and characterize a class of nonlinear systems for which a high gain observer can be designed.
Abstract: This paper deals with the problem of fault detection and isolation for nonlinear systems. The proposed approach is based on nonlinear disturbance decoupling techniques and nonlinear observers. First, we give sufficient conditions and a design procedure for the synthesis of residual generators. Next, we characterize a class of nonlinear systems for which a high gain observer can be designed. Finally, the two above developments are illustrated through a real application dealing with the detection and isolation of three failures in a hydraulic process. The design of the residual generators is shown and their performances are discussed.
84 citations
TL;DR: A general input-to-state stability (ISS)-type small-gain result is presented that specializes to a small- gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form.
Abstract: A general input-to-state stability (ISS)-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems.
83 citations
TL;DR: The design methods of dissipative static state feedback and dynamic output feedback controllers are developed such that the closed-loop system is quadratically stable and strictly ( Q, S, R )-dissipative.
Abstract: This paper deals with the problem of delay-dependent dissipative control for a class of linear time-delay systems. We develop the design methods of dissipative static state feedback and dynamic output feedback controllers such that the closed-loop system is quadratically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative controllers are obtained by using linear matrix inequality (LMI) approach. Furthermore, a procedure of constructing such controllers from the solutions of LMIs is given. It is shown that the solvability of a dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H∞ control and passive control.
81 citations
TL;DR: It is shown that by suitable substitution for the roots in the general result that the solution corresponding to each of the three cases can be obtained.
Abstract: A unified theory is presented for obtaining the transient response of nth order nonlinear systems with small nonlinearities by Krylov–Bogoliubov–Mitropolskii method. The method is a generalization of Bogoliubov's asymptotic method and covers all three cases when the roots of the corresponding linear equation are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the roots in the general result that the solution corresponding to each of the three cases can be obtained. The method is illustrated by examples.
51 citations
TL;DR: Numerical simulations indicate that the onset of chaos is characterized by break of torus as the torque of the magnetic forces is increased.
Abstract: This paper deals with chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit near the equatorial plane of the earth. The dynamical model of the problem is derived. The Melnikov analysis is carried out to prove the existence of a complicated nonwandering Cantor set. The dynamical behavior is numerically investigated by means of time history, Poincare map, power spectrum and Lyapunov exponents. Numerical simulations indicate that the onset of chaos is characterized by break of torus as the torque of the magnetic forces is increased.
16 citations
TL;DR: In this paper, the performance of the first-and second-order TDTLs under noise-free conditions was analyzed in the presence of additive Gaussian noise for different values of the loop parameters.
Abstract: Recently, a new non-uniform sampling digital phase-locked loop, the time-delay digital tanlock loop (TDTL), has been proposed. We have analyzed in a previous work the first- and second-order TDTLs under noise-free conditions. In this work, we analyze the performance of the TDTL in the presence of additive Gaussian noise for different values of the loop parameters. It is shown that the expected value of the steady-state phase errors at the input and the output of the phase error detector are equal to the noise-free steady-state values, while the variance is significantly reduced when the signal-to-noise ratio is increased or the phase shift introduced by the time-delay approaches 90°. The locking ranges of the TDTL parameters under noise-free conditions are unchanged by the presence of noise.
15 citations
TL;DR: A novel dual-sensor estimator that uses a merging formula that is based upon a different function of the residuals that is contrasted with an estimator using a single sensor and with another dual-Sensor algorithm that requires fewer on-line calculations.
Abstract: In a multimodal, system, the growth in the number of possible modal paths makes state estimation difficult. Practical algorithms bound complexity by merging estimates that are conditioned on different modal path fragments. Commonly, the weight given to these local estimates is inversely related to the normalized magnitude of the residuals generated by each local filter. This paper presents a novel dual-sensor estimator that uses a merging formula that is based upon a different function of the residuals. Its performance is contrasted with an estimator using a single sensor and with another dual-sensor algorithm that requires fewer on-line calculations.
13 citations
TL;DR: Simulation results indicate that the modified controller is better than the traditional PID controller and the PI σ D controller from the accuracy and stability point of view.
Abstract: The purpose of this study is to modify the traditional PID controller in order to improve its performance (stability and tracking) by changing the length of integration interval. The performance of the traditional PID controller was improved by changing the length of integration interval to make the most of the returns of the PID and PI σ D controllers. The asymptotic stability domain, in terms of the feedback gains, is derived for systems of second order using the modified controller which will be identified as PII σ β D . Comparing this controller with the traditional PID controller and PI σ D controller proposed in [1] , it proves that it is more accurate and more stable. For illustration and comparison, two examples have been simulated to evaluate the performance of the modified controller. All simulation results indicate that the modified controller is better than the traditional PID controller and the PI σ D controller from the accuracy and stability point of view.
13 citations
TL;DR: The design and implementation of digital controllers for a flywheel energy storage device that incorporates a radial flux hybrid permanent magnetic bearing are presented and it is indicated that the LQR controller with approximate system velocities is easier to implement than the LG controller, and also provides superior performance.
Abstract: This paper describes the design and implementation of digital controllers for a flywheel energy storage device that incorporates a radial flux hybrid permanent magnetic bearing. Although the uncontrolled device is asymptotically stable, active control is required to: (i) ensure that a finite radial air gap is maintained at all times, and (ii) attenuate the oscillations of the flywheel which reduce the efficiency of the motor generator. The paper presents the design of gain scheduled discrete time linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controllers for this rotordynamic system. Real time experiments are conducted to investigate the performance of the controllers. The result indicates that the LQR controller with approximate system velocities is easier to implement than the LQG controller, and also provides superior performance.
13 citations
TL;DR: The analysis methodology of time- Delay systems was generalized to that of the hybrid systems with time-delay and uncertainty, which developed a design procedure of sampled-data control for time- delay systems and results were described as linear matrix inequalities.
Abstract: The sampled-data systems are hybrid ones involving continuous time and discrete time signals, which makes the traditional analysis and synthesis methodologies of time-delay systems unable to be directly used in the cases of hybrid systems with time-delay. The primary disadvantages of current design techniques of sampled-data control are their inabilities to deal effectively with time-delay and the model uncertainty. In this paper, we generalized the analysis methodology of time-delay systems to that of the hybrid systems with time-delay and uncertainty, which developed a design procedure of sampled-data control for time-delay systems. Asymptotic stability of the time-delay hybrid systems was developed. The time-delay dependent robust sampled-data control for the time-varying delay of an uncertain linear system was then discussed. The results were described as linear matrix inequalities, which can be solved using newly released LMITool.
TL;DR: In this paper, the actuator fault diagnosis problem for a class of bilinear systems with uncertainty is discussed and an adaptive observer can be designed such that, under certain conditions, the observer error dynamics is stable.
Abstract: In this paper, the actuator fault diagnosis problem for a class of bilinear systems with uncertainty is discussed. The system is transformed into two different subsystems. One is not affected by actuator fault, so an adaptive observer can be designed such that, under certain conditions, the observer error dynamics is stable. The other whose states can be measured is affected by the faults. The observation scheme is then used for model-based fault diagnosis. Finally, an example of a semiactive suspension system is used to illustrate the applicability of the proposed method.
TL;DR: Semiglobal asymptotic stability and semiglobal practical signal tracking of the controlled system are proven using results from the theory of nonlinear singularly perturbed systems.
Abstract: The PI control configuration for stabilization and signal tracking of nonlinear systems is investigated. Semiglobal asymptotic stability and semiglobal practical signal tracking of the controlled system are proven using results from the theory of nonlinear singularly perturbed systems.
TL;DR: This paper extends a variety of results and constructive procedures that were developed in previous work for computations that take place in an abelian group to a more general setting that considers computations in semigroups and applies these techniques to linear time-invariant dynamic systems and Petri net models of discrete event systems.
Abstract: The traditional approach to fault-tolerant computation has been via modular hardware redundancy. Although universal and simple, modular redundancy is inherently expensive and inefficient. By exploiting particular structural features of a computational architecture or an algorithm, arithmetic codes and recently developed algorithm-based fault tolerance (ABFT) techniques manage to introduce “analytical redundancy” and offer more efficient fault coverage at the cost of narrower applicability and harder design. In this paper, we extend a variety of results and constructive procedures that were developed in previous work for computations that take place in an abelian group to a more general setting that considers computations in semigroups. We demonstrate possible encodings for semigroup operations of interest and use our extension to design concurrent error detection and correction schemes for group and semigroup machines. The method provides insight regarding the role of decomposition in fault-tolerant algebraic machines and results in a general, hardware-independent characterization of concurrent error detection and correction in finite semiautomata. We also demonstrate that by extending this approach to other dynamic systems, with specific hardware implementations and failure modes, we can systematically obtain fault-tolerant architectures. More specifically, we apply these techniques to linear time-invariant dynamic systems and Petri net models of discrete event systems.
TL;DR: The presented discrete-time model significantly facilitates analysis and design of a system when it faces the unavoidable inherent time delay and the computation time delay which can be modeled as a part of delay at the system input, in practice.
Abstract: The discrete-time model of the two-dimensional continuous-time input time-delay system is newly presented in this paper, and the solution of the continuous-time input time-delay system is then solved based on the newly presented discrete-time model. The presented discrete-time model significantly facilitates analysis and design of a system when it faces the unavoidable inherent time delay and the computation time delay which can be modeled as a part of delay at the system input, in practice.
TL;DR: An algorithm is developed to apply Hann, Hamming, Blackman and related windows directly in the transform domain for the discrete cosine transform and discrete sine transform.
Abstract: In this paper, an algorithm is developed to apply Hann, Hamming, Blackman and related windows directly in the transform domain for the discrete cosine transform and discrete sine transform. These algorithms are useful in applications where windowing is required in order to minimize edge effects caused by implicit symmetries in the transform domain that are not replicated in the real-world data. Examples of such applications include data communication, adaptive system identification and filtering, real-time analysis of financial market data, etc. Software implementations in C language are also given.
TL;DR: In this paper, the effect of optimal control strategies on the power and energy requirement of control devices is investigated.
Abstract: The performance enhancement of dynamic systems is accomplished by the application of active control components. Control strategies are derived to accomplish the task. Among the various control strategies, those that are designed to minimize a specified cost function while satisfying the necessary system constraints are referred to as optimal controllers. An important constraint is the amount of power and energy consumed by the control device. In this paper, the effect of optimal control strategies on the power and energy requirement of control devices is investigated.
TL;DR: The algorithm developed is based on a previously proposed method adapted now for the case of multi-component signals and combines an adaptive smoothing procedure with a noise resistant Fourier filter to generate an algorithm with an extremely fine frequency resolution.
Abstract: In this paper we are concerned with the problems of (1) tracking or estimating the unknown, time-varying instantaneous frequency (IF) of a chirp signal from a multi-component signal (we assume our multi-component signal to be formed of additive chirp signals, disjoint in the time–frequency domain, and Gaussian noise) and (2) reconstructing a specific chirp signal based on the estimate of its IF found at (1). The algorithm we developed is based on a previously proposed method adapted now for the case of multi-component signals. It combines an adaptive smoothing procedure with a noise resistant Fourier filter to generate an algorithm with an extremely fine frequency resolution. The method is non-parametric, that is, we assume no prior knowledge about the form of the time-varying IF of the chirp or about the chirp itself. We demonstrate how the method works on simulated data and compare its performance to other presently used procedures.
TL;DR: The proposed transitional filter nomographs provide the engineer with increased insight into the selection of classical transitional filters with optimum frequency response.
Abstract: The construction of nomographs for transitional classical filters is described. Gain functions of classical filters are related to filter requirements resulting in a formulation for the general gain nomograph. The transitional filters that are products of approximating polynomials are incorporated into the general gain nomograph resulting in transitional filter nomographs that are sums of the individual nomographs. Nomographs for transitional filters using alternative forms where poles are interpolated are also considered. The resulting nomographs allow for quick optimization of transitional filter frequency response in many cases. Design examples are submitted and discussed. The proposed transitional filter nomographs provide the engineer with increased insight into the selection of classical transitional filters with optimum frequency response.
TL;DR: The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ -polynomials of degrees 2 and 2 n in the interval (0,1).
Abstract: In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1− λ ) p 0 ( s )+ λp 1 ( s ), where λ ∈[0,1] and p 0 ( s ) and p 1 ( s ) are n th-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ -polynomials of degrees 2 and 2 n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure.
TL;DR: It is indicated that the full rank MSE corresponding to some data length N can be attained by a low-rank estimator corresponding to a length significantly smaller than N, and three methods for choosing the transformation matrix that reduces the mean-square error associated with the low- rank HOS estimates are proposed.
Abstract: Higher-order statistics (HOS) are well known for their robustness to additive Gaussian noise and ability to preserve phase. HOS estimates, on the other hand, have been criticized for high complexity and the need for long data in order to maintain small variance. Since rank reduction offers a general principle for reduction of estimator variance and complexity, we consider the problem of designing low-rank estimators for HOS. We propose three methods for choosing the transformation matrix that reduces the mean-square error (MSE) associated with the low-rank HOS estimates. We also demonstrate the advantages of using low-rank third-order moment estimates for blind system estimation. Results indicate that the full rank MSE corresponding to some data length N can be attained by a low-rank estimator corresponding to a length significantly smaller than N.
TL;DR: A new graphical user interfaces interpretation tool for thenon-linear frequency response function is proposed and the application of the non-linear auto-regressive moving average model with eXogenous input (NARMAX) identification methodology has been fully demonstrated and shown to have great potential in modelling real systems.
Abstract: There are two major contributions which are described in this paper. Firstly, a new graphical user interfaces interpretation tool for the non-linear frequency response function is proposed. The tool is developed by pv-wave package to provide better ways and user friendly of displaying, interpreting, and analysing of non-linear systems with significant non-linear effects. Secondly, the application of the non-linear auto-regressive moving average model with eXogenous input (NARMAX) identification methodology has been fully demonstrated and shown to have great potential in modelling real systems. To demonstrate the improved visualisation and interpretation of the multi-dimensional non-linear frequency response functions and the application of the NARMAX methodology, two cases have been analysed in detail as bench test to obtain the generalised higher-order frequency response functions for both continuous time non-linear differential equations and identified discrete time NARMAX models. The results obtained have shown that frequency response functions computed directly from the fitted models are very consistent with the actual frequency response functions.
TL;DR: Nomographs for determining the filter order of classical filters based on selectivity requirements are presented and can be used to gauge filter performance and combined with optimization techniques can yield superior classical filter designs.
Abstract: Nomographs for determining the filter order of classical filters based on selectivity requirements are presented. The selectivities for a variety of standard classical filters are summarized in equation form and the general selectivity nomograph is constructed. The selectivity equations are then converted into nomograph form by applying the relationship between the transfer function and the response slope. Design examples are presented to demonstrate the usefulness of the selectivity nomographs. These nomographs can be used to gauge filter performance and combined with optimization techniques can yield superior classical filter designs.
TL;DR: It is shown that the well-known Muntz–Szasz condition can be interpreted in terms of an equivalence relation, thereby proving that the standard MuntZ–SZasz formulation is equivalent with certain alternative formulations.
Abstract: New results pertaining to the completeness of a system of complex exponentials in L p spaces are presented. It is shown that the well-known Muntz–Szasz condition can be interpreted in terms of an equivalence relation, thereby proving that the standard Muntz–Szasz formulation is equivalent with certain alternative formulations.
TL;DR: The inverse control of discrete-time single-input/single-output linear systems is extended to multivariable systems and a feedback control algorithm suggested is based on decoupling and compensating the plant by preceding it with the inverse controller.
Abstract: The inverse control of discrete-time single-input/single-output linear systems is extended to multivariable systems. The extension considered is far from being trivial when a multivariable system possesses interactions and multiple delays, leading to ill-conditioning or even singularity of the problem. A feedback control algorithm suggested is based on decoupling and compensating the plant by preceding it with the inverse controller. The inverse controller is derived by using the regularization of the pseudoinverse of the plant convolution matrix. In this way a regularized multivariable control with a minimum norm is provided. A numerical example of the inverse control of a distillation column is presented.
TL;DR: The main objective of the scheduling algorithm and network interface is to maximize the performance measures by studying the problem of receiver collision phenomena at destination that multichannel nature of WDM networks introduces.
Abstract: In this paper, we propose the design and analysis of a reservation-based protocol for synchronous WDM multi-channel optical networks. The network architecture is based on a passive star topology and a new architecture for the network interface per station. The main objective of the scheduling algorithm and network interface is to maximize the performance measures by studying the problem of receiver collision phenomena at destination that multichannel nature of WDM networks introduces. We develop an analytical model based on a finite number of tunable receivers and a finite number of stations, following the “tell and go” policy for the access to communication system. Numerical results are showing the performance behavior for various number of channels, stations, and tunable receivers. Also, simulation results are presented for comparison with the results obtained by the performance analysis.
TL;DR: The system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minmax estimate and two Riccati equations for its ellipsoid matrix (optimal gain matrix of the filter) and the optimal regulator gain matrix.
Abstract: This paper presents solution of the optimal linear-quadratic controller problem for unobservable integral Volterra systems with continuous/discontinuous states under deterministic uncertainties, over continuous/discontinuous observations. Due to the separation principle for integral systems, the initial continuous problem is split into the optimal minmax filtering problem for integral Volterra systems with deterministic uncertainties over continuous/discontinuous observations and the optimal linear-quadratic control (regulator) problem for observable deterministic integral Volterra systems with continuous/discontinuous states. As a result, the system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minmax estimate and two Riccati equations for its ellipsoid matrix (optimal gain matrix of the filter) and the optimal regulator gain matrix. Then, in the discontinuous problems, the equation for the optimal controller and the equations for the optimal filter and regulator gain matrices are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the dual results in the optimal control problem for integral systems. The technical example illustrating application of the obtained results is finally given.
TL;DR: Basic properties of a new class of strictly positive real (SPR) functions are stated and examples for simultaneous SPR closed-loop systems via constant controllers and synthesis of simultaneous SPR feedback plants are presented.
Abstract: Basic properties of a new class of strictly positive real (SPR) functions are stated. Four problems are studied. The first deals with SPR preservation of transfer functions, obtained under the composition of polynomials with SPR0 functions. The second deals with Hurwitz stability preservation of the numerator of transfer functions, obtained under the composition of polynomials with SPR0 functions. The third deals with making a Hurwitz closed-loop plant, an SPR0 function by substituting s by SPR0 functions. The four deals with the synthesis of simultaneous SPR feedback plants. For the new class of SPR0 functions, a characterization is presented. For the first and second problems, sufficient conditions are presented using the new class of SPR0 functions. For the third and four problems, two examples are presented, the first being for simultaneous SPR closed-loop systems via constant controllers. The second is for simultaneous stabilization via universal feedback adaptive control.
TL;DR: The results demonstrate that the main features of statistical characteristics of the noise envelope are reproduced rather well with the help of a bistate system with random structure.
Abstract: Dynamic system with a random structure described by a set of the first-order stochastic differential equations (SDE) is used as a generating model of nonstationary pulse stochastic processes Physically the system presents the combination of the so-called partial filters related to the isolated states of the considered process, switched by a Poissonian point process and excited by a vector delta-correlated stream of impulses with the randomly distributed energy The filters’ outputs are components of the vector Markov continuous-jump process with statistics depending on the partial SDEs operators, intensity of switching process and distributions of the exciting impulses’ energies The approach proposed was used as a simulation model of the Middleton “Class-A “generally non-Gaussian noise The results demonstrate that the main features of statistical characteristics of the noise envelope are reproduced rather well with the help of a bistate system with random structure