High-order Linear Time-invariant Systems Research Articles

Time-Periodic and High-Order Time-Invariant Linearized Models of Rotorcraft: A Survey

The objective of this paper is to summarize the relevant published research studies on the extraction of linear time-periodic (LTP) systems and their higher order linear time-invariant (LTI) reformulations from rotorcraft physics-based models and on the identification of LTP systems from rotorcraft experimental data. The paper begins with an introductory overview of LTP system theory. Next, the relevant methods for the extraction of LTP and high-order LTI systems from physics-based models are presented. The paper continues with an overview of LTP model identification methods, followed by a discussion on the application of these methods toward the identification of the rotor dynamics alone and the coupled rigid-body/rotor dynamics. Final remarks summarize the overall findings of the study and identify areas for future work including, but not limited to, the context of the Future Vertical Lift (FVL) program.

Order reduction of linear time-invariant systems using Eigen permutation and Jaya algorithm

ABSTRACTThis article presents a new mixed method for order reduction of higher order linear time-invariant systems using Eigen permutation and the Jaya optimization algorithm. The Jaya algorithm is an algorithm-specific parameter-free optimization which requires tuning of standard control parameters only. On the other hand, the Eigen permutation retains the dominant poles of the original system with simultaneous cluster formation of the remaining real and complex poles. The numerator and the denominator polynomials of the reduced order model are determined using the Jaya optimization and Eigen permutation approaches, respectively. The proposed method results in a stable reduced order model for a stable higher order system. The effectiveness of the proposed method is validated using numerical examples of single-input–single-output and multiple-input–multiple-output systems. Furthermore, the results are compared with well-known existing techniques available in the literature.

Soft Computing Approach for Model Order Reduction of Linear Time Invariant Systems

Most of the physical systems can be represented by mathematical models. The mathematical procedure of system modeling often leads to a comprehensive description of a process in the form of higher-order differential equations which are difficult to use either for analysis or for controller synthesis. It is, therefore, useful and sometimes necessary to find the possibility of some equations of the same type but of lower order that may be considered to adequately reflect almost all essential characteristics of the system under consideration. This paper proposes a new method for order reduction of higher-order linear time invariant systems based on stability equation method and particle swarm optimization algorithm. Reduced-order model will definitely be stable if the original model is stable. The superiority of the proposed method is illustrated by numerical examples of single-input, single-output systems and multiple-input and multiple-output systems. The results are compared with well-known methods available in the literature.

H.Z. Alisoy; On the Harmonic Oscillation of High-order Linear Time Invariant Systems

— Linear time invariant (LTI) systems are widely used for modeling of dynamics systems in science and engineering problems. Harmonic oscillation of LTI systems is an outstanding case of LTI system behavior and it is employed for modeling of many periodic physical phenomenon in nature. This study investigates sufficient conditions to obtain harmonic oscillation by using high-order LTI systems. A design procedure for controlling harmonic oscillation of single-input single-output high-order LTI systems is presented. LTI system coefficients are calculated by solving equation sets, which imposes a stable sinusoidal oscillation solution for the characteristic polynomials of LTI systems. Moreover, these analyses are extended to fractional order LTI systems. Simulation examples are demonstrated for high-order LTI systems and the control of harmonic oscillations are discussed by using Hilbert transform and spectrogram of oscillation signals

System reduction using eigen spectrum analysis and Padé approximation technique

A mixed method is proposed for deriving reduced-order models of high-order linear time invariant systems using the combined advantages of eigen spectrum analysis and the Padé approximation technique. The denominator of the reduced-order model is found by eigen spectrum analysis, the dynamics of the numerator are chosen using the Padé approximation technique. This method guarantees stability of the reduced model if the original high-order system is stable. The method is illustrated by three numerical examples.

System reduction using factor division algorithm and eigen spectrum analysis

A mixed method is proposed which combines the factor division algorithm with the eigen spectrum analysis for deriving reduced order models of high-order linear time invariant systems. Pole centroid and system stiffness of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the other well known existing methods of order reduction. The method is illustrated by four numerical examples including one example of a multivariable system.

Best conditioned parametric identification of transfer function models in the frequency domain

It is shown that rational transfer function models based on orthogonal Forsythe polynomials minimize the condition number of the Jacobian of estimators in a least-squares framework. As a result, very high order linear time-invariant systems can be identified. The numerical stability of the estimation of the parameters and their derived quantities (zeros, poles, ...) are obtained. Statistical uncertainty bounds are provided. The method is illustrated on a 100th order simulated system and a 120th order measured beam-structure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Relative Stability using Simplified Routh Approximation Method (SRAM)

A new Simplified Routh Approximation Method (SRAM) for model reduction of high order linear time-invariant systems is proposed. The Routh Approximation Methods for model reduction discussed in literature are based on α and β parameters. This paper presents a new method (SRAM) for model reduction involving only α-parameters to make the method simple. The proposed method is a direct method for deriving a kth-order approximant. The main advantage is that, in order to find the parameters of the kth-order approximant, it will no longer be necessary to previously obtain those of all pth-order approximants (p⩽k-1) as is the case with Routh Approximation Methods [3, 5, 6]. The additional advantageous feature of SRAM is that it always gives a stable reduced order model if the original system is stable. New algorithms are proposed to obtain the numerator and denominator polynomials of the reduced order models using only α-parameters, thus avoiding the use of β-parameters and recursive formulae. The method is illust...

A New Model Reduction Technique for Linear Systems

A new method of reduction of high order linear time-invariant systems to low order is presented. New algorithms are proposed to obtain the reduced order model. When a zero-leading row appears in the α-table of the Routh Approximation method, the models cannot be formulated as the α-parameter will be indefinite. In this paper, new α-β tables are formulated in a way different from the Routh's table to overcome this problem. The new technique is simple and direct since it involves no computation of eigen values and residues and avoids the use of recursive formulae unlike in the Routh Approximation Methods. It always gives a stable reduced order model if the original system is stable. The method is illustrated with several numerical examples. The frequency response of the proposed model is more closely following that of the original system than the responses of the models by Routh Approximation and stability equation method. This feature is advantageous in the analysis and design of non-linear systems using frequency domain techniques.

Simplification of Linear Time Invariant Systems Using Foster Canonical Form

A new method for obtaining reduced order approximate model for high order linear time-invariant systems has been presented. The method is simple and always yields a stable reduced order model if the actual high order model is stable. The method is applicable to continuous-time as well as discrete-time multivariable systems. An example is given. This example illustrates the method as well as shows the effectiveness of the method.

Interactive Optimization of Controller and Plant Parameters in the Case of Multiple Design Objectives

This paper presents a design method for simultaneous optimization of a large number of controller and plant parameters of high-order linear time-invariant systems. User-friendly supervision and control of several design objectives is achieved through an interactive graphics-supported design process. The application of the design package for optimal matching of construction and controller parameters is demonstrated in great detail taking as an example a vehicle model with actively controlled tandem wheel suspension.

1st-order-type models for multivariable process control

It is well known in classical feedback control that many high-order linear time-invariant systems can be approximated, for the purpose of feedback design, by a low-order state-space model due to the presence of approximately cancelling poles and zeros in the system-transfer function. The paper presents an equivalent technique in the case of a multivariable system described by a strictly proper m × m, minimum-phase and invertible transfer-function matrix G(s) by the application of the contraction-mapping theorem. It is shown that, in many cases of practical interest, a multivariable 1st-order-type model is adequate for the purpose of control-system design, and that such a model can be determined directly from transient response data or, equivalently, by the analysis of the high- and low-frequency characteristics of the system. The application of the technique is illustrated by the analysis of a high-order binary-distillation-column model and the dynamics of a counter-flow heat exchanger.