Continuous Interval Systems Research Articles

An improvement of Gamma approximation for reduction of continuous interval systems

An improvement of Gamma approximation for reduction of continuous interval systems

Kharitonov Polynomial-Based Order Reduction of Continuous Interval Systems

Kharitonov Polynomial-Based Order Reduction of Continuous Interval Systems

Design of FOPID controller for higher order continuous interval system using improved approximation ensuring stability

This contribution deals with the design of a fractional-order proportional-integral-derivative (FOPID) controller through reduce-order modeling for continuous interval systems. First, a higher order interval plant (HOIP) is considered. The reduced-order interval plant (ROIP) for considered HOIP is derived by multipoint Padé approximation integrated with Routh table. Then, FOPID controller is designed for ROIP to satisfy the phase margin and gain cross over frequency. Thus obtained FOPID controller is implemented on HOIP also to validate the performance of designed FOPID on HOIP. A single-input-single-output (SISO) test system is taken up to elaborate the entire process of controller design. The outcomes affirm the validity of the designed FOPID controller. The designed FOPID controller produced stable results retaining the phase margin and gain cross-over frequency when implemented on HOIP. The results further proved that FOPID controller is working efficiently for ROIP and HOIP.

Anderson Corollary Based on New Approximation Method for Continuous Interval Systems

In this research, a new technique is developed for reducing the order of high-order continuous interval systems. The model denominator is derived using Anderson corollary and Routh table. Numerator is derived by matching the formulated Markov parameters (MPs) and time moments (TMs). Distinctive features of the proposed approach are: (i) New and simpler expressions for MPs and TMs; (ii) Retaining not only TMs but also MPs while deriving the model; (iii) Minimizing computational complexity while preserving the essential characteristics of system; (iv) Ensuring to produce a stable model for stable system; (v) No need to invert the system transfer function denominator while obtaining the TMs and MPs; and (vi) No need to solve a set of complex interval equations while deriving the model. Two single-input-single-output test cases are considered to illustrate the proposed technique. Comparative analysis is also presented based on the results obtained. The simplicity and effectiveness of the proposed technique are established from the simulation outcomes achieved.

Improved approximation of SISO and MIMO continuous interval systems

Improved approximation of SISO and MIMO continuous interval systems

Improved approximation of SISO and MIMO continuous interval systems

Recently, some engineering systems are modelled as interval systems. In this investigation, an improved approximation method is first presented for reducing the order of single-input-single-output ...

Sine Cosine Algorithm Assisted FOPID Controller Design for Interval Systems Using Reduced-Order Modeling Ensuring Stability

The focus of present research endeavor was to design a robust fractional-order proportional-integral-derivative (FOPID) controller with specified phase margin (PM) and gain cross over frequency (ωgc) through the reduced-order model for continuous interval systems. Currently, this investigation is two-fold: In the first part, a modified Routh approximation technique along with the matching Markov parameters (MPs) and time moments (TMs) are utilized to derive a stable reduced-order continuous interval plant (ROCIP) for a stable high-order continuous interval plant (HOCIP). Whereas in the second part, the FOPID controller is designed for ROCIP by considering PM and ωgc as the performance criteria. The FOPID controller parameters are tuned based on the frequency domain specifications using an advanced sine-cosine algorithm (SCA). SCA algorithm is used due to being simple in implementation and effective in performance. The proposed SCA-based FOPID controller is found to be robust and efficient. Thus, the designed FOPID controller is applied to HOCIP. The proposed controller design technique is elaborated by considering a single-input-single-output (SISO) test case. Validity and efficacy of the proposed technique is established based on the simulation results obtained. In addition, the designed FOPID controller retains the desired PM and ωgc when implemented on HOCIP. Further, the results proved the eminence of the proposed technique by showing that the designed controller is working effectively for ROCIP and HOCIP.

Improved Approximation for SISO and MIMO Continuous Interval Systems Ensuring Stability

In the recent literature, some practical systems have been modeled as interval systems. In this investigation, an improved approximation technique is first proposed for model reduction in single-input-single-output continuous interval systems; then, the proposed technique is extended to reduce multi-input-multi-output continuous interval systems. The proposed technique is based on a multipoint Pade approximation. Additionally, the technique generates a stable model for a given stable system. The results show that the Routh table integrated multipoint Pade approximation is a good way to reduce continuous interval systems.

An improved method for reduction of continuous interval systems using Anderson corollary

Engineering systems are modeled as interval systems recently. In this paper, an improved technique for model reduction of high-order continuous interval systems is presented using Anderson corollary and Routh approximation. The distinguishing features of the proposed method are: (i) it ensures exact matching of responses of reduced-order interval model and high-order interval system at steady-state; (ii) it retains interval-value of steady-state of high-order interval system; and (iii) it produces interval model for interval system. Firstly, the denominator of the reduced-order model is obtained based on Routh table. Then, the numerator is obtained by matching the interval-values of steady-state of high-order interval system and reduced-order interval model. A single-input-single-output (SISO) test system is considered to explain the efficiency of the proposed method. The step responses of SISO test systems are obtained and presented for comparative study. From the results, it is observed that the proposed method provides better approximants.

Best-case, worst-case and mean integral-square-errors for reduction of continuous interval systems

In this brief, best-case integral-square-error, worst-case integral-square-error and mean integral-square-error are defined for model reduction of continuous interval systems. These integral-square-errors (ISEs) can be used for comparison of responses of system and model. First, rational transfer functions of interval system and those of the model are obtained using Kharitonov theorem and then different ISEs are derived with the help of alpha and beta parameters obtained for rational transfer functions. The ISEs are obtained for impulse response and can be treated as measure of goodness for model reduction of continuous interval systems. The whole procedure is explained with the help of one numerical example. The goodness of model reduction is proved with the help of different quantitative and qualitative results obtained for considered system and model.

Best-case, worst-case and mean integral-square-errors for reduction of continuous interval systems

Best-case, worst-case and mean integral-square-errors for reduction of continuous interval systems

Model Order Reduction and Stability Analysis of Interval System

The model order reduction tool has been utilized fordecrementing the order of the interval model. The main prospective of this paper is to demonstrate the procedure for determining stability analysis of continuous time interval system. This paper concentrate mainly on, how we get the Kharitonov polynomials and how to use the algorithms given by Kharitonov for plotting Kharitonov rectangle. With the plot of Kharitonov rectangle we may determine the stability of interval system graphically. The conventional method for determining stability is also compared with the graphical method for determining the stability. The presented paper demonstrates stability analysis of decreasedorder system in accordance to the original higher order interval system. The stability analysis has been performed by using Kharitonov algorithm and MATLAB tool. Simulation results have been shown for comparison of stability of higher order interval system and decreased system.

On Time Moments and Markov Parameters of Continuous Interval Systems

In this paper, two expressions are derived for calculating the time moments and Markov parameters of continuous interval systems. The expressions presented are computationally simple and do not require inversion of denominator of the system transfer function unlike other techniques. The usefulness of expressions derived is shown with the help of Routh–Padé approximation of interval systems. The derived Routh–Padé approximants retain not only the time moments but also some Markov parameters of high-order interval system. Some improvement is also found in system approximation when these time moments/Markov parameters are used. One numerical example is included to illustrate the effectiveness and simplicity of proposed method.

A New Biased Model Order Reduction for Higher Order Interval Systems

This paper presents a new biased method for order reduction of linear continuous time interval systems. This method is based on the Stability equation method, Pade approximation and Kharitonov’s theorem. The higher order interval system is represented by four Kharitonov transfer functions using the Kharitonov’s theorem, and then reduced order models are obtained by the general form of the Stability equation method and Pade approximation. The Stability equation method is used to obtain a reduced order denominator polynomial while the Pade approximation is used for reduced order numerator coefficients. This method generates a stable reduced order model if the original higher order interval system is stable. The proposed method is illustrated with the help of typical numerical examples considered from the literature, and these are compared with well-known methods to show the efficacy of the proposed method.

Model Order Reduction of Linear Time Interval System Using Stability Equation Method and a Soft Computing Technique

This paper deals with a new method for model order reduction of linear continuous time interval system. This new method is based on the Kharitonov’s theorem, the Stability equation method and the error minimization by Differential Evolution. The reduced order interval model is determined by using Kharitonov’s polynomials, which make use of the Kharitonov’s theorem and general form of the stability equation method for denominator, while the numerator is obtained by minimizing the integral square error between the transient responses of original and reduced order models using Differential Evolution algorithm. This method generates stable reduced order interval system if the original higher order system is stable and retains the steady-state value. The proposed method is illustrated with the help of typical numerical example considered from the literature.

A New Model Order Reduction for Linear Continuous Time Interval Systems

A New Model Order Reduction for Linear Continuous Time Interval Systems

Suitability of Redesigned Digital Control Systems Having an Interval Plant via an Evolutionary Approach

In this paper, a quantitative index is proposed to address the performance evaluation and design issues in the digital redesign of continuous-time interval systems. From the perspective of signal energy, a worst-case energy resemblance index (WERI), defined as the ratio of the worst-case continuous signal energy (WCSE) of the continuous-time interval system over the worst-case discrete sequence energy (WDSE) of the redesigned digital system, is established for evaluating the closeness of the system performance between the redesigned digital control system and its continuous-time counterpart. Based on the WERI, performance of the redesigned digital systems can be evaluated for different discretization methods at different sampling times. It is found that no discretization method outperforms the others for all sampling times. Because of serious nonlinearities and nonconvexity involved, the determination of WCSE and WDSE is first formulated as an optimization problem and subsequently solved via an evolutionary algorithm. To guarantee stability of the redesigned digital system, the largest sampling time allowed is also evolutionarily determined to establish a sampling-time constraint under which robust Schur stability of the redesigned digital system can be ensured. For design purposes, sampling time required can be determined according to the user-specified WERI, which serves as a performance specification for fine tuning the performance of the redesigned digital control system.

DELAY-DEPENDENT ROBUST H∞ FILTERING FOR INTERVAL SYSTEMS WITH STATE DELAYS

This paper deals with the problem of robust H∞ filtering for a class of linear continuous-time interval systems with delay dependence and structured uncertainties, which are not restricted to the matched uncertainty or the norm-bounded uncertainty. The problem aims at designing a stable linear filtering assuring asymptotic stability and a prescribed H∞ performance level for the filtering error system. A sufficient condition for the existence of such a filter is developed in terms of linear matrix inequalities. A numerical example demonstrates the validity of the newly developed theoretical results.

Robust Kalman filtering for delay-dependent interval systems

In this paper, we study the problem of Kalman filtering for a class of linear continuous-time interval systems with delay-dependent conditions. By employing a Lyapunov-Krasovskii functional approach, it is proven that the dynamics of the estimation error is stochastically exponential stable in the mean square. Sufficient conditions are proposed to guarantee the existence of the desired robust Kalman filters by solving linear matrix inequality which is delay dependent. A numerical example is worked out to illustrate the validity of the theoretical results.

Robust [formula omitted]-stability of discrete and continuous time interval systems

Necessary and sufficient conditions are presented for the robust Schur and Hurwitz stability of the dynamic interval systems. An interval matrix can be expressed as a linear fractional transformation of an interconnection matrix with structured real parametric uncertainties. Consequently, the robust stability problem is converted to a robust nonsingular problem. An explicit condition in terms of the structured singular value is provided to ensure the stability robustness of dynamic interval systems. This systematic approach is feasible for both discrete-time and continuous-time cases. The proposed technique can be applied directly to D -stability for performance requirements.