Impulse energy approximation of higher-order interval systems using Kharitonov’s polynomials

Abstract

This research work proposes a method to obtain a stable reduced-order interval model from its stable higher-order interval plant. The reduced-order interval numerator and denominator polynomials are determined by using Kharitonov’s polynomials and a general form of the Routh approximation method. The proposed reduction algorithm retains stability and full impulse response energy of the higher-order interval system in its reduced-order interval model. In addition to this, the proposed method has useful features like matching of time moments and mathematical simplicity. Moreover, a few numerical examples in the literature are taken into consideration and simulated through MATLAB to illustrate the effectiveness of the proposed method.

Anderson Corollary Based on New Approximation Method for Continuous Interval Systems

“…From the data tabulated in Table 4, . From these values, it is evident that TMs due to the techniques proposed by Kumar et al [32], Hote et al [34], Singh et al [35], Bandyopadhyay et al [36], Sastry et al [37], and Kumar et al [38] are having larger deviation from those of the system. Also, it can be noted here that the TMs of the model proposed by Hote et al [34] is having non-interval values.…”

“…Zhang and Yang [31] developed a new control strategy that guarantees the prescribed tracking performance for a class of uncertain nonlinear single system with unknown control direction. Kumar et al [32] developed a technique to derive denominator and numerator of an interval model from Routh approximation using Kharitonov polynomials. In article [33], a class of control problems for multi-input-multi-output (MIMO) unknown Euler-Lagrange systems with output constrained are investigated, and also fault-tolerant control technique is effective to compensate for the actuator faults which ensure reliability of the dynamic system like inverted pendulum.…”

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

“…The goal of model order reduction is to compute an equivalent model which is simpler than the original complex systems and preserves the essential properties of the original system. The model diminution of higher order dynamical systems is a popular theme within the field of biological models (Javed and Ahmad, 2019; Snowden et al, 2017), control systems (Gautam et al, 2019; Kumar et al, 2016; Vasu et al, 2019), electromagnetic theory (Celo et al, 2005; Ng et al, 2020), mechanical engineering (Ischinger et al, 2019; Lin and Nikravesh, 2006; Veraszto et al, 2020), power systems (Al-Iedani and Gajic, 2020; Luo and Dhople, 2014; Wang and Long, 2020), chemical engineering (Nguyen et al, 2014, 2020; Tong et al, 2014) and so forth.…”

Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

“…It generates a much smaller system to approximate the original system such that the small system can retain some important properties (Jiang, 2010). Up to now, a lot of model reduction methods have emerged, such as Krylov subspace methods (Villemagne and Skelton, 1987; Yuan and Jiang, 2017), polynomials-based model reduction methods (Jiang and Chen, 2012; Kumar et al, 2016; Wang et al, 2016) and H 2 optimal model reduction methods (Qiu et al, 2018; Van Dooren et al, 2010).…”