Original Higher Order System Research Articles

Dual Channels Event-Triggered Asymptotic Consensus Control for Fractional-Order Nonlinear Multiagent Systems.

This article investigates the event-triggered leaderless consensus control problem for fractional-order multiagent systems (FOMASs), where both the agent-to-agent communication channel and the controller-to-actuator communication channel are based on the events. A filter is introduced to transform the original high-order system into a first-order one, greatly simplifying the complexity of controller design compared to the traditional backstepping. Further, the convergence of filtered output signals is proved to be consistent with that of the outputs of agents themselves. Superior to the traditional event-triggered scheme, two dynamic variables are designed for the triggering conditions of the communication among agents and the controller update, respectively. Via elaborately constructing the dynamic variables, zero-error leaderless consensus can be achieved instead of only ultimately uniformly bounded result. It is proved that the proposed control strategy can guarantee better control performance of leaderless consensus under limited communication resources, and Zeno behavior is excluded. Finally, two examples are provided to verify the effectiveness of our proposed control approach.

Identification and Control of Flexible Joint Robots Based on a Composite-Learning Optimal Bounded Ellipsoid Algorithm and Prescribe Performance Control Technique

This paper presents an indirect adaptive neural network (NN) control algorithm tailored for flexible joint robots (FJRs), aimed at achieving desired transient and steady-state performance. To simplify the controller design process, the original higher-order system is decomposed into two lower-order subsystems using the singular perturbation technique (SPT). NNs are then employed to reconstruct the aggregated uncertainties. An adaptive prescribed performance control (PPC) strategy and a continuous terminal sliding mode control strategy are introduced for the reduced slow subsystem and fast subsystem, respectively, to guarantee a specified convergence speed and steady-state accuracy for the closed-loop system. Additionally, a composite-learning optimal bounded ellipsoid algorithm (OBE)-based identification scheme is proposed to update the NN weights, where the tracking errors of the reduced slow and fast subsystems are integrated into the learning algorithm to enhance the identification and tracking performance. The stability of the closed-loop system is rigorously established using the Lyapunov approach. Simulations demonstrate the effectiveness of the proposed identification and control schemes.

Order Reduction using Basic Characteristics and Factor Division Method

Abstract: The authors propose a mixed method for reducing the order of the high order dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the basic characteristics of the higher order system which are maintained in the reduced model while the coefficients of the numerator are obtained by using factor division method. This method is fundamentally simple and generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical example taken from the literature.

Transient Stability Analysis for a Multi-VSC Parallel System Based on the CFND Method

Because of the control complexity of voltage source converters (VSCs), transient stability analysis of multi-VSC parallel systems is challenging, and there are still no effective methods to solve this problem. Inspired by the decoupling principle and combined with the normal form method, an innovative coupling-factor-based nonlinear decoupling (CFND) method is proposed. According to the coupling factors that can be used to evaluate the nonlinear coupling degree among different state variables, the CFND method approximately transforms a high-order nonlinear multi-VSC parallel system into multiple decoupled low-order modes. Thus, the transient stability of the original high-order multi-VSC system can be reflected indirectly by the mature inversing trajectory method and the phase plane method. The CFND method has universality, flexibility, and insensitivity to system order, and no need to construct corresponding Lyapunov functions for different nonlinear systems, breaking through the inherent limitations of traditional analysis methods. Furthermore, this paper derives a reduced-order large-signal model and the corresponding truncated model for a single VSC grid-connected system. The effectiveness of the reduced-order model is verified through simulation waveforms and ROAs partitioning. Subsequently, a generalized model of the multi-VSC grid-connected system is developed. Finally, taking the grid-connected system with three VSCs as an example, the proposed CFND method is used to analyze typical operation cases, and the conclusions of transient stability analysis are verified using the hardware-in-loop (HIL) experiments.

Output Feedback Control of Fuzzy Systems via Reduced-Order Approximation Technique

This article focuses on the problem of designing the reduced-order dynamic output feedback (DOF) controller for discrete-time T–S fuzzy plants. Differing from the existing methodologies, the reduced-order approximation technique is applied to simplify the pregiven high-order DOF controller. The key point is to construct a reduced-order closed-loop model to approximate the original high-order closed-loop system. First, a new error auxiliary system between the high-order closed-loop system and the reduced-order closed-loop model is obtained. The sufficient conditions to guarantee that the corresponding error system is asymptotically stable with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$</tex-math> </inline-formula> performance index are developed. Then, the parameters of the desired reduced-order controller are derived by utilizing the projection lemma and the cone complementary linearization algorithm. Finally, the advantages of the proposed technique are illustrated by a series of simulation analysis.

Design of Controller for Large-Scale Uncertain Systems Adopting Affine Arithmetic

In this article presents a new controller design technique for large scale uncertain systems. The new controller is designed through a reduced order system from certain high order system. In the projected reduction method, the numerator coefficients are obtained with γ-table while the denominator polynomial is achieved with δ - table. An optimised reduced order model is derived with minimum value of ISE. In this proposed method gives better stability of the reduced order model, if consider the original stable high order system. A PID controller is designed for the high order original systems through its proposed reducer order model. Consider several numerical examples are available in the literatureto illustrate the usefulness of the proposed method andit gives sufficientoutcome.

Model Order Reduction Algorithm Based on Preserving Dominant Poles

In recent years, model order reduction (MOR) has been interested in more and more scientists. A lot of MOR algorithms have been introduced by many different approaches, among which preserving the dominant poles of the original system and Hankel singular values of the original system in order reduction system are appropriate approaches with many advantages. The article introduces a new MOR algorithm applied for stable and unstable linear systems, based on the idea of preserving the dominant poles of the original system during the order reduction. The algorithm will switch matrix-A of the original high-order system into the upper triangular matrix, then arrange the poles under the measure of dominance- H, H2, and mixed points on the main diagonal of upper triangular matrix-A, in order to attain a small error order reduction and preserve dominant poles simultaneously. The effectiveness of the new algorithm is illustrated through the order reduction of the high-order controller. Simulation results have proven the correctness of the algorithm.

An Improvement in LQR Controller Design based on Modified Chaotic Particle Swarm Optimization and Model Order Reduction

The diverse engineering and scientific applications are stated through complex and high-order systems. The significant difficulties of these systems are the complications of modeling, analyzing, and controlling. It is easier to examine simpler models for more physical insights than more complex models and result in lower-ordering controllers that are easier to implement. The model order reduction (MOR) was used to simplify the computational difficulty of such complications and was later developed intensively for use with increasingly CDS. In this paper, a new Modified Chaos Particle Swarm Optimization (MCPSO) technique is employed to get a reduced-order model of a large scale system and design a Linear Quadratic Regulator (LQR) based controller. The mod uses the combination of advantages of basic PSO algorithms and chaotic algorithms. It becomes an excellent algorithm with fast convergence, few control parameters, simple execution, and avoidance of local extremes. In addition to combining the chaotic algorithm, CPSO also improved the weight parameter w, adjusting it to the dynamic attenuation direction. First, efficient reduced-order model parameters are obtained for original higher-order systems based on the MCPSO. Then linear quadratic regulator (LQR (controller parameters optimized for the reduced-order model. The goodness of the proposed method is evaluated through a numerical example. The experimental results indicate that the proposed technique’s reduced order model provides an excellent close approximation to the original system.

Design of Controller for Large Scale Uncertain Systems via Reduces Order Model

In This paper, a method of designing the Controller for large scale uncertain systems. The Controller is designed via a reduced order model for a given high order system. An optimized reduced order model is derived with minimum ISE. The proposed method guarantees stability of the reduced model, if the original high order system is stable system. A PID controller is designed for the high order original systems through its low order model proposed. This paper presents an improvement to generalized least squares method of model order reduction. The improvement enhances the flexibility of the method with very little computational requirement. The reduction procedure is simple, efficient and always generates stable reduced models for the stable high order systems. The proposed method is illustrated with typical numerical examples taken from the literature and the results are compared with the other existing methods to show its superiority.

Lower Order Approximation of Bounded-Parameter Uncertain Systems using Amplitude Matching and Whale Optimization Algorithm with Constriction Factor

Lower order modelling of uncertain bounded systems is presented in this paper using amplitude matching and Whale Optimization Algorithm (WOA) with Constriction Factor (CF). The amplitude matching technique ensures to retain the stability and dynamics of the original higher-order systems. The proposed optimization algorithm for minimum Integral Square Error (ISE) approximates the model so that the responses match closely. The results are validated by comparing the ISE values of existing models. The presented technique is applicable for both Linear Time Invariant Continuous Systems (LTICS) and Linear Time Invariant Discrete Systems (LTIDS) without any need for tedious calculation of domain transformation.

Reduced order model based FOPID controller design for power control in Pressurized Heavy Water Reactor with specific gain –phase margin

The substantial portion of the existing power generation comes from Pressurized Heavy Water Reactor (PHWR). However, PHWR is a nonlinear and high order system and designing a controller for such a high order system is not an easy task. Therefore, it is required to design a controller for a reduced order PHWR system which will give the same response as that on the original higher order system. The focus of the present research endeavor is to propose a design methodology for a fractional-order proportional integral derivative controller for the power control of reduced order PHWR system. The reduced order models of PHWR have been obtained using Balanced Truncation method and a robust FOPID controller has been designed using the stability boundary locus method with specific gain-phase margin. The simulation results illustrate a better set point tracking performance with the use of proposed FOPID controller at 30% control drop and varied initial power levels.

A novel method based on pole clustering technique and differential evolution for model order reduction

This paper strives to present a model order reduction (MOR) method for complex high order linear time-invariant (LTI) single input-single output (SISO) systems. The recommended method utilises the benefits of pole clustering method and differential evolution algorithm. In this suggested method, approximated denominator polynomial is obtained by pole clustering method whereas; approximated numerator is obtained using differential evolution algorithm. To indicate the effectiveness of the suggested method over existing MOR techniques, a comparison on the basis of a performance index known as integral square error (ISE) is depicted in this paper by using simulation graphs and in tabular form. Further, the suggested method is extended for MIMO systems also. Numerical examples are solved to give better understanding of the propound technique for SISO and MIMO systems. The recommended method derives and guarantees a stable approximated ROM if the original higher order system (HOS) is stable.

A two-phase approach for the design of two-degree-of-freedom of robust controller for higher order interval system

This paper proposes a novel method for the design of the robust controller to retain both the robust stability and performance of the higher order interval system via reduced order model using the differential evolution (DE) algorithm. A stable reduced interval model is generated from a higher order interval system using DE in order to minimise the cost and reduce the complexity of the system. The reduced order interval numerator and denominator polynomials are determined by minimising the integral squared error (ISE) using the DE. From the reduced order interval model, a robust PI controller is designed based on the new stability conditions of interval system. The designed robust controller from the reduced order interval model will be attributed to the higher order interval system. The designed PI controller from the proposed method not only stabilises the reduced order model, but also stabilises the original higher order system. Finally, with the help of frequency domain method a pre-filter is constructed to improve the performance of interval system. The viability of the proposed methodology is illustrated through a numerical example for its successful implementation.

Optimal Model Approximation of Linear Time-Invariant Systems Using the Enhanced DE Algorithm and Improved MPPA Method

In this paper, the authors propose a novel model order reduction method integrating evolutionary and conventional approaches for higher-order linear time-invariant single-input–single-output (SISO) and multi-input–multi-output (MIMO) dynamic systems. The proposed method makes use of a differential evolution algorithm with enhanced mutation operation for the determination of reduced order model (ROM) denominator polynomial coefficients. In addition, an improved multi-point Pade approximation method is used to determine the optimal ROM numerator polynomial coefficients. The optimum property of the ROM is measured by minimising the integral square of the step response error between the original high-order dynamic system and the ROM. In the case of the MIMO system reduction approach, an optimal ROM transfer function matrix is determined by minimising a single objective function. This objective function is defined by a linear scalarising of the multi-step error function matrix components $$ \left( {E_{ij} } \right) $$. The proposed method guarantees the preservation of the stability, passivity and accuracy of the original higher-order system in the ROM. The proposed method is validated by applying it to a ninth-order SISO system, as well as to the tenth- and sixth-order linearised single-machine infinite-bus power system model with and without an automatic excitation control system. The simulation results and the comparison of the integral square error and impulse response energy values of the ROM demonstrate the dominance of the proposed method over the latest reduction methods available in the literature.

Model Order Reduction of Commensurate Fractional-Order Systems Using Big Bang – Big Crunch Algorithm

ABSTRACT In this paper, a soft computing based scheme is proposed for the model order reduction of single input-single output commensurate fractional-order (FO) systems. The fractional-order system is first converted into an integer order (IO) system. The reduced order model of the corresponding integer order system is then determined via big bang – big crunch (BBBC) optimization algorithm. Finally, the reduced IO transfer function is transferred back to its FO form through an inverse substitution. The proposed approach is substantiated by two numerical examples of different orders. The effectiveness of the technique is demonstrated by the comparison of two performance indices, i.e. integral square error (ISE) and error and the response characteristics in time and frequency domain with the existing techniques from the literature. It is revealed that the response of the proposed BBBC based reduced order model is much closer to that of the original higher-order system.

Firefly artificial intelligence technique for model order reduction with substructure preservation

Model order reduction (MOR) is a process of finding a lower order model for the original high order system with reasonable accuracy in order to simplify analysis, design, modeling and simulation for large complex systems. It is desirable that the reduced order model preserves the fundamental properties of the original system. This paper presents a new MOR technique of multi-input multi-output systems utilizing the firefly algorithm (FA) as an artificial intelligence technique. The reduction operation is proposed to maintain the exact dominant dynamics in the reduced order model with the advantage of substructure preservation. This is mainly possible for systems that are characterized as multi-time scale systems. Obtaining the reduced order model is achieved by minimizing the fitness function that is related to the error between the full and reduced order models’ responses. The new approach is compared with recently published work on firefly optimization for MOR, in addition to three other artificial intelligence techniques; namely, invasive weed optimization, particle swarm optimization and genetic algorithm. As a result, simulations show the potential of the FA for the process of MOR.

Improved pole clustering-based LTI system reduction using a factor division algorithm

In this paper, a novel technique is proposed to approximate the high-order linear continuous-time and discrete-time systems. The proposed methodology is based on the improved pole clustering (IPC) and factor division algorithm (FDA). The IPC technique is employed to estimate the coefficients of reduced-order denominator polynomial while FDA computes the coefficients of numerator polynomial. The distinctive feature of the proposed scheme is that, the approximants turn out to be always stable, if the original high-order system (HOS) is stable. The efficacy of the proposed scheme is tested by considering six numerical examples from the existing literature. Further, the superiority of the proposed technique over existing techniques of order reduction is verified through performance indices, time and frequency responses.

Order Reduction of Linear Dynamic Systems by Improved Routh Approximation Method

ABSTRACTIn this paper, a new simplified Routh approximation technique is proposed for the model order reduction (MOR) of large scale linear time-invariant systems. In reduced order modeling, the Routh approximation technique described in the literature is based on the alpha and beta parameters. This paper presents a new simplified Routh approximation technique for the MOR involving only alpha parameters to make the proposed technique simple. In this technique, the denominator polynomial of the lower order system is obtained by the Routh approximation technique and the numerator polynomial is computed by a simple mathematical algorithm as discussed in the proposed scenario. The additional advantage of the proposed method is that it always gives a stable reduced model if the original higher-order system is stable. To illustrate the proposed method, the fourth-order DC–DC converter model is reduced to its second-order reduced model. The modeling of DC–DC converter in continuous conduction mode is also developed and whose final output is a complete linear circuit model. In order to check the effectiveness and accuracy competitive to other popular and recent techniques in the literature, the proposed method has been applied on various standard numerical examples.

Analysis and design of single-phase power factor corrector with genetic algorithm and adaptive neuro-fuzzy-based sliding mode controller using DC–DC SEPIC

This paper proposes a methodology for single-phase power factor correction with DC–DC single-ended primary inductance converter (SEPIC) using cascade control strategy which comprises of genetic algorithm-based outer PI controller and an inner current controller which uses an adaptive neuro-fuzzy inference system-based sliding mode controller. DC–DC SEPIC is a fourth-order converter, and in order to reduce the complexity in controller design, reduced-order model of the original higher-order system is obtained by using Type-I Hankel matrix method. The performance of the proposed system is analysed using MATLAB/Simulink-based simulation studies. In order to ensure the robustness of the proposed controller, the performance parameters such as percentage total harmonic distortion, power factor, % voltage regulation, and % efficiency are analysed. From the simulation results, it is inferred that the proposed method provides efficient tracking of output voltage and effective source current shaping for load, line, and set point variations.

A Novel Method Based on Pole Clustering Technique and Differential Evolution for Model Order Reduction

This paper strives to present a model order reduction (MOR) method for complex high order linear time-invariant (LTI) single input-single output (SISO) systems. The recommended method utilises the benefits of pole clustering method and differential evolution algorithm. In this suggested method, approximated denominator polynomial is obtained by pole clustering method whereas; approximated numerator is obtained using differential evolution algorithm. To indicate the effectiveness of the suggested method over existing MOR techniques, a comparison on the basis of a performance index known as integral square error (ISE) is depicted in this paper by using simulation graphs and in tabular form. Further, the suggested method is extended for MIMO systems also. Numerical examples are solved to give better understanding of the propound technique for SISO and MIMO systems. The recommended method derives and guarantees a stable approximated ROM if the original higher order system (HOS) is stable.