Model order reduction for discrete-time systems is often required to preserve accuracy over a prescribed frequency interval rather than across the entire frequency range. It is observed that a few existing methods based on frequency-constrained Gramians yield significant approximation errors for discrete-time systems owing to the eigenvalue imbalance in some of the intermediate matrices. Therefore, in this paper, a novel model reduction technique is proposed for discrete-time systems by constructing new frequency-constrained Gramians. A novel set of pseudo-input and output matrices is formed that precisely approximates the higher-order system to a lower-order system within the specified frequency interval. The proposed method guarantees a stable reduced model for a given stable system and provides an a priori error bound for the desired frequency interval. The simulation results of numerical examples illustrate the effectiveness of the proposed technique.

Single-ended primary-inductor converters (SEPICs) face output voltage regulation challenges owing to right-half-plane zeros and complex fourth-order dynamics, which severely restrict their control implementation. Traditional methods struggle to provide fast and stable regulation during sudden disturbances, especially when the input or load undergoes significant changes. Therefore, specialized controllers are required to address the slow response of the system and ensure stability over the operating range. This study presents a modified two-degree-of-freedom internal model control (MTDF-IMC) strategy for the output voltage regulation of SEPICs by unifying the IMC and model order reduction. In the current work, the proposed MTDF-IMC structure develops an internal model for control design, which is derived by reducing the fourth-order SEPIC through Padé approximation. The proposed control strategy incorporates the Pelican optimization algorithm to optimize the disturbance rejection performance and set-point tracking. The effectiveness of the proposed controller is assessed using MATLAB simulations across two operating scenarios of SEPIC. The results validate the efficacy of the proposed methodology and emphasize its potential for practical applications in power electronics, where precision and computational efficiency are vital.

This study presents an innovative cascade control architecture to regulate frequency deviations caused by load disturbances in single-area and multi-area thermal power systems (TPSs) incorporating renewable energy sources. Two dual-loop control structures are developed: (i) proportional fractional-order integral-derivative-proportional-integral-filtered derivative ((PID)-D-lambda-PIDF) and (ii) proportional-derivative-PIDF (PD-PIDF). In these configurations, the (PID)-D-lambda and PD controllers are employed in the primary loops, while the PIDF controller serves as the secondary controller in the inner loops. Proper tuning of the controller parameters is crucial for effectively mitigating frequency deviations. Therefore, a recently developed artificial-ecosystem-based optimizer (AEO) is employed to determine the optimal parameter values for the proposed controllers. Initially, the performance of the proposed controllers is evaluated on a single-area TPS, with and without renewable sources, under load fluctuations. The results of the cascade configurations are also compared with the other controllers to confirm the superiority of the proposed (PID)-D-lambda-PIDF and PD-PIDF schemes in terms of error criteria, peak overshoots/undershoots, and settling time. Furthermore, the applicability of the proposed methodology is examined on a three-area reheated TPS to emphasize its effectiveness and contribution. The simulated results confirm that the optimized AEO-based method offers improved system performance under varying load demands and system nonlinearities. Finally, the resilience of the proposed controllers is validated under +/- 50% variations in the system's key parameters.

Effective frequency weighted model reduction (FWMR) is essential for complex signal processing and high-speed digital filtering in two-dimensional (2-D) discrete-time systems. However, the fundamental limitations of contemporary FWMR techniques have limited their applicability. These drawbacks include the significant computational expense of iterative FWMR algorithms, the complexity of Lyapunov inequalities, and the unacceptably large errors resulting from the unequal eigenvalue distribution in the current FWMR approaches. To address these critical issues, this study introduces a unique parametrized FWMR approach for 2-D decoupled denominator-type discrete-time systems by incorporating two free parameters. Applying a direct block-diagonalization technique to weighted controllability and observability Gramian matrices is a fundamental innovation of the proposed approach. Additionally, the stability of the reduced-order models is guaranteed by the proposed methodology under single-and double-sided frequency weighting functions. Three numerical examples and their performance analyses were used to validate the efficacy of the proposed method using MATLAB simulations.

This paper presents an analytical method for designing fractional-order proportional-integral (FOPI) controllers for fractional-order systems with integer time delay and fractional time delay. The tuning parameters of the proposed FOPI controller are obtained by imposing frequency-domain design specifications to ensure better performance and enhanced robustness of the resulting closed-loop system. As the proposed methodology involves fractional-order nonlinear equations, a graphical approach is used to obtain the respective solutions. The comparison with the related methods confirms that the proposed methodology achieves better time-domain performance and greater robustness. The control signal generated by the proposed FOPI controller is non-aggressive, quick, and smooth, making it an excellent choice for reliable and practical implementation. The proposed controller is tested under the influence of disturbance as well as under the effect of measurement noise. The obtained results showcase the disturbance and measurement noise rejection capability of the proposed FOPI controller. Unlike conventional optimization-based tuning methods, the proposed approach offers an intuitive and systematic design. The proposed method is numerically straightforward, as it employs a graphical approach and is less computationally expensive owing to the alternative design specifications.

As the domestic load is increasing day by day, it is necessary to have a better energy management system for home appliances. This paper presents a solution for the above problem as a fuzzy-based home energy management system that can counter time-varying electricity costs, i.e., the nominal tariff (NT). As many houses use energy storage systems (ESSs) for their solar power generation, the proposed approach schedules ESSs to reduce electricity costs by changing the operations in ESSs. The charging of an ESS must be appropriately scheduled to lower the electricity bill. Therefore, we suggest the Mamdani-based fuzzy logic control approach, which decides the charging, discharging, and idle conditions for ESSs as per the NT and available renewable energy resources. The proposed system does not use power from the grid during peak hours to maintain the peak-to-average ratio by considering user's comfort and waiting time for appliances.

This study presents a novel configuration of frequency-limited controllability and observability Gramians to establish a new singular perturbation approximation-based model reduction approach. The proposed approach minimizes errors within designated frequency ranges for given higher-order models. The proposed method produces stable, simpler models and offers improved approximations compared to current methodologies. Two numerical examples are used to evaluate the efficacy of the presented method.

This study presents a novel square-root frequency-weighted truncated realization-based model reduction technique for designing reduced-order two-dimensional (2-D) separable denominator-type discrete-time infinite impulse response filters. The suggested method utilizes truncated balanced realisation, which works with both single- and double-sided weights. The efficacy of the suggested approach is demonstrated by analyzing a numerical example of a $(12,12)$ order 2-D low-pass Butterworth filter, and the results validate the proposed approach.

This paper presents a novel configuration of frequency-limited controllability and observability Gramians to establish a new square-root truncated realization-based model reduction approach, which minimizes errors within designated frequency regions. The proposed method produces stable, simpler models and offers improved approximations compared to current methodologies. Two numerical examples are employed to evaluate the efficacy of the presented method, demonstrating through error plots and comparisons that the suggested reduced models adequately approximate the actual models within the designated frequency band.

This paper presents the novel 1 + proportional derivative-proportional-integral derivative with filter controller for enhancing automatic voltage regulator (AVR) operation in a power system under external disturbances. The Grey wolf optimizer (GWO) is followed to determine the optimal settings of the proposed controller using integral-time-absolute error. The suggested GWO-based controller performance is validated in terms of steady-state and transient responses. Then, it is compared with recently developed controllers optimized by different optimizers. The results revealed that the suggested controller offers excellent performance in terms of minimum overshoot and settling time in AVR system response under unit step voltage. Finally, the recommended controller response is also examined in the presence of system’s parametric uncertainties to demonstrate it’s robustness.

This paper introduces a new interval model reduction approach for simplifying the dynamic modeling of a Zeta converter using Hurwitz polynomial and Padé approximation. A Zeta converter, characterized as a fourth-order DC-DC buck-boost converter with a non-inverting output, typically exhibits complex dynamic behavior due to variations in its components. To address this, the converter is modeled as an interval system, accounting for $\pm 2\%$ and $+10\%$ variations in system parameters. The interval model is then reduced to a lower-order system by applying the proposed technique. The effectiveness of the reduced-order models is evaluated through time response analysis. The results confirm that the proposed method reduces the model's complexity while preserving essential characteristics, demonstrating the robustness and practicality of the suggested technique.

This paper presents a novel frequency-weighted singular perturbation approximation-based model reduction technique which is implemented for the design of reduced-order two-dimensional (2-D) separable denominator-type discrete-time infinite impulse response (IIR) filters. The proposed technique uses a singularly perturbed balanced realisation that can be applied with single- and double-sided weights. A numerical example of a (12,12) order low-pass 2-D Butterworth filter is examined to establish the effectiveness of the proposed method.

In this paper, we demonstrate a novel solution for the continuous-time frequency-weighted and frequency-interval Gramians-based reduced-order modeling problems using a new structure of input and output matrices. It has been observed that reduced-order models (ROMs) of some methodologies produce unstable ROMs, and the generated ROMs differ substantially from the actual model, resulting in substantial approximation inaccuracy. The proposed frequency-weighted strategy is beneficial as it offers stable ROMs when input and output weightings are utilized. Further, the frequency-interval Gramians-based proposed algorithm also generates stable ROMs. The effectiveness of the presented strategies are shown by numerical examples, and the findings are compared to other well-established frequency-weighted and frequency-interval Gramians-based model order reduction (MOR) methods.

The frequency-limited model order reduction (FLMR) problem considers the model approximation within a desired frequency interval. It is observed that some of the existing FLMR methods tend to provide large approximation errors due to uneven distribution of intermediate eigenvalues. Hence, a new FLMR method based on novel frequency-limited Gramians is proposed in this article to obtain a lower approximation error. The proposed technique gives a stable reduced-order model due to the unique configuration of the Gramian matrices, which is obtained using intermediate fictitious input and output matrices. A comparative analysis using four numerical examples is provided, and it is found that the presented method produces better results than the prevailing methods.

Model order reduction (MOR) streamlines higher-order systems (HOSs) by creating lower-order approximations while preserving essential dynamics, aiding in efficient analysis and control design. Despite advancements in MOR techniques, achieving an optimal balance among accuracy, stability, and computational efficiency continues to pose a challenge, particularly for complex multi-input-multioutput (MIMO) systems. In this paper, a novel approach is introduced to determine the reduced-order model (ROM) of HOSs by integrating the Eigen permutation with the dandelion optimisation algorithm. This approach yields a stable ROM for a stable HOS. The efficiency of the presented approach is evaluated through numerical simulations of single-input singleoutput and MIMO systems. Furthermore, the proposed results are benchmarked against existing approaches, demonstrating their effectiveness.

Model order reduction preserves the intrinsic characteristics of a complex system while approximating it with a relatively lower-order model. To effectively control a higher-order system, the main goal is to determine a low-order model with fewer states. The well-known balanced realization approach with frequency weights is used in this work to reduce the order of continuous-time systems. Fictive matrices are developed, and singular value decomposition of the formed matrices is considered to obtain the reduced model. The suggested method produces a stable reduced model for a higher-order system, even with double-sided weights. A case study from the literature is considered to illustrate the effectiveness of the suggested method, and a comparison with alternative approaches is also provided.

Fractional-order systems (FOSs) present unique modeling challenges due to their non-integer order dynamics. This paper aims to enhance the computational efficiency of commensurate and incommensurate FOSs while maintaining their properties through reduced-order modelling. The proposed method begins with the rational approximation of incommensurate FOSs using the Oustaloup approximation, transforming them into integer-order models (IOMs). Subsequently, the Salp Swarm Optimization Algorithm (SSOA) is employed to reduce the complexity of these higher-order IOMs. The efficacy of the proposed order reduction method is compared with several strategies, including Genetic Algorithm, Balanced Truncation, Routh Approximation, and Big-Bang Big-Crunch Algorithm. The results demonstrate that the presented SSOA-based reduction method effectively retains the fundamental traits and characteristics of the original FOS.

This work presents a simulation-based study for the output voltage regulation of a non-ideal DC-DC buck converter. A modified two-degree-of-freedom internal model controller (MTDF-IMC) is designed for set-point tracking and disturbance rejection. The motivation for selecting an MTDF-IMC approach lies in the fact that it can easily handle the set-point tracking and the load-disturbance rejection separately. The presented controller is tested with (i) sudden input voltage variation, (ii) parametric uncertainty in the plant model, and (iii) presence of step disturbances to showcase the effectiveness and supremacy of the proposed work. The performance of the designed controller is compared with the TDF-IMC and IMC-PID control strategies, and the results show that the designed MTDF-IMC controller outperforms TDF-IMC and IMC-PID control strategies.

In this paper, we introduce the salp swarm optimization algorithm (SSOA)-based novel model reduction algorithm for simplifying commensurate and incommensurate fractional-order systems. In the case of commensurate fractional-order systems (CFOSs), the presented method converts it into a non-fractional-order system first. Then, we implement the SSOA with the stability equations to find a non-fractional-order approximant. Finally, the non-fractional-order approximant is transformed to determine the proposed reduced-order CFOS. It is also demonstrated using numerical examples that some existing methods fail to achieve the stability claim. On the other hand, the stability of the proposed fractional-order approximants is ascertained by incorporating stability equations along with SSOA. Further, the proposed method is extended for the model reduction in incommensurate and unstable fractional-order systems. In this case, the Oustaloup approximation is used along with the SSOA and stability equations to obtain the proposed non-fractional-order approximation. The simulation results corroborate the performance of the suggested method in both cases and establish its transcendency. The obtained results showcase the efficacy of optimization in simplification of fractional-order systems. The work also highlights the importance of order reduction in practical engineering and scientific applications of fractional-order systems.

In this work, a novel configuration of frequency-limited controllability and observability Gramians is constructed to develop a new truncated balanced realization for minimizing the error of higher-order models in specified frequency intervals. The suggested technique generates stable simplified models and approximates better than existing techniques. Two numerical examples are used to assess the performance of the presented approach, and it is found through the error plots and comparison that the proposed reduced models approximate the actual models satisfactorily in the specified frequency band.