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This study investigates the development of an advanced robust control strategy for a quarter-car active suspension system to optimize ride comfort and road handling. Traditional PID controllers struggle with trade-offs between comfort and stability under real-world conditions like variable road profiles and parametric uncertainties. To address this, we propose a novel H∞ robust control integrated with μ-synthesis, explicitly handling uncertainties in suspension parameters (sprung/unsprung mass, stiffness, damping, tire stiffness). Mathematical modeling and MATLAB/Simulink simulations demonstrate significant improvements: a 54% reduction in peak vertical body acceleration (3.95 m/s 2 to 1.816 m/s 2 ) and a 35% decrease in suspension deflection (0.078 m to 0.020 m) compared to passive systems. Frequency-domain analysis shows a 92.42% reduction in resonance peaks at 10 rad/s, with over 30% energy savings. Time-domain simulations confirm stability under transient disturbances, with actuator forces constrained to ±1.3 kN. The integration of μ-synthesis with H∞ control efficiently manages parametric variations and unmodeled dynamics. Comparative evaluations highlight the approach’s superiority over passive and conventional active systems, offering promising applications for autonomous and electric vehicles. This work lays the groundwork for future research on adaptive, energy-efficient suspension systems.

This study introduces a robust multivariable control approach for a permanent magnet synchronous motor (PMSM), designed to maintain stability and performance despite parametric uncertainties. A multi-input multi-output (MIMO) model of the PMSM is established in the (d,q) reference frame, leveraging field-oriented control (FOC) to effectively decouple the d- and q-axis dynamics. Six key parameters stator resistance, d- and q-axis inductances, magnetic flux linkage, moment of inertia, and viscous friction are treated as uncertain, with variations up to ±30%. The controller is developed using μ-synthesis within the$H \\infty / \\mu$framework, incorporating diagonal frequency weighting functions to balance performance, disturbance rejection, and control effort. A D-K iteration process is employed to derive a reduced-order controller, ensuring robust stability across the uncertainty range. Simulations in Simulink validate the controller’s effectiveness in tracking references and rejecting disturbances. This work demonstrates the efficacy of μ-synthesis for robust PMSM control in challenging, uncertain conditions.

Isolated microgrids, which are crucial for supplying electricity to remote areas using local energy sources, have garnered increased attention due to the escalating integration of renewable energy sources in modern microgrids. This integration poses technical challenges, notably in mitigating frequency deviations caused by non-dispatchable renewables, which threaten overall system stability. Therefore, this paper introduces decentralized fixed structure robust μ-synthesis controllers for continuous-time applications, surpassing the limitations of conventional centralized controllers. Motivated by the increasing importance of microgrids, this work contributes to the vital area of frequency regulation. The research challenge involves developing a controller that not only addresses the identified technical issues but also surpasses the limitations of conventional centralized controllers. In contrast to their centralized counterparts, the proposed decentralized controllers prove more reliable, demonstrating enhanced disturbance rejection capabilities amidst substantial uncertainties, represented through normalized co-prime factorization. The proposed controllers are designed using the D-K iteration technique, incorporating performance weight filters on control actions to maintain low control sensitivity and ensure specific frequency band operation for each sub-system. Importantly, the design considers unstructured uncertainty up to 40%, addressing real-world uncertainties comprehensively. Rigorous robust stability and performance tests underscore the controller's superiority, demonstrating its robustness against elevated uncertainty levels. Robust stability is verified for all controllers, with the proposed controller showing robust stability against up to 171% of the modeled uncertainty. Notably, the controller boasts a fixed structure with lower order compared to other H-infinity controllers, enhancing its practical implementation. Comparative analyses against Coronavirus Herd Immunity Optimizer tuned Proportional-Integral-Derivative (CHIO-PID) controller and CHIO tuned Fractional-Order Proportional-Integral-Derivative (CHIO-FOPID) controller further validate the superior performance of the proposed solution, offering a significant step towards ensuring the stability and reliability of microgrid systems in the face of evolving energy landscapes.

In this paper, a control strategy based on the inverse system decoupling method and μ-synthesis is proposed to control vibration in a rigid rotor system with active magnetic bearings that are built into high-speed motors. First, the decoupling method is used to decouple the four-degrees-of-freedom state equation of the electromagnetic bearing rigid rotor system; the strongly coupled and nonlinear rotor system is thus decoupled into four independent subsystems, and the eigenvalues of the subsystems are then configured. The uncertain parametric perturbation method is used to model the subsystem, and the multi-objective ant colony algorithm is then used to optimize the sensitivity function and the pole positions to obtain the optimal μ-controller. The closed-loop system thus has the fastest possible response, the strongest internal stability, and the best disturbance rejection capability. Then, the unbalanced force compensation algorithm is used to compensate for the high-frequency eccentric vibration; this algorithm can attenuate the unbalanced eccentric vibration of the rotor to the greatest extent and improve the robust stability of the rotor system. Finally, simulations and experiments show that the proposed control strategy can allow the rotor to be suspended stably and suppress its low-frequency and high-frequency vibrations effectively, providing excellent internal and external stability.

Frequency regulation in isolated microgrids is challenging due to system uncertainties and varying load demands. This study presents an optimal µ-synthesis robust control strategy that regulates microgrid frequency while enhancing system performance and stability—a proposed fixed-structure approach for selecting performance and robustness weights, informed by subsystem frequency analysis. The controller is optimized using multi-objective particle swarm optimization (MOPSO) and multi-objective genetic algorithm (MOGA) under inequality constraints, employing a Pareto front to identify optimal solutions. Comparative analyses demonstrate that the MOPSO-optimized controller achieves superior robustness and performance, tolerating up to 236% uncertainty compared to 171% for conventional µ-synthesis controllers. Additionally, it significantly reduces frequency deviation and enhances transient response. Nyquist stability analysis confirms robustness across renewable energy uncertainties. The results highlight the proposed controller’s effectiveness in isolated microgrid frequency regulation, with future work focused on discrete-time implementation for practical digital signal processing (DSP) applications.

This paper designs, implements, and compares the performance of a H2, H∞, H2/H∞, and μ‐synthesis approach for a V94.2 gas turbine mounted in Damavand combined cycle power plant. The controllers are designed to maintain the speed and exhaust temperature within their desired intervals and to ensure the robust performance of the gas turbine power plant (GTPP) in the presence of uncertainties and load demand variations. A linear model of the GTPP is first estimated using V94.2 gas turbine real‐time data and an autoregressive with exogenous input (ARX) identification approach, and then verified by residual analysis tests and steady‐state performance. The H2, H∞, H2/H∞, and μ‐synthesis controllers are then designed and implemented to the ARX model of the GTPP. The performance of the approaches is assessed and compared in terms of tracking capability, robustness, and transient performance. Additionally, the controllers' performance is compared to that of a conventional PID approach. Despite the slight variations in the performance, all the controllers exhibited robust stability and good overall performance in the presence of model uncertainties and load variations. A linear model for the gas turbine unit in a combined cycle power plant nonlinear system is estimated. The estimated model is evaluated using the steady‐state diagram for the power plant model. Four different H2, H∞, H2/H∞, and μ‐synthesis robust controllers are designed, implemented and assessed for the speed and temperature control loops. A comparison study between the robust controllers in the presence of model uncertainty is presented. All the robust controllers are able to guarantee the robust stability and performance and improve speed and temperature responses.

This paper presents an end-to-end method to design passivity-based controllers (PBC) for a class of input-affine nonlinear systems, named quasi-linear affine. The approach is developed using Krasovskii’s method to design a Lyapunov function for studying the asymptotic stability, and a sufficient condition to construct a storage function is given, along with a supply-rate function. The linear fractional transformation interconnection between the nonlinear system and the Krasovskii PBC (K-PBC) results in a system which manages to follow the provided input trajectory. However, given that the input and output of the closed-loop system do not have the same physical significance, a path planning is mandatory. For the path planning component, we propose a robust controller designed using the μ-synthesis mixed-sensitivity loop-shaping for the linearized system around a desired equilibrium point. As a case study, we present the proposed methodology for DC-DC converters in a unified manner, giving sufficient conditions for such systems to be Krasovskii passive in terms of Linear Matrix Inequalities (LMIs), along with the possibility to compute both the K-PBC and robust controller alike.

The control of systems like: bipedal locomotion robots, space launch vehicle, offshore wind turbines, and active vibration control systems in buildings and bridges, have to ensure, besides stability and accuracy, the system's insensitivity to parameters' uncertainties, unmodeled dynamics, external disturbances, and measurements noise. In such systems analysis and controller design, a triple inverted pendulum can be used as a benchmark to mimic systems characteristics and effect of different sources of uncertainty. μ-synthesis is a robust control method which seeks a controller that minimizes the robust H-infinity performance of the closed-loop system through D-K iteration. The D-K iteration is not guaranteed to converge to a global, or even local minimum. Hence this paper proposes the enhancement of controller design by applying gazelle optimization technique to shape the fictitious output by determining the parameters of the performance weighting matrix. The incorporation of optimization with controller design allows avoiding getting unnecessarily conservative system at the expense of performance. The developed control system is simulated using Matlab R2023b for different scenarios of system uncertainty. The results show that the requirements of robustness and performance can be balanced through the right choice of cost function. The robust performance measure obtained is 0.6432 which leads to good response for both stabilization and tracking in the presence of uncertainty. The results also show that even the baseline μ-synthesis design achieves higher robust stability margin about 2.818, the proposed optimized method stabilizes the system with overshoot been reduced by 67.65% and steady state error reduced by 5.69% without sacrificing robustness.

Internal oscillations among multiple generation systems in low-voltage stand-alone nanogrids and small-scale microgrids can cause instability in the entire generation system. This issue becomes worse when the coupling strength between the generation systems increases, which is a result of a shorter distance between them and a smaller reactance to resistance ratio. Previous approaches, which were based on the independent control design and considered the coupling effect as disturbances, may fail to tackle this issue when the two generation systems become strongly coupled. Therefore, in this paper a novel method is proposed to handle this coupling effect by designing robust decentralized controllers in a sequential manner to address the problem of voltage and frequency control in a nanogrid. This proposed sequential design is a general technique that is applicable to multiple inverter-based generation systems in a nanogrid or small-scale microgrid. For the ease of demonstration, in this paper the case of two interconnected inverters with LC output filters is studied. Two robust decentralized controllers are designed for the two inverter systems by using the μ-synthesis technique. The sequential design takes into account the interconnection line between the two inverters. Moreover, the controllers are designed to be robust against all the parameter variations in the system including the LC filter and interconnection line parameters. The simulation results demonstrate the superior performance of the proposed controller over the independently-designed controllers for the case of two generation systems that are highly coupled due to the short distance between them. Moreover, the proposed controller is shown to be robust against the LC filter and interconnection line parameter uncertainties as compared to the sequentially-designed linear quadratic Gaussian controllers.

In this paper, the secondary load frequency controller of the power systems with renewable energies is investigated by taking into account internal parameter perturbations and stochastic disturbances induced by the integration of renewable energies, and the power unbalance caused between the supply side and demand side. For this, the μ-synthesis robust approach based on structure singular value is researched to design the load frequency controller. In the proposed control scheme, in order to improve the power system stability, an ultracapacitor is introduced to the system to rapidly respond to any power changes. Firstly, the load frequency control model with uncertainties is established, and then, the robust controller is designed based on μ-synthesis theory. Furthermore, a novel method using integrated system performance indexes is proposed to select the weighting function during controller design process, and solved by a differential evolution algorithm. Finally, the controller robust stability and robust performance are verified via the calculation results, and the system dynamic performance is tested via numerical simulation. The results show the proposed method greatly improved the load frequency stability of a micro-grid power system.