Μ-synthesis Control Research Articles

Modeling of dynamic characteristics and μ-synthesis control of piezoelectric positioning platform

Abstract The dynamic hysteresis nonlinearity and various uncertainties of the piezoelectric positioning platform are critical factors limiting its high-precision applications. To address this, the dynamic characteristics of the piezoelectric positioning platform under various loads are identified based on the linearization of the Prandtl-Ishlinskii inverse model. The inverse compensation error and load disturbances are attributed to model uncertainties, which are modeled in the frequency domain. A μ-synthesis controller is designed to improve the tracking accuracy of the piezoelectric positioning platform under uncertainty disturbances. Experimental results indicate that with the μ-synthesis controller, the piezoelectric positioning platform achieves a relative error (RE) of less than 2.71% when unloaded. The RE is less than 6.03% for load disturbances of 100g, 200g, and 300g, respectively. These results demonstrate that the designed controller meets the high-precision positioning performance requirements under various load disturbance conditions.

Robust active vibration control of flexible smart beam by μ-synthesis

This paper presents a comprehensive method for designing a robust active vibration control system to suppress low-frequency vibrations in smart structures. A novel finite element method based on the first-order shear deformation theory is used to calculate the dynamic response of a smart beam. Through a comprehensive system identification process, the uncertain model of the smart beam is extracted considering both the magnitude and phase. The model fits the experimental data successfully. In addition, a generalized low-frequency vibration control performance function is designed for the piezoelectric smart beam. Using a linear fractional transformation, the system is converted into a standard μ-synthesis control framework, and the controller K is synthesized using structural singular values μ. The effectiveness of the proposed method is experimentally validated using a setup with a piezoelectric smart beam. The experimental results suggest that the proposed control method exhibits robust stability and robust performance, effectively enhancing the performance of smart structure control in various scenarios. The proposed control framework utilizes structured singular value analysis to provide optimal robust stability margins and superior robust control performance, effectively addressing system uncertainties and non-linearities.

Continuous-time robust frequency regulation in isolated microgrids with decentralized fixed structure μ-synthesis and comparative analysis with PID and FOPID controllers

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.

Dual-Loop μ-Synthesis Direct Thrust Control for Turbofan Engines

As the power unit of an aircraft, the engine’s primary task is to provide the demanded thrust, making research on direct thrust control crucial. However, being a complicated multivariable system, effective multivariable direct thrust control methods are currently lacking. The main content of this paper is threefold. First, it presents a dual-loop multivariable μ-synthesis direct thrust control scheme for mixed-exhaust low-bypass turbofan engines, which is a typical rotationally symmetric machine. The scheme adjusts fuel flow for thrust control and nozzle area to control the turbine pressure ratio, ensuring thrust tracking while maintaining the engine’s key parameters within safe limits. Second, a fast, accurate thrust estimation algorithm based on aerodynamic thermodynamics and component characteristics is introduced. At last, considering the model uncertainties between off-design and design points, a weight function frequency shaping μ-synthesis control design method is proposed to address internal loop coupling and external disturbance suppression. Nonlinear simulations within the flight envelope show that μ-synthesis direct thrust control achieves robust servo tracking and disturbance rejection, with a maximum steady-state thrust error of no more than 0.1%, and the key parameters are not over their safety boundaries.

Robust H-infinity and μ-synthesis controllers to mitigate sub-synchronous control interaction in DFIG wind farms considering time delay

Robust H-infinity and μ-synthesis controllers to mitigate sub-synchronous control interaction in DFIG wind farms considering time delay

μ-Analysis and μ-Synthesis Control Methods in Smart Structure Disturbance Suppression with Reduced Order Control

In this study, we created an accurate model for a homogenous smart structure. After modeling multiplicative uncertainty, an ideal robust controller was designed using μ-synthesis and a reduced-order H-infinity Feedback Optimal Output (Hifoo) controller, leading to the creation of an improved uncertain plant. A powerful controller was built using a larger plant that included the nominal model and corresponding uncertainty. The designed controllers demonstrated robust and nominal performance when handling agitated plants. A comparison of the results was conducted. As an example of a general smart structure, the vibration of a collocated piezoelectric actuator and sensor was controlled using two different approaches with strong controller designs. This study presents a comprehensive simulation of the oscillation suppression problem for smart beams. They provide an analytical demonstration of how uncertainty is introduced into the model. The desired outcomes were achieved by utilizing Simulink and MATLAB (v. 8.0) programming tools.

Development of a Ship's Course Controller using μ-synthesis

The article describes the procedure for designing a robust controller for controlling the course of sea vessels exposed to sea waves using µ-synthesis. To this end, practical knowledge of the vessel is used to obtain a linear design model with parametric uncertainties describing the dynamics of the vessel. Appropriate frequency weighting functions are selected to provide the required performance characteristics during the controller design phase. The proposed model and then the weighting functions are used to design a robust controller. The problem of wave filtering in the low-frequency range is also considered during the modeling and design of the controller. The key contribution of the paper is that it provides system designers with a methodology for obtaining uncertain linearized ship models that naturally fit within the framework of µ-synthesis control theory, and it describes, in a systematic manner, the various stages of the controller design process. In addition, the document contains detailed information on methods for analyzing robust systems and their modeling.

Active vertical vibration suppression of high-speed railway vehicles by controlling internal pressure of the air spring using μ-synthesis control

In recent years, railway vehicles have become lighter since it corresponds not only to the improvement of the running speed but also to the reduction of running cost and environmental noise. On the other hand, this causes an increase in the vertical elastic vibration of the car body and the riding comfort has deteriorated. Therefore, various strategies to reduce vertical vibration have been studied. In this study, vertical vibration reduction, by controlling the internal pressure of the air spring using µ-synthesis control, is proposed. The merit of µ-synthesis control is that it can guarantee robust performance. A controller by µ-synthesis was designed for vibration reduction of a 1/6 scale railway model and compared nominal performance and robust performance with H∞ control theory. Moreover, a feasibility study of this strategy was investigated for full-scale railway vehicles through simulation.

μ-Synthesis control with reference model for aeropropulsion system test facility under dynamic coupling and uncertainty

Due to the dynamic coupling and multi-source uncertainties, it is difficult to accurately control the pressure and temperature of the Aeropropulsion System Test Facility (ASTF) in the presence of rapid command and large disturbance. This paper presents the design of μ-synthesis control to solve the problem. By incorporating the pressure ratio into the linear equation of the control valve, the modeling error of ASTF in the low frequency range is effectively reduced. Then, an uncertain model is established by considering various factors, including parameter variations, modeling error in the low frequency range, unmodeled dynamics, and changes in the working point. To address the dynamic coupling, a diagonal reference model with desired performance is incorporated into μ-synthesis. Furthermore, all weighting functions are designed according to the performance requirements. Finally, the μ-controller is obtained by using the standard μ-synthesis method. Simulation results indicate that the μ-controller decouples the pressure and temperature dynamics of ASTF. Compared with the multivariable PI controller, integral-μ controller, and double integral-μ controller, the proposed μ-controller can achieve higher transient accuracy and better disturbance rejection. Moreover, the robustness of the μ-controller is demonstrated by Monte Carlo simulations.

Formula omitted]-Synthesis robust coordinated control of variable speed wind power generators and electric vehicles to regulate frequency

Variable speed wind power generators (VSWPGs) can inevitably introduce power fluctuations and reduce the system inertia in modern power systems. On the other hand, VSWPGs also have certain frequency support ability due to the fast control characteristics of the power electronics in the converters. Therefore, it is urgently required for VSWPGs to regulate the frequency of the power system. Taking into consideration the internal and external uncertainty in the power systems and that frequent regulation actions of VSWPGs might lead to mechanical failures and aggravate the aging process of the wind power generators, a coordinated control method of VSWPGs and electric vehicles (EVs) for frequency regulation on the basis of μ-synthesis control is proposed in this paper. The EVs are modeled as energy aggregators, the VSWPGs are modeled under the derating control using the small-signal analysis method, and the dynamic frequency response model for the system with uncertainty is then built. Considering the power system parametric uncertainty, a μ-synthesis controller is implemented to tackle the coordinated control problem of VSWPGs and EVs regulating system frequency by means of the D-K iterative method. Then the comparisons through time-domain simulations are conducted to verify the presented coordinated strategy is able to overcome influence of uncertainty on system frequency and also has better dynamic frequency performance.

가변속 냉동시스템의 견실 온도 제어를 위한 구조화 불확실성 기반의 μ-Synthesis 제어기 설계

This paper investigates μ-synthesis robust control for a variable speed refrigeration system to enhance robustness against model uncertainty and external disturbance. As the practical transfer function model obtained by experiments to design a controller inevitably contains model uncertainties such as unmodeled dynamics and modeling errors, a robust controller is necessary to track references in the system. Target temperature and superheat were simultaneously controlled in the system by adjusting rotating speed of compressor and opening angle of an electronic expansion valve respectively. Moreover, the μ-synthesis controller treats model uncertainty as structured perturbation; it is designed using structured singular value. It is shown that the μ-synthesis approach which takes structured uncertainties into account provides robust control performance against both dynamic perturbations including modeling errors and external disturbances. The validity of the proposed method was demonstrated by simulations and experiments.

μ-Synthesis FO-PID for Twin Rotor Aerodynamic System

μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters values. However, the free parameters available for tuning must be involved only in classical arithmetic operations, which leads to a problem for the fractional-order operator or for its integer-order approximation, exponential operations being involved. The main goal of the current article consists of presenting a possibility to integrate a fixed-structure multiple-input-multiple-output (MIMO) fractional-order proportional-integral-derivative (FO-PID) controller in the μ-synthesis optimization problem. The solution consists in a possibility to find a set of tunable parameters isomorphic with the fractional-order such that the coefficients involved in the approximation of the fractional element, along with the formulation of a fixed-structure mixed-sensitivity loop shaping μ-synthesis control problem. The proposed design procedure is applied to a twin rotor aerodynamic system (TRAS) using both MATLAB numerical simulation and practical experiments on laboratory scale equipment. Moreover, a comparison with the unstructured μ-synthesis is performed, highlighting the advantages of the proposed solution: simpler form and guaranteed robust stability and performance.

Generic Uncertainty Parameter Analysis and Optimization of Series–Series Wireless Power Transfer System for Robust Controller Design

In a typical wireless power transfer (WPT) system, the load, the mutual inductance, and the required tuning frequency can vary in a particular range. Variation of each parameter can substantially impact the dynamic characteristics of the system. Thus, they can be considered as sources of uncertainty in the system. To address this, robust control methods such as μ-synthesis are developed to deal with possible system uncertainties. This article first undertakes the generic dynamic analysis of the series–series WPT compensation network for two modes of operation, i.e., constant output voltage (COV) mode and constant output current (COC) mode, in the presence of three aforementioned uncertainty sources. Subsequently, the frequency detuning as a function of the compensation capacitor variation is explored and broadened as a technique to obtain the optimized compensation capacitor value that can lead to a plant with minimized dynamic deviations from its nominal system in the operating range between COC and COV modes. As such, this approach offers a design procedure for a least conservative robust controller, which can significantly improve the system performance. The optimized structure and the corresponding designed μ-synthesis controller are comprehensively elaborated. The theoretical achievements and experimental results show superior dynamic performance of the optimized structure and the corresponding designed controller in the presence of three uncertainty sources compared to the COC and COV modes of operation.

Robust Controller Synthesis and Analysis in Inverter-Dominant Droop-Controlled Islanded Microgrids

This work investigates the problem of controller design for the inverters in an islanded microgrid. Robust μ-synthesis controllers and local droop controllers are designed to regulate the output voltages of inverters and share power among them, respectively. The designed controllers alleviate the need for additional sensors to measure the states of the system by relying only on output feedback. It is shown that the designed μ-synthesis controller properly damps resonant oscillations, and its performance is robust to the control-loop time delay and parameter uncertainties. The stability of a droop-controlled islanded microgrid including multiple distributed generation (DG) units is analyzed by linearizing the nonlinear power flow model around the nominal operating point and applying theorems from linear algebra. It is indicated that the droop controller stabilizes the microgrid system with dominantly inductive tie-line impedances for all values of resistive-inductive loads, while for the case of resistive-capacitive loads the stability is conditioned on an upper bound on the load susceptances. The robust performance of the designed μ-synthesis controller is studied analytically, compared with the similar analysis in an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control (benchmark) framework, and verified by simulations for a four DG benchmark microgrid. Furthermore, the robustness of the droop controllers is analyzed by Monte Carlo simulations in the presence of local voltage fluctuations and phase differences among neighboring DGs.

μ-Synthesis for Fractional-Order Robust Controllers

The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with D–K iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets the stability and performance criteria for a family of plants. Because this control problem is NP-hard, it is usually solved using an approximation, the most common being the D–K iteration algorithm, but, this approximation leads to high-order controllers, which are not practically feasible. If a desired structure is imposed to the controller, the corresponding K step is a non-convex problem. The novelty of the paper consists in an artificial bee colony swarm optimization approach to compute the nearly optimal controller parameters. Further, a mixed-sensitivity μ-synthesis control problem is solved with the proposed approach for a two-axis Computer Numerical Control (CNC) machine benchmark problem. The resulting controller using the described algorithm manages to ensure, with mathematical guarantee, both robust stability and robust performance, while the high-order controller obtained with the classical μ-synthesis approach in MATLAB does not offer this.

Robust current control scheme for single‐phase PWM rectifiers based on improved μ ‐synthesis in electric locomotive

The parameter perturbation of grid-side equivalent inductance is a significant feature of the uncertainty in the single-phase pulse-width modulation rectifiers system for the electric locomotive. This characteristic tends to reduce the robustness of the rectifier system. This study handles these problems in the framework of the structured singular value, which helps to reduce the influence of model parameter perturbation, caused by measurement error and operation condition change, on the robustness. However, the conventional μ-synthesis robust controls only reflect tracking and anti-disturbance performance by weighting functions and ignoring the dynamic response performance. Herein, a direct current control (DCC) scheme based on improved μ-synthesis is proposed. A desired closed-loop transfer function is introduced to the conventional μ-synthesis control structure to ameliorate the performance of the dynamic response. Furthermore, considering the external disturbances on the system control output, a suitable weighting function is used to restrict the external disturbance. The input–output relationship of the generalised open-loop plant can thus be constructed accordingly. The proposed control scheme is compared with the widely applied proportional–integral-based DCC scheme and the conventional μ-synthesis DCC scheme. Hardware-in-the-loop experiment results show promising dynamic performance as well as stronger robustness against parameter perturbation and external disturbances.

Computational Cost Reduction of MIMO Controllers for Active Magnetic Bearing Systems

Abstract Generalized multiple-input-multiple-output (MIMO) controllers such as H∞ and μ have not been widely adopted in the magnetic bearing industry, partially due to high computational cost relative to simpler single-input-single-output schemes. Computational cost is important to industrial magnetic bearing vendors as their controller hardware is based on embedded processors that have limited bandwidth. Studies to mitigate the problem of high-order controllers show the limit of the existing methods in order reduction while still maintaining satisfying robust performance. A novel method is proposed to reduce the computational cost of robust controllers by identifying bounds in their dynamic response, such that an implementation of a controller within those bounds results in the robust performance. The bounds are used to develop two computational cost reduction schemes for controller implementation, i.e., (1) identifying a dual-rate implementation of a single-rate controller which uniformly reduces the computational cost via interlacing technique, and (2) redesign of a controller by identifying its negligible dynamics based on the identified bounds in the controllers' dynamic response. The results of both approaches are demonstrated on two active magnetic bearing (AMB) systems, a model of a 300 kW turbine generator with permanent magnet biased AMBs, and an experimental high-speed AMB machining spindle. μ-synthesis controllers are designed for both systems, and the proposed method and schemes are applied accordingly. The comparison of standard implementations of the synthesized controllers and the proposed new implementations is presented. The results demonstrate considerable reduction in the computational cost in terms of required number of multiply accumulate (MAC) operations.

Uncertainties Investigation and µ-Synthesis Control Design for a Full Car with Series Active Variable Geometry Suspension

Linear robust control schemes, for example the H∞ control, are commonly utilized in the control design of an active suspension system, with a linearized and time-invariant state-space model of the system adopted. However, the vehicle parameter uncertainties are mainly ignored and their effect on the control robustness is not investigated. In this paper, a µ-synthesis-based control scheme is synthesized for a full car with the recently introduced Series Active Variable Geometry Suspension (SAVGS), to mainly enhance the ride comfort and road holding performance, with two significant practical uncertainties in the sprung mass and the suspension damping taken into account. Numerical simulations with a high fidelity nonlinear vehicle model are performed, with the cases of the fixed and swept values of the sprung mass tested, to assess the control robustness and performance of the developed scheme against the passive suspension as well as the H∞ -controlled SAVGS. The proposed µ-synthesis control scheme is proved to be more effective for realistic applications as it is capable of maintaining the suspension performance improvement regardless of variations of system parameters associated with the uncertainties, while the H∞ control performance tends to deteriorate when a notable deviation from the nominal values occurs.

On robustness of an AMB suspended energy storage flywheel platform under characteristic model based all-coefficient adaptive control laws

A characteristic model based all-coefficient adaptive control law was recently implemented on an experimental test rig for high-speed energy storage flywheels suspended on magnetic bearings. Such a control law is an intelligent control law, as its design does not rely on a pre-established mathematical model of a plant but identifies its characteristic model while the plant is being controlled. Extensive numerical simulations and experimental results indicated that this intelligent control law outperforms a μ-synthesis control law, originally designed when the experimental platform was built in terms of their ability to suppress vibration on the high-speed test rig. We further establish, through an extensive simulation, that this intelligent control law possesses considerable robustness with respect to plant uncertainties, external disturbances, and time delay.

Robust [formula omitted] control of miniaturized optical image stabilizers against product variabilities

This paper presents uncertainty modeling and robust controller design for 3 degrees-of-freedom miniaturized optical image stabilizers (OISs) against product variabilities. To develop a mathematical model of OISs with product variations, both model and uncertainty structures are determined by finite element analysis. The model parameters are identified based on experimental frequency responses. A robust H∞ controller design method is applied to the model, in order to guarantee robust stability of the closed-loop system and optimize OIS performance against the hand-induced vibrations of the OIS body. The proposed modeling and controller design method is experimentally validated with large-scale OIS prototypes. The experimental results demonstrate that the robust H∞ controller outperforms conventional and μ-synthesis controllers.