Multi-objective Robust Control Research Articles

Multiple classical noise mitigation by multiobjective robust quantum optimal control

Multiple classical noise mitigation by multiobjective robust quantum optimal control

Parameter uncertainty modeling for multiobjective robust control design. Application to a temperature control system in a proton exchange membrane fuel cell

Advanced control systems are tuned using dynamic models and optimization techniques. This approach frequently involves satisfying multiple conflicting objectives. Tuning robust controllers requires considering a framework that represents the system uncertainties, and its definition is not a trivial task. When dealing with a nonlinear model with many parameters, a high-quality representation requires a massive sampling of variations. In many cases, this represents an inaccessible computational cost for the optimization process.This work presents a new methodology for parameter uncertainty modeling that is oriented to tuning robust controllers based on multiobjective optimization techniques. The uncertainty modeling formulated represents a feasible computational cost and leads to robust solutions without attributing excessive conservatism. The novelty of this process consists in using the multiobjective space to define a set of scenarios with highly representative properties of the global uncertainty framework that formulate the control problem under a predefined minimization strategy.To demonstrate the effectiveness of this methodology, we present a temperature control design in a micro-CHP system under worst-case minimization. Based on the results, particular interest is given to verifying the appropriate formulation of the uncertainty modeling, which represents a 92.8% reduction of the computational cost involved in solving the robust optimization problem under a global uncertainty framework.

A multi-model multi-objective robust damping control of GCSC for hybrid power system with offshore/onshore wind farm

In the recent decade, the power network has experienced a remarkable energy transition due to the large-scale integration of wind energy resources, especially converter-interfaced modern wind turbines. The increasing/decreasing wind penetration, on the other hand, unexpectedly affects the low frequency oscillations of the modern power grid. In this context, the proposed work adopts a multi-model multi-objective robust control framework to design a supplementary damping controller for the gate-controlled series capacitor (GCSC) to stabilize the hybrid power system with a permanent magnet synchronous generator (PMSG)-based off-shore wind farm (OSWF) and a doubly-fed induction generator (DFIG)-based onshore wind farm (ONWF). A bilinear matrix inequality (BMI) optimization problem, formulated as multi-objective synthesis considering H2/H∞ performance along with pre-defined pole placement, is presented for the GCSC control design, which is solved by a two-step linear matrix inequality (LMI) approach. In addition, all LMI constraints are constructed based on the multi-model control framework to incorporate multiple operating conditions. Afterward, the significant improvement in the damping characteristics of the closed-loop system, covering a wide operating range, is confirmed using eigenvalue analysis. The effectiveness of the scheme is validated using two case studies based on the hybrid power system, subject to various disturbances and uncertainties. The simulation results show the robustness and higher damping performance of the proposed multi-model strategy, compared to a conventional and a robust damping controller, for mitigating power system oscillations alongside voltage fluctuations of the wind farms.

D-decomposition-based multi-objective robust resilient control for blade pitch of wind energy conversion system

The uncertainties due to the load variations and wind speed fluctuations represent the biggest challenges to the stabilization of the wind energy conversion systems (WECS). In this regard, this paper develops a new resilient control approach for blade pitch of WECS as well as a low computational burden to tackle the uncertainty issue instead of the metaheuristics techniques. The proposed approach is formulated via a graphical D-decomposition strategy to identify the optimal region on the stability profile of the WECS that achieves the desired damping performance as well as minimum oscillation, settling time, and overshoot. Furthermore, the proposed approach takes into account a set of segment plants to achieve the robust performance and resiliency objectives simultaneously for the controller gains. The proposed approach is designed mathematically without hypothesis or probability as well as simple structure compared with metaheuristics techniques. Various performance indices are taken into account to assert the proposed approach accomplishment. Besides, the performance of the WECS based on the designed controller via D-decomposition is compared with different techniques in the literature. The results confirm that the proposed approach demonstrates better damping performance including less overshoot around 2.2329% and settling time around 9.2626 s than metaheuristics techniques. Furthermore, the robustness and resiliency of the designed controller are emphasized in the case of different test aspects including load variations and wind speed fluctuations compared with other techniques.

Robust multiobjective control of singularly perturbed systems using linear matrix inequality

International Journal of Adaptive Control and Signal ProcessingVolume 36, Issue 9 p. 2341-2341 ERRATUMFree Access Robust multiobjective control of singularly perturbed systems using linear matrix inequality This article corrects the following: Robust multiobjective control of singularly perturbed systems using linear matrix inequality Xigen Wang, Volume 36Issue 7International Journal of Adaptive Control and Signal Processing pages: 1746-1758 First Published online: May 30, 2022 First published: 28 July 2022 https://doi.org/10.1002/acs.3474AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Subsequent to publication, an error was identified in the ‘Correspondence’ section of Wang.1 The section has been corrected below. Correspondence Xigen Wang, College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201,620, China. Email: 15221619759@139.com The Publisher apologizes for this error. REFERENCE 1Wang X. Robust multiobjective control of singularly perturbed systems using linear matrix inequality. Int J Adapt Control Signal Process. 2022; 36(7): 1746- 1758. Wiley Online LibraryWeb of Science®Google Scholar Volume36, Issue9September 2022Pages 2341-2341 ReferencesRelatedInformation

Robust multiobjective control of singularly perturbed systems using linear matrix inequality

SUMMARYThe article investigates the issue of designing H∞ output feedback controller for a fuzzy nonlinear singularly perturbed systems (SPSs). From overall perspective, we design a series of linear matrix inequalities conditions, which provides the optional stability bounds Ɛ0, verifies the existence of Ɛ0 and ensures that the T–S fuzzy SPSs are asymptotic stable for all Ɛ ∈ (0, Ɛ0]. According to the characteristics of SPSs, we design the asymmetric auxiliary matrix P(Ɛ), which reduces the conservatism and expands the application scope of Ɛ in contrast to the previous results. The approach gives the Ɛ‐dependent Lyapunov function and deduces the fuzzy Ɛ‐dependent robust controller. It is not only can be applied to the standard or nonstandard nonlinear systems but also eliminates the ill‐conditioned problems. Finally, a numerical example testifies the feasibility of conclusion.

Quadratic Stabilization of Takagi-Sugeno Fuzzy Discrete-time Uncertain Networked Systems

For one class of Takagi-Sugeno uncertain time-delay discrete-time systems this paper proposes an extended way to account related constraints in problem solving of the networked control system quadratic stability reflecting sensor drifts and communication delays. The new design conditions are proposed, exploiting a set of linear matrix inequalities to guaranty the closed-loop system quadratic stability where a specific Lyapunov-Krasovskii functional is exploited. Combining into the functional the disturbance transfer function H∞ norm upper bound, the design task is defined as a multi-objective robust control problem, while only the set of time-invariant control law gains are used in the fuzzy parallel structure of the controller realization. A numerical example is included to assess the feasibility of the technique and its applicability.

Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance

This paper proposes a novel scheme of the multi-objective robust control design for a class of uncertain nonlinear systems in strict-feedback-form based on Takagi–Sugeno fuzzy model (TSFM). The nonlinear system contains both the matched and the unmatched uncertainties and also subjected to the external disturbances. The TSFM provides the generalization of the linear systems concepts to the nonlinear systems field in a convex framework. First, a new sliding surface is defined using a convex combination of the surfaces which are defined for each fuzzy rule consequence local linear subsystems. Then, their gains are designed optimally via a generalized eigenvalue problem (GEVP). Also, the upper-bounds of the matched and unmatched uncertainties are estimated using the adaptive update laws. The multi-objective control aims not only to satisfy the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization performance, but also, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability region is formulated to improve the transient response performance. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization characterization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability design conditions are derived in terms of new linear matrix inequalities (LMIs) conditions. Finally, the effectiveness of the proposed approach is demonstrated by considering a comparative practical example.

Multi-objective robust generalised H 2 control

A novel multi-objective robust control problem is studied for systems with norm-bounded structured uncertainty and robust generalised norms as criteria. Necessary conditions for Pareto optimality are formulated from which it follows that Pareto optimal solutions are to be among optimal solutions for scalar multi-objective costs in the form of Germeyer convolution. The upper bounds of the multi-objective costs are used to compute Pareto suboptimal controllers in terms of linear matrix inequalities, while the lower bounds to estimate a ‘difference’ between Pareto suboptimal and unavailable Pareto optimal controllers. Two-criteria robust control problem for a mathematical model of the rotor rotating in active magnetic bearings is considered as an application of this theory.

Multi-Objective Robust Control for Vehicle Active Suspension Systems via Parameterized Controller

A parameterized controller design approach is proposed to solve the problem of multi-objective control for vehicle active suspension systems by using symbolic computation. The considered model is a quarter-vehicle model of the active suspension system. The multi-objective robust control performances include the sprung mass acceleration, suspension deflection, and tire deflection. Based on dissipative Hamiltonian systems and Lyapunov function, a multi-objective $H_{\infty }$ controller design approach is developed, which can avoid solving Hamilton-Jacobi-Issacs equations. Then, an algorithm of solving semi-positive definite polynomial with tuning parameters is proposed by using symbolic computation. Furthermore, a method of parameter optimization is proposed. Simulations and comparation show that the control performance is significantly improved comparing with passive controlled systems and existing other control systems for active suspension systems.

Robust Controller Synthesis for Airborne Electro-Optical Device Line-of-Sight Stabilization System with Saturating Actuators

A technique of multiobjective robust controller synthesis for an electro-optical device line-of-sight stabilization system with saturating actuators is developed on the basis of polytopic linear parameter-varying system theory. From the computational point of view, the synthesis procedure is reduced to convex optimization under constraints expressed in the form of linear matrix inequalities. The multiobjective synthesis of the robust control law for the stabilization system being considered is performed.

Active vibration control of a blade element with uncertainty modeling in PZT actuator force

The aim of this research is to attenuate the vibrations of a blade structure with an attached piezoelectric actuator using robust multi-objective control. The force obtained from a piezoelectric patch loading has uncertainties due to the complicated shape (airfoil) of the blade element. A parameter-dependent model of the force equation is developed to understand the possible variation range of the actuation force. The modal analysis of the blade is performed to find vibration mode frequencies, and an aerodynamic load is generated experimentally to create steady-state vibration on the blade. A state-space model is obtained by considering certain vibration modes and the parameter-dependent part of the force in the input vector is taken outside of the plant model. The robust stability filter is modified with parameter dependency to have a cluster of the filter. Two different multi-objective controllers are designed with different design objectives. The designed controllers are implemented in experiments and performances of the controllers are compared using frequency and time domain responses. It is shown that the flexible blade vibrations are successfully suppressed with the proposed mixed norm robust controllers under the effect of steady-state aerodynamic disturbance with different air speeds. It is observed in experimental results that the performances of the controller are better than the controller.

Robust multi-objective blood glucose control in Type-1 diabetic patient.

In this study, an automatic robust multi‐objective controller has been proposed for blood glucose (BG) regulation in Type‐1 Diabetic Mellitus (T1DM) patient through subcutaneous route. The main objective of this work is to control the BG level in T1DM patient in the presence of unannounced meal disturbances and other external noises with a minimum amount of insulin infusion rate. The multi‐objective output‐feedback controller with H∞, H2 and pole‐placement constraints has been designed using linear matrix inequality technique. The designed controller for subcutaneous insulin delivery was tested on in silico adult and adolescent subjects of UVa/Padova T1DM metabolic simulator. The experimental results show that the closed‐loop system tracks the reference BG level very well and does not show any hypoglycaemia effect even during the long gap of a meal at night both for in silico adults and adolescent. In the presence of 50 gm meal disturbance, average adult experience normoglycaemia 92% of the total simulation time and hypoglycaemia 0% of total simulation time. The robustness of the controller has been tested in the presence of irregular meals and insulin pump noise and error. The controller yielded robust performance with a lesser amount of insulin infusion rate than the other designed controllers reported earlier.

A New Active Control Strategy for Pantograph in High-Speed Electrified Railways Based on Multi-Objective Robust Control

In high-speed railways, the quality of current collection of high-speed train is directly determined by the contact force between the contact wire of the catenary and the registration strip of the pantograph. In order to ensure a stable contact force, this paper proposes a control strategy for active pantographs by minimizing the acceleration of pantograph collector. The model of pantograph-catenary interaction is established based on the finite element approach and the multibody dynamics. A Kalman filter is designed to obtain the states of the pantograph considering complex electromagnetic circumstances and severe physical environments. According to the equation of motion for the pantograph-catenary system, the implicit expression of pantograph-catenary contact forces is derived. The factors causing the fluctuation of the contact force are analyzed to determine the three control targets, which are minimize the acceleration of pantograph collector, limit the control force and displacement constraint. At last, a multi-objective robust control method based on state estimation is designed. The robustness and effectiveness of the control method are verified on a nonlinear pantograph-catenary system model under different work conditions. The results show that the error between the estimated value and the true value of the pantograph is between 0.06% and 3.46%. The standard deviation of contact force is reduced by 29.55%, 25.26%, and 20.86% under different operational speeds, respectively. The standard deviation of the contact force was still reduced considering the parameter perturbation of pantograph and the unevenness of contact lines. The result of proposed control strategy is better than previous work, even though the proposed controller requires a lower energy consumption. In addition, With the proper pre-treatment of the active control force, the movement number of the actuator is reduced and the control performance is still fine.

Multiobjective Robust Controller Synthesis for Nonlinear Mechanical System

In the paper multiobjective robust controller synthesis problem for nonlinear mechanical system described by Lagrange’s equations of the second kind is considered. Such tasks have numerous practical applications, for example in controller design of robotic systems and gyro-stabilized platforms. In practice, we often have to use uncertain mathematical plant models in controller design. Therefore, ensuring robustness in presence of parameters perturbations and unknown external disturbances is an important requirement for designed systems. Much of modern robust control theory is linear. When the actual system exhibits nonlinear behavior, nonlinearities are usually included in the uncertainty set of the plant. A disadvantage of this approach is that resulting controllers may be too conservative especially when nonlinearities are significant. The nonlinear H∞ optimal control theory developed on the basis of differential game theory is a natural extension of the linear robust control theory. Nonlinear theory methods ensure robust stability of designed control systems. However, to determine nonlinear H∞-control law, the partial differential equation have to be solved which is a rather complicated task. In addition, it is difficult to ensure robust performance of controlled processes when using this method. In this paper, methods of linear parameter-varying (LPV) systems are used to synthesize robust control law. It is shown, that Lagrange system may be adequately represented in the form of quasi-LPV model. From the computational point of view, the synthesis procedure is reduced to convex optimization techniques under constraints expressed in the form of linear matrix inequalities (LMIs). Measured parameters are incorporated in the control law, thus ensuring continuous adjustment of the controller parameters to the current plant dynamics and better performance of control processes in comparison with H∞-regulators. Furthermore, the use of the LMIs allows to take into account the transient performance requirements in the controller synthesis. Since the quasi-LPV system depends continuously on the parameter vector, the LMI system is infinite-dimensional. This infinitedimensional system is reduced to a finite set of LMIs by introducing a polytopic LPV representation. The example of multiobjective robust control synthesis for electro-optical device’s line of sight pointing and stabilization system suspended in two-axes inertially stabilized platform is given.

Multiobjective Robust Controller Synthesis for Airborne Electro-Optical Device Line-of-Sight Stabilization System

A technique of multiobjective robust controller synthesis for airborne electro-optical device line-of-sight stabilization system is developed. The multiobjective synthesis of the robust control law for the stabilization system being considered is performed.

Robust multi-objective control design for underground coal gasification energy conversion process

ABSTRACTThe efficiency of an underground coal gasification (UCG) energy conversion process can be increased by maintaining a desired heating value of the product gases. In literature this task has been accomplished by adopting nonlinear model-based control strategies. To exploit the flexibility of the linear control design techniques, a linear model of the UCG process has been developed, which retains the dynamics of the nonlinear model around the operating point of interest. To account for external disturbance and modelling inaccuracies, an output-based robust multi-objective H2/H∞ control law integrated with pole placement has been proposed. The problem is solved by formulating linear matrix inequality (LMI) constraints for performance and robustness. The simulation results show that the designed controller gives adequate performance in the presence of modelling inaccuracies and external disturbance. Moreover, it has been shown that performance of the designed controller is better as compared to the standard PI controller.

LMI based robust control design for multi-input–single-output DC/DC converter

Utilizing linear matrix inequalities (LMI) framework, in this paper a robust control model for multi-input–output DC/DC converter is presented based on its analytical study. This converter is composed of two conventional converters, buck-boost and boost, which can supply the load when one of the inputs fails to do so. Employing the LMI method makes it possible to modelize the nonlinearities and uncertainties as a convex polytope. So, by considering LMI constraints, a certain rejection level of noise and an area for pole location are guaranteed robustly. Utilizing this method along with standard optimization algorithms can set the multi objective robust controller automatically. The simulation results are derived by MATLAB for a low efficiency implementable state-feedback and are compared with a conventional PID controller.

Investigating Achievable Performances for Robust Broadband Active Noise Control in an Enclosure

This brief presents a complete methodology for evaluating achievable performances in applications of active noise control aiming robust broadband attenuation. A comparison between different control architectures, the influence of the number of available actuators and sensors on attainable performances, and the impact of considering the perturbation as measured or not are all discussed. First, a generic experimental device, specifically designed to study active noise attenuation, is identified as a multi-input multi-output system. Then, robust multiobjective control is considered, using a $\mathcal {H}_{\infty }$ criterion, and recasts as $\mathcal {H}_{\infty }$ optimization under constraints. Appropriate indicators are proposed for comparison purposes. Finally, quantified results are presented and validated experimentally. Intrinsic limitations introduced by nonminimum phase zeros are illustrated and discussed.

Robust multiobjective control method for power sharing among distributed energy resources in islanded microgrids with unbalanced and nonlinear loads

This paper proposes a robust control method for power sharing among dispatchable electronically-coupled distributed energy resources (DERs) in an autonomous microgrid. The DER units operate in parallel to meet the total aggregated load demand. The aggregated load is assumed to be uncertain, unbalanced and/or nonlinear, thus it is considered as a source of unmodeled dynamics. The main objective of this paper is to design an H∞ robust controller to enable tracking reference commands of the voltages at the output of the DERs in the presence of unmodeled dynamics. In addition, the H∞ control design problem is combined with other control methods, such as constrained optimal control and regional pole placement, to achieve an optimal control objective, and to improve transient response. The optimal controller is achieved by minimizing an upper bound on H2 performance. The regional pole placement is achieved by defining a linear matrix inequalities (LMI) region. This multiobjective H2/H∞ problem, combined with regional pole placement are expressed as a set of LMIs, and solved by using standard convex optimization algorithms. To show the effectiveness of the proposed method in maintaining the desired voltage at the DER outputs, in presence of unbalanced and nonlinear loads, simulation results are provided for a single DER unit, and the performance of the proposed control strategy is compared with three different controller strategies. Power sharing among multi DER units in autonomous networks is then demonstrated through digital time-domain simulation studies using MATLAB/SimPowerSystems Toolbox.