LFT models of continuous biotechnological processes

A linear fractional transformation (LFT) model of the linearized equation of the lateral-directional axes of the X-38 crew return vehicle is developed to facilitate the analysis of e ight control systems. The LFT model represents uncertainty in nine aerodynamic stability derivatives at a given e ight condition with frequency-domain performance specie cations. The X-38 LFT model combined with a controller at specie c e ight conditions is used to determine the aerodynamic coefe cients that result in the worst-case performance and gain/phase margin of the closed-loop system. The objective is to verify that a given controller remains stable and achieves desired performance objectives for all predee ned aerodynamic variations at select operating conditions along its e ight trajectory.

On computational complexity of invalidating structured uncertainty models

Software engineers have to cope with uncertainties and changing requirements. Agile methods provide flexibility towards changes and the emergence of continuous delivery has made regular feedback loops possible. The abilities to maintain high code quality through reviews, to regularly release software, and to collect and prioritize user feedback, are necessary for continuous software engineering (CSE). However, there exists no software process metamodel that handles the continuous character of software engineering. In this paper, we describe an empirical process metamodel for continuous software engineering called CSEPM, which treats development activities as parallel running workflows and allows tailoring and customization. CSEPM includes static aspects that describe the relations between specific CSE concepts including reviews, releases, and feedback. It also describes the dynamic aspect of CSE, how development workflows are activated through change events. We show how CSEPM allows to instantiate linear, iterative, agile and continuous process models and how it enables tailoring and customization.

This paper proposes a new Linear Fractional Transformation (LFT) modeling approach for uncertain Linear Parameter Varying (LPV) multibody systems with parameter-dependent equilibrium. Traditional multibody approaches, which consist in building the nonlinear model of the whole structure and linearizing it around equilibrium after a numerical trimming, do not allow to isolate parametric variations with the LFT form. Although additional techniques, such as polynomial fitting or symbolic linearization, can provide an LFT model, they may be time-consuming or miss worst-case configurations. The proposed approach relies on the trimming and linearization of the equations at the substructure level, before assembly of the multibody structure, which allows to only perform operations that preserve the LFT form throughout the linearization process. Since the physical origin of the parameters is retained, the linearized LFT-LPV model of the structure exactly covers all plants, in a single parametric model, without introducing conservatism or fitting errors. An application to the LFT-LPV modeling of a robotic arm is proposed; in its nominal configuration, the model obtained with the proposed approach matches the model provided by the software Simscape Multibody, but it is enhanced with parametric variations with the LFT form; a robust LPV synthesis is performed using Matlab robust control toolbox to illustrate the capacity of the proposed approach for control design.

In this paper, the development of a software tool for linear parameter varying (LPV)/linear fractional transformation (LFT) modeling and data-based validation techniques is described. This tool represents a step towards industrialization of these techniques, which although still suffering from a certain theoretical complexity are increasingly shown to help deal effectively with important real world applications. The tool is a key component for the development of an integrated LPV/LFT framework for control modeling, analysis, and design which is also a necessity for successful transfer of LPV/LFT techniques to industry. The focus of this paper is on describing the development of the integrated modeling/validation software and examining the applicability problems associated with these techniques. The technical readiness of the tool is exemplified through the development of validated LFT models used for LPV control design and analysis of a nonlinear longitudinal model of the NASA HL-20 re-entry vehicle.

This work compares Several analytical approaches are compared for in-flight flutter margin calculations for an F-16A/B in heavy store configuration. Nominal flutter model formulations are developed in terms of the dynamic pressure and the Macb number. These analysis models are expressed within the linear fractional transformation (LFT) framework for the determination of flutter onset conditions using the structured singular value μ analysis. The results obtained from classical analysis tools such as the P and P-K method, as well as the μ method are compared with each other and validated using actual flight-test data. The LFT model parameterization in terms of match-point Mach number is novel and permits a natural and efficient flight-test procedure for flutter envelope clearance. Structural parameter variations such as changes in wing mass, as well uncertainties in damping and/or stiffness, are also incorporated in the LFT formulation and permit the calculation of robust match-point flutter margins. The μ-analysis results obtained from such model formulations incorporating several simultaneous parameter variations reveal and explain the complex physical mechanisms that have led to limit-cycle oscillation conditions encountered during the flight tests.

This paper deals with uncertain model structures, model validation and robust performance analysis of active magnetic bearings. The dynamics of active magnetic bearing systems are characterized by their instability and complex dynamics of rotor and electromagnets. The feedback control is indispensable to stabilize the system, further the closed-loop systems of magnetic bearings should have robustness for stability and performance against model uncertainties. First we derive a nominal mathematical model of AMBs as a linear state-space model under some assumption and idealization, then we consider the discrepancy between the real physical systems and the obtained nominal design model. This discrepancy can be expressed as the structured uncertainties by Linear Fractional Transformation. These uncertainties include linearization error, parametric uncertainties, unmodeled dynamics, and gyroscopic effect. Then we set the interconnection structure which contains the above structurally represented uncertainties. Next we design a robust controller which achieves robust performance condition. Finally, we validate the interconnection structure with the nominal model and uncertainties, and analyze the robustness of stability and performance of the closed-loop system via the mixed structured singular value.

This paper considers an application of the structured singular value, μ, to the robust performance of active filter circuits that are subject to real parameter component uncertainty. The focus is on the different linear fractional transformations that are required for the calculation of safe upper bounds on filter performance without using conventional Monte-Carlo based frequency gridding techniques. State-space μ results are applied so that worst case maximum and minimum filter gain are separately determined using a non-probabilistic test on a static matrix. The methodology is illustrated by a typical analysis on an active Butterworth low pass filter of order 4.

Centralized wide area control design using system-wide data has been suggested to enhance large interconnected power system dynamic performance. Because of the nature of wide area interconnections, communication delay cannot be ignored in wide area control. A long time delay may be a detriment to system stability and degrade system robustness. The general linear fractional transformation (LFT) method to describe the time delay uncertainty can lead to a conservative design. In this paper, a gain scheduling (GS) method based on linear matrix inequality (LMI) is proposed to design a dynamic controller to accommodate time delays in supervisory power system stabilizer (PSS) design. The new approach achieves better performance than the general LFT method, and the order of the controller remains the same with that of the system plant.

The output voltage of a dual LCL inductive power transfer (IPT) system varies with the load and mutual inductance, which can affect the system performance, e.g., the charging speed of electrical equipment. This paper proposes a robust controller to maintain constant output voltage against the load and mutual inductance variations. A μ-synthesis method is proposed based on structured singular value to design the dual LCL IPT closed-loop system. The frequency-domain nominal model of the system is established by using the generalized state-space averaging (GSSA) method. A standard M-Δ configuration is generalized through separating the nominal and uncertain block by upper linear fractional transformation (LFT). The μ-controller is finally obtained by D-K iteration. The robust performance analysis and time-domain performance analysis are also carried out. The simulation and experimental results verified the effectiveness of the proposed modeling and controller design, and demonstrated the robust stability and robust performance of the dual LCL IPT system.

This paper presents a transformation-based robust nonlinear control design framework based on the concepts of incremental nonlinear dynamic inversion (INDI) and quasi-linear parameter-varying (q-LPV) control. The duality between these popular control design paradigms is investigated. Control-oriented q-LPV model representations of INDI and nonlinear dynamic inversion (NDI)-based closed-loop systems are presented for various inversion strategies, which creates a basis for robust synthesis and analysis of INDI and NDI-based designs in the LPV sense. This includes extensions to singular perturbations that limit exact inversion in reality. The presented approach is demonstrated in a design case study for a nonlinear aeroservoelastic system, where INDI-based controllers are synthesized and quantitatively compared with direct q-LPV control based on linear fractional transformations.

This paper presents a H∞ loop-shaping controller for controlling dc-link voltage by regulating the switching signal of the inverter associated with a grid-connected single-phase photovoltaic system. To facilitate a robust control design, state-space realisation of the system model is made with uncertainties represented by linear fractional transformation. The controller is achieved through H∞ synthesis followed by obtaining desired loop shapes through the choice of the proper weighting functions. The controller order is reduced by Henkel-norm method for facilitating its practical implementation. Controller performance is evaluated through carrying out simulations on MATLAB/Simulink platform under standard and changing atmospheric conditions, and fault condition.

The controlled atmospheric re-entry associated with the precision soft-landing of Reusable Launch Vehicles (RLVs) on Earth is very challenging as it depends on multiple parameters [1]. Over the last decade, the cost-effectiveness of such a technology has been finally demonstrated with the successful recoveries of SpaceX’s Falcon 9 first-stage rocket first [2], then followed by other companies such as the Rocket Lab’s Electron micro-launcher [3]. This breakthrough has been made possible by the development of advanced and robust computational methods able to generate in real time the flight conditions and to command the optimal vehicle's deflections accordingly to achieve a safe pinpoint landing. Indeed, during an Earth atmospheric re-entry, the vehicle is subjected to fast system dynamics changes partly induced by external loads associated with the terrestrial environment (e.g., lift, drag, wind and gusts), but also by the actuation commands to answer the landing constraints satisfaction and the vehicle integrity preservation. All those involve uncertainties and nonlinearities, which lead to vehicle’s instability and therefore give reason why for a highly performant Guidance, Navigation and Control system implementation [4]. More particularly, one of the critical aspects is the design of a robust control strategy capable of counteracting the previously defined disturbances and uncertainties while satisfying the strict accuracy requirements associated with the pinpoint landing [5]. As demonstrated by the current state-of-the-art on control design for launchers [6-7], the classical linear control theory represents a rich heritage with a lot of applications. This choice was motivated by its relative easiness of implementation and the possibility to use gain-scheduling techniques to adapt to nonlinear systems. Nevertheless, these techniques are well-adapted to the control system design of single-input single-output systems, such as for example a reusable rocket using a Thrust Vector Control (TVC) system as the unique actuator. The implementation of multiple-input multiple-output control systems becomes then complex since every channel is addressed in a single-loop fashion. This capability is however required for the future generation of reusable rocket, using also aerodynamic steering based on fins in addition to the TVC system for enhancing control authorities. Moreover, model uncertainties are not accurately considered in the design process, developed only with nominal conditions and stability margin requirements. For all these reasons, it results in an extensive (both in terms of time and cost) Verification and Validation campaign with many iterations and Monte-Carlo analyses to assess the performance and robustness of the control system. To overcome these drawbacks, the H-infinity family of methods, introduced a few years ago [8], provides with a powerful solution for robust control design. It relies on defining the control requirements in the frequency domain in terms of weighting functions and minimising the maximum gain of the resulting weighted system from the exogenous inputs to the outputs to be controlled. Moreover, the control-plant interaction is modelled through a Linear Fractional Transformation (LFT) representing the feedback action. Finally, the structured H-infinity method [9] allows to directly impose a specific control structure – like a Proportional-Integral-Derivative (PID), enabling the re-use of gain-scheduling techniques – and to consider parametric uncertainties for enhanced robustness. This paper studies the synthesis of a robust control system via structured H-infinity for the RLV atmospheric re-entry problem. First, the nonlinear 6-Degree-of-Freedom (6-DoF) RLV re-entry dynamics are simplified into a linear model and then linearised along a reference trajectory to get the nominal LFT of the system, then augmented with parametric uncertainties. The model covers the atmospheric re-entry and vertical landing of a first-stage rocket equipped with a TVC system and steerable planar fins. The controllers are built at different points of the re-entry trajectory, using the structured H-infinity framework through PID-like structures. Weighting functions considering the control objectives and requirements of a realistic RLV re-entry scenario are implemented. A robust stability analysis of the obtained system is performed via classical stability margins and structured singular value. Finally, the controllers are gain-scheduled and validated via Monte-Carlo analyses, using a nonlinear 6-DoF RLV re-entry dynamics simulator equipped with successive convex optimisation guidance. The performance of the resulting guidance and control architecture is compared with the baseline developed in previous works [10], using a TVC system only and classical linear feedback control through gain-scheduled PID controllers. This study lies within the ASCenSIon (Advancing Space Access Capabilities - Reusability and Multiple Satellite Injection) project, an innovative training network funded within H2020.

In this paper, instructional material on the design of robust controllers that applies to introductory graduate or advanced undergraduate courses on control is provided. The main objective is the presentation of key concepts and interpretations that help students learn robust control design. The use of recently developed techniques in robust control such as H/sub /spl infin//, /spl mu/ analysis, and synthesis is explored. Emphasis is given to the modeling of the robust control problem with the system requirements described in a unified approach using weighting functions and linear fractional transformations (LFTs). Also, the results of a conventional lead-lag are included to reinforce the concept of robustness. The students should understand the basics of robust control using the MATLAB/Simulink platform and a hardware-in-the-loop experiment with a magnetic levitation system, which is considered a good plant for analysis and control design since it is a nonlinear unstable plant with practical use in high-speed transportation and magnetic bearings. The hardware-in-the-loop experiments are suitable for assessment during the final two semesters of engineering courses and are useful to further develop the students' skills in control engineering. The control algorithms are evaluated in the LabVIEW environment, which introduces the students to industrial platforms.

Due to the universal approximation capability of Takagi–Sugeno (T–S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T–S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T–S fuzzy models and LPV models provides a new perspective of the control problems for T–S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gain-scheduling control design approach for T–S fuzzy systems is presented to ensure globally asymptotical stability and optimize H∞ performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.