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Passivity-based Robust Control of Aerospace Systems

This report provides a brief summary of the research work performed over the duration of the cooperative research agreement between NASA Langley Research Center and Kansas State University. The cooperative agreement which was originally for the duration the three years was extended by another year through no-cost extension in order to accomplish the goals of the project. The main objective of the research was to develop passivity-based robust control methodology for passive and non-passive aerospace systems. The focus of the first-year's research was limited to the investigation of passivity-based methods for the robust control of Linear Time-Invariant (LTI) single-input single-output (SISO), open-loop stable, minimum-phase non-passive systems. The second year's focus was mainly on extending the passivity-based methodology to a larger class of non-passive LTI systems which includes unstable and nonminimum phase SISO systems. For LTI non-passive systems, five different passification. methods were developed. The primary effort during the years three and four was on the development of passification methodology for MIMO systems, development of methods for checking robustness of passification, and developing synthesis techniques for passifying compensators. For passive LTI systems optimal synthesis procedure was also developed for the design of constant-gain positive real controllers. For nonlinear passive systems, numerical optimization-based technique was developed for the synthesis of constant as well as time-varying gain positive-real controllers. The passivity-based control design methodology developed during the duration of this project was demonstrated by its application to various benchmark examples. These example systems included longitudinal model of an F-18 High Alpha Research Vehicle (HARV) for pitch axis control, NASA's supersonic transport wind tunnel model, ACC benchmark model, 1-D acoustic duct model, piezo-actuated flexible link model, and NASA's Benchmark Active Controls Technology (BACT) Wing model. Some of the stability results for linear passive systems were also extended to nonlinear passive systems. Several publications and conference presentations resulted from this research.

Kelkar, Atul G.↗

Hybrid Hydraulic-Electric Architecture (HHEA) for Mobile Machines (Final Report)

Traditionally, off-road mobile machines such as excavators and wheel loaders are primarily powered by hydraulics, and throttling valves are used to control their work circuits. In recent years, two general trends are towards more energy efficient systems and electrification. With electrification, both efficiency and control performance can be improved by the elimination of throttling losses and the use of high-bandwidth inverter control. Electrification is generally accomplished with Electro-hydraulic actuators (EHA) but they are limited to lower powered systems due to the high cost of electric machines capable of high power or high torque. This project proposes a new system architecture for off-road vehicles - Hybrid Hydraulic Electric Architecture (HHEA) to improve efficiency and control performance without requiring large electric machines. The widely applicable architecture combines hydraulic power and electric power in such a way that the majority of power is provided hydraulically while electric drives are used to modulate this power. In particular, HHEA utilizes multiple common pressure rails to transmit the majority of power and small electric machines to modulate the power. The energy-saving potential of the the HHEA has been validated for the work circuits of a variety of mobile machines, from small 5-ton excavators to medium sized 20-ton excavators and wheel loaders, and representative duty cycles to reduce energy input by 50-80% compared to the commercial state-of-art load-sensing systems. In addition, the corner power requirements of the electrical machines can be downsized by 85% compared to the EHA approach. Various tradeoff studies have also been conducted, including sensitivities to individual components performances, controllers, accumulator sizes, and variations of the system architecture etc. A control strategy has been developed to maintain or exceed the motion control precision compared to current systems. The motion control strategy consists of a nominal controller, based on a passivity-based backstepping design, and a transition controller, based on least-norn feedforward design. The nominal controller is used in between common pressure rail switches whereas the transition controller compensates for any disturbance that common pressure rail switchings inflict on the system. The control strategy has been experimentally validated on both a medium pressure (200bar) hardware-in-the-loop (HIL) testbed and a high pressure (300+bar) HIL testbed. An efficient and power-dense integrated electric-hydraulic machine consisting of an axial flux electric machine and a radial hydrostatic piston hydraulic machine has been designed, constructed and tested. The machine has an active material power density of 6.1kW/kg, a rated speed of 12500 RPM, and a design efficiency of 85%. This is among the highest power density electric machines using conventional materials. While the integrated machine was designed for modulating the hydraulic power within the HHEA, it can also be used in other applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Synthesis of Optimal Constant-Gain Positive-Real Controllers for Passive Systems

This paper presents synthesis methods for the design of constant-gain positive real controllers for passive systems. The results presented in this paper, in conjunction with the previous work by the authors on passification of non-passive systems, offer a useful synthesis tool for the design of passivity-based robust controllers for non-passive systems as well. Two synthesis approaches are given for minimizing an LQ-type performance index, resulting in optimal controller gains. Two separate algorithms, one for each of these approaches, are given. The synthesis techniques are demonstrated using two numerical examples: control of a flexible structure and longitudinal control of a fighter aircraft.

Mao, Y.↗

Synthesis of Optimal Constant-Gain Positive-Real Controllers for Passive Systems

This paper presents synthesis methods for the design of constant-gain positive real controllers for passive systems. The results presented in this paper, in conjunction with the previous work by the authors on passification of non-passive systems, offer a useful synthesis tool for the design of passivity-based robust controllers for non-passive systems as well. Two synthesis approaches are given for minimizing an LQ-type performance index, resulting in optimal controller gains. Two separate algorithms, one for each of these approaches, are given. The synthesis techniques are demonstrated using two numerical examples: control of a flexible structure and longitudinal control of a fighter aircraft.

Mao, Y.↗

Robust Control of Non-Passive Systems via Passification

This paper presents methods which enable the use of passivity-based control design techniques to control non-passive systems. For inherently non-passive finite- dimensional linear time-invaraint systems, passification methods are presented to render such systems passive by suitable compensation. The passified system can then be controlled by a class of passive linear controllers. The idea is to exploit the robust stability properties of passivity-based control laws for uncertain systems. The proposed passification methods are demonstrated by application to the ACC benchmark problem and to pitch-axis control of an F-18 High Alpha Research Vehicle (HARV) model.

Kelkar, A. G.↗

Wideband Impedance Passivation of MMCs for Suppressing Harmonic Oscillations

Harmonic instability and associated oscillation events have become one of the main concerns in MMC-based HVdc systems. These oscillations can appear in the range from a few hundred hertz to several kilohertz, and the root cause is identified as delay-induced negative damping of MMC impedance appearing at the system resonance frequency. Here, this paper introduces a wideband impedance reshaping method through MMC control to eliminate such negative damping for both grid-following (GFL) and grid-forming (GFM) MMCs, which makes the MMC impedance completely passive from the second harmonic frequency upward, thus preventing all harmonic oscillations. First, simplified impedance models of MMCs are derived for the harmonic stability analysis and the impedance reshaping control design. Next, a passivity-based impedance reshaping method is presented, as well as practical considerations for its implementation. In addition, to maintain the MMC's disturbance ride-through capability, an adaptive activation scheme is developed, which enables the wideband impedance reshaping control only in the presence of harmonic oscillation events. The effectiveness of the proposed method is validated by frequency domain analysis and by electromagnetic transient (EMT) simulations of two typical MMC-based power systems.

17 WIND ENERGY↗

Method and system to perform energy-extraction based active noise control

A method to provide active noise control to reduce noise and vibration in reverberant acoustic enclosures such as aircraft, vehicles, appliances, instruments, industrial equipment and the like is presented. A continuous-time multi-input multi-output (MIMO) state space mathematical model of the plant is obtained via analytical modeling and system identification. Compensation is designed to render the mathematical model passive in the sense of mathematical system theory. The compensated system is checked to ensure robustness of the passive property of the plant. The check ensures that the passivity is preserved if the mathematical model parameters are perturbed from nominal values. A passivity-based controller is designed and verified using numerical simulations and then tested. The controller is designed so that the resulting closed-loop response shows the desired noise reduction.

Kelkar, Atul↗

Synthesis Methods for Robust Passification and Control

The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.

Kelkar, Atul G.↗

Virtual Self-Excited Induction Generator-Based Grid-Forming Inverter Control for Robust Voltage Regulation Under Nonideal Loading

This paper presents a generator-inspired control methodology for grid-forming (GFM) inverters that deliberately emulates a self-excited induction generator so that the inverter can hold its voltage and frequency under difficult loading and severe terminal disturbances across wide voltage and frequency ranges. The design integrates a Lyapunov energy function-based inner loop to provide high bandwidth and strong disturbance rejection, and it complements this with a passivity-based argument that furnishes a coherent large-signal stability guarantee beyond small-signal limits. Analytical insights are developed via the Krylov-Bogoliubov-Mitropolsky averaging method, which reveals an intrinsic resistive droop characteristic; these closed-form relations both explain the observed dynamics and yield simple, decentralized tuning rules. The methodology is validated on a controller-hardware-in-the-loop platform and exercised in real time across balanced, unbalanced, and nonlinear loads, as well as during parallel operation. Across these scenarios, the inverter maintains balanced three-phase voltages, limits harmonic content, settles quickly with well-damped transients, and remains resilient when multiple units operate in parallel. The contributions are a self-excited-machine-inspired GFM controller with enhanced dynamic performance and robustness, a single stability rationale grounded in passivity, closed-form expressions that guide tuning, and comprehensive hardware-in-the-loop validations demonstrating effectiveness and superiority under challenging operating conditions.

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