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Load Alleviation Control using Dynamic Inversion with Direct Load Feedback
Abstract
This paper addresses the use of dynamic inversion with direct load feedback to provide combined load alleviation and flight control of rotorocraft. The method is applied to a compound utility rotorcraft with similar airframe properties as a UH-60A along with a lifting wing. The controller makes use of flaperons and horizontal stabilizer in addition to the conventional main rotor / tail rotor blade pitch controls to track pilot commands while also minimizing pitch link loads. The nonlinear simulation is developed in FLIGHTLAB ® with structural models of the rotor blades and control system. This model must be linearized to a linear time-invariant (LTI) system to support linear Dynamic Inversion control design. The vehicle dynamics and critical fatigue load are modeled with a linear time-periodic (LTP) model which is converted via harmonic decomposition into a high-order LTI model. This model is then reduced to design controllers across a range of airspeeds. The controllers are tested both in linear model simulations and using the full nonlinear FLIGHTLAB ® model. The results show that the load alleviating controller achieves significant reduction in the pitch link peak-to-peak loads with minimal change in response characteristics, indicating that load alleviation can be achieved with no degradation in handling qualities.
... However, this limitation can be relaxed using the harmonic decomposition method that originated from the rotorcraft community [35][36][37]. Within the context of rotorcraft, harmonic decomposition models have been used to: (1) study the interference effects between higher-harmonic control (HHC) and the aircraft flight control system (AFCS) [35,[38][39][40]; (2) design load alleviation control (LAC) laws (the PI's efforts in [41][42][43]; and (3) prediction and avoidance of flight envelope limits [43][44][45]. A survey by the PI on the use of harmonic decomposition models in the rotorcraft field can be found in [46]. ...
... However, this limitation can be relaxed using the harmonic decomposition method that originated from the rotorcraft community [35][36][37]. Within the context of rotorcraft, harmonic decomposition models have been used to: (1) study the interference effects between higher-harmonic control (HHC) and the aircraft flight control system (AFCS) [35,[38][39][40]; (2) design load alleviation control (LAC) laws (the PI's efforts in [41][42][43]; and (3) prediction and avoidance of flight envelope limits [43][44][45]. A survey by the PI on the use of harmonic decomposition models in the rotorcraft field can be found in [46]. ...
... The state vector is conveniently partitioned into rigid-body and rotor states: (43) x x x T = u v w p q r x y z 0 0D 1c 1ṡ0̇0Ḋ1ċ1s 0 0D 1c 1ṡ0̇0Ḋ1ċ1s 0 1c 1s 0T ...
This article investigates vibrational stabilization effects in rotorcraft flight dynamics. This study is motivated by recent results in flapping-wing flight, which showed that the time-varying aerodynamic and inertial loads due to the insect wing periodic motion induce a vibrational stabilization mechanism in hover. The dynamics of flapping-wing flyers and rotary- wing vehicles are both described by time-periodic systems so vibrational stabilization mechanisms can also have an effect on stability characteristics of rotary-wing vehicles. The article extends the use of the harmonic decomposition method to vibrational stability analysis of rotorcraft. Two cases are considered: vibrational stability due blade imbalance at hover, and vibrational stability due to number-of-blades-per-rotor-revolution (Nb/rev) in high-speed forward flight. Results show that while vibrations induced by rotor blade imbalance do not stabilize the hovering dynamics of a helicopter, these vibrations can still have a significant effect on the hovering dynamics. Rotor blade imbalance results in a symmetric effect on the roll and pitch axes, in that it tends to decrease the frequency of the subsidence modes of the hovering cubic, while the unstable oscillatory modes tend to increase in frequency and decrease in damping (destabilizing effect). On the other hand, the yaw/ heave dynamics are relatively unaffected compared to the lateral and longitudinal axes. Moreover, Nb/rev rotor loads in forward flight are shown to reduce the damping of the coupled roll/pitch oscillation mode.
... Recently, LTI reformulations of LTP systems were employed in the design of load alleviation control laws (Refs. [11][12][13] and the prediction and avoidance of flight envelope limits (Refs. 14, 15). ...
... A total of n(2N + 1) constraints are formed by requiring that the state derivative Fourier coefficients in Eq. (11) and the state Fourier coefficients in Eq. (8a) satisfy the integral relations in Eq. (13). This leads to the definition of the error vector at the iteration k as ...
... The n(2N + 1) = 288 constraints are given by Eq. (13), with the exception of the zeroth harmonic of the derivative of the x position state which is set to the desired forward speed (i.e.,ẋ 0 = 80 kt). Because there are m(2M + 1) = 4 unknowns more than there are constraints, the zeroth harmonics of the position states (x, y, z) and yaw angle ψ, denoted as x 0 , y 0 , z 0 , and ψ 0 , are removed from the problem and set to arbitrary values. ...
This paper discusses the development of a numerical method for the approximation of the nonlinear time-periodic rotorcraft flight dynamics with higher order linear time-invariant (LTI) models. The method relies on a per-rotor revolution perturbation scheme, which is of particular importance for the linearization of simulation models that do not allow for per-time-step perturbations, and for those output measures that necessitate the solution of partial differential equations and thus require several time steps to be computed. The paper demonstrates the application of the proposed methodology to obtain high-order LTI models capable of predicting vibrations for a generic utility helicopter. Simulations are used to validate the response of the linearized models against those from nonlinear simulations and from competing approaches in the literature. The proposed method is shown to predict accurately the nonlinear response for the case shown and for small amplitude maneuvers. Frequency-domain validation is also performed to compare the linear models derived with the proposed method with those obtained with harmonic decomposition, a competing approach based on a per-time-step perturbation scheme. Interestingly, the proposed algorithm yields nearly identical numerical results compared to harmonic decomposition, suggesting that the two methods are in fact equivalent but rely on different formulations.
... 28, 31-33); (ii) design load alleviation control (LAC) laws (the PI's efforts in Refs. [34][35][36]; and (iii) prediction and avoidance of flight envelope limits (Refs. [36][37][38]. ...
... [34][35][36]; and (iii) prediction and avoidance of flight envelope limits (Refs. [36][37][38]. A survey by the PI on the use The paper starts from a simple example involving an inverted pendulum to demonstrate the use of the harmonic decomposition method (Ref. ...
This paper investigates vibrational stabilization effects in rotorcraft flight dynamics. This study is motivated by the fact that eigenvalues of the rotorcraft flight dynamics identified from flight test often differ from those computed with physics-based simulations, and that some commonly observed mismatches may be ascribed to vibrational stability effects due to rotor blade imbalance or other periodic disturbance on the rotorcraft. Starting from a simple example involving an inverted pendulum, the paper demonstrates the use of the harmonic decomposition method for the study of vibrational stabilization effects. The concept is then extended to analyze the effect of blade imbalance on the flight dynamics of a helicopter. Additionally, vibrational stablization of a slung load in forward flight is investigated using small-amplitude and disturbances on an active cargo hook. Results show that while vibrations induced by rotor blade imbalance do not stabilize the hovering dynamics of a helicopter, these vibrations still have a significant effect on the hovering dynamics. Rotor blade imbalance results in a symmetric effect on the roll and pitch axes, in that it tends to decrease the frequency of the subsidence modes of the hovering cubic, while the unstable oscillatory modes tend to increase in frequency and decrease in damping. On the other hand, the yaw/heave dynamics are relatively unaffected compared to the lateral and longitudinal axes. Moreover, small-amplitude oscillations of an active cargo hook were shown to significantly decrease the amplitude of the limit cycle oscillation of a slung load in forward flight and to stabilize its dynamics. This constitutes a practical solution to the semi-active control of a suspended load.
... 23,[25][26][27], to design load alleviation control (LAC) laws (Refs. [28][29][30], to predict and avoid flight envelope limits (Refs. [30][31][32], and to examine the stability of flapping-wing flyers (Refs. ...
... [28][29][30], to predict and avoid flight envelope limits (Refs. [30][31][32], and to examine the stability of flapping-wing flyers (Refs. 33). ...
This paper demonstrates the extension of the harmonic decomposition methodology, originally developed for rotorcraft applications, to the study of periodically-forced fluid flows. Starting from a dynamic systems approach to fluid flows, application of the harmonic decomposition method is demonstrated through two examples involving an oscillating cylinder in an inviscid compressible flow and in a viscous incompressible flow. High-order time-invariant linearized approximations are obtained by linearizing the nonlinear dynamics about its periodic solution and, subsequently, performing a harmonic decomposition. Numerical simulation results from the harmonic decomposition models are validated against the results from the nonlinear equations. Order reduction methods are explored to guide the development of linearized models that provide a better runtime performance than the nonlinear and the linearized harmonic decomposition models while ensuring accurate predictions of the harmonic content of the flow.
... However, the reliance on state transition matrices to approximate LTP systems with higher-order LTI systems was recently relaxed by a numerical method that originated from the rotorcraft community known as "harmonic decomposition" [33,34]. High-order LTI approximate models obtained using harmonic decomposition have been used to study the interference effects between higher-harmonic control (HHC) and the aircraft flight control system (AFCS) [33,[35][36][37], in the design of load alleviation control (LAC) laws [38][39][40], and in the prediction and avoidance of flight envelope limits [40][41][42]. When coupled with a harmonic balance scheme, harmonic decomposition can also be used to compute the periodic solutions for flight vehicles with NLTP dynamics [30]. ...
... However, the reliance on state transition matrices to approximate LTP systems with higher-order LTI systems was recently relaxed by a numerical method that originated from the rotorcraft community known as "harmonic decomposition" [33,34]. High-order LTI approximate models obtained using harmonic decomposition have been used to study the interference effects between higher-harmonic control (HHC) and the aircraft flight control system (AFCS) [33,[35][36][37], in the design of load alleviation control (LAC) laws [38][39][40], and in the prediction and avoidance of flight envelope limits [40][41][42]. When coupled with a harmonic balance scheme, harmonic decomposition can also be used to compute the periodic solutions for flight vehicles with NLTP dynamics [30]. ...
This paper demonstrates the extension of the harmonic decomposition methodology, originally developed for rotorcraft applications, to the study of the nonlinear time-periodic dynamics of flapping-wing flight. A harmonic balance algorithm based on harmonic decomposition is applied to find the periodic equilibrium and approximate linear time-invariant dynamics about that equilibrium of the vertical and longitudinal dynamics of a hawk moth. These approximate linearized models are validated through simulations against the original nonlinear time-periodic dynamics. Dynamic stability using the linear models is assessed and compared to that predicted using the averaged dynamics. In addition, modal participation factors are computed to quantify the influence of the higher harmonics on the flight dynamic modes of motion. The study shows that higher harmonics play a key role in the dynamics of flapping-wing flight, inducing a vibrational stabilization mechanism that increases the pitch damping and stiffness while reducing the speed stability. This results in stabilization of the pitch oscillation mode and thus of the longitudinal hovering cubic. In addition, the proposed methodology is used to derive open-and closed-loop control laws for attenuating arbitrary state harmonics and to enhance the dynamic response characteristics.
... The authors also developed methodologies for assessing the fidelity of LTI approximations of LTP systems [13]. More recently, studies [23,24,63] at Penn State have used the LTI models of coupled body/rotor/inflow dynamics of Refs [13] and [62] for the development of life extending control schemes in the form of load alleviation control (LAC) strategies. ...
... The flight control law used in this work to track the desired flare trajectory is nonlinear dynamic inversion (NDI), a popular model-following scheme among aircraft and rotorcraft manufacturers, and within the aerospace flight control community in general. Application of NDI control laws to rotorcraft can be found in, e.g., [17][18][19][20][21][22][23][24][25][26]. One convenient feature of NDI is that it inverts the plant model in its feedback linearization loop, which, compared to other more conventional model-following control strategies such as explicit model following (EMF), eliminates the need for gain scheduling. ...
A novel trajectory generation and control architecture for fully autonomous autorotative flare that combines rapid path generation with model-based control is proposed. The trajectory generation component uses optical Tau theory to compute flare trajectories for both longitudinal and vertical speed. These flare trajectories are tracked using a nonlinear dynamic inversion (NDI) control law. One convenient feature of NDI is that it inverts the plant model in its feedback linearization loop, which eliminates the need for gain scheduling. However, the plant model used for feedback linearization still needs to be scheduled with the flight condition. This key aspect is leveraged to derive a control law that is scheduled with linearized models of the rotorcraft flight dynamics obtained in steady-state autorotation, while relying on a single set of gains. Computer simulations are used to demonstrate that the NDI control law is able to successfully execute autorotative flare in the UH-60 aircraft. Autonomous flare trajectories are compared to piloted simulation data to assess similarities and discrepancies between piloted and automatic control approaches. Trade studies examine which combinations of downrange distances and altitudes at flare initiation result in successful autorotative landings.
... Recently, LTI reformulations of LTP systems were employed in the design of load alleviation control (LAC) laws (Refs. [11][12][13] and in the prediction and avoidance of flight envelope limits (Refs. 14,15). ...
The objective of this paper is to summarize the relevant published research studies on the extraction of linear time-periodic (LTP) systems and their higher order linear time-invariant (LTI) reformulations from rotorcraft physics-based models and on the identification of LTP systems from rotorcraft experimental data. The paper begins with an introductory overview of LTP system theory. Next, the relevant methods for the extraction of LTP and high-order LTI systems from physics-based models are presented. The paper continues with an overview of LTP model identification methods, followed by a discussion on the application of these methods toward the identification of the rotor dynamics alone and the coupled rigid-body/rotor dynamics. Final remarks summarize the overall findings of the study and identify areas for future work including, but not limited to, the context of the Future Vertical Lift (FVL) program.
This paper focuses on the integration of generalized rotor-on-rotor interactional aerodynamics models in state-variable form within flight dynamics simulations of multi-rotor unmanned aircraft systems (UAS), and on their subsequent linearization. The aircraft chosen for this investigation is a resupply coaxial quadcopter. Upon trimming the flight dynamics at hover, linearized models of said dynamics are compared to nonlinear simulations, and with linear and nonlinear adopting dynamic inflow models that do not account for rotor-on-rotor inflow interference effects. Model-order reduction methods are investigated to guide the development of linearized models that are tractable for flight control design while still predicting the effect of rotor-on-rotor interactions on the vehicle flight dynamics. Model-following flight control laws based on these reduced-order linearized models that account for the rotor-on-rotor interactions are developed and tested against similar control laws based on linearized models that do not account for rotor-on-rotor interactions. It is found that, for the coaxial quadcopter configuration in consideration, rotor-on-rotor interactions result in a lower magnitude roll/pitch rate response to lateral/longitudinal velocity and in a lower pitch/roll damping. These changes in stability derivatives yield roll and pitch subsidence modes at a lower frequency and roll and pitch oscillation modes with a lower natural frequency. Additionally, roll and pitch on-axis frequency responses indicate that the interactional inflow dynamics results in higher gains and phases at low to medium frequencies (ap-proximately 0.1 to 4 rad/s). No significant improvements are detected by designing model-following control laws based on reduced-order models that account on rotor-on-rotor interactions.
This article describes the development, implementation, and validation of a generic tilt-rotor simulation model with coupled flight dynamics, state-variable aeromechanics, and aeroacoustics. A major novelty of this work lies in the integration of the flight dynamics with a state-space free-vortex wake code that adopts a near-wake vortex-lattice model. This way, the flight dynamics are augmented by the vortex wake dynamics so that the coupled flight and wake dynamics are self-contained and inherently linearizable. The model is implemented for a Bell XV-15 tiltrotor and validated against U.S. Army/NASA XV-15 flight-test data and other data in the literature. Flight control design is performed to provide desired stability, performance, and handling-quality properties and to allow for a fully autonomous transition between hover in helicopter mode and high-speed flight in aircraft mode. The simulation model has clear applications in the development and testing of advanced flight control laws, aeromechanics analysis, and the prediction of aerodynamically generated noise in generalized maneuvering flight.
This paper describes the development, implementation, and validation of a generic tilt-rotor simulation model with coupled flight dynamics, state-variable aeromechanics, and aeroacoustic. A major novelty of this work lies in the integration of the flight dynamics with a state-space free-vortex wake code that adopts a near-wake vortex-lattice model. This way, the flight dynamics are augmented by the vortex wake dynamics so that the coupled flight and wake dynamics is self-contained and inherently linearizable. The model is implemented for a Bell XV-15 tiltrotor and validated against U.S. Army/NASA XV-15 flight-test data and other data in the literature. Flight control design is performed to provide desired stability, performance, handling-quality properties and to allow for a fully-autonomous transition between hover in helicopter mode and high-speed flight in aircraft mode. The simulation model has clear applications in the development and testing of advanced flight control laws, aeromechanics analysis, and in the prediction of aerodynamically-generated noise in generalized maneuvering flight.
The objective of this paper is to demonstrate the use of the Julia language for developing complex flight simulation models and performing flight control design. Three simulation models are developed: a simple helicopter model (J-SimpleHel), a higher-fidelity helicopter model (J-GenHel), and a fighter jet model (J-F16). These models are validated against flight test data, when available, and are used to predict the dynamic characteristics of the three aircraft in consideration. Model-following control laws are implemented for each aircraft to enhance the response characteristics.
Accurate and real-time load monitoring of vital components located in the rotor system is important for not only
inferring usage and estimating fatigue in those components, but also for developing load alleviation /limiting
control schemes. An approach previously developed for online estimation of rotor component loads is evaluated
in this paper in which a linear time invariant (LTI) model of helicopter coupled body/rotor dynamics is combined
with a Linear Quadratic Estimator (LQE), that is designed to correct LTI model state response using fixed system
measurements. The estimation fidelity of the LTI/LQE scheme is evaluated in simulations using a nonlinear
model of a generic helicopter for online prediction of rotor blade pitch link loads arising from vehicle maneuvers.
Flight control design for rotorcraft is challenging due to high-order dynamics, cross-coupling effects, and inherent instability of the flight dynamics. Dynamic inversion design offers a desirable solution to rotorcraft flight control as it effectively decouples the plant model and effectively handles non-linearity. However, the method has limitations for rotorcraft due to the requirement for full-state feedback and issues with non-minimum phase zeros. A control design study is performed using dynamic inversion with reduced order models of the rotorcraft dynamics, which alleviates the full-state feedback requirement. The design is analyzed using full order linear analysis and non-linear simulations of a utility helicopter. Simulation results show desired command tracking when the controller is applied to the full-order system. Classical stability margin analysis is used to achieve desired tradeoffs in robust stability and disturbance rejection. Results indicate the feasibility of applying dynamic inversion to rotorcraft control design, as long as full order linear analysis is applied to ensure stability and adequate modelling of low-frequency dynamics.
Two approaches to gains optimization of dynamic inversion control laws have been developed to facilitate the shipboard operation of rotorcraft. The first approach is a frequency-based method to optimize the tradeoff between stability margins and disturbance rejection properties; the second approach uses direct optimization of gains to enhance tracking performance in the time domain. Comparative studies show that both methods tend to use high gain design for improvement of tracking error while rejecting airwake disturbances and following station-keeping commands over a moving deck. The frequency domain based method provides firm information on the margin to instability, although this is done via analysis of each axis independently. The direct optimization approach directly addresses tracking error performance in all axes, but the method resulted in only moderate improvements over the baseline gains for the particular case studied.
The objective of this research effort is to assess the impact of load alleviation control on the quantitative handling qualities specifications (also known as predicted handling qualities) of both conventional helicopters and compound rotorcraft in forward flight. First, an overview on how the harmonic decomposition methodology is used toward load alleviation control is presented. Next, flight control laws are developed based on an explicit model-following architecture. Parametric studies are performed to provide insights on how both the feedforward and feedback paths of the model-following control laws can be used to alleviate the rotor loads. The impact of load alleviation on predicted handling qualities is studied. It is shown that, for the standard helicopter configuration considered, load alleviation comes at the cost of a degradation in handling qualities. However, for the compound rotorcraft considered, allocation of the control signal to the redundant control surfaces provides load alleviation without degradation in predicted handling qualities. The flight control laws are subsequently optimized using the Control Designer’s Unified Interface (CONDUIT) to meet a comprehensive set of stability, handling-qualities, and performance specifications for specific mission task elements while minimizing the unsteady rotor loads.
The present study considers two notional rotorcraft models: a conventional utility helicopter, representative of an H-60, and a wing-only compound utility rotorcraft, representative of an H-60 with a wing similar to the X-49A wing. An explicit model following (EMF) control scheme is designed to achieve stability and desired rate command / attitude hold response around the roll, pitch, and yaw axes, while alleviating vibratory loads through both feed-forward and feedback compensation. The harmonic decomposition methodology is extended to enable optimization of primary flight control laws that mitigate vibratory loads. Specifically, linear time-periodic systems representative of the periodic rotorcraft dynamics are approximated by linear time-invariant (LTI) models. The LTI models are subsequently reduced and used in linear quadratic regulator (LQR) design to constrain the harmonics of the vibratory loads. Both fuselage state feedback and rotor state feedback are considered. A pseudo-inverse strategy is incorporated into the EMF scheme for redundant control allocation on the compound configuration. Simulations of the load alleviating controllers are compared to results from a baseline controller. Finally, an analysis is performed to assess the impact that load alleviating control action, rotor state feedback, and pseudo-inverse have on handling qualities in terms of ADS-33E specifications.
Several methods for analysis of linear time periodic (LTP) systems have successfully been demonstrated using harmonic decompositions. Onemethod recently examined is to create a linear time invariant (LTI) model approximation by expansion of the LTP system states into various harmonic state representations, and formulating corresponding LTI models. Although this method has shown success, it relies on a second-order formulation of the original LTP system. This second-order formulation can prove problematic for degrees of freedom not explicitly represented in second-order form. Specifically, difficulties arise when performing the harmonic decomposition of body and inflow states as well as interpretation of LTI velocities. Instead this paper presents a more generalized LTI formulation using a first-order formulation for harmonic decomposition. The new first-order approach is evaluated for a UH-60A rotorcraft model and is used to show the significance of particular harmonic terms, specifically that the coupling of harmonic components of body and inflow states with the rotor states makes a significant contribution to LTI model fidelity in the prediction of vibratory hub loads.
A weighted least-squares eigenstructure assignment technique and a balanced singular value Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) technique are used to develop rotor loads alleviation control laws for the V-22 Osprey aircraft. These techniques were applied to alleviate rotor yoke chord loads as part of a comprehensive Bell-Boeing structural loads limiting control law design effort. The control laws developed using these modern control techniques reduce precession generated rotor aerodynamic moments while allowing the pilot to exploit the maneuverability and agility of the tiltrotor configuration. Robustness to feedback sensor failures is ensured through a model following port limiting architecture derived using low order estimation techniques. Analysis and design of the rotor loads alleviation control laws using linear and nonlinear aircraft math models and piloted simulation is discussed.
Recent results on singular perturbations are surveyed as a tool for model order reduction and separation of time scales in control system design. Conceptual and computational simplifications of design procedures are examined by a discussion of their basic assumptions. Over 100 references are organized into several problem areas. The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.
2019 Nikolsky Lecture: Design Advantages of an Integrated Cyber-Physical Aircraft
- N D Lappos
Lappos, N. D., "2019 Nikolsky Lecture: Design Advantages of an Integrated Cyber-Physical Aircraft," Proceedings of the 75 th Annual Forum of the Vertical Flight
Society, Philadelphia, PA, May 13-16, 2019.
Optimizing Control of a Compound Rotorcraft in Quasi-Steady Maneuvers
- A T Thorsen
- J F Horn
- G T Ozdemir
Thorsen, A. T., Horn, J. F., and Ozdemir, G. T., "Optimizing Control of a Compound Rotorcraft in Quasi-Steady Maneuvers," Proceedings of the 5 th Decennial
AHS Aeromechanics Specialists' Conference, San Francisco, CA, Jan 2014.