Document
Incorporating Handling Qualities Analysis into
Rotorcraft Conceptual Design
Ben Lawrence San Jose State University Research Foundation NASA Ames Research Center, Moffett Field, CA, USA Abstract This paper describes the initial development of a framework to incorporate handling qualities analyses into a rotorcraft conceptual design process. In particular, the paper describes how rotorcraft conceptual design level data can be used to generate flight dynamics models for handling qualities analyses. Also, methods are described that couple a basic stability augmentation system to the rotorcraft flight dynamics model to extend analysis to beyond that of the bare airframe. A methodology for calculating the handling qualities characteristics of the flight dynamics models and for comparing the results to ADS-33E criteria is described. Preliminary results from the application of the handling qualities analysis for variations in key rotorcraft design parameters of main rotor radius, blade chord, hub stiffness and flap moment of inertia are shown. Varying relationships, with counteracting trends for different handling qualities criteria and different flight speeds are exhibited, with the action of the control system playing a complex part in the outcomes. Overall, the paper demonstrates how a broad array of technical issues across flight dynamics stability and control, simulation and modeling, control law design and handling qualities testing and evaluation had to be confronted to implement even a moderately comprehensive handling qualities analysis of relatively low fidelity models. A key outstanding issue is to how to ‘close the loop’ w ith an overall design process, and options for the exploration of how to feedback handling qualities results to a conceptual design process are proposed for future work.
Notation Vehicle moments of inertia about Aerodynamic stability derivative of ͳ ߲ ߲ܮ ܫ ܫ ǡ ܫ ǡ ௫௫ ௬௬ ௭௭ roll, pitch and yaw axes ܮ ൌ body axis roll moment force due to ܫ ௫௫ roll rate perturbation perturbation in body axis rolling ்ܮο ை் moment ܰ Main rotor number of blades Total perturbation in body axis ்ܴ Tail rotor radius ்ܺο ை் longitudinal force ܵ Area of vertical tail fin Height of rotor above vehicle center ݄ Aerodynamic control derivative of ோ ͳ ߲߲ܺ of gravity body axis longitudinal force due to ܺ ൌ ఏ భೞ ܯ ߠ Height of tail rotor above vehicle ଵ௦ longitudinal cyclic perturbation ்݄ center of gravity Aerodynamic stability derivative of ͳ ߲߲ܺ Height of vertical tail fin above body axis longitudinal force due to ܺ ൌ ݄ ௨ vehicle center of gravity ܯ ݑ longitudinal velocity perturbation ȳ Tail rotor angular speed Total body axes roll and yaw angular ݎ ሶǡ ሶ accelerations Side force coefficient due to sideslip ܥ ௬ഁ derivative ߠ Trim pitch attitude ௧ Vehicle product of inertia between ߣ Main rotor flap frequency ratio ఉ ܫ ௫௭ roll and yaw axes Partial derivative of tail rotor thrust ߲ ܥ ߲௧் ܭ Pitch rate error feedback gain coefficient with tail rotor normalized ߤ ௭் vertical velocity ܭ Pitch attitude error feedback gain ఏ Perturbation in body axis ܺο Aerodynamic stability derivative of ௩௧௬ ͳ ߲ ߲ܮ longitudinal force due to gravity body axis roll moment force due to ܮ ൌ ఉ భೞ ܫ ߚ ௫௫ ଵ௦ rotor lateral flap perturbation Presented at the AHS Rotorcraft Handling Qualities Specialists’ Meeting, Huntsville, AL, Feb 19-20. This material is declared a work of the U.S. Government and is not subject to copyright protection Perturbation in body axis roll, pitch Total body axes roll and yaw angular ݎο ǡݍο ǡο ݎ ǡݍǡ and yaw rates rates Perturbation in body axis ߙ Angle of attack ݑο , ݓο ǡݒο longitudinal, lateral, and vertical ߚ Angle of sideslip velocities Main rotor Lock number ȳ Main rotor angular speed ర ఘ ோ ߛ బ ൌ ூഁ ܸ Vehicle airspeed ߤ Main rotor advance ratio Acceleration due to gravity ݃ most conceptual design tools, uses low fidelity Introduction modeling to facilitate rapid calculations and is typically In ref [1], Padfield notes that 25-50% of flight testing sufficient to analyze the flight performance of an time in an aircraft development program might be spent aircraft in terms of characteristics such as range, on fixing handling qualities problems. Furthermore, in payload, maximum speed, cruise speed etc. for a set of the same paper associated with this lecture, he went on flight conditions and missions. NDARC, as typical for to suggest that handling qualities were not given their conceptual design tools, has no capability to consider proper place in the early design trade-space, and were handling qualities as part of its sizing and design often left until flight test to discover and ‘put right’. It is optimization routine.
not difficult to justify the argument that these handling qualities fixes are not only time consuming, but Aircraft conceptual design has long lacked sufficient expensive. Padfield also recognized that part of the analyses that consider stability, control, and handling reason was that during the early days of helicopter qualities. Traditionally, conceptual design has been development handling qualities were extremely difficult limited to static analyses of the bare-airframe designs, to predict.
particularly for fixed-wing aircraft where designs tended to stay close to a well understood 'tube-and-wing' design Traditional approaches relied on heuristic data and rules with stiff structures and little aerodynamic interactions, of thumb and even with the help of numerical criteria as highlighted in ref [3]. This work, and another paper, and that they were justifiably treated as an outcome of ref [4], both encapsulate the multiple issues regarding the series of complex design decisions relating to the the estimation of the vehicle flight dynamics based on overall performance of the vehicle, its layout, structural the conceptual design data available and whether to integrity, and fixing other issues such as vibration perform handling qualities or stability and control problems. In these situations, it may have been analysis of the bare-airframe or to incorporate a control advantageous to be able to analytically consider system.
handling qualities factors on a design before it became somewhat ‘frozen’ , either to predict issues or to provide Ref [4] specifically addresses the issue of predicting sufficient margins in the design to facilitate ‘easier handling qualities with conceptual design level design fixes’ to any unforeseen handling qualities problems data by incorporating probabilistic techniques to that might occur later in the development process.
evaluate the uncertainties in the modeling. Sensitivity studies were demonstrated that not only inform the Conceptual design tools consist of analysis, synthesis, designer of handling qualities sensitivities to design and optimization routines to size flight vehicles to find parameters, but also provide a sensitivity to the the best configurations to meet the required operational uncertainty in the flight dynamics characteristic capabilities and performance, as well as reveal trends on parameters themselves. This looks to be a promising the relative benefits certain configuration choices have effort that could add robustness to future approaches, on the resulting aircraft performance. The NDARC where a conceptual design process incorporating (NASA Design and Analysis of Rotorcraft) tool [2] handling qualities is focused on finding regions of the provides such a capability to model general rotorcraft design space with maximum probability of achieving an configurations, and estimate the performance and objective target, instead of just maximizing the attributes of advanced rotor concepts. NDARC, like deterministic value of the objective.
Ref [3] takes a greater focus on the control aspects, and control derivatives could be generated at any point in describes an approach that uses actuator and closed-loop the ‘ trimmable ’ flight envelope to create linear state- pole placement constraints to optimize a control system space models, and their eigenvalues and response for satisfactory handling qualities characteristics. The transfer functions evaluated. However, this tool did not authors echoed the same sentiments of those in ref [4], attempt any feedback of the handling qualities whose control law developments were still a work-in- information into a design process or optimization.
progress, in that the purpose is not to design operational The challenges of incorporating handling qualities flight control laws, but to include closed loop design analyses into conceptual design begin with the fact that variables in the conceptual designer's toolbox so that the conceptual design tools typically do not include the questions can be answered: 'Can this aircraft modeling necessary to represent the flight dynamics or a configuration fly, and can it do so in a satisfactory flight control system. Then there is the question of manner?'. They state that conceptual designers have a performing the handling qualities analyses, should the high level need to know whether a suite of control bare-airframe be considered, or an aircraft with a flight effectors or a particular geometric configuration is control system? These questions are particularly capable of achieving mission goals. Without a challenging when many rotorcraft airframes are preliminary control system design, they are unable to inherently unstable, making automatic analyses approximate the closed-loop dynamic performance, a problematic. Finally, there are questions about how necessity for the analysis of any modern aircraft.
handling qualities analyses can contribute to conceptual In the rotorcraft domain, ref [5] describes a rotor design design; is it appropriate to include it all? If so, how does optimization study that simultaneously takes into the inclusion of handling qualities considerations affect account rotor dynamics and flight dynamics. The the evolution of a design at a conceptual design phase, objective was to maximize the damping ratio of the least and which design issues might be realistically addressed damped rotor mode, namely the lag progressive mode. with the models available?
The design variables comprised rotor, airframe, and In the search for answers to a number of these flight control system parameters. The behavior questions, this paper describes the initial development constraints included rotor stability, rotor loads, and of a framework to incorporate handling qualities several handling qualities constraints from ADS-33, [6].
analyses into a rotorcraft conceptual design process.
The simulation model included flexible blade dynamics, The initial goal is to outline a methodology and a detailed representation of fuselage and incorporating a set of potential solutions in a tool while empennage. Although the design case demonstrated is presenting the lessons learnt. In particular, the paper somewhat beyond what conceptual design might describes how output from the NDARC rotorcraft consider, it showed that a multidisciplinary approach conceptual design tool was used to generate flight yielded successful results and evidence of counteracting dynamics models appropriate for handling qualities handling qualities and aeromechanics constraints in the analyses. Also, methods are described that couple a optimization of the design. This investigation also basic stability augmentation system to the rotorcraft incorporated closed loop control, and handling qualities flight dynamics model to enable analyses that extend constraints that encompassed more than the linear beyond that of the bare airframe. Next, the development system poles used in the fixed-wing studies just and performance of analyses capable of calculating the mentioned, with ADS-33 bandwidth and quickness handling qualities characteristics of the flight dynamics criteria evaluated (longitudinal axis only).
models are described. This is followed by the A more complete attempt at a whole vehicle study at a presentation of preliminary results of conducting similar level of information as conceptual design is handling qualities analyses on models that feature reported in ref [7]. This paper described work to extend variations of the input conceptual design data. In the a performance oriented code 'JANRAD' with a stability final discussion, the analysis of the results will guide a analysis capability. An approach to modeling the six discussion of proposed methods to quantify and use degree of freedom flight dynamics of conventional handling qualities metrics for their incorporation in an helicopter configurations is reported, where stability and overall design process.
Figure 1 Tasks for proposed methodology to incorporate handling qualities into a NDARC-based conceptual design process parameters from NDARC included the geometric, Technical Approach aerodynamic and trim data required to generate the The key actions to incorporate a handling qualities flight dynamics simulation models.
analysis into an NDARC-based conceptual design process outlined in this paper are shown in Figure 1.
Flight Dynamics Modeling The process includes the following key tasks: Read in a To generate the flight dynamics models, an approach vehicle configuration from NDARC, generate a flight based on linear stability and control derivatives was dynamics model, apply a control system, perform a selected. A number of factors contributed to this, firstly handling qualities analysis and then assess those a well-established theoretical approach based on linear handling qualities against various criteria and either stability and control derivatives exists to model the output the results to the user or feed them back to flight dynamic properties of rotors and vehicles using NDARC to influence the design optimization. This the kind of parameters usually defined by conceptual section of the paper describes the development, design analyses. Secondly, using closed expressions to implementation and performance of each these key calculate the stability derivatives directly, although constituent steps before going onto evaluating the initially time consuming to define, is computationally process as a whole. The methodology was developed efficient. This is an advantageous feature in the context using MATLAB/SIMULINK which provided a suite of of design studies where the goal is normally to assess a tools to support the prototyping of the required broad design space evaluating numerous parameter algorithms and models.
variations Importing Data from NDARC Typically, conceptual design tends to work with high- NDARC generates an array of text-file based outputs level ‘global’ parameters defining the overall vehi cle and tools were developed that parsed these text files into and its major components. For example, rotors would be MATLAB structure workspace variables. Key defined with a single radius, chord, blade inertia, and flap frequency ratio, linear twist etc., other components approach to the ‘hybrid’ model described in ref [8], such as fuselages, wings and empennage surfaces would where the flapping equations have dropped the terms be defined similarly, using overall dimensions such as involving flap acceleration (i.e. no inertia). This span, chord, area and orientation. Aerodynamic data is simplification retains a representation of the regressive normally limited to linear lift curve slopes and linear flapping mode, which typically has a natural frequency derivatives to represent other forces and moments. around half the rotor speed frequency. This is the primary rotor mode of concern for handling qualities, Finally, using closed form expression linear stability flight dynamics and control. This approach allows in a derivative-based modeling confers engineering insight relatively simple formulation a representation of as interactions can also be assessed by directly fuselage – rotor couplings that a 6-DoF model alone examining the mathematical expressions. The linear cannot capture. A similar notation of ref [8] to represent models generated are also more manageable from a the flapping moment terms, the bar on the term denotes robustness perspective - typically, these models tend to the differences to the aforementioned reference as be less susceptible to numerical instabilities and follows, where ߬ is the rotor-flap time constant, for ‘ crashes ’ than more sophisticated full force and moment example, for the lateral flap moment: models or models featuring significant non-linear ഇభ modeling. This is a desirable feature when automated ݁ Ǥ ݃Ǥ݂ܮ തതത ൌ (1) ఏ భ ఛ analysis sweeps may be left unattended to explore a wide range of input parameters, which may be The stability and control derivatives for which unbounded, over long periods of time. expressions have been derived are shown below in the ܣ and ܤ matrices respectively in equation 2. Note that (a), Stability Derivative expression development where a term is zero, it is explicitly not computed, and A set of semi-analytical, closed-form expressions were (b) that certain common terms such as the inertial and developed to compute the stability and control gravitational terms are not included in the matrices – derivatives. The expressions are currently capable of these effects, along with the calculation of the vehicle calculating the stability and control derivatives for a Euler angles, are handled separately by other elements conventional 4-bladed single main rotor helicopter with in the stitched model architecture, as described in the tail and fin surfaces, fuselage, and anti-torque tail rotor.
following section.
The expressions cover the derivatives for the Six- Example expressions for key terms in the roll axis Degree-of-Freedom (6-DoF) rigid body states and 2 equation: the roll moment due to roll rate derivative, ܮ , rotor multi-blade coordinate states of lateral and Τ roll moment due to lateral flap, ߲ ߲ܮ ߚ , lateral ሽ ଵ௦ longitudinal flapping, ߚ ǡݎǡ ݍǡ ǡ ݓǡ ݒǡ ݑሼ ൌ ݔ ߚ ǡ and ଵ௦ ଵ flapping rate due to roll rate, ߲ ሶ ߚ Τ , and finally, 4 control inputs of main rotor collective, longitudinal ߲ଵ௦ lateral flapping rate due to lateral cyclic input, and lateral cyclic, and tail rotor collective ൌ ݑ Τ ߠሼ ሽ ߲ ሶ ߚ ߠ , are shown in equations 3, 4, 5 and 6 ߠ ǡ ߠ ǡ ߠ ǡ . The flapping dynamics are modeled ߲ଵ௦ ଵ ଵ௦ ଵ ் respectively.
using a first order approximation, following a similar Ͳ ܺͲ ܻͲ ܺ௨ ܺ௩ ܺ௪ ܺ ఉ ఏ ఏ ఏ ܻభ ܺబ ܺభೞ భ ܺۍ ې ܺۍ ې ܼͲ ܻ௨ ܻ௩ ܻ௪ ܻ ܻ ܻ ఉ ఏ ఏ ఏ ఏ భೞ ܻబ ܻభೞ ܻభ ܼబ ێ ۑ ێ ۑ Ͳ ܼͲ Ͳ Ͳ ێ ۑ ێ ۑ ܼ௨ ܼ௩ ܼ௪ ఉ ఉ ఏ ఏ ܼభೞ భ ܼబ భೞ ێ ۑ ێ ۑ ܮ ܮ ܮ ܮ Ͳ ܮ ܮ ܮ ܮ ܮ ܮ ܮ ௨ ௩ ௪ ఉ ఉ ఏ ఏ ఏ ఏ భೞ భ బ భೞ భ బ ێ ۑ ێ ۑ ൌ ܣ ൌ ܤ (2) ܯ ܯ ܯ ܯ ܯ Ͳ ܯ ܯ ܯ ܯ ܯ ܰͲ ௨ ௩ ௪ ఉ ఉ ఏ ఏ ఏ భೞ ܰభ బ భೞ భ ێ ۑ ێ ۑ ێ ۑ ێ ۑ ܰ௨ ܰ௩ ܰ௪ ܰ ܰ ܰ ఉ ఉ ఏ ఏ ఏ ఏ ܰభೞ భ ܰబ ܰభೞ ܰభ బ ێ ۑ ێ ۑ തതത തതത തതത തതത തതത തതത തതത തതത തതത തതത തതത ݂ܮ ݂ܮ ݂ܮ Ͳ ݂ܮ ݂ܮ ݂ܮ ݂ܮ ݂ܮ ݂ܮ ݂ܮ ݂ܮ ఏ ఏ ఏ ௨ ௩ ௪ ఉ ఉ భೞ భ బ భೞ భ ێ ۑ ێ ۑ തതതത തതതത തതതത തതതത തതതത തതതത തതതത തതതത തതതത തതതത തതതത ݂ܯ ݂ܯ ݂ܯ ݂ܯ ݂ܯ ݂ܯ ݂ܯ ݂ܯ ݂ܯ ݂ܯ ݂ܯ Ͳ ۏ ے ۏ ے ௨ ௩ ௪ ఉ ఉ ఏ ఏ ఏ భೞ భ బ భೞ భ మ మ ఘௌ ഁ ఘஐ ோ గோ డ ଶ ߲ܮ ܮ ߲ൌ ൌ (3) ൗ ଶூೣೣ ூೣೣ డఓ ்݄ ே್ ଶ ߲ܮ ଶ ଶ ଶ ሻ ܮ ߲ൌ ൗ ൌ ߣ൛൫ െ ͳ൯ܫ ȳ ൟ െ ߩሺȳܴ ܴߨ ܥ (4) ఉ ఉ ఉ ݄௧ ோ భೞ ߚ ଶூೣೣ ଵ௦ തതത തതത Τ ݂ܮ ሶ ߚ ߲ൌ ൌ ͳ ݂ܮ (5) ߲ଵ௦ ఉ ோ ݄ೡ మ ஐ ଵ ఓ ሶ ߚ ߲ଵ௦ തതത ൘ ݂ܮ ߲ൌ ൌ ቆቀ ቁ ቀͳ ቁቇ (6) ఏ మି మ భ ߠ భల భ ర ఊ ଶ ଵ ൬ଵାቀ ቁ ቀ ఓቁ ൰ ം మ య Figure 2 Comparison of stability derivatives from semi-analytical calculations to derivatives extracted from comparable non-linear full force and moment models.
Figure 2 shows a comparison of a subset of the compare reasonably well, with most major trends derivatives computed by the closed expressions to those captured. There are some mismatches, some of which from two models that are similar to the Bo-105 and UH- are attributed to poor estimates for input trim data that 60 helicopters. The Bo-105 – like calculations are were unavailable for the Bo-105.
compared to derivatives published in ref [3], whereas Furthermore, it should be noted that the data from both the UH-60 calculations are compared to linear reference models are from full force-and-moment derivatives computed from linearization of a models that include a number of effects not accounted comparable FLIGHTLAB model.
for in the calculated stability derivatives, including The derivatives are compared for a range of speeds from dynamic inflow, aerodynamic interference and other hover up to forward flight. In order to facilitate the higher order effects. Nevertheless, considering the comparison, the derivatives for the handling qualities relative simplicity of the modeling and input data, analysis models have been computed by reducing the appreciably similar derivatives are being computed for flapping effects back to their quasi steady effect, leaving rotorcraft of reasonably different size and rotor hub the 6-DoF rigid body states only. The comparisons are systems. This outcome confers confidence in the initial generally favorable especially for dominant derivatives development phase of the research, providing a firm such as roll and pitch damping derivatives, ܯ and ܮ foundation for future modeling developments, and for and the speed damping derivatives such as ܺ and ܻ .
௨ ௩ the overall methodology.
Other important terms such as ܯ and ܯ , and ܮ also ௪ ௨ Trim data Rotor control inputs: ߠ ߠ ǡ ߠ ǡ ߠ ǡ , Trim attitudes , ߰ǡ߶ǡ ߠ , Rotor Thrust coefficient : ଵ ଵ௦ ் f(Airspeed,…) ܥ , Atmospheric density , ߩ ௧ Geometry data Rotor : radius, chord, angular speed, location, Number of blades, linear twist rate, shaft tilt, flap moment of inertia, ܫ , Hinge offset, ݁ , and/or Hub stiffness, ܭ , delta3 angle ఉ ఉ Vehicle : Center of gravity location, Radii of Gyration, ܭ ܭ ǡ ܭ ǡ , Vehicle mass, ܯ ௫ ௬ ௭ Aerodynamic surface s: location, span, chord or area Aerodynamic Rotor: blade lift curve slope data Aerodynamic surfaces : lift curve slope f( ߙ or ߚ ), angle of incidence for zero lift Fuselage : reference area, force and moment linear derivatives with incidence Table 1 Parameters required for stability derivative-based single main rotor flight dynamics model conferred on those. Currently, NDARC simply takes a Flight Dynamics Model Data Requirements user input of the radii of gyration, thus either an a priori Table 1 shows the full set of parameters required from knowledge of those parameters or a user estimate is NDARC (or any other design source) to calculate the required to define a variable important for flight flight dynamics for the single main rotor configuration dynamics. For the test models in this paper the inertias used in this paper. The total number of variables used to are known, however, in the future, where the NDARC fully compute all the derivatives for the demonstration design vehicle configuration is changing iteratively with configuration (1 main rotor, tail rotor, fuselage, tail, fin) a handling qualities analysis in a closed loop, an inertia is of the order of around 50 variables, with a mixture of estimation capability will be required, either provided trim, geometric and aerodynamic data required. There by NDARC or the handling qualities model generation are optional data input choices, such as defining the code.
rotor with an equivalent hinge offset or a hub spring (or both) for modeling articulated and hingeless rotors. A Stitched Modeling approach key factor is that a certain amount of the flight state data A ‘ s titched’ model architecture, ref [10] , using a ‘quasi - such as the trim controls, attitudes and thrust coefficient, Linear Parameter Varying’ or ‘qLPV’ model technique , are inputs, rather than being computed by the handling ref [11], was used for the overall flight dynamics qualities analysis model. Importing this information simulation model. The approach effectively ‘stitches’ from the NDARC conceptual design tool is crucial to together numerous fixed-point linear state-space models facilitating the use of a stability derivative based to create a single model with a continuous approach, as several of the trim states and controls are representation of the vehicle dynamics across the full required for the derivative calculations. NDARC’s flight envelope. In this architecture, the derivatives for performance-oriented calculations require reasonably each fixed-point state space model are entered into accurate estimates of trim and therefore are likely to be lookup tables that are a function of typical parameters satisfactory for handling qualities purposes. Using the such as flight speed, altitude, or vehicle configuration.
NDARC calculated parameters also helps with the An example of this was developed for the tiltrotor consistency of modeling as only the dynamic model in ref [12], where the second independent lookup characteristics are computed and use as much of the input variable was nacelle angle (airspeed was the first NDARC calculation as possible, i.e. the dynamics lookup table independent input variable).
model does not re-compute trim thrust coefficients or One key characteristic of the stitched model technique, flap angles etc.
in addition to the lookup tables for the stability and For conceptual design analysis and design optimization, control derivatives, (the ‘A’ and ‘B’ Matrices) , is that mass is a crucial parameter, and as such, NDARC has the model includes lookup tables of the trim control algorithms for the estimation and accounting of vehicle inputs and states. The stitched model uses these to mass. However, for the estimation of the flight reproduce trim characteristics such as input gradients dynamics the vehicle mass must be accompanied by the and attitude changes across the flight envelope, as well moments of inertia. However, the moments of inertia as to act as the datum point from which the perturbation are not required for the trim and performance linear dynamics are referenced to.
calculations of NDARC and therefore less attention is Another characteristic of the stitched model is that it motion piloted simulation handling qualities models a certain amount of nonlinearity by separately experiments for a large civil tiltrotor. This work computing the non-linear gravity component force demonstrated that the stitched model can be used as a perturbation. The 6-DoF perturbation aerodynamic basis for a piloted simulation.
forces and moments are computed by multiplying the A Stability and Control Augmentation and B matrix derivatives by the perturbations in the appropriate states and controls, these terms are summed Many bare-airframe rotorcraft designs are inherently unstable, often in more than one axis, and also feature a for each equation and then multiplied by the according number of control and dynamic response cross- mass or inertia term. Examples of this are shown for the longitudinal and roll equations of motion in equations 7 couplings. Therefore it was considered prudent to to 12. The two features of nonlinear gravity forces and provide a certain amount of stability augmentation to the models generated from the conceptual tool airframe nonlinear equations of motion, along with the trim and designs. There are a couple of important reasons for state lookup, give the stitched model quasi-nonlinear characteristics, and as such acts as a hybrid between a this: firstly, the relevance of bare airframe analysis in an fixed-point, linear state space model and a full force- age when all modern and future rotorcraft designs feature sophisticated flight control systems is and-moment model. Further details on the theory and questionable, and therefore a representation of the implementation of stitched models are in refs [10] and action of stability and control augmentation was [12].
considered realistic and also potentially informative.
ܺο ܯ ൌ ݊݅ݏ൫ ݊݅ݏ െ ሻߠሺ ߠሺ ሻ൯ (7) ௩௧௬ ݃ ௧ Secondly, if the flight dynamics are unstable, it can make the testing required for ADS-33E handling ்ܺο ܯ ൌ ܺ൫ ܺ ݑο ܺڮ ݓο ߠο ڮ൯ ை் ௨ ௪ ఏ ଵ௦ భೞ qualities criteria assessment problematic, due to ܺο (8) ௩௧௬ divergence of the simulation model from the intended test trim point, especially in the off-axis response.
்ܮο ܫ ൌ ܮ൫ ܮ ݒο ܮ ο ߠο ڮ൯ (9) ை் ௫௫ ௩ ఏ ଵ భ The two main requirements to implement a control law ο ೀಲಽ for the conceptual design-based handling qualities ݑሶ ൌ െሺ ݍݓെ ݎݒሻ (10) ெೌ models were as follows: ሺሶି ሻାο ൫ூ ூ ൯ାூೣ ି ೀಲಽ 1. The control law architecture should be generic ൌ ሶ (11) ூೣೣ enough to deal with a variety of vehicle configurations and sizes and widely varying ߶ሶ ൌ ݍ ߶ ߠ ݎ ߶ ߠ (12) stability and control characteristics 2. A process to automatically select the gains to Although the testing presented in the methodology in meet some form of stability or handling this paper is predominantly at point conditions, and thus qualities target criteria was required.
the stitched model may be seen as unnecessary, the stitched model provided a convenient way to keep a A simple approach based on the use of model-following general approach to the methodology development control law architecture (Figure 3), combined with a without making too many predeterminations on the root locus control feedback gain selection algorithm was nature of the subject models, either current or future.
selected. Although it is recognized that there are tools This is important in the context of the development of that support the design of control systems, such as the overall methodology – the use of stitched model has CONDUIT (ref [16]), the simple approach presented caused the analysis to be developed in a way that few herein was considered more appropriate at this stage as assumptions have been made about the analysis model it gave greater control of the individual component such that changes in modeling approach (e.g. linear or processes involved. The following sections will describe non-linear, full-force and moment etc.) can be more the key features of the control law architecture used in easily incorporated by the analysis in the future.
this study and how it was configured, including the Furthermore, the author has used these models in other development of a gain selection algorithm for the research (ref [13], [14] & [15]) projects featuring full- feedback of the control laws.
Input Command Inverse Control Vehicle Vehicle + + + Plant limits Model Model Response Feedback Error + + - Figure 3 Model-following control architecture The model following architecture consists of two key forward input to the appropriate rotor inputs to give the functions: 1. A command and inverse plant model desired response shape. The control system uses a which convert pilot stick inputs to idealized responses reduced order inverse plant model in each axis. For and then to swashplate input, 2. A feedback or regulator lateral cyclic control, the inverse plant model transfer path which tries to minimize the error between function is: measured aircraft response and the desired response ሺ௧ሻൈ coming from the command model. A convenient ߠ ሺݐሻ ൌ െ (14) ଵ ഇభ structure is provided whereby the command model response characteristics can be varied independently of The feedback function of the control law is designed to the feedback control response stabilization augment the stability of the vehicle. The feedback uses rate and attitude feedback with proportional gains characteristics and vice-versa. The command model was chosen to have a rate-response type, which is the most applied to the rate response errors ( ሻݓǡ ݎǡ ݍǡ and to basic response type, and, as per ADS-33, it can be used errors in the roll and pitch attitudes ( ߠ ǡ߶ ), where the in most mission task elements across the flight envelope error is defined as the commanded variable minus the by rotorcraft in fully attended operations and non- current observed state, e.g.
degraded visual environments (ref [6]). This is a ൌ െ (15) convenient aspect, as the rate command based control law does not require mode switching or require blending Commanded attitudes are calculated via the integration at speed thresholds between hover and low speed of the command model rate signals ݁ ߠ Ǥ ݃Ǥ ݍ ൎ ௗ ௗ operations and forward flight. The rate response in the as such, the feedback gain on the error of the st roll, pitch, yaw and vertical axes use 1 order dynamic commanded attitude (in pitch and roll only) follows response shaping functions in the command model as that of Attitude Hold architectures, but the objective follows: was only attitude stabilization and not a hold capability.
K p
lat cmd Feedback gain selection
e.g. (13)
1 s
The main challenge was to develop a method that lat lat selected gains for each of these feedbacks that conferred Here, the desired rate response is governed by a stability improvements, but without requiring overly proportional gain, ܭ and a response time constant, ௧ large actuator demands as to be unrealistic, or cause ߬ which are respectively set to notional values of 1 ௧ new instabilities and/or oscillations due to high gain and 0.3 for all axes for this study. The desired response control. An approach based on a root locus design signal is then split in two paths, one as the reference for methodology was developed in order to select the gains.
the error calculation in the feedback control, and the The gain selection process is outlined in the flowchart other is fed to the inverse plant. The signal passed to the shown in Figure 4.
inverse model provides a certain amount of feed- Figure 4 Flow-chart describing feedback gain selection process The first stage is to split the full-order, coupled ܯ is the feedback control allocation matrix, determining linearized state-space model into 2 reduced-order 4-state which inputs are applied to which feedback states e.g.
models of the decoupled longitudinal ሻߠǡ ݍǡ ݓǡ ݑሺ and for the 4-state reduced order representation of the lateral-directional ߶ ǡݎǡ ǡ ݒሺ ) dynamics by partitioning longitudinal dynamics: the A matrix. The next stage calculates the eigenvalues Ͳ Ͳ Ͳ Ͳ for the reduced order closed loop systems for ܯൌ ቂ ቃ (18) Ͳ Ͳ ͳ ͳ combinations of gains from predetermined arrays of gains. The starting gain arrays cover a range of values ఏ ఏ ܺబ ܼభೞ ܺۍ ې of 0 to 0.5 degree of control per degree error – ఏ ఏ ܼబ భೞ ێ ۑ ܤ ൌ (19) ܯ ܯ considered to be conservative, low gain values. The use ێ ۑ ఏ ఏ బ భೞ ۏ ے Ͳ Ͳ of the reduced order decoupled models greatly accelerates this process where only 2 gain arrays are ܹെ ߠݏܿ݃െ ܺ௨ ܺ௪ ܼ ܺۍ ې considered for longitudinal dynamics and 3 for the ܷ ߠ݊݅ݏ݃െ ܼ௨ ܼ௪ ێ ۑ ܣ ൌ (20) lateral-directional dynamics. A full matrix search on the ܯ ܯ ܯ Ͳ ێ ۑ ௨ ௪ fully coupled systems becomes computationally ۏ ے Ͳ Ͳ ͳ Ͳ expensive and unwieldy. The closed loop dynamics are This is done for each combination of elements in the computed as follows: arrays of each gain, for example, for the longitudinal ܣ ܣ ൌ ܤ ܭܯ (16) ௦ௗ axis, if there are ݊ ܭ ൈ gains and ݉ ܭ ൈ gains then ఏ ݊ ݉ൈ gain combinations are evaluated. This process is where ܭ is a matrix of the feedback gains, e.g. for the illustrated in Figure 5, shown in black are the longitudinal axis: eigenvalues evaluated for all the combinations of gains Ͳ Ͳ Ͳ Ͳ from the ܭ and ܭ arrays. T he ‘identified’ critical ఏ Ͳ Ͳ Ͳ Ͳ eigenvalue pairs are plotted green, which are the ܭൌ ൦ ൪ (17) Ͳ Ͳ ܭ Ͳ eigenvalues for gain sets meeting the following criteria: Ͳ Ͳ Ͳ ܭ ఏ also shown for comparison. All three un-augmented No unstable modes vehicles exhibit at least one unstable mode at the hover Any oscillatory modes above a certain frequency flight condition, which after the gain selection, is (to ignore very low frequency modes) stabilized, as shown by the square symbols.
Within a certain percentage of a target damping ratio, in this case a value of 0.707, indicated by the blue line extending from the origin.
(a) Bo-105 Figure 5 Closed loop eigenvalues for reduced order, longitudinal models for varying pitch rate and attitude gains The downselected gain sets for the longitudinal axes are then combined with the downselected lateral-directional gains determined by the same process and applied to the full order (11-state) linear state-space model to check that the coupled system remains stable. If all the eigenvalues of the closed-loop full order model are stable, the process is then complete and the final gains are chosen by either maximizing or minimizing the least stable closed loop pole (user specified), if not, then the (b) UH-60-like process is repeated with gain search arrays with increased values.
The algorithm has been tested on three test models, two of which are single main rotor models generated by the semi-analytical expressions, one approximating to the Bo-105, and the other approximating to the UH-60A.
The third test model is of a Large Civil Tiltrotor (LCTR2), with predefined flight dynamics and control allocation, developed for the studies in refs [12] to [15].
Figure 6 (a) through (c) show the comparison of the open loop (bare airframe) eigenvalues to the closed-loop systems after the feedback gain selection algorithm has been run for the three aforementioned test models at (c) LCTR2 hover. In the figures, the ADS-33E boundaries for the Figure 6 Comparison of open-loop and closed-loop hover and low-speed longitudinal/lateral oscillations are poles after application of feedback gains Figure 7 Comparison of time histories of the response of Bo-105, UH-60-like and LCTR2 models to step pulse in longitudinal control before and after stability augmentation A further comparison of the performance of the gain at zero to low amplitudes is stability, and as amplitude selection algorithm for the three test models is shown in increases issues of response become the focus up until Figure 7, which compares time responses to a the maximum limits of maneuver response are reached.
longitudinal input of the vehicles at hover, with and This follows a natural physical relationship that the without the feedback applied. It shows that the long- highest frequency responses cannot be large amplitude term response of the vehicles are generally improved and vice-versa, with various mechanisms from actuator with reduced deviation from the trim state, and a stable, rate limits, control saturation, aerodynamic force and rather than oscillatory divergent response, in both the on structural limits all playing their role in enforcing this.
and off-axis response (roll/yaw), especially for the Bo- The US Army Aeronautical Design Standard, ADS- 105 and UH-60-like models. 33E-PRF, ref [6] provides a suitable framework and methodology for analyzing the handling qualities of rotorcraft across the span of dynamic response Handling Qualities Testing characteristic behaviors. Implementing automatic Once the vehicle model is generated and the control handling qualities analyses based on ADS-33 will be system defined and configured, a handling qualities described in the remainder of this section.
assessment can be performed. Ref [3] describes how the maneuver envelope of an aircraft can be expressed in Use of ADS-33E as a basis terms of the frequency and amplitude of the dynamic Across the rotorcraft industry, the concepts, response. A spectrum of short-, mid-, and long-term methodology and criteria of ADS-33 have become frequencies and small, moderate, and large input common parlance for assessing rotorcraft handling amplitudes encompass all the task demands that the qualities. Developed through the 1970s, 80s and into pilot and vehicle are likely to encounter. This the 1990s, ADS-33 was a distinct step forward in framework naturally delineates into the three handling qualities engineering with its philosophy based fundamental flight dynamics analyses: trim, stability on the construct of the Mission Task Element (MTE) and response. At zero to very low frequency is trim, and and laying down clearly quantified and objective criteria the problem without overburdening the overall for measurable parameters which are strongly development process by implementing every possible substantiated by flight test and simulation research. In test. Table 2 lists the ADS-33 handling qualities tests its typical usage, ADS-33 uses a complementary currently implemented. Also indicated in the table are approach of subjective piloted assessment in the MTEs the specific ADS-33E-PRF requirements being tested providing Handling Qualities Ratings (HQRs) combined and their approximate location in the frequency- with the objective criteria for an overall assessment of amplitude response spectrum.
handling qualities.
The majority of the ADS-33 testing is performed The objective ADS-33 vehicle response characteristic through the generation of time histories from simulation criteria are founded in the concepts introduced in the runs, the exception being the pole-zero stability previous subsection with criteria broken down along analyses. For each flight condition, hover or straight and lines of response amplitude and frequency. Frequency level forward flight at various speeds, the model is and time domain analyses are used to evaluate the full initialized by trimming to obtain the equilibrium control range of frequency and amplitude responses from low inputs and roll and pitch attitudes. Next, test inputs are amplitude/high frequency using parameters such as defined and applied in a series of simulation runs which bandwidth, mid-term agility parameters such as may feature frequency sweeps, pulse or step inputs or a quickness, out to maximum maneuver capability control linearization process.
response criteria. The ADS-33 objective criteria Finally, the simulation output is recorded and processed constitute well-defined parameters and methodologies for the final handling qualities assessment. This for their identification and are the natural basis for any approach was chosen over linear systems analyses that quantitative handling qualities assessment of rotorcraft.
directly calculate the system characteristics from state- Handling qualities testing methodology space or transfer function models because it offered a A set of algorithms were developed to run a selected certain amount of future-proofing to developments in range of key ADS-33 handling qualities criteria tests on terms of using non-linear models or transferring the the rotorcraft models. As described in the introduction, algorithms to other codes or languages, i.e. a the primary focus of the research initially was to methodology was desired that did not overly rely on a develop the overall methodology, including a basic particular software analysis toolbox or implementation.
capability in each of the tasks outlined in Figure 1. As The following subsection considers a subset of the tests such, the development of the handling qualities testing listed in Table 2 (highlighted in gray) for further component was designed to encompass a sufficient description to demonstrate how the handling qualities variety of ADS-33 criteria tests to be representative of analyses are performed.
Roll Pitch Yaw Vertical Small Amplitude/High Attitude Attitude Bandwidth Attitude Bandwidth - Frequency Bandwidth (3.3.2.1) (3.3.5.1, 3.4.8.1) (3.3.2.1, 3.4.6.1) Small Amplitude/ Oscillatory Oscillatory Oscillatory - Low/Medium Frequency Requirements 4 Requirements Requirements (mode stability) (3.3.2.3, 3.4.9.1) (3.3.2.3, 3.4.1.2) (3.4.9.1) Medium Amplitude/ Attitude Attitude Quickness Attitude Response to Medium Frequency Quickness (3.3.3) Quickness (3.3.6) Collective (3.3.3, 3.4.6.2) (3.3.10.1, 3.4.3.2) Large Amplitude/Low Large amplitude Large amplitude Large amplitude - Frequency attitude change attitude change attitude change (3.3.4, 3.4.6.3) (3.3.4) (3.3.8) Interaxis coupling Roll due to pitch Pitch due to roll Yaw due to - (3.3.9.2, 3.3.9.3, (3.3.9. 2, 3.3.9.3, colle ctive 3.4.5.2, 3.4.5.4) 3.4.5.3, 3.4.5.4) (3.3.9.1) Table 2 ADS-33E-PRF Handling qualities criteria tests implemented Attitude Bandwidth Testing (Roll Axis) where if the parameter is to be compared to regions on The attitude bandwidth testing is based on a frequency an ADS-33 criteria chart, then the data point is plotted domain analysis of the vehicle attitude response to a on the chart and evaluated to be within a particular sinusoidal frequency sweep input applied in a region defined by the appropriate ADS-33 handling simulation run. The time histories of typical inputs and qualities boundaries.
outputs for a roll axis attitude bandwidth test for the Bo- 105 example model with a stability augmentation control system enabled are shown in Figure 8(a). These time histories are used to calculate the magnitude, phase and coherence of the roll attitude frequency response to the lateral input, as plotted in Figure 8(b). From these, the phase and gain bandwidth, and phase delay, are evaluated as defined in ADS-33.
Figure 9 Bo-105 Roll axis attitude bandwidth and phase delay on ADS-33E-PRF handling qualities criteria chart Attitude Quickness Testing (Roll Axis) Attitude quickness is considered a moderate amplitude vehicle response criterion by ADS-33. It requires the vehicle to undergo rapid attitude changes from one steady attitude to another. The criterion seeks to identify in the time domain the maximum ratio of the peak rate (a) Time history of frequency sweep response to the attitude change achieved in a maneuver over a range of attitude changes. The test algorithm for this criterion uses a two stage process; Firstly, an open loop step input in the control axis of interest is made to generate an estimate of the relationship between input magnitude and the steady rate response. This information is used to initialize the second stage of the process whereby the vehicle is run in a sequence of simulation runs using square pulse inputs of varying size and length, as shown in Figure 10. The process (b) Bode plot starts with a selected minimum input length and begins Figure 8 Time history of roll-axis frequency sweep by first increasing the input amplitude up until the and computed Bode plot of frequency response to maximum attitude change required is achieved. This compute attitude bandwidth and phase delay process then loops over a range of input lengths, each The final stage of the test is the evaluation against the pulse input increasing in period after each loop of ADS-33 criteria – this is illustrated in Figure 9. Here the increasing input amplitudes. As such, the process minimum value between the roll attitude phase and gain generates a collection of attitude quickness curves bandwidth, which is the procedure for a rate response shown in Figure 11, from which the analysis code type according to ADS-33, is plotted against the selects the maximum quickness achieved. Attitude computed phase delay. It can be seen that against the quickness differs somewhat to criteria such as ADS-33 criteria, the roll attitude bandwidth is well into bandwidth in that it is not defined by a single point, so a the Level 1 region. This is the technique used method was devised as to adjudge whether a collection throughout the handling qualities analysis routines of points are overall Level 1, 2, or 3. The current method looks at the percentage of points occupying criteria, as it simply requires maximum control input each region, currently a threshold point of 90% or more steps to be made and then the maximum rate or attitude in a single region (can be set to whatever the user response to be measured. However, for the current level requests) determines the assigned handling qualities of model fidelity, more philosophical issues arose level, otherwise the worse region that the curve enters is around the meaningfulness of such a test. This is the assigned handling quality level. This aspect is not because the linear models used feature little or no from the ADS-33 methodology but provides some physical limitations, i.e. there are no nonlinear flexibility for users to make a judgment whether they aerodynamic effects such as aerodynamic stall or high consider a certain majority of points from the simulation angle of attack drag increase or limits such as rotor analysis to give the appropriate result. It also confers a thrust, engine power, actuator or structural limits way to provide some robustness to a spurious point that represented. This aspect also somewhat applies to the might otherwise skew the overall outcome. quickness testing but there are two justifications for retaining this type of test at this stage. (a) Maintaining a general approach to the methodology development – the current model is linear and generally not applicable for large amplitude motion but subsequent developments may lead to the use of higher fidelity models that are more appropriate. (b) A simplified synthesis of the effect on this handling qualities parameter can be evaluated on a linear model by limiting the control inputs. In this way an effect on the large amplitude criteria can be generated by using simple position saturation limits on the value of the rotor cyclic, collective or aerodynamic surface inputs applied to the vehicle model. This prevents the test procedure from applying a control input of any size to the model to Figure 10 Time histories of roll axis attitude generate the desired Level 1 response, and thus when quickness testing input and output parameters comparing designs, gives a sense of the maximum control force/moment and damping capability for some equivalent maximum control input size.
Figure 12 (a) and (b) show the typical output from a roll-axis large amplitude response handling qualities test, the results shown are for the UH-60-like rotorcraft model in hover. The plots show the time response of both the roll rate and roll attitude. There are three pairs of axes for each test run with each plot having different criteria applied to enforce the plot color for the ADS-33 limited, moderate and aggressive agility categories. In this way, the curve is colored according to the agility category used; this is evident in Figure 12(b) where, as an example, the rotor input limits were reduced to 33% Key: of the nominal values. In this case, it can be seen that Level 1 achieved Level 2 achieved Level 3 achieved although vehicle maximum rate response for the vehicle st for limited agility (1 column of plots) category Figure 11 ADS-33E Quickness criteria (roll axis) remained Level 1 (green) when compared to its 100% Large Amplitude Response (Roll Axis) input limit cases in (a), the handling qualities for the The large amplitude response testing was a relatively moderate and aggressive MTE categories were degraded straightforward test to implement compared to the other to Levels 2 (magenta) and 3 (red) respectively.
In the current implementation, each axis of large Key: amplitude attitude change response testing confers three Level 1 achieved Level 2 achieved Level 3 achieved distinct handling quality level scores for each of the MTE categories of limited, moderate and aggressive agility. In forward flight, ADS-33 specifies criteria only for the roll axis, thus a fourth HQ score is provided in forward flight testing (not shown) . Looking forward, the provision of a score for all the possible categories may be unnecessary, as part of a future implementation Limited Moderate Aggressive Agility Agility Agility the overall conceptual design problem definition might include an interpretation of the NDARC mission into a more refined set of ADS-33 requirements and thus specify which of the agility requirements should be used. In fact, this idea is applicable to a number of the ADS-33 test parameters which are evaluated against a range of criteria that is dependent on the MTE, visual conditions and pilot attentional demands relevant to the (a) 100% Rotor input limits mission intended for the vehicle in question.
Preliminary Results Preliminary results from the execution of the majority of the process outlined in Figure 1 are presented and discussed in the following section. The element omitted from the process is the final feedback of the handling Limited Moderate Aggressive qualities analysis results back to the conceptual design Agility Agility Agility process, i.e. the NDARC tool, an aspect that will be discussed further in the final discussion. Nevertheless, the following results represent a near complete analysis loop demonstrating a method that includes the import of conceptual design data, flight dynamics model generation, the application and configuration of a control law, and then the execution and presentation of a (b) 33% Rotor input limits handling qualities analysis using those models.
Figure 12 Time histories from roll axis large amplitude testing Figure 13 Table of handling qualities Levels assigned generated from handling qualities methodology Figure 13 shows complete results from a handling the rotor radius across the frequency-amplitude response qualities analysis of the UH-60-like model at hover, spectrum. Figure 14 (a) shows the roll axis with the stability augmentation enabled. The table bandwidth/phase delay criteria, it can be seen that shows the handling qualities Levels achieved by the although all the points reside within the level 1 region model for each axis applicable to each criterion for the (All other MTEs, full attended operations and UCE=1 ADS-33E criteria currently. A prominent result is that a category), the variation in the roll axis bandwidth is 0.5- great deal of the criteria is assigned Level 1 handling 1 rad/s between the lowest bandwidth at 75% radius and qualities. This is an outcome that has been observed for highest for the 125% rotor. This is a reasonably all the test models (Bo-105-like and LCTR2, not shown) significant variation, especially when it is considered and is probably the outcome of two key factors, firstly that there is only a difference of 1.5 rad/s from the Level the two vehicles that are representative of existing 1 to the Level 3 boundary. The phase delay is more designs (UH-60 and Bo-105-like) are likely to have significantly affected, with the 75% rotor more than reasonably good basic handling qualities in the light of twice the value of the 100% rotor. This is intuitive, as their longevity of use and successful service. The level the key contribution to the lag represented by the phase of modeling fidelity is also important, in particular there delay is the rotor flap time constant, which is inversely are a variety of un-modeled lags, delays, nonlinearities proportional to rotor radius to the power of 4 via the and couplings that would be attributed to actuator Lock number (equation 21, hover approximation) – the dynamics and limits, engine power, torque and dynamic smaller the radius, the greater the flap time constant (all limits and aerodynamic effects such as inflow dynamics, other aspects fixed).
stall, and interference effects that all would contribute to ͳ ߬ ൌ ൗ (21) ȳߛ handling qualities degradations.
Similar trends are observed for the quickness parameter This raises one of the research questions highlighted in in Figure 14 (b), where the 75% rotor exhibits worse the introduction of this paper – ‘ what can be learned by handling qualities with borderline Level 1 and Level 3, a handling qualities analysis at this level of modeling while the 125% rotor is better. As seen for the fidelity ?’ a level that is consistent with the vehicle bandwidth, the variation with airspeed is not distinct, modeling/information/data available from the with no particular difference with speed observed for a conceptual design process. In light of the handling given radius. Figure 14 (c) shows the roll axis large qualities results just presented, an argument could be amplitude response (control limits applied) for the made that greater modeling fidelity is required, radius and speed variations, for the 4 agility categories.
especially if an accurate appraisal of the absolute level Here, the trends do not follow those observed for the of handling qualities is required. However, there is a bandwidth and quickness, with the 75% radius rotor trade-off to be considered; adding modeling complexity having a lower large amplitude response capability than and fidelity will incur cost, in terms of computational the 100% radius, but not much observable difference cost, data requirements and perhaps reduced between the 100% and 125% rotor. Figure 14 (d) shows engineering insight. An alternative viewpoint is perhaps the low speed roll/pitch midterm response criteria, the criteria as they now exist need to be somehow which is essentially an analysis of the vehicle stability.
adjusted to factor in the level of modeling fidelity used This criterion is only applicable to hover and low speed, for the conceptual design handling qualities analysis.
hence only the hover (0kts) and 40kt points are shown.
Handling Qualities sensitivity analysis No discernable trends are observed, which is somewhat A demonstration of the handling qualities sensitivity to to be expected, as these results are strongly influenced design parameters is illustrated in Figure 14(a)-(d) and by the action of the stability control augmentation.
Figure 15(a)-(d). Figure 14(a)-(d) illustrates a subset of Ultimately, the action of the control system is to return the handling qualities parameters evaluated for the roll similar stability characteristics for each of the vehicles axis of the UH-60-like configuration model, (control with the varied rotor radius. What is not indicated by and stability system applied) for a variation of the main this analysis, and perhaps a useful handling qualities rotor radius design parameter, and a range of speeds. indicator, is how much feedback control activity is The handling qualities parameters have been selected to required to achieve these similar stability provide an impression of the effect of the variation of characteristics, a subject discussed later in this paper.
(a) Roll axis bandwidth and phase delay (b) Roll axis attitude quickness (c) Roll axis large amplitude response (d) Hover/Low-speed Pitch/Roll oscillations Figure 14 Results of main rotor radius variations on various ADS-33E Handling qualities (roll axis) criteria at hover and forward flight for UH-60-like model Figure 15(a) to (d) presents a different comparison, in demonstration and helps somewhat in reducing the this instance, a single handling qualities criteria, roll complexity in interpreting the input-output axis bandwidth/phase delay, is compared for the dependencies.
variation of 4 vehicle model input parameters: main The radius variation is the same result as plotted in rotor radius, main rotor blade chord, main rotor hub Figure 15(a) and is included for comparison only.
spring stiffness, and main rotor flap moment of inertia.
Figure 15(b) shows that the effect due to chord Each of the parameters was varied entirely variation, again for a 75%/125% variation from a independently, with no consideration made for real- nominal 100%, has a similar but much reduced effect to world interdependencies, such as variation in radius also that for a radius change, with the 75% chord generally impacting flap moment of inertia. This would differ producing the lowest bandwidth, and the 125% chord from an analysis fully integrated into a conceptual the highest and the inverse relationship for the phase design process, where the design code would provide a delay. The effect due to a variation in the hub spring fully ‘ consistent ’ input dataset. Nevertheless, the single stiffness, and blade inertia shown in Figure 15(c) and parameter variation analysis provides a useful initial (d) are minimal for this handling qualities parameter. numerator and denominator of the Lock number but are This is due to the fact that the command and inverse only linearly proportional to the rotor flap time constant model in the control system compensates for any and so have a less significant effect than the rotor radius variations in the bare airframe dynamics to return variation.
similar bandwidth characteristics. The variation of blade inertia has the inverse effect on the roll bandwidth to that of the chord. Both terms respectively appear in the (a) Main rotor radius variation (b) Main rotor blade chord variation (c) Main rotor hub stiffness variation (d) Main rotor blade inertia variation Figure 15 Results of 4 design parameter variations on ADS-33E Handling qualities roll axis bandwidth/phase delay criteria at hover and forward flight for UH-60-like model one possible option. However, use of the handling Final Discussion qualities level ratings in their integer form may not In summary, the results in the previous section confer enough granularity, especially if points go demonstrated that the analysis for a limited subset of beyond a Level 3 or Level 1 boundary, as illustrated by design parameter variations, output handling qualities the results in Figure 14 (a) where all the results are parameters, and evaluation flight conditions, generated a Level 1, but with different margins. As such, the points complex picture. Even the analysis using single for each criterion could be converted to a continuous parameter variations did not always produce clearly form to provide sensitivity within each handling discernable dependencies and trends. This is not an qualities level, as demonstrated by ref [16]. For the unsurprising result as the underlying expressions overall handling qualities assessment a single overall governing the flight dynamics of the vehicles have a handling qualities score could be a possibility, although complex relationship with the input design parameters, a greater breakdown is likely to be desirable. Options with the same terms often appearing multiple times in could be to divide the handling qualities into subgroups many counteracting stability and control derivatives.
along the lines of axis of response, roll, pitch, yaw, The action of the control system also masked the effects vertical, etc. An alternative approach might be to of the design parameter variations on the handling categorize along the lines of the frequency-amplitude of qualities parameters and so closer inspection of the response, with a single handling qualities score control system actions is crucial.
computed for short term response (bandwidth), However, calculating the effect of the input design moderate amplitude (quickness), and large amplitude parameters on higher-level handling qualities (control power), with other categories for interaxis parameters helps to provide a more direct reflection on couplings and stability, in this format, the different axes the complex handling qualities relationships than of response are subsumed within each category. Modern techniques that purely examine the fundamental flight optimization tools may render these concerns dynamics terms might. Nevertheless, it is evident that unnecessary and ultimately the number of parameters the outstanding challenge of translating handling included is dependent on the ‘weight’ that handling qualities analysis to a form suitable for a conceptual qualities are conferred by the conceptual designer and design process is not insignificant. The remainder of on the ‘ confidence ’ in the results calculated.
this section of the paper will review the progress of the Two particular issues arose when considering these work, encompassing both the results and methodology, types of unpiloted handling qualities evaluations. First is to guide a discussion of areas requiring further one of the questions raised in the introduction, is it more development and analysis.
appropriate to compare bare-airframe designs or To reiterate, the ultimate goal of the work presented in vehicles with stability and control augmentation this paper is the realization of a design process that fully applied? Arguments can be made for either case; on the integrates handling qualities into a rotorcraft conceptual one hand, comparing bare-airframes without design process. The progress so far indicates that there augmentation would seem to be a more fair and are multifarious handling qualities parameters and unambiguous approach without the effect on control law relationships between those parameters and possible augmentation obfuscating a direct comparison.
design variables; the question is how to quantify the However, on the other hand, it is somewhat unrealistic handling qualities to guide a design downselection or to analyze bare-airframes as no modern sophisticated optimization process? Incorporating all the possible rotorcraft would fly without some form of control handling qualities parameters individually as design augmentation. In such a scenario, poor bare-airframe targets might be unwieldy and difficult to converge a stability characteristics might unduly count against a design upon, and thus some form of grouping of the design that might otherwise possess desirable criteria may be required to reduce the number of characteristics and would be perfectly feasible to variables.
operate once stability and control augmentation were applied. Furthermore, comparisons in stability Using the handling qualities Levels assigned for each augmentation margins, and other control related factors criterion to either compute a total score or an average is will be important when comparing designs as the handling qualities parameter variations may be minimal Overall, the work presented in this paper has but the control system compensation may not. Secondly, demonstrated how a broad array of technical issues a practical aspect exists as many of the rotorcraft across flight dynamics stability and control, simulation designs are likely to exhibit a large amount of instability and modeling, control law design and handling qualities in their natural (bare-airframe) flight dynamic response, testing and evaluation had to be confronted to as well as strong control and dynamic response inter- implement even a moderately comprehensive handling axis couplings. Using a control law to ameliorate and qualities analysis of relatively low fidelity models.
mitigate these effects is desirable to make the testing Although it is too early to determine many conclusions more tractable by protecting against model divergence about what questions such a methodology might most induced by unstable dynamics. However the bare- effectively answer and how best it might be deployed, it airframe should not be completely forgotten, depending is considered that a good foundation for the next phase on the 'reliability' of the augmentation. ADS-33 allows, has been established. The following conclusions and -3 with a probability of less than 2.5 x10 per flight hour, lessons learnt are submitted: degradations to level 2 within the operational flight The output data of the conceptual design tool envelope, and Level 3 within the service flight NDARC provided sufficient information to define a envelope. Other specific failures are defined, such as basic rotorcraft flight dynamics model. A caveat is single failures that cause complete or partial loss of the that the vehicle moment of inertia characteristics flight control syst em ‘shall not cause dangerous or will require estimation if the NDARC tool does not intolerable flying qualities’. Whether this is something provide them.
handling qualities analysis at a conceptual design level The application of a control system to primarily can address is an open question but it indicates that the augment the stability of the bare-airframe flight bare- airframe cannot be completely ‘unflyable’, dynamics models is advantageous as it provides certainly if current standards are applied.
models with better baseline characteristics for Finally, as indicated in the previous paragraph, the handling qualities analysis, reducing the risk of presence of the control and stability augmentation offers model divergence. It also offers additional handling alternatives to directly comparing the ADS-33 handling qualities analysis options such as evaluating the qualities for designs. Two designs with equivalent level of augmentation and actuator demands handling qualities might be dissociated from another by required to achieve certain stability and response examining how much stabilization and control action is characteristics.
required to attain a particular level of handling qualities.
Preliminary results from variations of example One of the indicators for evaluating this aspect could be vehicle design variables showed measurable to look at the magnitude of the feedback gains required handling qualities outcomes. However, assigning to confer certain levels of stability and damping of the them a Level 1,2 or 3 rating may not be a suitable response. A vehicle design requiring more gain than method of quantifying the handling qualities in a another might be deemed inferior as high gain might vehicle design optimization and a more continuous lead to negative effects such as high actuator activity, measure of ‘handling quality’ may be required.
rate limiting or saturation. These actuator aspects could The current ADS-33 handling qualities boundaries also be evaluated directly through the examination of may not be meaningful for fidelity of the flight actuator RMS (e.g. ref [16]), or the use of control dynamics models currently being derived from the system criteria such as the Open-Loop Onset Point conceptual design data. Possible options are to (OLOP) design criteria (ref [17]), which is used to move the boundaries to compensate for modeling predict the potential handling qualities impact simplifications, to increase fidelity, or to represent associated with actuator rate limiting.
higher fidelity effects indirectly by using techniques such as equivalent delays, etc.
Summary and Conclusions This paper has described a process to generate and Future Work analyze the handling qualities of models derived from Referring back to Figure 1, one of the key outstanding the output of the NDARC conceptual design tool.
issues is how to ‘close the loop’ with an overall conceptual design process. A number of avenues for examined including tiltrotors, co-axials and winged exploration of how to feedback useful handling qualities compounds.
results have been proposed, and will form the core Addressing the modeling fidelity aspects is an ongoing aspects of future work which will most likely effort. Thus far, the analysis applicable to this area has encompass these aspects: been limited to the comparisons presented in the flight 1. Determining handling qualities boundaries dynamics modeling section. These have demonstrated appropriate for conceptual design. This may entail that the stability and control derivatives being computed adjustment of boundaries of current criteria to from the input data are reasonably representative when reflect modeling simplifications or the estimated compared to other modeling codes. However, if this tool margins that simplified dynamics confer, or is to be used in actual studies, additional validation introduction of higher fidelity effects or their effort is required, including comparisons to handling representation through synthesized delays or other qualities analyses conducted on equivalent vehicles techniques. from higher fidelity simulations or flight test.
2. An analysis of the control system requirements in Furthermore, greater involvement of conceptual design terms of the level of augmentation required, subject matter experts in the future developments will actuator demands and margins against future be an important factor to developing an understanding unforeseen handling qualities issues (i.e. achieving of the design questions that have a strong interaction greater than Level 1-2 boundary in a conceptual with handling qualities, which will ultimately guide how design). to best deploy the methodologies being developed.
Acknowledgements Another key area for future analysis and development A number of individuals require acknowledgement for relates to the modeling capabilities of the tool. Two their support, guidance and discussions with the author aspects are of particular interest: 1. The number of on a variety of topics that encompassed the work in this vehicle configurations that can be modeled 2.
paper. From NASA Ames Research Center, Colin Developing a greater understanding of the trade-offs Theodore, Wayne Johnson and Carlos Malpica are between model fidelity and complexity and the design acknowledged. Chris Blanken, Mark Tischler, Tom process, i.e. what can be credibly assessed and what is Berger and Hossein Mansur of the US Army the most critical aspect – accuracy, or the ability to Aeroflightdynamics Directorate at Ames Research rapidly predict handling qualities trends over a broad Center are also acknowledged. Gareth Padfield, array of design cases.
Professor Emeritus from the University of Liverpool, is Adding modeling capability to increase the types of also thanked for review comments and providing vehicle configurations is the logical next step once the technical papers.
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