Aerospace Science and Technology 13 (2009) 92–104 www.elsevier.com/locate/aescte Flight testing of a rate saturation compensation scheme on the ATTAS aircraft ✩ O. Brieger b,∗ , M. Kerr a,1 , D. Leißling b , I. Postlethwaite a,1 , J. Sofrony a,1 , M.C. Turner a,1 a Department of Engineering, University of Leicester, Leicester LE1 7RH, UK b Institute of Flight Systems, German Aerospace Centre (DLR), Lilienthal Platz 7, 38108 Braunschweig, Germany Received 5 December 2006; received in revised form 7 September 2007; accepted 8 May 2008 Available online 27 May 2008 Abstract This paper presents the application of a rate saturation compensation scheme to the DLR Advanced Technologies Testing Aircraft (ATTAS) and the results of the subsequent flight tests. Details of the design philosophy and the flight tests, termed SAIFE (Saturation Alleviation InFlight Experiment), which employed the HQDT (Handling Qualities During Tracking) test technique, are presented, as well as pilot flight test reports (PFRs). The rate saturation compensators were designed based on the anti-windup (AW) control philosophy, with the aim to reduce the deleterious effects of rate saturation on the piloted aircraft dynamics, and hence provide an increased flight envelope (operating envelope) for acceptable aircraft handling qualities and reduced PIO (Pilot-in-the-Loop/Pilot-involved Oscillation) tendencies. The achievement of this goal was primarily determined by subjective pilot handling qualities ratings and PIO ratings, and secondly by supporting flight test data. The results show that the compensation scheme greatly reduced the level of rate saturation in all instances (flight conditions), making the aircraft less PIO prone in almost all investigated cases, while exhibiting either unchanged or improved handling qualities. Most notably, the flight tests demonstrated the definite potential for well designed AW compensators to improve the safety and handling qualities of aircraft during rate saturation, with some flight conditions exhibiting dramatic improvements.  2008 Elsevier Masson SAS. All rights reserved. Keywords: Handling qualities; Pilot-in-the-loop oscillations (PIO); Rate saturation; Anti-windup compensation; Flight test; Handling qualities during tracking (HQDP) 1. Introduction It is well known that rate limits present a problematic nonlinearity, whether superimposed on the surface deflection commands in a flight control system or defined by the physical constraints of the actuation system itself. Rate limiting adversely affects both the stability and performance properties of the system, potentially catastrophically. A number of spectacular accidents during the development phase of fly-by-wire (FBW), 4th generation fighter aircraft, such as the JAS 39 Gripen and ✩ This article was presented at the German Aerospace Congress, 2006. * Corresponding author. E-mail address: oliver.brieger@dlr.de (O. Brieger). 1 Research supported by the UK Engineering and Physical Sciences Research Council. 1270-9638/$ – see front matter  2008 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ast.2008.05.003 the YF-22, have been attributed to the destabilising effects of actuator rate limiting. These destabilising effects have been determined to be a major factor in CAT II PIOs. CAT II PIOs are predominantly quasi-linear pilot vehicle system (PVS) oscillations with rate and/or position limiting as the only explicitly nonlinear elements [13]. PIO behaviour associated with rate limiting has been observed in both civilian and military aircraft, with the alleviation of such PIO tendencies being an objective of the aeronautical community over the last 15 years (see, e.g. [12,13]). Subsequently, the issue of PIO proneness of an aircraft, including the specific effect of rate saturation, has become an important design consideration in modern FBW aircraft. Within the GARTEUR (Group for Aeronautical Research in Europe) framework, Action Group 15 (AG15) is currently involved in advancing PIO research in the field of analysis and test techniques, as well as online rate saturation compen- O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 sation algorithms, which are the focus of this research. Online algorithms, such as nonlinear filters, phase compensators and feedback schemes have already been proposed [11,12,16]. However, while these methods have been implemented successfully, they are typically designed in an ad-hoc manner, and thus may not provide reasonable guarantees for system stability and performance. One key objective of AG15 has been to develop methods to rigorously and systematically design rate saturation compensation algorithms that provide stability and performance guarantees, and hence are more likely to alleviate the effects of rate saturation in practice. This paper presents the results from the design of such an algorithm, as proposed in [19], that is based on the anti-windup (AW) philosophy, and its evaluation via flight tests, termed SAIFE (Saturation Alleviation In-Flight Experiment), on the DLR Advanced Technologies Testing Aircraft (ATTAS) at DLR, Braunschweig, Germany in July of 2006. In the experiments, in order to exploit fully the AW compensator capability, the software-imposed rate limits within the experimental control laws were reduced to a degree that rate limiting would occur during high frequency, large amplitude pilot inputs. This degradation was only applied to the roll axis, since the ATTAS testbed is comparatively agile in roll, whereas structural load limits would have compromised a rigorous evaluation of the pitch axis. Testing was conducted in a build-up approach in three phases at various flight conditions, allowing for a thorough analysis of system dynamics at up-andaway and landing-approach flight conditions. The paper is outlined as follows. Initially, an overview of the effects of rate limiting on the aircraft dynamics is given which serves as motivation for the research undertaken. This is followed by a discussion of SAIFE and a description of the experimental test aircraft (ATTAS), as well as the test methods employed, providing both handling qualities ratings (HQRs) [3] and PIO ratings (PIORs) [3]. The subsequent test results are to be used to determine the effects of the AW scheme on the piloted-aircraft system and the ability to improve handling qualities and reduce PIO susceptibility. The AW design philosophy is presented thereafter, where it is shown how this aims to alleviate the effects of saturation in a theoretically rigorous manner. The design of the AW controllers for the ATTAS aircraft is presented, which gives an overview of the design trade-offs involved in the synthesis and the specific methodology employed. Finally, the results of the experimental evaluation of the AW controller on the ATTAS aircraft for a range of up-andaway flight conditions and offset landing tasks are presented. These results are discussed with reference to pilot flight reports (PFRs), time domain data and preliminary analysis. Conclusions are given in Section 8. 2. Motivation: Aircraft with rate limiting The effects of rate limiting of aircraft actuators have been well studied (see [2,4,9,12,13] and the references therein). The following review provides the technical basis for the discussion of rate limiting effects in the paper, while also motivating the compensation philosophy employed in the present research. The problem of saturation is ubiquitous, with all physical sys- 93 Fig. 1. Phase lag caused by rate limit. Slew rate limit of ±1 unit/second; sine wave of 2 rad/s applied. tems subject to constraints on their inputs and outputs at some level. Both amplitude and rate limitations will be present, both physically and often as software limits. Furthermore, for aircraft systems, and specifically PIO phenomena, the effects of rate saturation have been identified as a leading factor in degraded aircraft response and stability [9,13]. This is because, unlike amplitude saturation, rate saturation is a dynamic nonlinearity, and as such contributes additional phase lag to the response of the system. It is this phase lag that is often the major cause of degraded system performance during saturation, as it can greatly reduce the stability margins of the closed-loop system, potentially giving rise to unstable or oscillatory (limit cycle) responses by significantly affecting the magnitude response of the closed loop system. Such observations have led to successful analysis tools for PIO behaviour, notably the OLOP criterion [2]. The dynamics of full rate limiting can be quantitatively observed in Fig. 1.2 This shows the standard saw tooth triangle response of the rate limiter when it is completely activated (full saturation). Note that, in addition to the reduced amplitude of the signal, there is a phase difference between the peaks which gives rise to the detrimental phase lag. To model the rate limiter, time domain equations can be derived, but to facilitate control system design and frequency domain analysis, two other approaches are commonly used. The first is to analyse the time domain response of the system using harmonic balance methods, which provides a quasi-linear frequency domain model of the system [9]. The second is to model the rate saturation element as a first order feedback system, as shown in Fig. 2. This simplified actuator model gives an accurate description of the low frequency behaviour, and is suitable for model based control. This can also be analysed based on 2 The rate limiter can operate in three modes: no limiting, partial limiting, where the limiter only acts over part of the signal period, and full limiting, where it acts continuously on the signal over several periods, as depicted in Fig. 1. The frequency ranges of these modes are also shown in Fig. 3. 94 O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 Fig. 2. Feedback representation of the rate limited actuator. Fig. 4. Control loops in PIO analysis. Fig. 5. ATTAS testbed. Fig. 3. Rate limiter describing function Bode plot. harmonic balance methods to give a similar quasi-linear model of the system [2]. This model, termed the describing function of the rate saturation, is described by the following equation [2]: πr N(a, ω) = (4r/πωa)e−j arccos( 2ωa ) (1) where ω and a are the frequency and amplitude of the sinusoidal input, and r is the rate saturation limit. Fig. 3 shows the Bode plot of the magnitude and phase characteristics of this quasi-linear model of the rate limiter. Note the phase and magnitude loss at higher frequencies where rate saturation is more pronounced. Based on these models of the rate limiter, analysis can be performed to determine the effect of rate saturation on the piloted aircraft. For example, in [2,12,16] it is shown how the frequency response of the aircraft changes during full rate saturation and the subsequent effects on stability and handling qualities. A particular concern is sustained or divergent oscillations in the aircraft response, as associated with PIO behaviour, and for this limit cycle analysis based on the describing function provides a useful, albeit approximate, first order analysis, which can be supplemented with analysis based on nonlinear simulations and bifurcation theory. The difficulty with such analysis is the fidelity of the models of the pilot behaviour during the demanding tasks where rate limiting often presents severe problems. Often simple gain or first order models are employed, with the overall piloted aircraft system being represented as in Fig. 4. As the accuracy of the pilot model is always questionable, high fidelity analysis of piloted-aircraft behaviour is difficult. However, existing analysis techniques, such as OLOP and other more recent derivatives, have been found to give a good indication of the PIO tendencies [12]. From such analysis it has generally been agreed that the effect of the additional phase lag, as seen in Fig. 3, is a leading cause of poor aircraft behaviour during rate saturation. Furthermore, rate limiting, potentially combined with other nonlinear effects, can evidently have a drastic and sometimes catastrophic effect on the piloted aircraft behaviour, mandating its consideration in FCS design for FBW aircraft. Based on the above, methods have been proposed to alleviate the detrimental effects of rate saturation. Examples include nonlinear pilot input filtering and smart rate limiters that preserve phase, and more advanced techniques, such as phase compensators and AW techniques [4,11,12,16]. Of these, those based on the AW philosophy have often been successful. Such an AW approach is employed herein, with details of the design philosophy given in Section 5. In short, it aims to reduce the effects of rate saturation on the overall aircraft response, which implicitly includes reducing the error (magnitude and phase) between the input and output of the rate limiter, and more importantly explicitly includes the provision of improved stability properties and performance during saturation. 3. ATTAS aircraft The ATTAS is a highly modified VFW 614 aircraft which has been operated by DLR as a testbed and inflight simulator since 1986 (see Fig. 5). It features various customized systems, such as direct lift control, enabling rigid body manipulations in 5 degrees of freedom, an adaptive fly-by-wire flight control system, capable of hosting different controller designs and emulating vehicle dynamics of model-based virtual aircraft (InFlight Simulation – IFS), an experimental cockpit and extensive flight test instrumentation. The safety concept realised on the aircraft, with a safety pilot and a mechanical back-up control system as primary assets, allow for the assessment of flight control software in the authentic environment by an evaluation pilot, without having to meet extensive certification requirements. In cases where flight O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 95 Fig. 7. Pilot input schematic. Fig. 6. Test points within the ATTAS envelope. safety may be compromised, the safety pilot can always override commands generated by the experimental control laws via the mechanical back-up system. For the SAIFE flight test campaign, the aircraft was equipped with a passive side stick as primary control inceptor at the evaluation pilot’s station to facilitate high frequency, large amplitude inputs and potentially precipitate ‘bang-bang’ control. The AW compensator design was based on the basic ATTAS VFW 614 dynamics, including the scheduled control laws engaged in the FBW mode. 4. Planned flight tests To demonstrate the effectiveness of the AW compensation, four up-and-away flight conditions and one landing-approach flight condition were selected to assess different compensator designs (see Fig. 6 and Tables 2 and 3). Two test pilots from the German Armed Forces Technical and Airworthiness Centre for Aircraft participated in the trial and acted as evaluation pilots, one previously known to be a high gain pilot and one a low gain pilot. As mentioned earlier, testing focused on the roll axis. To degrade system performance and handling qualities, the software imposed aileron command rate limits were reduced to 50% (12.5 deg/s) and 60% (15 deg/s) of the full authority values for up-and-away and landing-approach test cases, respectively. All test conditions were assessed with the AW compensator both engaged and disengaged, while the rate limit degradation was retained throughout. Pilots were not aware if the AW compensation was active and plainly evaluated aircraft response. Prior to any flight testing, procedures and test methods were trained using the fixed base ATTAS simulator, which also provided an insight into the expected real aircraft response. 4.1. Up-and-away testing Testing at all up-and-away flight conditions was conducted in cruise configuration, in a build-up approach, consisting of three test phases [14,21]: • Phase I testing comprised semi-closed loop and closed loop bank angle capture tasks, to enable the pilot to become familiar with the aircraft dynamics, requiring qualitative pilot comments. • Phase II testing involved the application of the HQDT test technique, which currently is the only method that allows for systematic, high bandwidth PIO resistance testing, and is therefore sometimes also referred to as handling qualities stress testing. This test method was developed to investigate the entire range of possible pilot input commands with respect to frequency and amplitude which may occur during a flight under certain circumstances, as depicted in Fig. 7. When tracking becomes necessary, i.e. an error signal exceeds a certain threshold prompting the pilot to close the control loop, many pilots naturally adopt the lowest gain3 (lowest aggressiveness) piloting technique that is consistent with satisfactory task performance. However, when pilots experience stress, anxiety or fear they assume a high gain (high aggressiveness) control technique. In order to ensure that in such an event system stability is not compromised, which could promote a PIO, and stability margins are sufficient to accommodate such changes in pilot dynamics, the HQDT test technique was devised to uncover deficiencies caused by high gain pilot inputs, including system degradation due to saturation. Its aim is to artificially increase pilot aggressiveness, i.e. the frequency and amplitude content, by requiring the pilot to track a precision aim point as aggressively and assiduously as possible, correcting even the smallest tracking error as rapidly as possible. Initially commencing with small amplitude and low frequency inputs, control is gradually tightened, progressing to higher frequencies and amplitudes up to ‘bangbang’ control, until finally the pilot behaves like a switching function, reversing the control input in the instant the piper or other aircraft fixed reference moves through the aim point. The degree to which an aircraft follows these violent inputs is quantified using PIORs using the PIO Rating Scale [3]. The PIORs give an indication of PIO tendency, as determined by the pilot based on a decision-tree. During the SAIFE campaign the pilot was tasked to apply the HQDT technique while capturing a wings level roll attitude from an initial 30 deg offset using the roll attitude indicator in the main head down display (MHDD) as reference. 3 Here high gain and low gain refer to the aggressiveness with which the pilot attempts to perform a certain task and is a combination of pilot input frequency and amplitude, as shown in Fig. 7. This is similar to the definition of pilot gain in [13], except here the frequency content is also of explicit interest. 96 O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 Fig. 10. Performance criteria for tracking task. Fig. 8. Generic tracking task in MHDD. criteria were defined as illustrated in Fig. 10. Desired performance is achieved when the WL-symbol overlaps or touches the aircraft symbol. Adequate performance is achieved when the WL-symbol can be positioned within the wingspan of the aircraft symbol. Display latency was not found to be a factor during the assessment. 4.2. Landing-approach testing Fig. 9. Generic tracking task sequence. • Phase III testing evaluates handling qualities in an operationally relevant context. A target tracking task was defined, requiring the pilot to closely track a generic birdy (aircraft symbol) projected into the MHDD with the aircraft water line (WL) symbol (refer to Fig. 8). The birdy performed a predefined sequence of ramp and step-type roll attitude changes, requiring the pilot to perform and assess gross acquisition and fine tracking handling qualities. The tracking task in roll ideally required no compensation in pitch, as the birdie was initiated at the trimmed pitch angle. If such deviations were induced, the pilot was required to correct for the pitch deviations to achieve the roll task in accordance with Fig. 10. The birdy tracking task is depicted in Fig. 9 and was originally devised to assess pitch axis dynamics. It has been successfully used by the US Air Force Test Pilot School on the NF-16D VISTA [7] as a heads-up display (HUD) tracking task and features a range of large amplitude step and ramp alterations, intended to evoke aggressive pilot inputs and consequently actuator saturation. For the SAIFE flight tests the task amplitudes were scaled to fit the ATTAS roll capability. Evaluation pilots were tasked to provide Handling Qualities Ratings (HQRs) [3] to quantify system performance during gross acquisition and fine tracking, respectively. Performance As an additional operational task, offset landings were performed at Schwerin–Parchim airfield (EDOP) to evaluate the effectiveness of various compensator designs during the landing-approach phase of flight. For these landings, the aircraft was reconfigured with flaps set to 14 deg and the landing gear extended. The pilot was tasked to establish a nominal approach flight path on the active runway with an initial 200 m lateral offset to the runway centreline. When passing through 500 ft AGL (Above Ground Level) the pilot was required to aggressively capture runway centreline and maintain the nominal flight path to attempt to hit a specified touch down point within the desired touch down zone marked on the runway. System performance was evaluated by means of HQRs and PIORs. Since the primary focus was on the evaluation of the lateral/directional dynamics, and the combined task proved to be too complex with such a degraded system, the precision touch down requirement was dropped in favour of precise centreline control. 5. Anti-windup philosophy Section 2 discussed basic properties of rate limited systems and the need to alleviate their potentially deleterious effects. In order to reduce such effects of rate limits on system performance, three obvious choices are available to the flight control system designer: 1. Limit the aggressiveness of pilot reference inputs at the output of the stick. This entails either saturating or filtering the pilot command inputs to the flight control system so as to ensure that demands, which would require control signals of too high rates, are not commanded [11]. Effectively, this ensures that the rate limits are not excited by pilot inputs. The problem with this approach is that the pilot’s ability to control the aircraft may be reduced and that external disturbances, such as wind gusts, are not catered for and hence may induce saturation. 2. Re-design the linear controller to explicitly cater for rate limits. Although feasible in principle, such an approach is O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 potentially fraught with problems. Firstly, it may be difficult to design a controller which simultaneously meets small signal (linear) and large signal (rate limited) performance specifications. Moreover, it may not be costeffective to perform a complete re-design if much time and effort have been invested in the flight testing of the original linear compensation. 3. Augment the existing linear controller with an additional element which is only active when rate limiting occurs. The advantage of this approach is that the baseline controller can be maintained and will function normally, except in cases when the actuators undergo rate limiting. This allows small signal performance to be handled by the linear controller and large signal performance to be enhanced by the additional element. In this paper we take the third approach to catering for rate limited actuators. This approach is arguably the most pragmatic and is probably the one most studied, both within the aerospace industry and within the academic community. In fact, the socalled phase compensation methods developed by SAAB and the former DASA are examples of this latter approach [8,23]. In the phase compensation methods, a filter, which only becomes active during rate limiting, attempts to keep the phase-lag between the input and output of the rate limited actuator to a minimum. In terms of Fig. 1, the objective of the phase compensation techniques is to minimise the phase delay which occurs between the input sine and the output saw-tooth waveform. As mentioned earlier, although these so-called phase compensation methods, particularly those developed by SAAB [16], have had success in coping with rate limited actuators, they also suffer from several drawbacks: • They are not rigorous design approaches; stability and performance guarantees are not provided. • There are no systematic methods to design or tune these compensators; the choice of filter parameters is essentially ad-hoc. • They take no account of the specific aircraft dynamics or the existing linear flight control system. • They simply aim to alter the control signals injected into the actuators, with no consideration given to signals measuring aircraft response. 5.1. An anti-windup approach The phase compensation method developed by SAAB [16] is actually very similar to a class of control augmentation elements called AW compensators. In the case of rate limits, these are linear filters which become active only when rate limiting occurs and act to retain stability and limit performance degradation during rate limiting. The generic structure of an AW scheme is shown in Fig. 11. In this figure G(s) represents the aircraft dynamics, K(s) the baseline controller and Θ(s) the AW compensator. G(s) is assumed to have state-space realisation {Ap , Bp , Cp , Dp }. The pilot command input is r(t) and the aircraft response is represented by y(t). The nonlinear 97 Fig. 11. Control scheme with generic AW compensator. (rate limited) actuators are represented by the nonlinear operator N (.). Note that Θ(s) only becomes active when the signal ũ = u − ur is non-zero, that is, when the plant input is different from the controller output (i.e. rate limiting has occurred). Thus the AW compensator remains inactive until rate limiting occurs and, when it does occur, has the authority to modify the controller’s behaviour through the signals θ1 (t) and θ2 (t). Roughly speaking, θ1 (t) allows rapid modification of controller output for improved performance and θ2 (t) allows the AW compensator to stabilise any unstable (integrator) controller dynamics during periods of saturation. 5.2. Rate limit anti-windup Although its significance in the control of aircraft has been fairly modest, AW compensation is a standard method in the control field and has been studied by many researchers over recent years. Good summaries can be found in [5,10,22], for example. Most of these studies have concentrated on magnitude limits and studies of the AW technique applied to rate limiting are less common (see [15] for some related aircraft work). This fact was one of the motivators for the studies in [17], in which an existing technique for AW synthesis for magnitude limited actuators [18] was extended to systems with actuator rate limits. This scheme makes extensive use of the representation of the rate limit shown in Fig. 2, in which the actuator is modelled by a linear first order low-pass filter with saturation on the rate. For large values of H , this serves as a good approximation to a ‘true’ rate limiter, and also gives a simple model of the linear dynamics of actuators for smaller values of H , where H represents the actuator bandwidth. For this work it is assumed that the signals either side of the saturation block in Fig. 2 are available for measurement. Although this would rarely be the case for a physical rate limit, software imposed rate limits within the control laws are common and this assumption is plausible in most modern aircraft. In fact, for the ATTAS study described here, the aircraft was artificially degraded using software rate limits and hence the assumption on these measurements was entirely reasonable. 5.3. A decoupled design problem The AW compensator used in this paper is synthesised according to the methodology described in [17] (see also [6, 18,20], for related work). The basic architecture is shown in 98 O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 depicted in Fig. 12, which are both defined by the free parameter F . This relationship is given by ⎤ ⎡ Ã + B̃F B̃ M(s) − I Θ1 (s) ⎥ ⎢ = =⎣ Θ(s) = 0 ⎦ . (5) F Θ2 (s) N (s) D̃ C̃ + D̃F One of the motivations behind this parameterisation of Θ(s) is that through manipulating the block diagram, one can then redraw Fig. 12 as Fig. 13. Although Fig. 13 does not represent an implementable AW scheme, this figure is mathematically equivalent to Fig. 12 and thus any analysis conducted using this representation also holds for Fig. 12. The advantage of the alternative representation in Fig. 13 is that it gives a more lucid representation of the AW problem, as it decouples the ideal linear response from the effect of saturation. In particular, it is easy to observe that, providing the nominal system (i.e. aircraft plus linear controller) is stable and M(s) is also stable, then the nonlinear stability problem is translated into ensuring that the nonlinear loop in Fig. 13 is stable. Furthermore, the degradation of linear performance can be measured by the magnitude ′ ]′ , or alternatively, the ‘gain’ from d to ỹ . of ỹd := [yd′ xrd lin d For minimal degradation of linear performance due to saturation, we would like the gain of the map Tp : dlin → ỹd to be as small as possible. Fig. 12. Control scheme with generic AW compensator. Fig. 13. Equivalent representation of system with AW parameterised by M(s). 5.4. Anti-windup synthesis and tuning Fig. 12. In this structure the rate limit, as represented in Fig. 2, has been ‘broken’ into two linear parts and the saturation nonlinearity (see [17]). One linear part is then subsumed into an augmented controller, K̃(s), which is described by the relation ⎤ ⎡ r d = H [K1 K2 − I ] ⎣ y ⎦ , (2)    xrm K̃(s) where xrm is the output of the rate limit and K1 and K2 are the feedforward and feedback components of the linear controller K, respectively. The second linear part (the integrator) is subsumed into an augmented linear plant, G̃(s), which is described by the relation ỹ := y xrm = G(s) I   G̃(s) 1 dm , s  (3) where dm is the saturated rate command to the actuator, as shown in Figs. 2 and 12. With G(s) having state-space realisation {Ap , Bp , Cp , Dp }, the augmented plant is ⎡ ⎤ 0 Ap Bp  ⎥  ⎢ I ⎥ 0 ⎢ 0 Ã B̃ ⎥= G̃(s) = ⎢ . (4) ⎢ ⎥ C̃ D̃ ⎣ Cp D p 0 ⎦ 0 I 0 In this scheme, the AW compensator, Θ(s), is interpreted in terms of two transfer function matrices M(s) and N (s), as Considering Fig. 13, the ‘size’ of the nonlinear map Tp : ′ ]′ indicates how performance of the sysdlin → ỹd = [yd′ xrd tem degrades from that of the linear system during rate limiting. A natural design objective would therefore be to minimise Tp , using a suitable metric, while also ensuring that the nonlinear loop is stable. Unfortunately, the integrator in the rate limit creates problems in achieving unconditional global asymptotic stability of the nonlinear loop. In [17] a method for designing AW compensators for rate limited systems was introduced. Essentially the method produced an AW compensator, Θ(s), which ensured that the local L2 (RMS) gain of Tp is less than a certain value, γ , and that the nonlinear loop is stable in a certain subset, E, of the region of attraction. The synthesis algorithm is described in detail in [17] and in [19] and [1] the tuning algorithm was refined. Here a simplified form of the synthesis equations in [19] and [1] are presented to highlight the main features of the method. Based on the derivations given in [19] and [1], the synthesis problem for Θ(s) guaranteeing stability in a subset E of the state-space and L2 gain of Tp less than γ , amounts to the following steps: (i) Choose design parameters ρ > 0 and ε ∈ (0, 1). (ii) Solve the following Riccati equation for P : Ã′ P + P Ã − ρP B̃ B̃ ′ P + C̃ ′ C̃ = 0. (6) (iii) Construct Θ(s) via Eq. (5) above, with F= −ρ B̃ ′ P . (1 − ε) (7) 99 O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 The gain of the performance map Tp is then bounded by γ = √ 1/ ρ , and an ellipsoidal approximation of the region of attraction for stability is as follows, where d̄i is the rate limit in the ith channel and B̃i is the ith column of B̃: E = {x: x ′ P x  cmax }; cmax = min i d̄i2 ρ 2 B̃i′ P B̃i . (8) From these equations the design-tradeoffs that govern the tuning of the compensator are evident. In choosing ρ, large values give good performance (small γ ) but also reduce the region of attraction as quantified by cmax . Thus there is a clear trade-off between minimising the local L2 gain and maximising the size of the estimate of the region of attraction; the two cannot be achieved simultaneously (see [1,17,19] for more details). Additionally, the design parameter ε ∈ (0, 1) influences the local nature of the results obtained. As epsilon nears unity, the system properties and in particular the L2 gain bound, tend to hold almost globally (i.e. for very large actuator commands), but as epsilon becomes smaller, the L2 gain bound is valid only for much smaller actuator command levels. Due to its influence on F via Eq. (7), epsilon also plays a role in determining the magnitude of the AW compensators poles, with the poles moving further into the left-half complex plane as ε approaches unity. 6. Anti-windup designs for ATTAS In [19], a single AW compensator was designed for the entire ATTAS flight envelope. The flight condition which was expected to cause the most problematic behaviour during rate limiting was selected as the design point. Linear and nonlinear simulations revealed that the AW compensator delivered reasonably robust performance across the flight envelope. However, performance did degrade as the flight condition was varied. To reduce the potential effects of varied flight condition on the performance of the compensators, it was deemed prudent that, for each flight condition to be tested, a specific AW compensator was designed and subsequently tested. The procedure to design the AW controller for each flight condition was to make an initial choice of AW design parameters ε and ρ based on the designs in [19]. These were then tested at the appropriate flight condition using linear and nonlinear simulations to assess their properties. This involved both open-loop responses and closed-loop tracking tasks with a simple pilot model. Based on these simulations, and the tuning logic in the previous section, the AW coefficients were adjusted to give more desirable responses. It should, however, be noted that, due to the presence of the nonlinearity, the response of the system is strongly input dependent, making the tuning process quite difficult. Based on the above design method, as shown in Table 2, at all up-and-away flight conditions tested a specific AW controller was designed using the following choice of AW coefficients: ε = 0.97, ρ = 1e–7. It was found that this choice worked well across all the up-and-away flight conditions to be tested. To also provide an initial assessment of the effect of different design parameters and on the response of the system, at FC2 (up and away) an additional compensator was designed, termed Table 1 Key to HQR/PIO ratings PIO-c HQR-g HQR-f PIO-b HQR-cl HQR-t PIO-t PIO rating: bank angle capture HQR: gross acquisition, birdy HQR: fine tracking, birdy PIO rating: birdy HQR: centreline capture HQR: touch-down zone PIO rating: touch-down zone Table 2 Up-and-away flight conditions Flight condition No Height [ft] Speed (VIAS) [knts] 1 2 2 5 6 8 8 10000 10000 10000 20000 20000 500 500 164 220 220 180 224 135 135 Comp ρ ε L2 gain 1 2 3 5 6 8 9 1e–7 1e–7 1e–5 1e–7 1e–7 1e–8 1e–6 0.97 0.97 0.96 0.97 0.97 0.97 0.95 3162.28 3162.28 316.23 3162.28 3162.28 10000.0 1000.0 Comp 3, in Table 2. For Comp 3 the AW coefficients were chosen to be ε = 0.96, ρ = 1e–5, which should give improved performance at the expense of a reduced region of attraction. For the landing approach task, two compensators were also tested, termed Comp 8 and Comp 9. For Comp 8 the AW coefficients were chosen to be ε = 0.97, ρ = 1e–8. For Comp 9 the AW coefficients were chosen to be ε = 0.95, ρ = 1e–6, which should give improved performance over Comp 8 at the expense of a reduced region of attraction. All the designed compensators were found to deliver reasonably robust performance (in desktop simulation) around their respective trim points in the flight envelope. It was found that increasing ρ beyond these values led to less aggressive compensators which seemed better at preserving linear performance for small amounts of rate limiting but which failed to provide enough protection for extensive rate limiting. All the AW compensators were of 16th order, being equal to the order of the plant plus the dimension of the control vector, and were flight tested without model reduction. However, Hankel modelreduction to between 6th and 8th order was found to be possible without loss of performance in desktop simulation. 7. Flight test results 7.1. Pilot ratings As mentioned earlier, at each flight condition two pilots evaluated a series of tasks (HQDT, birdy tracking task, offset landings) for the degraded ATTAS aircraft, both with and without AW compensation. At each flight condition, the pilots assigned PIORs (on the PIO rating scale [3]) and HQRs (using the standard Cooper–Harper rating scale [3]) for the aircraft both with and without AW compensation. The results for the up-and-away flight conditions are tabulated in Table 3 and the results for the offset landing approach in Table 4. The key tasks which were rated are summarised in Table 1. The final two columns in both 100 O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 Table 3 Up-and-away flight conditions FC Comp 1 1 2 2 2 5 5 6 6 Pilot 1 (high gain) none 1 none 2 3 none 5 none 6 Pilot 2 (low gain) HQR-g HQR-f PIO-b PIO-c HQR-g HQR-f PIO-b Pilot 1 Pilot 2 4 4 5 4 3 5 5 5 3 6 5 6 5–6 5 (w/l) 7 7 6 5 (w/l) 5 5 5 5 (w/l) 4 6 6 5 4 3 3 4 3 2 5 5 n/a 3 4 3 4 2 2 4 4 5 3 6 5 6 5 5 (w/l) 7 (w/l) 5 6 (w/l) 5 5 5 5 4 4 6 5 5 4 (w/l) 4 3 4 4 2 4 4 4 2 – slight – minor major – none – major – minor – major major – minor – major Table 4 Landing approach flight conditions FC Comp Pilot 1 (high gain) Pilot 2 (low gain) Improvement HQR-cl HQR-t PIO-t HQR-cl HQR-t PIO-t Pilot 1 Pilot 2 8 8 8 none 8 9 5 4 4 6 5 6 Improvement PIO-c 4 3 4 6 4 3 t/d t/d 3 t/d 5 t/d – some slight – some major Tables 3 and 4 summarise the indicated improvement provided by the use of the specific AW controller relative to testing without AW engaged. In the tables the notation ‘w/l’ indicates that the rating given was due to the workload involved. Note that for FC6, for the case of no AW compensation, no rating was assigned for the PIO tendency during HQDT testing (PIO-b), as denoted by ‘n/a’ in Table 3. This was due to a failure in the recording process and is not related to the response of the aircraft for this configuration. Note also that due to the difficulty of the offset landing task, in four cases HQR and PIO ratings were not assigned, and this is denoted by ‘t/d’ in Table 4. From the tables it can be inferred that, based on the PIORs and HQRs, the presence of AW compensation generally improved the handling qualities and reduced the PIO susceptibility of the aircraft at all flight conditions. The results for the up-and-away and offset landing approach tasks are specifically discussed below. 7.1.1. Up-and-away testing Four up-and-away flight conditions were examined, two at low speeds (conditions 1 and 5) and two at higher speeds (conditions 2 and 6). Table 3 indicates that at the lower speed flight conditions the AW compensation bestowed minor improvements in aircraft handling, with HQRs and PIORs given by both pilots typically being the same or slightly lower than without AW compensation. For higher speed flight conditions (conditions 2 and 6), it is clear that the AW compensators led to major handling improvements, again according to both pilots. For instance, at Flight Condition 2 both pilots gave the birdy tracking task a PIOR of 4 when AW compensation was not employed; this dropped to a 2 when AW compensator 3 was used. Similar improvements in PIORs were seen at Flight Condition 6. Moreover, in addition to PIO rating improvements, the HQRs awarded by the pilots at the high speed flight conditions were also improved when the AW compensators were engaged. 7.1.2. Offset landing approach testing Table 4 shows the pilot ratings awarded for the offset landing approach. It is more difficult to make confident deductions about the results at this flight condition because in several instances the task proved too difficult to complete, as noted by the pilots, and thus no HQRs or PIORs were awarded. It does appear that the use of AW compensators improved the ease in which the pilots could achieve centreline capture, with pilot 2 in particular awarding a significantly lower HQR when compensator 9 was engaged. On average the HQRs and PIORs tended to be a little lower when AW compensation was used to those awarded when it was not. However, it must be mentioned that Pilot 2 did encounter a likely PIO in roll on the final approach for the case of AW compensator 8, and hence with an AW compensator active. It is not clear why this occurred, nor whether it can be attributed to the presence of the compensator. Initial analysis has indicated that this PIO may be type I rather than type II, as the stick magnitude and actuator rate limits were only slightly violated. As such, AW compensation would not have been a major factor, as it is only active during periods of rate saturation and only has a marked effect during periods of significant saturation. 7.2. Time histories The data recorded in the flight tests was gathered in three parts, each of which concentrates on certain areas of the flight envelope; low altitude, landing approaches and high altitude. This section presents exemplary data from the high altitude (20 k feet) flight condition at a speed of 224 kts (i.e. Flight Condition 6). This set of data was recorded last, and the data without AW compensation was the last manoeuvre sequence recorded, giving some assurance that the learning factor will not play a role in the pilot’s appreciation of the aircraft’s manoeuvrability. Figs. 14 and 15 show experimental time histories of the birdy tracking tasks for Pilot 1 and Pilot 2 for the cases with and without AW compensation. The signals shown are the roll angle φ, pilot stick command, and control signals u and ur at the input and output of the rate limiter, respectively (see Figs. 2 and 11). RMS levels for the tracking error are given in all cases. Although the task is demanding, and generally the steps are given in quick succession, the time response plots do give a rough indication of the aircraft’s performance. The responses for each O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 Fig. 14. Lateral tracking task for Pilot 1 and Flight Condition 6 (20 kft, 224 kts). 101 102 O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 Fig. 15. Lateral tracking task for Pilot 2 and Flight Condition 6 (20 kft, 224 kts). O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 pilot are discussed below, with the following criteria of particular interest: • The level of oscillatory response of both the aircraft (roll angle) and pilot (stick command). • The difficulty the pilot has to stabilise the system and the ability to track the reference signal. • The level of rate limiting and subsequently how far the system is from linear operation. Pilot 1 (Fig. 14). The left hand plots in Fig. 14 indicate the aircraft response without AW compensation. Note that the roll angle exhibits some oscillatory behaviour and high overshoots. There are also instances when it appears that a divergent oscillation may be developing and the pilot is ‘lowering his gain’ to counter this tendency. It is important to note that the system experiences very high levels of rate limiting and operates outside its linear range most of the time. From the right hand plots in Fig. 14, with AW compensation employed, some improvement in the aircraft behaviour can be observed, with a lower RMS error level and perhaps with finer tracking achievable and less oscillatory behaviour. However the level of stick activity appears greater. Note the markedly reduced rate limiting in the lower graphs, with the rate limited signal remaining much closer to the commanded control signal. Pilot 2 (Fig. 15). With no AW compensation, observe that the roll angle has frequent, large overshoots and fine tracking seems poor. Tracking capabilities of the system are deeply affected by rate limiting; significant oscillations develop, especially when the pilot initiates abrupt manoeuvres. Notice that the pilot uses full stick commands most of the time in order to control the system, increasing the work load and tendency to PIO. In addition, the control signal remains rate limited frequently and there is a large difference between the commanded and actual control signal. When AW compensation was introduced, the roll angle has noticeably better tracking properties, with overshoot and oscillation dramatically reduced and a much lower RMS error. The pilot commented that “although the aircraft response appears to be more sluggish, fine tracking is possible but with an increase in workload”. It is important to observe that the conditioned control signal is less aggressive, and therefore the system is outside linear behaviour for shorter periods of time. Pilot stick commands are reduced, suggesting that, with the exception of fine tracking, pilot workload is lower. 7.3. Discussion The goal of reducing the deleterious effects of rate saturation on the piloted aircraft dynamics was achieved in the flight tests, albeit to different degrees at different flight conditions. The qualitative pilot ratings, which were used as the primarily indicator of the advantages of AW compensation, show clear benefits from the employment of AW compensation. This seems to be true for all flight conditions, although the advantages of AW compensation are most striking at higher speeds (conditions 2 and 6), where Table 3 indicates PIO rating improvements by two points in some cases and also improvement 103 in the HQRs. While improvements are also seen in the PIORs and HQRs in Table 4, the advantages of AW compensation are not as clear. This may indicate that the choice of AW compensation parameters for the landing approach task requires further investigation. The supporting time-histories for Flight Condition 6 most clearly show an improvement due to AW for the case of Pilot 2, where a definite reduction in pilot workload and oscillatory response can be observed when AW compensation is employed (see Fig. 15). It is thus not surprising that Pilot 2 records some of his best PIORs/HQRs for AW compensation at this flight condition and these ratings are substantially better than those with no AW. The correspondence between the time-domain data and Table 3 is less clear for Pilot 1. Although Table 3 shows that this pilot preferred the response of the aircraft with AW compensation, with ratings similar to Pilot 1, it is less evident how this is manifested within the time-domain data. While some improvement in tracking, together with a reduction in rate limiting, may be observed in Fig. 14, the improvement is not striking and stick activity appears greater. However, it should be pointed out that the pilots do consciously, and may unconsciously, adjust their ‘gain’ and piloting technique as the task progresses. Indeed, close inspection of Fig. 14 reveals that the pilot stick command is zero for short periods, perhaps as the pilot removes himself from the loop to prevent oscillations building up (the pilot remarked on this during the flight). More generally, both pilots remarked that they felt that AW improved the predictability of the aircraft response, although they mentioned that the aircraft also felt more sluggish at times. On the basis of these flight tests it is not clear whether AW compensators which improve the handling and preserve the predictability of the aircraft can be obtained, without making the response more sluggish; an investigation into this is desirable, and is one of several avenues of research that will be pursued in further planned flight tests. 8. Conclusions This paper has presented results from a flight test campaign (SAIFE) of a rate limit compensation scheme conducted at DLR, Braunschweig, Germany. The SAIFE tests were successful and demonstrated the definite potential of anti-windup (AW) compensation to improve the safety and handling qualities of aircraft during periods of rate saturation. Pilot ratings and inspection of recorded time-domain data show clearly the attainable performance improvement when AW compensation is employed, particularly at high speed, up-and-away flight conditions. An important characteristic of the results, and one that was expected, is the reduction in the level of rate limiting of the control signal when AW compensation is present, reducing the system’s deviation from linear behaviour. The precise effects of changes in the AW tuning parameters are not clear from these flight tests and further tests would be required to obtain clearer tuning guidelines, particularly for landing approach configurations. Overall, the test results are very encouraging and should contribute towards the development of PIO-free aircraft. 104 O. Brieger et al. / Aerospace Science and Technology 13 (2009) 92–104 Acknowledgements The authors gratefully acknowledge the test pilots Lt. Col. Ritter and Lt. Col. Rüdinger for their piloting expertise and invaluable comments, along with the crew of the ATTAS aircraft, the safety pilots and flight engineer. The support of the members of the GARTEUR Action Groups 12 and 15 is also appreciated. References [1] O. Brieger, M. Kerr, D. Leibling, I. Postlethwaite, J. Sofrony, M.C. Turner, Anti-windup for compensation of rate saturation in an experimental aircraft, in: American Control Conference, 2007. [2] H. Duda, Prediction of pilot-in-the-loop oscillations due to rate saturation, Journal of Guidance, Control and Dynamics 20 (3) (1997) 581–587. [3] Flying Qualities Testing, Chapter 22, US Air Force Test Pilot School, Edwards Air Force Base, February 2002. [4] S.L. Gatley, M.C. Turner, I. Postlethwaite, A. 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