Linghai Lu

Issues of numerical accuracy and stability in inverse simulation

Abstract Inverse simulation algorithms based on integration have been widely applied to predict the control input time histories required for aircraft to follow ideally defined manoeuvres. Several different inverse simulation algorithms are available but these different methods are all subject to a number of numerical and stability problems, such as high frequency oscillation effects and also lower frequency oscillatory phenomena termed “constraint oscillations”. Difficulties can also arise in applications involving discontinuous manoeuvres, discontinuities within the model or input constraints involving actuator saturation. This paper has shown that the dynamic response properties of the internal system are the cause of the so-called “constraint oscillation” phenomenon. In addition, a new inverse simulation approach based on the constrained derivative-free Nelder–Mead search-based optimisation method has been developed to eliminate problems of discontinuities and saturation. Simulation studies involving nonlinear ship models suggest that this new approach leads to improved properties in terms of convergence and numerical stability.

Sensitivity-analysis method for inverse simulation application

An important criticism of traditional methods of inverse simulation that are based on the Newton–Raphson algorithm is that they suffer from numerical problems. In this paper these problems are discussed and a new method based on sensitivity-analysis theory is developed and evaluated. The Jacobian matrix may be calculated by solving a sensitivity equation and this has advantages over the approximation methods that are usually applied when the derivatives of output variables with respect to inputs cannot be found analytically. The methodology also overcomes problems of input-output redundancy that arise in the traditional approaches to inverse simulation. The sensitivityanalysis approach makes full use of information within the time interval over which key quantities are compared, such as the difference between calculated values and the given ideal maneuver after each integration step. Applications to nonlinear HS125 aircraft and Lynx helicopter models show that, for this sensitivity-analysis method, more stable and accurate results are obtained than from use of the traditional Newton–Raphson approach.

Tau Guidance in Boundary-Avoidance Tracking: New Perspectives on Pilot-Induced Oscillations

DOI: 10.2514/1.54065 Tau theory, introduced to the flight control discipline as a model for natural guidance, is shown to provide an approach to predicting a class of adverse aircraft-pilot couplings described as boundary-avoidance tracking events and pilot-induced oscillations. These have previously been modeled a posterior as discrete events using timedependent feedback gains. Drawing on the prospective nature of the time-to-contact variable optical tau � , a new method is proposed for modeling such phenomenon and also for determining the critical incipience for this class of aircraft-pilotcoupling.Inthepresentstudy,theapproachhasbeenappliedtotauguidanceinarotorcrafttrajectory tracking maneuver, to predict the conditions under which aircraft-pilot couplings may occur. In addition, a strong correlation between motion and control activity and the derivatives of tau adds substance to the hypothesis that the pilot’sperceptualsystemworksdirectlywithinvariantsintheoptical flowduringvisualguidance.Resultsfrom flight simulation tests conducted at the University of Liverpool and complementary flight tests carried out with the National Research Council (Canada) advanced systems research aircraft in-flight simulator support the tau control hypothesis. The theory suggests ways that pilots could be alerted to the impending threat of such adverse aircraftpilot couplings.

Investigation of inverse simulation for design of feedforward controllers

This paper describes the use of inverse simulation to develop feedforward controllers for model-based output-tracking control system structures, thus avoiding the more complicated techniques of model inversion. Similarities and shortcomings of the inverse simulation and model inversion approaches are explored. It is found that, with suitable values of discretized time interval, the method based on inverse simulation may be preferable for minimum-phase systems. Depending upon zero redistribution within the process of inverse simulation, non-minimum-phase problems for linear systems can also be handled. The conclusions are demonstrated using a non-linear HS125 aircraft model, a linearised Lynx helicopter model and a container ship model for ship steering control and roll stabilization.

Prediction and Simulator Verification of Roll/Lateral Adverse Aeroservoelastic Rotorcraft–Pilot Couplings

The involuntary interaction of a pilot with an aircraft can be described as pilot-assisted oscillations. Such phenomena are usually only addressed late in the design process when they manifest themselves during ground/flight testing. Methods to be able to predict such phenomena as early as possible are therefore useful. This work describes a technique to predict the adverse aeroservoelastic rotorcraft–pilot couplings, specifically between a rotorcraft’s roll motion and the resultant involuntary pilot lateral cyclic motion. By coupling linear vehicle aeroservoelastic models and experimentally identified pilot biodynamic models, pilot-assisted oscillations and no-pilot-assisted oscillation conditions have been numerically predicted for a soft-in-plane hingeless helicopter with a lightly damped regressive lead–lag mode that strongly interacts with the roll mode at a frequency within the biodynamic band of the pilots. These predictions have then been verified using real-time flight-simulation experiments. The...

Tau Coupling Investigation Using Positive Wavelet Analysis

The investigation of motion guidance and its subsequent application using tau (τ) theory relies on the accurate calculation of the coupling term between the τ (time to contact) of the motion and the appropriate τ guide. However, the traditional approach for this calculation can be numerically unstable, requires experience and skill to execute in a meaningful manner, is sensitive to the data selected, and has limited application when the motion information is incomplete or deviates from the ideal. To deal with these issues, a new approach, based on positive wavelet analysis, is proposed in this paper. The mother wavelet is constructed using the desired τ-guide shapes, with its scale considered to be defined by the maneuver period. The scale and time information of interest are found by searching for the best local correlation within the whitened original signal. An inverse dewhitening process is then used to reconstruct an approximation to the original motion signal. The adequacy of the positive wavelet me...

Development of the Phase-Aggression Criterion for Rotorcraft—Pilot Coupling Detection

Significant effort has been expended to develop criteria to predict the susceptibility of an air vehicle to so-called pilot-induced oscillations . Much of this work has been carried out for fixed-wing aircraft and it is only recently that their applicability to rotorcraft has started to be assessed. Real time pilot-induced oscillation identification methods provide an alternative means to at least warn the pilot that a pilot-induced oscillation is in progress so that preventative action can be taken. Existing methods, however, have some limitations and have rarely been used for rotary-wing purposes. Specifically, the existing methods assessed in this paper do not provide an indication of the severity of the event and mask the underlying data that are being used to generate the warning. This paper proposes and presents a new method to identify pilot-induced oscillations, either in near real time or as a postprocessing aid for recorded flight-test data, that addresses both of these issues. The new method, e...

Investigation of Rotorcraft-Pilot Couplings under Flight-Path Constraint below the Minimum-Power Speed

In some situations, closed loop control by the pilot can result in the combined pilot-aircraft system becoming marginally stable or even unstable. This can happen whether the pilot is controlling attitude or flight path. In this paper, an investigation into helicopter stability under flight-path constraint below the minimum-power speed is reported. The work provides a theoretical basis for flight path handling qualities criteria particularly for flight on the, so-called, back-side of the power curve. The research uses the theory of weakly coupled systems by partitioning the helicopter longitudinal dynamics to investigate three interacting subsystems – classically the surge mode, the phugoid mode and the heave mode. Under certain conditions, strong control of flight path or vertical speed is shown to drive the aircraft-pilot system unstable and a conflict is shown to exist between feedback gain values to guarantee stability of both the surge and the flight path motions. This conflict constitutes a potential source of adverse rotorcraft-pilot couplings. The problems are exacerbated in cases when the use of collective control is restricted. The phenomenon is explored in both ground based simulation and flight test to provide a verification of the theory

Multiloop Pilot Model for Boundary-Triggered Pilot-Induced Oscillation Investigations

This paper presents the development of a multiloop pilot model for use in boundary-triggered pilot-induced oscillation investigations. In doing so, the point-tracking and boundary-avoidance elements of the pilot control strategy are assumed to act simultaneously for a point-tracking-dominant task during a boundary-avoidance tracking event. The theoretical analysis indicates that the essence of the boundary-avoidance tracking phenomenon consists of an additional requirement for the pilot to provide lead equalization as the boundary is approached as the task transitions from a full-attention point-tracking task to both a point-tracking and boundary-avoidance task. This process leads to a narrower open-loop system bandwidth and a larger tracking error, or the triggering of a pilot-induced oscillation. It is also found that the severity of the boundary-avoidance influence can be reduced by including the effects of vestibular and proprioceptive cues into the model. The boundary-avoidance tracking pilot model e...

Development of Occupant-Preferred Landing Profiles for Personal Aerial Vehicles

With recent increased interest in autonomous vehicles and the associated technology, the prospect of realizing a personal aerial vehicle seems closer than ever. However, there is likely to be a continued requirement for any occupant of an air vehicle to be comfortable with both the automated portions of the flight and their ability to take manual control as and when required. This paper, using the approach to landing as an example maneuver, examines what a comfortable trajectory for personal aerial vehicle occupants might look like. Based upon simulated flight data, a “natural” flight trajectory is designed and then compared to constant deceleration and constant optic flow descent profiles. It is found that personal aerial vehicle occupants with limited flight training and no artificial guidance follow the same longitudinal trajectory as has been found for professionally trained helicopter pilots. Further, the final stages of the approach to hover can be well described using the Tau theory. For automatic ...