The Pennsylvania State University The Graduate School Department of Aerospace Engineering SIMULATION AND CONTROL OF A HELICOPTER OPERATING IN A SHIP AIRWAKE A Thesis in Aerospace Engineering by Dooyong Lee c 2005 Dooyong Lee Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2005 The thesis of Dooyong Lee has been reviewed and approved* by the following: Joseph F. Horn Assistant Professor of Aerospace Engineering Thesis Adviser, Chair of Committee Lyle N. Long Professor of Aerospace Engineering Edward C. Smith Professor of Aerospace Engineering Qian Wang Assistant Professor of Mechanical Engineering George Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering *Signatures are on file in the Graduate School. Abstract This thesis describes a study in simulation and control of a helicopter operating in proximity to a ship. The helicopter/ship combination used in the study is a UH-60A helicopter operating off an LHA class ship. This represents the same aircraft ship combination used in the JSHIP program. The flight dynamics model is based on the GENHEL software and this flight dynamics model has been updated to include high-order dynamic inflow model and gust penetration effects of the ship airwake. To simulate the pilot control inputs for typical shipboard operations, an optimal control model of the human pilot is developed. The pilot model can be tuned to achieve different tracking performances based on a desired crossover frequency in each control axis and is designed to operate over a range of airspeeds using a simple gain scheduling algorithm. The pilot model is then used to predict pilot workload for shipboard operations in two different wind-over-deck conditions. Validation studies are conducted using both time and frequency domain analyses to understand the impact of a time-varying ship airwake on the pilot control activity for the approach and departure operations. The pilot control input autospectra predicted from the simulation model are compared to those of flight test data from the JSHIP program. It is found that the control activities are similar in low frequency range but underestimate iii in magnitude in the high frequency range (over 1.5 Hz). There is clear evidence that the human pilot is continually moving cyclic stick in the maneuver. At this stage of the study no attempt has been made to optimize the parameters of the human pilot model. The paper also discusses the application of a stochastic airwake model for more efficient simulation. This new airwake model is derived from the simulation with the full CFD airwake by extracting an equivalent six-dimensional gust vector. The spectral properties of the gust components are then analyzed, and shaping filters are designed to simulate the gusts when driven by white noise. It is proposed that the stochastic gust model can be used to optimize the automatic flight control system in order to improve disturbance rejection properties of the aircraft. A stability augmentation system (SAS) is optimized for a UH-60 helicopter operating in the turbulent ship airwake. For disturbance rejection, a new performance specification is designed based on the power spectral density of the transfer function from the gust inputs to aircraft rate responses. The baseline limited authority SAS is modified and optimized using CONDUIT (Control Designer’s Unified Interface) in order to improve handling-qualities and stability, and to minimize a weighted objective of gust responses. In addition, a H∞ controller is designed to provide an alternative SAS configuration. The optimized SAS and H∞ SAS are then tested using the non-linear simulation model with time-varying airwake. Time domain and frequency domain analyses of the simulation show that the modified SAS results in significant reduction of pilot workload. iv Contents List of Figures viii List of Tables xiv Acknowledgments xv 1 Introduction 1 1.1 Modeling of Helicopter/Ship Dynamic Interface . ......... 4 1.1.1 HelicopterFlightDynamicModel. 4 1.1.2 ModelingofRotorAerodynamics . 7 1.1.3 ShipAirwakeModel ........................... 11 1.1.4 FlightControlModel........................... 13 1.2 Simulation of Helicopter/Ship Dynamic Interface . .......... 16 1.3 Problem Statement and Research Objectives . ...... 18 2 Helicopter Flight Dynamics Model 20 2.1 OverviewoftheGENHELSimulationModel . 20 2.2 MATLABImplementation. 23 v 2.3 Peters-HeInflowModel ............................. 24 2.3.1 Background................................ 24 2.3.2 Basic Equations of Peters-He Inflow Model . 25 2.4 GustPenetrationModel . 29 3 Pilot Modeling 34 3.1 Optimal Control Model of the Human Pilot . 35 3.2 Nonlinear Elements of the Human Pilot . 41 3.2.1 Hysteresis................................. 41 3.2.2 Deadband................................. 42 4 Numerical Examples 44 4.1 Overview ..................................... 44 4.1.1 ShipboardDepartureTrajectory . 45 4.1.2 Shipboard Approach Trajectory . 46 4.2 EffectsofShipAirwakeModel. 48 4.3 EffectsofDifferentTrackingPerformance . ...... 65 4.4 ValidationwithFlightTestData . 70 4.4.1 FrequencyDomainAnalysis . 81 5 Task-Tailored Control Design 85 5.1 Overview ..................................... 85 5.2 StochasticAirwakeModeling . 88 5.3 Optimization of a Stability Augmentation System . ......... 110 vi 5.4 H∞ ControlofaHelicopterSAS . 128 5.4.1 Review of H∞ Control Design Method . 129 5.4.2 Design of H∞ Controller for a Helicopter SAS . 135 6 Conclusions and Future Works 154 6.1 Conclusions .................................... 154 6.2 Recommendations for Future Work . 157 Bibliography 160 vii List of Figures 1.1 TypicalWODenvelope(Ref. [2]) . ... 2 1.2 The modeling components of a helicopter (Ref. [3]) . ......... 4 1.3 Momentum theory flow model for axial flight (Ref. [3]) . ........ 8 1.4 Block diagram of coupled rotor and induced flow dynamics (Ref. [14]) . 9 1.5 Schematic of helicopter control system . ....... 14 2.1 Block diagram of GENHEL flight simulation model (Ref. [11]) ....... 21 2.2 Overall structure of MATLAB based simulation program . ......... 23 2.3 Comparisonsofinflowratio . 29 2.4 Vorticity magnitude iso-surface at t = 40 sec (Ref. [39]) . .......... 31 2.5 Gustpenetrationmodel . 32 2.6 The approach of the overlapped time history of airwake . ......... 33 3.1 Optimal control model of the human pilot . ..... 35 3.2 Augmented plant model in longitudinal axis . ....... 37 3.3 Effect of a sine wave passing through a hysteresis . ........ 42 3.4 Effect of a sine wave passing through a deadband . ...... 43 4.1 TopviewofanLHAclassship . 45 viii 4.2 Shipboard approach operation procedures . ....... 47 4.3 Helicopter position w.r.t. ship coordinate system - Departure task . 50 4.4 Helicopter velocity [ft/sec] - Departure task (30 knot, 0 degree WOD condition) 51 4.5 Helicopter attitude angles [deg] in the DI mesh - Departure task (30 knot, 0 degreeWODcondition) ............................. 52 4.6 Pilot inputs [%] in the DI mesh - Departure task (30 knot, 0 degree WOD condition)..................................... 53 4.7 Helicopter velocity [ft/sec] - Departure task (30 knot, 30 degree WOD con- dition)....................................... 54 4.8 Helicopter attitude angles [deg] in the DI mesh - Departure task (30 knot, 30degreeWODcondition) ........................... 55 4.9 Pilot inputs [%] in the DI mesh - Departure task (30 knot, 30 degree WOD condition)..................................... 56 4.10 Helicopter position w.r.t. ship coordinate system - Approach task . 58 4.11 Helicopter velocity [ft/sec] - Approach task (30 knot, 0 degree WOD condition) 59 4.12 Helicopter attitude angles [deg] in the DI mesh - Approach task (30 knot, 0 degreeWODcondition) ............................. 60 4.13 Pilot inputs [%] in the DI mesh - Approach task (30 knot, 0 degree WOD condition)..................................... 61 4.14 Helicopter velocity [ft/sec] - Approach task (30 knot, 30 degree WOD condition) 62 4.15 Helicopter attitude angles [deg] in the DI mesh - Approach task (30 knot, 30 degreeWODcondition) ............................. 63 ix 4.16 Pilot inputs [%] in the DI mesh - Approach task (30 knot, 30 degree WOD condition)..................................... 64 4.17 Helicopter position error [ft] - 30 knot, 0 degree WOD condition . 66 4.18 Pilot control input [%] - 30 knot, 0 degree WOD condition .......... 67 4.19 Helicopter position error [ft] - 30 knot, 30 degree WOD condition . 68 4.20 Pilot control input [%] - 30 knot, 30 degree WOD condition......... 69 4.21 Helicopter airspeed [knot] - 30 knot, 0 degree WOD condition........ 73 4.22 Helicopter altitude [ft] - 30knot, 0 degree WOD condition .......... 74 4.23 Angular rate [deg/sec] - 30knot, 0 degree WOD condition .......... 75 4.24 Pilot stick inputs [%] - 30 knot, 0 degree WOD condition . ......... 76 4.25 Helicopter airspeed [knot] - 30 knot, 30 degree WOD condition ....... 77 4.26 Helicopter altitude [ft] - 30 knot, 30 degree WOD condition ......... 78 4.27 Angular rate [deg/sec] - 30knot, 30 degree WOD condition.......... 79 4.28 Pilot stick inputs [%] - 30 knot, 30 degree WOD condition .......... 80 4.29 Pilot input autospectrum [dB] - 30 knot, 0 degree WOD condition . 83 4.30 Pilot input autospectrum [dB] - 30 knot, 30 degree WOD condition . 84 5.1 Task-tailored control system design scheme . ....... 87 5.2 Derivation of stochastic airwake disturbances . .......... 91 5.3 Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equiv- alentairwake)-0degreeWODcondition