AD-A266 718 TI C A/F9 J T-3/ ED/ N S ELECTE JUL 819931 C DEVELOPMENT OF AN AIR-TO-AIR REFUELING AUTOMATIC FLIGHT CONTROL SYSTEM USING QUANTITATIVE FEEDBACK THEORY THESIS Dennis W. Trosen Captain, USAF AFIT/GE/ENG/93J-03 93-15348 .0. 7 08 002 III I I IIII II , Approved for public release; distiibution unlimited AFIIT/GE/ENG/93I-03 DEVELOPMENT OF AN AIR-TO-AIR REFUELING AUTOMATIC FLIGHT CONTROL SYSTEM USING QUANTITATIVE FEEDBACK THEORY THESIS Presented to the Faculty of the School of Engineering of the Air Force Institute of Technology Air University In Partial Fulfillment of the Requirements for the Degree of Master of Science in Electrical Engineering Dennis W Trosen, B.S.E.E. Captain, USAF Acce-,iuy' cr June, 19,139 93 DTaICv no.T.mAbcc d [U Dist ibut ion I Avddi bility Codes Approved for public release, distribution unlimited i Avail a-idof Dist Specia IA Acknowledgements I send thanks to my parents, Patricia and Kenneth Trosen, for shaping me into the man I am today. Prof Houpis and Prof Pachter, thank you for the knowledge to accomplish this thesis. Kevin and Sean . you waited patiently for me, I love you and "daddy's all studied". I dedicate this work to my wife, Chris whose love and understanding provides my mctivation, you make my life whole, I love you very much. Dennis W. Trosen ii Table of Contents Acknowledgemnents..............................................ui Table of Contents..............................................1iii List of Piguc ................................................ Vill List of Tables................................................. xi Abstract..................................................... xii I. Introduction............................................... 1-1 1.1 Background........................................... 1-1 1.2 Problem Statement...................... ............... 1-2 1.3 Assumptions......................................... 1-3 1.4 Research Objectives..................................... 1-3 1.5 Scop,. .............................................. 1-4 1.6 Methodology........................................ 1-4 1.7 Overview of the Thesis................................. 1.5 1.8 Summary........................................... 1-5 HI. QFT and Output Disturbance Rejection............................ n-1 2.1 Intruduction .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2-1 2.2 Overview of QFT. .. .. .. .. .. .. .. .. .. .. ... .. .. ... .. ... 2-1 2.3 MIMO, QFT .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. ... .. .. .. 2-3 2.4 MIMO QFT with External Output Disturbance .................. 2-5 2.5 Summary . ... ........................... 2-14 111. Air-to-Air Refueling FCS Design Concept.......................... 3-1 3.1 Introduction.......................................... 3-1 3.2 C-13511 Modeling...................................... 3-1 3.3 Disturbance Modeling................................... 3-4 3.3.1 Pitch Plane Wind Induced Disturbance................. 3-4 3.3.2 Lateral Channel Wind Induced Disturbance.............. 3-8 3.3.3 Disturbance Due to Refueling .... . . . . . . . . 3-8 3.4 Plant and Disturbance Matrices . . . . . . . . . . . .. 3-10 3.5 Controil Problem Approach .. . . . . . . . . . . . . . 3-11 3.6 Summary........................................... 3-15 IV. LTI Plant and Disturbance Model Generation....................... 4-1 4,1 Introduction.......................................... 4-1 4.2 Plant Transfer Function Generation.......................... 4-1 4.3 Disturbance Transfer Function Generation..................... 4-5 iv 4.4 Summary . . . . .. . . . . . . . . . . . . . .. 4-8 V. QFT AFCS Design......................................... 5-1 5.1 Introduction.......................................... 5-1 5.2 Disturbance Rejection Specification......................... 5-1 5.3 Loop Shaping......................................... 5-3 5.3.1 Channel 2 Loop Design........................... 5-3 5.3.2 Channel I Loop Design........................... 5-7 5.3.3 Channel 3 Loop Design.......................... 5-11 5.4 Closed Loop Lm Plots.................................. 5-14 5.5 Summary.......................................... 5-15 VI. Air-to-Air Refueling Simulations................................6-1 6.1 Introduction......................................... 6-1 6.2 Linear Simulations.................................... 6-1 6.3 Nonlinear Simulations.................................. 6-2 6.4 Summary........................................... 6-3 Vfl. Conclusions and Recomnieidation ............................... 7-1 7.1 Discussion.......................................... 7-1 7.2 Conclusions......................................... 7-2 7.3 Recommendations..................................... 7-2 V Appendix A. C-135 Nondimensional Stability Derivatives ................ A-i A.i Nondimetnsional Stability Derivative Definitions .............. A-i A .1.1 Looitlldin41. ................................. A -I A .1.2 Lonitudinal ................................. A -i Appendix B. Plant Transfer Functions ............................. B-I B.1 Plant Case 1 - C , = 0.2 Gross Weight = 160,666 pounds ........ B-i 1 B.2 Plant Case 2 - CL = 0.6 Gross Weight = 160.666 pounds ........ B-I B.3 Plant Case 3 - CL = 0.2 Gross Weight = 207,316 pounds ........ B-2 B.4 Plant Case 4 - C , = 0.6 Gross Weight = 207,316 pounds ........ B-3 1 B.5 Plant Case S - C = 0.2 Gross Weight = 210,189 pounds ........ B-4 1 B.6 Plant Case 6 - CL = 0.6 Gross Weight = 210,189 pounds ........ B-4 13.7 Plant Case 7 - CL = 0.2 Gross Weight = 245,500 pounds ........ B-5 B8 Plant Case 8 - CL = 0.6, Gross Weight 245,500 pounds ........ B-6 B.9 Plant Case 9 - CL - 0.2, Gross Weight = 253,500 pounds ....... B-6 B.10 Plant Case 10 - CL = 0.6, Gross Weight = 253,500 pounds ...... B-7 B.11 Plant Case II - CL = 0.2, Gross Weight = 263,500 pounds ...... B-8 B.12 Plant Case 12 - CL = 0.6, Gross Weight = 263,500 pounds ...... B-8 B.13 Plant Case 13 - CL = 0.2, Gross Weight = 275,500 pounds ...... B-9 B.14 Plant Case 14 - CL = 0.6, Gross Weight = 275,500 pounds ..... B-10 B.15 Plant Case 15 - C = 0.2, Gross Weight = 277,500 pounds ..... B-10 1 B.16 Plant Case 16 - C, = 0.6, Gross Weight =- 277,500 pounds ..... B-1I 1 Vi Appendix C. C-135B and Autopilot Input Response...................... C-1 Appendix D. C-135B and Autopilot Disturbance Response.................. D-1 Appendix E. Templates and Boundary Plots...........................E-1 Appendix F. QFT Conmpenisators................................... F-I F.1 Channel 11c ompensator, g,............................... F- I F.2 Channel 2 compensator, :2...........................................F-i F.3 Channel 3 compensator. F-I 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Bibliography................................................ BIB-i1 Vita..................................................... VITA- I vii List of Figures Figure 2.1 QFT Controller Design ................................ 2-2 Figure 2.2 3x3 MISO Equivalent Loops ............................ 2-4 Figure 2.3 QFT Controller with Output External Disturbance .............. 2-6 Figure 2.4 3x3 MISO Equivalent Loops for External Output Disturbance ..... 2-9 Figure 3.1. Bare Aircraft Plant .................................. 3-2 Figure 3.2 C-135B Bare Aircraft with Autopilot ...................... 3-4 Figure 3.3 Control Problem Geometry ............................ 3-13 Figure 3.4. Control Problem . ................................... 3-14 Figure 4.1 P(s) Log M agnitude Plot ............................... 4-3 Figure 4.2 Q',s) Log M agnitude Plots .............................. 4-5 Figure 4.3 P,(s) Log M agnitude Plots .............................. 4-7 Figure 5.1 Disturbance Rejection Model Response to 10 ft/sec Impulse ....... 5-2 Figure 5.2 Channel 2 Loop Shaping P. = Plant Case 2 .................. 5-5 Figure 5.3 Channel 2 Nichols Plot all Plant Cases ..................... 5-6 Figure 5.4 Channel 1 Loop Shaping P,, = Plant Case 2 .................. 5-9 Figure 5.5 Channel 1 Nichols Plot all Plant Cases .................... 5-10 Figure 5.6 Channel 3 Loop Shaping P. = Plant Case 2 ................. 5-12 Figure 5.7 Channel 3 Nichols Plot all Plant Cases .................... 5-13 Figure 5.8 MISO Equivalent System Lm Plots ...................... 5-14 Figure 6.1 Linear Simulation - Z Separation Deflection all Plant Cases ....... 6-4 viii Figure 6.2 Linear Simulation - X Position Deflection all Plant Cases 6-5 Figure 6.3 Linear Simulation - Y Position Deflection all Plant Cases ........ 6-6 Figure 6.4 Nonlinear Simulation - X, Y, Z Position Defection, Plant 1 C, = 0 .2 . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . 6 -7 Figure 6.5 Nonlinear Simulation - Control Surface and Throttle Response, Plant 1............................. ................. 6-8 Figure 6.6 Nonlinear Simulation - X, Y, Z Position Deflection, Plant 2 CL = 0 .6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 -9 Figure 6.7 Nonlinear Simulation - Control Surface and Throttle Response, Plant 2 .. ............................................. 6-10 Figure C.1 Mach Hold Response to 1 ft/sec Step Input - CL = 0.2 .......... C-2 Figure C.2 Mach Hold Response to 1 ft/sec Step Input - CL = 0.6 .......... C-3 Figure C.3 Altitude Hold Response to 1 foot Step input - CL = 0.2 .......... C-4 Figure C.4 Altitude Hold Response to 1 Foot Step Input - C = 0.6 ......... C-5 Figure C.5 Rudder Control Response to 1 deg Step Input - CL. = 0.2 ......... C-6 Figure C.6 Rudder Control Response to 1 deg Step Input - CL = 0.6 ......... C-7 Figuie C.7 Aileron Controi Response to 1 deg Step input - CL = 0.2 ........ C-8 Figure C.8 Aileron Control Response to 1 deg Step Input - C.= 0.6 ........ C-9 1 Figure D.1 X, Y, Z Response to Longitudinal Wind Disturbance - CL = 0.2 ... D-2 Figure D.2 X, Y, Z Response to Longitudinal Wind Disturbance - C = 0.6 ... D-3 Figure D.3 X, Y, Z Response to Lateral Wind Disturbance - CL = 0.2 ....... D-4 Figure D.4 X, Y, Z Response to Lateral Wind Disturbance - CL = 0.6 ....... D-5 ix