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1 Journal of Northwestern Polytechnical University Apr. Vol No. 2 Neal-Smith CAP Neal-Smith PIO Neal-Smith V249 A Neal-Smith CAP Neal-Smith Neal-Smith 1 STT Step Target Tracking Neal-Smith Time-Domain Neal-Smith TDNS PIO 2 3 Ⅰ Ⅱ PIO 4 TDNS 1 PIO % ISE ITAE PIO 7 CAP

2 ITAE CAP - C * B 1 - C * 1 Neal-Smith Neal-Smith Neal-Smith θ e t ITAE ITAE TDNS T T ITAE = t y t - y ref t dt 1 0 y t y ref t

3 2 Neal-Smith ω n1 1 ω n1 TDNS TDNS 3 5 s ω n1 = 7 CAP ξ n1 ξ n1 = ξ n1 = ω n1 T θ2 = CAP T θ2 = 7 /6 GJB θ = 7 2 S F z S S K θ ( s + 1 θ F z s = T θ ) 2 s 2 + 2ζ sp ω sp + ω 2 sp e -τ e0s 2 3 ζ sp ω sp T θ2 τ e0 θ = 7 2 S F z S S S 2. 2 Neal-Smith 2 ξ n1 CAP TDNS ω n1 T θ2 ω n1 8 n /α T θ2 T θ2 n /α 1 /T θ2 ω n1 n /α ω n1 T θ2 CAP C-H ω n1 T θ Neal-Smith ξ n s A θ c s D 1 / A 3

4 TDNS ω n1 < 10 rad /s D D τ T N θ RMS D τ P = τ + T N 7 θ RMS 6 1 D 2 θ RMS Neal-Smith TDNS D Neal-Smith 1 8 ω BW - D ω BW - ω BW - 1 = D ln ( 1 40) 5 t P2 = T I = 1 ( - Tw ω BW ) s 1 t P1 = T L = t P2 ω 2 BW 10 1 / T w 8 k P τ θ RMS - PC PC = 57. 3tan -1 t P1 ω BW tan -1 t P2 ω BW 11 θ RMS PC D θ RMS 4 1 W P s = k p T L s + 1 e -τs T I s + 1 T N s k P 1 ~ 100 T L 0 ~ 1. 0 s T I 4 0 ~ 1. 0 s T N 0. 1 ± 20% s τ D 0. 2 ± 20% s 0. 2 s 0. 6 s 4 W P s = k p T L s + 1 T I s + 1 e -τ P s 8 τ P Step1

5 2 Neal-Smith D 2. 7 s θ RMS k P k t P1 t P2 t P1 0 1 t P2 0 1 Step2 ± 100 /s ± 25 PC Step3 δ P = K θ θ + K q q 12 ITAE 1 CAP TDNS K θ K q k P - T L T N K θ K q ITAE NSGA-II Pareto Pareto s 5 s D 5 5 s θ RMS TDNS Pareto 1 CAP TDNS 5 Neal-Smith CAP s 2. 7 s 4. 5 s PID NSGA-II 10 Pareto 6 TDNS s 7 8 TDNS 1 1

6 TDNS PIO 4 Ⅰ PIO Ⅱ PIO 1 PIO 11 2 D 1. 3 ~ 2 s θ RMS D d 2 θ RMS /dd PIO 3 CAP θ RMS D s 2. 5 s θ RMS D PIO 100 Ⅱ PIO TDNS PIO 1 Anderson M R. Unified Pilot-Induced Oscillation Theory Volume 3. PIO Analysis Using Multivariable Methods. Virginia Polytechnic Inst and State Univ Blacksburg Dept of Aerospace and Ocean Engineering Neal-Smith PID Ning Guodong Fang Zhenping. PID Multi-Objective Optimization Design Based on Pareto Optimality. Journal of Beijing University of Aeronautics and Astronautics in Chinses 3 Zhao Z Liu Y Yan S W et al. Pilot-Induced Oscillations PIO Susceptibility Evaluation Approach Based on Sequential Quadratic Programming. IEEE Bailey R E Bidlack T J. A Quantitative Criterion for Pilot-Induced Oscillations-Time Domain Neal-Smith Criterion Avanzini G Minisci E A. Evolutionary Design of a Full-Envelope Flight Control System for an Unstable Fighter Aircraft. IEEE Pareto PID

7 2 Neal-Smith 285 Liu Nannan Shi Yu Fan Shenghui. PID Multi-Objective Optimization Design Based on Pareto Optimality. Information and Control in Chinese 7. PID Li Xuebin. Multi-Objective Optimization and Multi-Attribute Decision Making for PID Controller Parameters Tuning in Ship Diesel Design. Journal of Naval University of Engineering in Chinese Gao Jinyuan Li Luyu Feng Yachang. Aircraft Handling Qualities. Beijing National Denfence Industry Press 2003 in Chinese 9 Bailey R E Bidlack T J. Unified Pilot-Induced Oscillation Theory. Volume 4. Time-Domain Neal-Smith Criterion. Calspan Advanced Technology Cenier Buffalo NY K D S A A P. A Fast Elitist Non-Domina2ted Sorting Genetic Algorithm for Multi-Objective Optimization NSGA2 II. Paris France PIO Zhao Zhizhong Liu Yan Gao Zhenghong. PID Susceptibility Evaluation Approach Based on Sequential Quadratic Programming. Flight Dynamics in Chinese A Fairly Successful Exploration of Multi-Objective Optimization of Aircraft Flight Control System Design Using Time-Domain Neal-Smith Criterion Nie Rui Zhang Weiguo Li Guangwen Liu Xiaoxiong Department of Automatic Control Northwestern Polytechnical University Xi'an China Abstract Sections 1 and 2 of the full paper explain what we believe to be a fairly successful exploration. Their core consists of 1 to match the pilot and the aircraft with the man-vehicle closed loop reference model we introduce the flight quality requirements into the optimization algorithm to design the aircraft flight control system 2 we establish the equivalent model of the aircraft with the CAP criterion 3 using the time-domain Neal-Smith criterion we perform the multi-objective optimization to obtain the optimal pilot reference models under different tasks 4 we select the optimal pilot reference model according to the flight quality requirements and combine it with the aircraft equivalent model to form the man-vehicle closed loop reference model 5 with the man-vehicle closed loop reference model we design the aircraft flight control system by using the multi-objective optimization algorithm. Section 3 simulates the multi-objective optimization of the pilot reference model and the man-vehicle closed loop reference model the simulation results given in Figs. 5 through 8 and their analysis show preliminarily that our multi-objective optimization algorithm can not only tune the parameters of the controller of the aircraft flight control system but also select the optimal pilot reference model under different tasks and use the optimization results to evaluate the PIO pilot-induced oscillation susceptibility. Key words aircraft algorithms analysis closed loop control systems design evaluation man machine systems models numerical control optimization parameter optimization requirements engineering tracking position sensitivity analysis simulation standards time domain analysis flight control systems multiobjective optimization flight quality reference model time-domain Neal-Smith criterion

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