A Time-Optimal Control Problem in Dynamics with Sampled Data Citation Radey, Kendrick (1962) A Time-Optimal Control Problem in Dynamics with Sampled Data. Engineer's thesis, California Institute of Technology. doi:10.7907/CXDE-J137. https://resolver.caltech.edu/CaltechETD:etd-12092005-132505 Abstract A two-degree-of-freedom dynamical system has been analyzed to determine an optimum control sequence which will drive the dynamical system from an arbitrary initial position and velocity to one of a prescribed set of terminal position and velocity's in minimum time. The basic complexities are: (1) that the forcing function can change only at discrete intervals of time, and (2) that the prescribed terminal states allow a multiplicity of solutions to prevail. A novel but not unique force program which is dependent upon the initial state of the system has been determined. This program consists essentially of the continuous application of a force of the proper sense and maximum allowable amplitude followed by a time during which no force is applied. This is followed by a time interval in which the forcing function has a maximum amplitude but is of the opposite sign to that used in the first part of the program. Item Type: Thesis (Engineer's thesis) Subject Keywords: (Aeronautical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Thesis Availability: Public (worldwide access) Research Advisor(s): Mullin, Francis J. Group: GALCIT Thesis Committee: Unknown, Unknown Defense Date: 1 January 1962 Record Number: CaltechETD:etd-12092005-132505 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-12092005-132505 DOI: 10.7907/CXDE-J137 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 4905 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 12 Dec 2005 Last Modified: 27 Nov 2023 20:41 Thesis Files Preview PDF (Radey_k_1962.pdf) - Final Version See Usage Policy. 2MB Repository Staff Only: item control page

A TIME-OPTIMAL CONTROL PROBLEM T ! I DYNAMICS WI?'H SAMPLED DATA Thesis by Kendrick Radey I n P a r t i a l Fulfillment of t h e Requirements f o r the Degree of Aeronautical Engineer California I n s t i t u t e of Technology Pasadena, California 1962 FIGURE I PORTRAYAL OF F I N A L STATE CONDITIONS IN C . PLANE T R A J E C T O R I E S F O R A = 1.0 A P P R O A C H T R A J E C T O R I E S FOR A = - 1.0 A P P R O A C H T R A J E C T O R I E S FOR A = 0 A P P R O A C H C = a , E = + 1.0 C =-- , E = - I .O E = 0 ,I C 1 A R B I T R A R Y FIGURE 2 PHASE PLANE TRAJECTORIES L I N E OF SYMMETRY FIGURE 3 INITIAL PARTIONING OF PHASE P L A N E B Y - FORCE ASSIGNMENT 2% : (*t;~, -A# 0) %&J@Q% f;o 43 : (&, O, -I)G W * ~ . %&t@ : &@g (a-bf C \ c =-I .OZ - - - - - - - - - -\- - \ -- \ a = (?I \ REGION \ -- \ \ \ \ \ A = - 1.0 \ R E G ION (1) A: I , 0 ,- 1 ) ( 2 ) A : (*I , - I , 0 ) A = + 1.0 C 1 I 1 1 I I\ \ \ \ \ I + I \ FIGURE 4 PHASE PORTRAIT SHOWING T R A J E C T O R I E S FOR A : ( + I , O , - 1 ) EQUIVALENT A N D A: ( + I , - I , O ) FIGURE 5 REPARTITIONED PHASE P L A N E A C C O R D I N G TO O P T I M U M F O R C E P R O G R A M S L I N E OF S Y M M E T R Y A = - 1.0 REGION A = +I.O REGION C FIGURE 6 T I M E - O P T I M A L SWITCHING REGIONS F O R PROPOSED S O L U T I O N FIGURE 7 P H A S E P O R T R A I T S H O W I N G EQUIVALENT TRANSFER P A T H S FOR A : ( +I, 0 , - I ) B e, I$# 1- E,,&+ kmw A far I maat@ 6- Web FIGURE 8 PHASE PLANE GEOMETRY FOR EVALUATING K ( m i d FIGURE 9 P H A S E PLANE GEOMETRY FOR E V A L U A T I N G