Open AccessPulse response based control for positive definite systems
Author(s) -
Raúl González Lima
Publication year - 2000
Publication title -
revista brasileira de ciências mecânicas
Language(s) - English
Resource type - Journals
ISSN - 0100-7386
DOI - 10.1590/s0100-73862000000200003
Subject(s) - reachability , control theory (sociology) , piecewise , positive definite matrix , interval (graph theory) , mathematics , pulse (music) , degrees of freedom (physics and chemistry) , actuator , sequence (biology) , set (abstract data type) , realization (probability) , control system , computer science , control (management) , mathematical analysis , algorithm , physics , engineering , telecommunications , eigenvalues and eigenvectors , statistics , quantum mechanics , combinatorics , artificial intelligence , detector , biology , electrical engineering , genetics , programming language
Pulse Response Based Control (PRBC) is a recently developed minimum time control method for flexible structures. The flexible behavior of the structure is represented through a set of discrete time sequences, which are the responses of the structure due to rectangular force pulses. The rectangular force pulses are given by the actuators that control the structure. The set of pulse responses, desired outputs, and force bounds form a numerical optimization problem. The solution of the optimization problem is a minimum time piecewise constant control sequence for driving the system to a desired final state. The method was developed for driving positive semi-definite systems. In case the system is positive definite, some final states of the system may not be reachable. Necessary conditions for reachability of the final states are derived for systems with a finite number of degrees of freedom. Numerical results are presented that confirm the derived analytical conditions. Numerical simulations of maneuvers of distributed parameter systems have shown a relationship between the error in the estimated minimum control time and sampling interva