3rd ENOC ProceedingsIndex



Nonlinear oscillations in a time-optimal feedback system

Wladyslaw Hejmo

Cracow University of Technology
31-155 Cracow
Poland



Abstract


There exists a very broad class of industrial devices which need to change their position in a minimum time. Dynamics of the above devices, called position mechanisms, depends essentially on the motion resistance and may be defined by planar non-linear and discontinuous differential equation. Time-optimal problem of this system will be understood as a transfer of any two dimensional initial state to any two dimensional target state in a minimum time. Time-optimality of the controlled processes of that controlled object may be ensured only in a closed-loop system which attributes to each of the state a time optimal value of the control function u. Thus, the open controlled system by a feedback system in which the control function depends on state of system. In real closed-loop system such as mentioned above both the internal uncertainty and external perturbations may appear. So, the created feedback system becomes a non-time-optimal one.

We create two spetial factors p and r those may be usefull in identification of divergent and convergent oscilatory process. It has been shown that if the function, created by controller, h differs from the time optimal one and 0 < p < 1 then the closed-loop system induces the convergent non-linear oscillations, i.e. state trajectory goes around the target state and reaches it in finite time after performing undefined number of encirclements. Instead, if the factor r > 1 then the closed-loop system induces the divergent non-linear oscillations, i.e. state trajectory goes around the target state divergently and tends to form the limit curve with the target state in its interior.



Document



Hejmo.pdf


Contact information


Wladyslaw Hejmo

Cracow University of Technology
ul. Warszawska 24
31-155 Cracow
Poland

e-mail: hejmo@kts.edison.pk.edu.pl
Phone: +48 (12) 632 59 71
Fax: +48 (12) 632 59 71



3rd ENOC ProceedingsIndex