On non-unique time-optimal control of a planar discontinuous dynamic object.

• Autorzy: Hejmo W. , Majewska K.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to present the solution of time-optimal problem of the controlled object, the dynamics of which is given by x=y, y=f(x)+u, where /u/<1, and motion resistance function f(x)=0 if x<0, f(x)=-A if x>0, 0,A<1. That model describes dynamics of of industrial devices called position mechanisms. It has been shown that in the formula defining resistance functionf(x) there exists a value Ab that plays an essential role in time-optimal structure formation. Namely, if A<Ab then the time-optimal control process is typical, analogous as in classical case x=u, /u/<1, i.e. there exists a switching curve formed by the trajectories of time-optimal solution reaching the target state and the time-optimal process formed by at most one switching operation. for the case A>Ab we will examine the following two singular phenomena. The first phenomenon appears if the target state z1=(0,0). Then, there exists the switching curve, dividing the state plane into two sets, however, only one in branch is formed by the time-optimal solution. None of the solutions form the second branch of the switching curve. Thus, the time-optimal process is generated by bang-bang control with none, one or two switching operations. The second singular phenomenon appears if the target state z1=(x1,0), x1>0. Then, there exists a set of starting states from which there start two trajectories reaching he target in the same minimal time. It appeared that only two starting points from which there start the non-unique trajectories, may be defined in algebraic open form. The next starting points may be calculated in numerical way only. There have been shown some examples of numerical solutions. Finally, several suggestions as to practical applications have been given, too.

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 1999
• Tom: Vol. 25, nr 3
• Strony: 37--55
• Opis fizyczny: Bibliogr. 4 poz., rys. 10

Twórcy

autor

Hejmo W.

autor

Majewska K.

• Cracow University of Technology, Institute of Control Engineering, ul. Warszawska 24, 31-155 Kraków, Poland.