THE CALCULATION OF THE SIMPLEST OPTIMUM RELAY SYSTEMS OF THE SECOND ORDER
Abstract
The problem of finding the optimum control law and of determining the structure of the optimum controlling portion of an automatic control system is treated. According to the general theory, an optimum process of a relay automatic control system, the roots of the characteristic equation of which are real (including the zero roots), consists of two intervals. Instead of an (n - 1)dimensional switching hypersurface in an n-dimensional phase space, there is a switching line on a phase plane. In the case of optimum secondorder systems the switching line on the phase plane of error coincides with the branches of the phase trajectories going towards the origin. If the roots of the characteristic equation of the linear part of an automatic control system are conplex, an optimum process (depending on the initial conditions) may consist of any number of intervals, and then the branches of the phase trajectories going towards the origin constitute only a part of the optimum switching line. Thus, in principle, the task of synthesizing the optimum control portion of a second-order automatic control system may be readily solved by the phase-plane method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 20, 1962
- Accession Number
- AD0287723
Entities
People
- A.a. Pavlov
- V.p. Poputsillo
Organizations
- National Air and Space Intelligence Center