# Accession Number:

## AD0262177

# Title:

## BANG BANG CONTROL OF REAL POLE SYSTEMS

# Descriptive Note:

# Corporate Author:

## CALIFORNIA UNIV BERKELEY ELECTRONICS RESEARCH LAB

# Personal Author(s):

# Report Date:

## 1961-06-15

# Pagination or Media Count:

## 1.0

# Abstract:

The control equations, for minimum response time operation, are presented for regulatory and tracking systems. The controlled plant is linear, time-invariant, with real, non-positive poles. The input to the plant is assumed amplitude saturated. The concept of the switching hypersurface leads to a system of nonlinear algebraic equations, which must be solved by the compensator. The optimal system is analyzed through its trajectories in phase space which define the switchin sets. Minimum response time implies the reduction of the error and its time derivatives to zero in minimum time. A sequence of switching sets and a switching hypersurface are defined in space. It is shown that the switching sets provide the unique, and optimal, path for the system trajectories. A distance function is defined, which indicates the relative position of the state point with respect to the switching hypersurface. To determine the distance function a compensator must solve a system of N-1 nonlinear algebraic equations, where N is the order of the plant. Author