ANALYTIC TIME-OPTIMAL CONTROL SYNTHESIS OF 4TH-ORDER SYSTEM AND MANEUVERS OF FLEXIBLE STRUCTURES

The analytic solution to the problem of minimum-time control of a four th-order linear system near the origin is obtained by using Gulko's su bsystem strategy. This system has two real eigenvalues (zeros) and two imaginary eigenvalues (vibrational. frequency), which represents a fl exible structure with one rigid-body mode and one flexible mode. The c omplete solution including the optimal switching times for the second- order subsystem is first obtained. Next, the geometry of the control s witching surface near the origin for the third-order subsystem is anal yzed through the phase-plane and phase-space technique. Then, the swit ching function for the full fourth-order system is constructed by usin g the roots of a quartic algebraic equation. This solution can be used to synthesize the feedback time-optimal control for the maneuvers of flexible structures. Numerical examples with one and more flexible mod es are illustrated to show the applications of the solution.