Robust time-optimal control - Frequency domain approach

Abstract

The design of nonrobust and robust time-optimal controllers for linear systems in the frequency domain is presented. The bang-bang profile is represented as the superposition of time-delayed step inputs or the output of a time-delay filter subject to a step input. A parameter optimization problem is formulated to minimize the final time of the maneuver with the constraint that the time-delay filter cancels all of the poles of the system. The issue of robustness to errors in the model is addressed by placing multiple zeros of the time-delay filter at the estimated locations of the poles of the system. The design technique is illustrated on representative models of large space structures, for rest-to-rest, time-optimal, and robust time-optimal maneuvers. Spin-up maneuvers are shown to be special cases of the general formulation.

Time Optimal Control of Flexible Systems Subject to Friction

“…It has been previously shown by Singh and Vadali,3 that time delay filters can be used to satisfy the boundary condition of the rest-to-rest maneuvers. However, the systems that are analyzed here are nonlinear systems and the concept of poles and zeros are nonexistent.…”

Minimax Design of Prefilters for Maneuvering Flexible Structures

“…They also showed that by cascading the time-delay filter designed to cancel the poles of the system, the resulting filter was insensitive to errors in modeled damping and frequency. The idea of locating multiple zeros * Associate Professor, Mechanical & Aerospace Engineering, Member AIAA † Graduate Student, Mechanical & Aerospace Engineering of a time-delay filter at the estimated location of the poles of the system has been exploited to design robust time-optimal control [9], [5], robust fuel-time optimal control [11], fuel constrainted time-optimal control [12] etc. Liu and Singh [4] extended this idea to nonlinear systems undergoing rest-to-rest maneuvers, by requiring the sensitivity of the system states with respect to uncertain parameters be zero at the final time.…”

Time‐optimal control of flexible systems subject to friction

“…2 Singh and Vadali proposed a time-delay filter which shapes the step input into bang-bang control input. 3 Driessen and Sadegh formulated a mixed integer linear programming problem to design a near time-optimal controller including the Coulomb friction effect. 4 However, finding an accurate optimal control profile with the mixed integer programming is computationally very expensive, and the accuracy is limited by the number of samples and convergence tolerance.…”