Rest-to-Rest Motion of an Experimental Flexible Structure Subject to Friction: Linear Programming Approach

Abstract

A linear programming approach designed to eliminate the residual vibration of the two-mass harmonic system subject to friction and undergoing a point-to-point maneuver is proposed and implemented on an experimental test bed. Techniques for design of positive pulse control profiles for nonrobust and robust open loop controller design are explored, where the positive pulses initiate motion and the friction force brings the system to rest. It is shown that consistent results can be obtained from experiments and the robustness against frequency uncertainty results in the reduction in residual vibration as well as steady-state error.

Robust model-based trajectory planning for nonlinear systems

“…By imposing that their values must be zero at a given point of a trajectory, the robustness with respect to the parameter is increased. The effectiveness of this approach has been shown both numerically (Hindle and Singh, 2000;Singh, 2010) and experimentally (Kased and Singh, 2005), but only for the design of closed-loop control systems for linear systems. For this reason the procedure followed in the aforementioned papers cannot be applied to the test cases used here, which involve nonlinear systems.…”

“…Moreover, the innovative method proposed here applies to nonlinear plants, and therefore it greatly enhances the field of application of the method presented by Singh (2010), Kased and Singh (2005), and Dieulot et al (2006), which is also based on the use of sensitivity functions. However, the mentioned method can be applied only to linear plants, and is used to design a closed-loop control system.…”