Proportional retarded control of a second order system

A strategy for the tuning of a second order system in closed loop with a proportional retarded control law, based on the root location analysis of the system, is proposed. It is validated by achieving a significant reduction of the oscillatory behavior of a cart pendulum experimental setup.

[1]  K. Cooke,et al.  Discrete delay, distributed delay and stability switches , 1982 .

[2]  K. Cooke,et al.  On zeroes of some transcendental equations , 1986 .

[3]  Vladimir L. Kharitonov,et al.  Exponential estimates for retarded time-delay systems: an LMI approach , 2005, IEEE Transactions on Automatic Control.

[4]  Wim Michiels,et al.  Static output feedback stabilization: necessary conditions for multiple delay controllers , 2005, IEEE Transactions on Automatic Control.

[5]  Ali H. Nayfeh,et al.  Dynamics and Control of Cranes: A Review , 2003 .

[6]  S. Niculescu,et al.  Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach , 2007 .

[7]  F. L. Chernous'ko Optimum translation of a pendulum , 1975 .

[8]  Vladimir L. Kharitonov,et al.  Exponential estimates for time delay systems , 2004, Syst. Control. Lett..

[9]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[10]  Pierre Rouchon,et al.  Generalized state variable representation for a simplified crane description , 1993 .

[11]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[12]  T. Kalmár-Nagy,et al.  Nonlinear Stability of a Delayed Feedback Controlled Container Crane , 2007 .

[13]  Il Hong Suh,et al.  Proportional minus delay controller , 1979 .

[14]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[15]  Ho-Hoon Lee,et al.  Modeling and Control of a Three-Dimensional Overhead Crane , 1998 .

[16]  C. Abdallah,et al.  Delayed Positive Feedback Can Stabilize Oscillatory Systems , 1993, 1993 American Control Conference.