State‐constrained stabilization of beam‐balance systems

We present nonlinear control techniques to stabilize a beam-balance system with state constraints. We consider two different actuator configurations: the first one is actuated by a cart moving on the beam, while in the second case, the actuation is by a single electromagnet. In the first case, the constrained stabilization problem is solved via an output feedback controller designed using feedback linearization, Luenberger-like observer and linear matrix inequality based optimization. In the second case, a Lyapunov-based controller is proposed that takes care of both the input and state constraints. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[2]  Panagiotis Tsiotras,et al.  Low-bias control of AMBs subject to saturation constraints , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[3]  E. Mosca,et al.  Nonlinear control of constrained linear systems via predictive reference management , 1997, IEEE Trans. Autom. Control..

[4]  Ali Saberi,et al.  Constrained stabilization problems for linear plants , 2002, Autom..

[5]  R. Mahony,et al.  Integrator Backstepping using Barrier Functions for Systems with Multiple State Constraints , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[6]  Alberto Bemporad,et al.  Model predictive control based on linear programming - the explicit solution , 2002, IEEE Transactions on Automatic Control.

[7]  H. Richter.  Robust positively invariant cylinders for constrained sliding mode control designs , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[8]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[9]  Ali Charara,et al.  Nonlinear control of a magnetic levitation system without premagnetization , 1996, IEEE Trans. Control. Syst. Technol..

[10]  Paul E. Allaire,et al.  Constrained Control Design for Magnetic Bearing Systems , 2005 .

[11]  Lichuan Li,et al.  Linearizing magnetic bearing actuators by constant current sum, constant voltage sum, and constant flux sum , 1999 .

[12]  Jiefang Li,et al.  Analysis of the combustion driven linear generator for electric gun applications , 1999 .

[13]  A. Isidori.  Nonlinear Control Systems , 1985 .

[14]  A. Germani,et al.  A Luenberger-like observer for nonlinear systems , 1993 .

[15]  Jean Lévine,et al.  A nonlinear approach to the control of magnetic bearings , 1996, IEEE Trans. Control. Syst. Technol..

[16]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..