Single‐input and single‐output (SISO) controller reduction based on the L1‐norm

This paper proposes a new method to solve the controller-reduction problem based on the L1-norm. This method uses a reduced-order closed-loop system to deduce reduced-order controllers. The problem of obtaining the required lower-order closed-loop system was formulated as an L1-norm optimization, and the conditions were provided for guaranteeing the internal stability and the existence of lower-order controllers from the obtained reduced-order closed-loop system. In addition, the particle swarm optimization and sequence linear programming were adopted to solve the resultant L1-norm optimization. Two numerical examples demonstrated the effectiveness of the proposed method.  2008 Curtin University of Technology and John Wiley & Sons, Ltd.

[1]  Yoshito Ohta,et al.  Rational approximation of L/sub 1/ optimal controllers for SISO systems , 1992 .

[2]  Jan Swevers,et al.  Experimental validation of different MIMO-feedback controller design methods , 2004 .

[3]  Mathukumalli Vidyasagar,et al.  Optimal rejection of persistent bounded disturbances , 1986 .

[4]  J. Pearson,et al.  l^{1} -optimal feedback controllers for MIMO discrete-time systems , 1987 .

[5]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[6]  M. O. Tokhi,et al.  Active Vibration Control of Flexible Structures Using Genetic Optimisation , 2006 .

[7]  Prasanta Sarkar,et al.  A Unified Approach for Controller Reduction in Delta Domain , 2004 .

[8]  Giovanni Muscato,et al.  Genetic algorithms for controller order reduction , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[9]  K. Poolla,et al.  An LMI approach to peak-to-peak gain minimisation: filtering and control , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[10]  A. Antoulas,et al.  Krylov-based controller reduction for large-scale systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[11]  Leon S. Lasdon,et al.  An Improved Successive Linear Programming Algorithm , 1985 .

[12]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[13]  Hsiao-Ping Huang,et al.  Decoupling Multivariable Control with Two Degrees of Freedom , 2006 .