H_∞ control design for unstable plants

HeZhen, MENG Fan-wei, Zhou Di, WANG Guang-xiong

Dept. of Control Science and Engineering,Harbin Institute of Technology,Harbin 150001,China



Abstract:

For the control of unstable plants,it is required that the Nyquist locus of the system should encircle anticlockwise the point-1+j0,and the performance weighting function must be selected based on the specific requirement of the mid-frequency gain. Besides,the performance limitation imposed by the Bode’s integral also must be considered. Therefore the H∞ design for unstable plants is different from that in the regular case. It is pointed out that the sensitivity function for unstable plants must remain constant over the mid-frequency range to ensure a robust design. The selection of weighting functions to meet these requirements in the H∞ design is discussed in detail in the paper. A mixed sensitivity H∞ design example is also given to demonstrate the special considerations of the design.

Key words:  unstable plant  H∞ design  mixed sensitivity  electromagnetic levitation

DOI：10.11916/j.issn.1005-9113.2010.03.020

Clc Number:TP273

Fund: