A quantitative design method for MIMO linear feedback systems having uncertain plants

Abstract

An improvement of the quantitative feedback theory (QFT) (Horowitz 1982) for MIMO systems is presented. The advantages of this approach are as follows, (a) In the ‘improved method’ the fundamental design relation (for the ith free function l_i ,) has the form |1 + l_i | > φ(b_uv , q_uv ) where b_uv are related to the performance tolerances of the closed loop, and q_uv to the plant parameters. We show that the right side can be replaced by a constant. This makes the design much easier and even more economical in terms of cost of feedback, (b) The SISO systems that replace the original MIMO problem are now defined by induction. This gives a better insight into the tradeoffs between the loop transmissions and make computer implementation easier. The attractive properties of this design method are: (1) The problem is reduced to successive single-loop designs with no interaction between them and no iteration necessary. (2)Stability over the range of parameter uncertainty is automatically guaranteed. (3) There is insight to the tradeoff between the loop transmissions. (4) The synthesis technique can handle the attenuation of plant disturbances. (5) This technique can be applied to all the plants P such that all the elements of P⁻¹ have no poles in the right half-plane. This new technique has been applied successfully to many examples, one of which is presented here.