Partial pole placement using static output feedback

For many dynamical systems it is required to specifically shift individual poles, especially when these poles are lightly damped or even unstable. To achieve that, a preferably large number of effectors and measurements are installed leading to multivariable control problems. In this paper, a novel control approach is presented for placing either a single pole or a conjugate complex pole pair at a predefined location using rank-one static output feedback. Rank-one feedback can be interpreted as blending inputs and outputs to define a single input and single output loop with a desirable root locus along which the pole is moved. The corresponding controller synthesis is reduced to an unconstrained optimization problem in a single variable that aims at minimizing the feedback gain. Although the approach is derived for a single pole or conjugate complex pole pair, it is easily extended to multiple poles. To this end, a repeated design and superposition of rank-one feedback gains is proposed. It is further shown how residual system dynamics as well as subsequently designed gains can be efficiently decoupled from each other in order to avoid undesired interactions and spillover effects. The effectiveness of the proposed control approach is demonstrated by means of a numerical example.