SYNTHESIS OF TWO-INPUT PSS BASED ON THE H∞ CONTROL THEORY

Abstract

In the standard mixed sensitivity weighting strategy for H∞ controllers, the designer can formulate desired requirements (desired loop shape) using frequency domain weighting functions. The ∞all pass∞ property of the optimal H∞ control laws ensures that the singular value Bode plots will precisely conform to those specified by the weighting functions. However, there is a serious drawback to this property; namely, the resulting standard H∞-PSS always cancels the stable poles of the plant (pole-zero cancellation). It is known that the cancellation of lightly damped poles can lead to poor robust stability and performance. In the case of multi-input H∞ controller, it becomes much more difficult to achieve good robust stability and performance. In this paper, a design of H∞-PSS is proposed to prevent the pole zero cancellation phenomenon and increase the damping of weakly damped modes. The design method consists of applying the bilinear transform to a stable poorly damped nominal plant in order to transform it into a fictitious unstable plant suitable for the standard mixed sensitivity design approach. A combination of additive and multiplicative uncertainty representation was used to achieve the robust stability for a wide range of operating conditions. The PSS designed based on the proposed approach was compared with those based on the standard H∞ approach and the conventional method. Simulation results show that the proposed PSS gives better performance and is more robust than the standard H∞-PSS and the optimally tuned conventional PSS.