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

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 IL 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 Hm 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 Hm 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.

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