V-gap metric-based simultaneous frequency-shaping stabilization for unstable multi-input multi-output plants - Pushpangathan, Jinraj V. (2021)
The solution to the simultaneous stabilization problem of a finite set of MIMO unstable plants considered in this Note is based on the frequency-shaped central plant and its sufficiency condition for simultaneous stabilization. The novel method proposed in this Note to acquire the frequency-shaped central plant from a finite set of MIMO unstable plants used v-gap metric between the plants, the frequency-shaping of the plants that used the pre- and post-compensators, and the robust stabilization theory. An optimization problem is formulated to obtain the pre- and post-compensators that reduce the minimum among the maximum v-gap metrics of all the frequency-shaped plants as well as induce required frequency characteristics on all the plants in the set without instigating pole-zero cancellation with any plants in the set. A novel iterative algorithm is developed to solve this optimization problem to attain the compensators. The plant with a maximum v-gap metric that is the minimum among the maximum v-gap metrics of all the frequency-shaped plants is identified as the frequency-shaped central plant. Also, the sufficiency condition of the frequency-shaped central plant is the most suitable sufficiency condition for the simultaneous stabilization. The capability of the iterative algorithm presented in this Note is demonstrated by a realistic design example. For that, the simultaneous stabilization of the finite set of MIMO unstable plants of the NAV is accomplished. The limitation of the method presented in this Note is that it is only applicable to the plants that have similar frequency characteristics.