Non-parametric H∞ control synthesis with suboptimal controller sets.

Abstract

The effectiveness of norm-based control methodologies heavily relies on the quality of the model that describes the dynamic behavior of the plant. In practical applications, the requirement to accurately describe the system at hand often results in high-order plant-models. On the other hand, low-order models are desired to end-up with low-order controllers that reduce implementational costs. The resulting trade-off between dynamical order and closed-loop performance can not be handled in a straightforward manner since the closed-loop behavior is unknown at the moment of plant-parametrization. This paper proposes a method to overcome this trade-off via non-parametric H ∞ control-synthesis, i.e. omitting parametrization of the plant. As a result, no data-reduction or data-interpolation is performed before synthesis. The resulting controller is represented as Frequency Response Sets for a given frequency grid. This data can be used as input for controller parametrization with explicit trade-off between closed-loop performance and controller order. This is achieved by considering the mixed-sensitivity problem as a model-matching problem based on Youla-parametrization. Via a specific conceptual choice of the coprime-factorization for the Youla parametrization, it is proved that the SISO H ∞ control synthesis problem can be solved in a non-parametric way based on the plant zeros and frequency response coefficients of the system solely. A simulation study is performed on a fourth-order system to illustrate the main steps in the approach.