Fundamental tradeoff between performance and robustness in control design

Control systems must fundamentally trade off performance with robustness to plant uncertainty. Hence, controller design aims at achieving an acceptable tradeoff between the conflicting goals of tracking or regulation performance versus robustness to plant uncertainty. This thesis investigates the tradeoff between robustness and performance for single-input single-output (SISO) systems and a tuning strategy for robust control of multiple-input multiple-out (MIMO) systems.; Robust Hinfinity or mu controller design is based on a set of weighting functions representing performance specifications and uncertainty sets with the goal of achieving the desired trade off between performance and robustness. However, once the robust controller is implemented, its parameters are fixed and no tuning is possible. Yet, plant uncertainty arises from the inevitable discrepancy between the true plant and its model. Thus, the capability of tuning the controller is often required in order to re-establish a favorable tradeoff between performance and robustness on-line.; Using a framework based on the internal model control (IMC) structure, we consider the fundamental tradeoff between performance and robustness by analyzing the tradeoff (|Wp(jo)|, | Wa(jo)|) where |W p(jo)| is the weighting for specifying performance and |Wa(jo)| is the maximum magnitude of the additive plant perturbation. In SISO systems and in certain MIMO systems, using only |Wp( jo)|, |Wa(jo)| and the nominal plant model Pn(jo) as input data, the optimal frequency response of the IMC controller Qopt(o) minimizing the structured singular value at each frequency can be obtained. This result provides the tradeoff (| Wp(jo)|, |Wa( jo)|) that yields the minimum of the structured singular value, which can help the control designer in the selection of appropriate weighting functions, and in judging different controller designs against the best achievable level of robust performance. Furthermore, the tradeoff theorem for SISO systems and the optimization algorithm for MIMO systems allow the computation of the optimal performance versus robustness tradeoff (rp(o),| Wa(jo)|), where r p(o) is the largest performance weight for which robust performance can be achieved for fixed |Wa( jo)|. On the other hand, the robust tuning requirement is achieved by fixing a |Wp(jo)| and adjusting |Wa(jo)| and therefore the tuned robust controller can be computed in a simple calculation which can be handled by plant engineers.; MIMO plants with a linear fractional uncertainty model are considered as a more general case for robust tuning design requirement. The framework is to reconfigure an interconnection of the Q-parameter and the uncertainty weights into the IMC-based structure. By defining a matrix H that maps Q into K in a linear fractional transformation, K □ F1( H,Q), the robust controller K can be obtained via a Q-parameter. The tuning strategy of the MIMO robust control design depends on this IMC structure. A systematic design procedure is presented to achieve a sub-optimal Q-parameter along with a tuning technique. A numerical example illustrates the MIMO robust control design and tuning procedure based on the optimization.