Integrated Robust Optimal Design Using Bilinear Matrix Inequality Approach Via Sensitivity Minimization

Abstract

A novel integrated robust control synthesis methodology is presented here which combines a traditional sensitivity theory with relatively new advancements in bilinear matrix inequality (BMI) constrained optimization problems. The proposed methodology is demonstrated using a numerical example of integrated control design problem for combine harvester header linkage. The integrated design methodology presented is compared with a traditional sequential design method and the results show that the proposed methodology provides a viable alternative for robust controller synthesis and often times offers even a better performance than competing methods.

Header height control of combine harvester via robust feedback linearization

“…The methodology presented in [1] proposed to use sensitivity theory to add robustness to feedback linearization. The basic concept is to minimize the sensitivity, which is defined as the change in performance as a result of perturbations in design variables.…”

“…With advancements in technology, symbolic computation has become easier and as a result, recent research has revisited sensitivity theory for robust control applications [22]. The method proposed in [1] and developed further in this thesis provides the least conservative design by using the sensitivity dynamics to add robustness to the feedback linearization controller. This is achieved by adjusting the nominal feedback linearization calculated input slightly to minimize the sensitivity with respect to uncertain parameters.…”

“…The methodology uses two separate control strategies, one for the multibody mechanical system and one for the hydraulic system. The former is fulfilled by Integrated Robust Optimal Design (IROD) proposed in [1,22] with the latter being the Robust Feedback Linearization (RFL) controller presented in this thesis. The RFL controller is made robust with respect to bulk modulus uncertainties.…”

“…It suggested that even the best optimal controller still may not be sufficient due to structural limitations. To overcome this, integrated plant and controller design was proposed in [22] and [53]. In doing this, certain mechanical plant parameters are designed concurrently with the controller to achieve a more optimal design than originally possible.…”

“…In doing this, certain mechanical plant parameters are designed concurrently with the controller to achieve a more optimal design than originally possible. In [53], a H ∞ controller is used, while in [22] a new methodology, IROD, is introduced which is shown to achieve better tracking performance than H ∞ . In both works, the focus is on the mechanical system and the hydraulic dynamics are idealized, such that the hydraulic actuator can provide perfect force.…”