In this work, we introduce several novel approaches to feedback controller design, known collectively as the “Robust Bode” methods, which adapt classical control principles to a modern robust control (H∞) framework. These methods, based on specially modified Bode diagrams extend familiar frequency-domain controller design techniques to linear and nonlinear, single–input/single– output (SISO) and multi–input/multi–output (MIMO) systems with parametric and/or unstructured uncertainties. In particular, we introduce the Contoured Robust Controller Bode (CRCBode) plots which show contours (level-sets) of a robust metric on the Bode magnitude and phase plots of the controller. An iterative loop shaping design procedure is then employed in an attempt to eliminate all intersections of the controller frequency response with certain forbidden regions indicating that a robust stability and performance criteria is satisfied. For SISO systems a robust stability and performance criterion is derived using Nyquist arguments leading to the robust metric used in the construction of the CRCBode plots. For open-loop unstable systems and for non-minimum phase systems the Youla parametrization of all internally stabilizing controllers is used to develop an alternative Robust Bode method (QBode). The Youla parametrization requires the introduction of state-space methods for coprime factorization, and these methods lead naturally to an elegant connection between linear-quadratic Gaussian (LQG) optimal control theory and Robust Bode loop-shaping controller design. Finally, the Robust Bode approach is extended to MIMO systems. Utilizing a matrix norm based robustness metric on the MIMO CRCBode plots allows cross-coupling between all input/output channels to be immediately assessed and accounted for during the design process, making sequential MIMO loop-shaping controller design feasible.

Recently, conductive polymer/carbon nanomaterials have drawn attention for use in corrosion inhibition, sensors, energy storage devices, and coatings for electromagnetic shielding applications due to their good mechanical properties and electronic conductivity. Therefore, efforts have been made to find fast and facile methods for the synthesis and development of these hybrids that allow control over key parameters, such as the thickness of the conductive polymer coating. In this study, such hybrids were prepared using polyaniline (PANI) as the conductive polymer and vapor-grown carbon nanofibers (VGCNFs) as the carbon nanomaterial or filler by a semi-dilute in situ polymerization method to be evaluated for their effectiveness as corrosion inhibitory additives to alkyd paints. Spectroscopic, colorimetric, and electric properties of PANI-coated VGCNFs were investigated. The thickness of the PANI coating, along with other parameters, impacts the behavior and mechanisms by which the nanomaterial performs its role in a given application, particularly in the corrosion inhibition processes. Thus, different synthesis conditions, including pretreatment of the nanofibers, the presence of sodium dodecyl sulfate (SDS) surfactant, PreT-VGCNF/ANI ratios (w/w), and polymerization times were tested and their effects on the PANI thickness were microscopically and statistically evaluated. It was found that only different PreT-VGCNF/ANI ratios allowed definite control of the PANI thickness. No clear effect on the thickness was observed after three hours of polymerization. The presence of SDS and pretreatment of VGCNFs displayed a synergistic effect on the appearance and thickness of the PANI film. PANI-coated VGCNF additives, with PANI in the leucoemeraldine base (LEB) and emeraldine base (EB) forms, were synthesized using a PreT-VGCNF/ANI ratio of 0.4 in the presence of SDS. Cold-rolled steel coupons were coated with 20-30 ìm thick alkyd paint coatings, and their electrochemical behavior was investigated by open circuit potential (OCP) and electrochemical impedance (EIS) measurements. The results indicate that, overall, EB/VGCNF additive performed better as a corrosion inhibitor, followed by PreT-VGCNF and LEB/VGCNF additives.