Theoretical and experimental assessment of Maxwell–Boltzmann type gain distribution for the vibration control of a generalized structural system

In this study, a linear frequency adaptive (LFA) optimal control was designed and investigated theoretically and experimentally for a generalized multi-degree-of-freedom structural system in its modal space. The designed control strategy followed Maxwell–Boltzmann type frequency distribution providing a concave type behavior similar to the uncontrolled structural mode to enable an improved control resistance at the regions of higher frequency responses of the system, and subsiding at the lower frequency response regions. The efficiency of the designed control was established to two existing control mechanisms, namely a frequency-sensitive lead compensated (LC) proportional control and the popular linear quadratic Gaussian (LQG) control. The theoretical evaluation was extended to include the noise effects in the closed-loop system. Based on the theoretical appraisal, thorough experimental investigations were conducted for the designed LFA and LQG control strategies applied on single-story and two-story steel shear frame models, considering diverse excitation scenarios across different frequency regions. The closed-loop test setup developed in a LabVIEW environment, interfaced with a data acquisition system to collect real-time data from the acceleration sensors attached to the structures, and the response integral in the form of convolution was used as output feedback. The results summarized that the LFA achieved the desired response with minimal control input compared to the existing control, even in the presence of significant noise uncertainty. Finally, a numerical validation was performed to compare the experimental results with the theoretical predictions, affirming the effectiveness and reliability of the designed control mechanism.