# Comparative Study Between Active AMD and ABS Devices by Using \(\mu\)-Synthesis Robust Control
###### Abstract
Therefore, the choice between the two depends on priorities: robustness to uncertainties or the optimization of energy consumption and performance. In our work, the focus was on structural uncertainties and the rejection of random disturbances such as seismic events. The \(\upmu\)-synthesis control method we employed is not strictly an H\(\infty\) control, though it uses H\(\infty\) principles in its design. It can be considered a robust extension of H\(\infty\) control, specifically more suited to applications where uncertainty is both significant and structured. It provides robust performance by minimizing the worst-case impact of disturbances and uncertainties, making it ideal for seismic protection in highly variable environments. Moreover, as with all previously discussed points, the choice of the control system device significantly influences the control performance. This choice appears to be just as important as the control method itself, as the actuator device has a tangible impact on the control design. Effectively, the actuators serve as active systems, translating control into a force that directly acts on the structure to counteract seismic effects; it is crucial to select the most suitable actuator for each structure. Two main active control devices in the active vibration control (AVC) field are the active bracing system (ABS) and the active mass damper (AMD). Base isolators are also specialized devices installed between a building's foundation and superstructure to reduce the amount of energy transferred to the structure by decoupling it from ground movements. Together, ABS, AMD, and seismic isolation provide seismic protection, each with unique advantages depending on the specific requirements and characteristics of the structure. The ABS device has an extra braking system with tendons connected to a servo-hydraulic actuator that is placed between the ground and the first floor of a building or between floors that follow each other. The AMD device, on the other hand, has an extra load on the last floor of the building [10]. An actuator connects the AMD to the structure. Thus, [PERSON] et al. [11] compared the results of a regular TMD with the use of an AMD to control the active vibrations of a 40-story building shook by strong winds. [PERSON] [12] proposed a guideline for the construction of active mass dampers (AMDs) to regulate a tall structure exposed to stationary random wind forces. [PERSON] and [PERSON] [13] used two controllers: fuzzy sliding mode control and variable structure control, for seismic-protected edifices equipped with active mass damper control systems. [PERSON] and [PERSON] [14] evaluated the efficacy of fuzzy logic and PD controllers in managing a 15-story frame fitted with AMDs on the first and fifteenth floors. [PERSON] et al. [15] conducted an experimental investigation on the fuzzy control of seismic structures utilizing an active mass damper (AMD). [PERSON] et al. [16] conductedcomputational and experimental evaluations of the AMD control system utilizing the model reference adaptive control method. ABS can decrease building vibrations by including active features between the ground and the first level. So, [PERSON] et al. [17] looked into how to use positive position feedback (PPF), direct velocity feedback (DVF), and integral force feedback (IFF) to control the active bracing of a seven-story building. However, [PERSON] and [PERSON] [18] investigated the Lyapunov method for vibration control in a SDOF building. [PERSON] [19] proposed a discrete-time modal control strategy, which is a very useful method to control the seismic response of building structures equipped with ABS. [PERSON] and [PERSON] [20] demonstrated a neural network-based vibration control method that effectively mitigated the shaking of an earthquake-damaged 3D multi-story building. They compared it to the traditional linear quadratic regulator (LQR) in terms of how it responded to displacement and how much force it used to control the building.