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Palizvan Zand J, Sabouri J, katebi J, Nouri M. An anti-windup robust PID controller based on H_∞ for structural vibration attenuation. MCEJ 2021; 21 (4) :127-140
URL: http://mcej.modares.ac.ir/article-16-48324-en.html

Successful implementation of active control technology requires an appropriate control algorithm to calculate the adaptive control force required by the actuators. Smart structures represent a new engineering approach that integrates the actions of digital sensors, actuators and control circuit elements into a single control system that can respond adaptively to environmental stochastic changes in a useful manner. The mathematical model of the system is an estimation of its actual dynamic behavior. In general, this difference can have a significant effect on the performance and stability of the control system. One of the important issues in active control algorithms is the evaluation of the control systemchr('39')s robustness to model uncertainties and the actuator saturation. In this paper, a Developed Robust Proportional Integral Derivative controller with uncertainties in the structural stiffness parameter, the sensing noise and saturation windup of the saturation is introduced. the PID control force is obtained in such a way that the infinity norm of the closed loop system transfer function from disturbance inputs to target outputs becomes minimal. By considering the parametric uncertainty in the structural stiffness parameters and multiplicative unstructured uncertainty and the windup phenomenon in the actuator model and existence of noise in the velocity sensor, PID control scheme has been developed in the form of state space. The PID control gains by taking advantage of the Hinfinity mixed sensitivity minimization criterion, are obtained simultaneously by considering the effects of all vibration modes of the building in such a way that the infinity norm of the closed loop transfer function from exogenous inputs to the controlled outputs becomes minimal. To demonstrate the robust performance and stability of the proposed algorithm, the results of numerical simulations on a 4-story structure equipped with an active tuned mass damper are used. The obtained results show the robust performance and stability of the proposed robust PID control scheme in comparison with conventional PID and linear quadratic regulator (LQR) control algorithms, both in time and frequency domains. According to the mean values ​​of performance indices, in average 11 and 7% more reduction in J1 , 7 and 5% in J2  and 10 and 6% in J3  in the proposed robust PID in comparison with the LQR and common PID for three models subjected to far field selected earthquake records. And in average 17 and 10% more reduction in J1 , 12 and 8% in J2  and 11 and 8% in J3  in the proposed robust PID in comparison with the LQR and common PID for three models subjected to near field selected earthquake records. And J4  which related to amount of control effort, for the proposed robust PID, LQR and conventional PID are 1.3e-2, 9.1e-3 and 7.9e-3 in average for the three models subjected to far field and 4e-2, 2.4e-2 and 2.7e-2 subjected to near field selected earthquake records. The obtained results show the robust performance and stability of the proposed controller in the presence of structural stiffness uncertainties, actuator saturation and measurement noise.