Robust Control of a Seismic Excited Building Facing to Structured Uncertainties KARIMA CHAKER, ABDELKRIM MOUSSAOUI, BADREDDINE SBARTAI Department of Electrical Engineering, Department of Civil Engineering University of Skikda, University of Guelma, University of Annaba Road of El Hadeik, B.P. 26 Skikda  B.P. 25, Guelma, B.P. 12, Annaba ALGERIA chakerkarima@yahoo.fr, a_k_moussaoui@yahoo.fr, bsbartai@hotmail.fr Abstract: Robust active controllers, designed to seismic excited building structure facing to parametric uncertainties (variations in mass, stiffness, damping coefficients…etc) were studied these last years with recent focus to non parametric ones (time delay, actuator saturation…etc). This study presents an evaluation of the robustness to variations in the model parameters of a t hree floors seismic exited structure (stiffness and damping coefficients) and modelling errors in the actuator dynamics of a robust controller designed on the base of the µ-synthesis approach chosen for its ability to directly incorporate performance and robustness objectives into multivariable control design. To further check the controller designed, we perform simulations using state feedback control and a seismic excitation source modelled by Kanai Tajimi filter attacked by a white noise. The resulting controller achieves closely similar performances (level of vibrations attenuation) in nominal and worst case of uncertainties variation while accounting for actuator limit and sensor noise considerations and presents a great benefit of costing low energy. At last, as the μ-synthesis generates controllers with too high order, a balanced realization method has been used to reduce the designed controller order without degrading its performance. Key-Words: Robust active control, Seismic excited building, μ-Synthesis, Structured uncertainties, 1 Introduction The research in structural robust active control field considerably increased these last two decades since the earthquake protection of structures represents a serious problem that looks for a way more and more efficient to dissipate the energy due to the seismic load for raising their safety and performance [1-2]. These last years, several papers investigate this domain employing number of robust control strategies (LQG, H ∞, adaptive control,...etc) and provided potentially significant reduction of the structure response to a seismic load in presence of uncertainties [3-5]. This being, the major concern of researchers is to insure that the designed controller will really be efficient in the real conditions of implementation. That implies to take into account in the control design procedure maximum of practical considerations which often occur as modelling errors (in coefficients of structure model), sensors noise, time delay [4-5] induced by the application of the actuator force (mechanical, hydraulic), physical actuator limits...etc. In fact, the modelling errors resulting from the evaluation of the parameters of the structural model (parametric uncertainties) or errors in the dynamics of the actuator and structure models (non parametric uncertainties) should be considered simultaneously. Incorporate all these aspects in the robustness and performance objectives design help to well evaluate the usefulness of a controller in a practical point of view [1]. Hence, the motivation of this work is to design a robust controller based on the structured singular value μ technique to a three-degree of freedom structure as its control law allow to account explicitly of robustness to dynamic and parametric uncertainties, in the present case modelling errors in the actuator dynamic and variations in stiffness and damping coefficients in the structure model. In addition to robustness considerations, the μ - synthesis problem formulation poses the performance objectives as minimizing the norm of weight transfer functions [6]. The quantification of these uncertainties as well as t he interpretation of the performance requirements in appropriate weighting functions represent the critical step in the problem formulation of this multivariable control technique [7]. To evaluate the designed controller, we perform simulations on a three floors building where an active bracing system (ABS) actuator is attached to the first floor [3] to attenuate the seismic WSEAS TRANSACTIONS on SYSTEMS Karima Chaker, Abdelkrim Moussaoui, Badreddine Sbartai E-ISSN: 2224-2678 19 Volume 16, 2017