properties are found via several assumptions done in material strengths calculations and variable loading. These

factors affect the mass and stiffness of the structure, but it is known that the main factor in the optimum design

of control systems is the frequency that is related to mass and stiffness, generally. In this study, the stiffness of

multiple degrees of freedom structure was reduced and increased to investigate the effect of the robustness of

optimum active control systems for uncertainties. The numerical examination is done for a structure with an

active tuned mass damper (ATMD) that is positioned on the top of the structure. For ±20 stiffness change of

structure, the efficiency of ATMD is between 0.99% and 12.63% for the reduction of maximum displacement.

Key-Words: - Robustness, uncertainties in structures, stiffness, active tuned mass damper

Received: May 26, 2021. Revised: December 27, 2021. Accepted: January 24, 2022. Published: February 15, 2022.

approximately 8 billion, the changing and

diversifying needs of people led to a rapid change in

the face of the world. This change occurs in almost

every aspect of life, such as the increase in the rate

of urbanization, the rise of buildings, the increase in

energy needs, the expansion of high-speed train

networks and highways due to the need for a global

supply chain and urbanization. However, this

change brings with it new problems that need to be

solved. This change and diversity in structural

frequently used in order to provide structural safety

and comfort against earthquake and wind-like

vibrations, especially in developed countries in the

earthquake zone. Tuned mass dampers have an

algorithm is better than LQG [5]. Active multi-tuned

mass dampers (AMTMDs) have also been

investigated and suggested to be used to reduce

structural vibration due to ground motion [6-10].

a method combining genetic algorithm (GA) and

FLC to suppress vibration of high rise buildings

derivative) control and FLC was proposed [13].

FLC algorithm was also modified with a self-

tunning mechanism to improve control strategy

[14]. Li et al. introduced a design methodology for

AMTMD to attenuate translational and torsional

responses in asymmetric structures [15]. In the other

study, Li also considered soil-structure interaction

(SSI) for AMTMD attached to asymmetric

structures [16]. A hybrid system consisting of

ATMDs was proposed for retrofit of irregular

regulator for building frames with ATMD. In the

study, the stochastic algorithm provided more

effective seismic control [19]. Amini et al.

employed particle swarm optimization (PSO) and

linear quadratic regulator (LQR) in the calculation

of active force. The study demonstrated that PSO

provides better solutions for the structures subjected

to near-fault excitations [20]. Fitzgerald et al.

implemented ATMD to a wind turbine to control in-

plane vibrations of blades [21].

objective methodology using GA and FLC in order

to mitigate dynamic vibrations due to earthquake

and wind loads. The method was tested on a

benchmark 76-story building in Australia,

Melbourne. However, the optimum design against

earthquake excitations was not adequate for the

reduction of wind-induced vibrations and vice versa

[24]. Considering similar building, the cuckoo

search (CS) algorithm was proposed to be involved

in the calculation process of active forces by Zabihi

are given of an ATMD using proportional derivative

integral (PID) type controllers that have optimum

mass (md,opt), stiffness (kd,opt), damping (cd,opt),

proportional gain (Kp,opt), derivative time (Td,opt) and

integral time (Ti,opt). The structure mass, stiffness

and damping coefficients are shown as mi, ki and ci,

respectively. i represent the story number. The

motions presented in FEMA P-695 [41] are used

and the results are presented for the most critical

excitation. F(t) represents the control force matrix

given as Eq. (2). x(t) (Eq.3) is the response matrix

including displacements of N story structure (xi to

xN) and ATMD (xd). M, K and C matrices are shown

as Eqs. (4)-(6). The control force (Fu) is calculated

via Eqs. (7)-(9). In these equations, Kf, iATMD, R, Ke,

u(t), td and e(t) are trust constant, armature coil,

resistance value, induced voltage constant of

bold in the Table 3 are NORTHR/MUL279 record

for -25% - -5% stiffness, and DUZCE/BOL090

record for others. Considering the critical

earthquakes, the increase in stiffnesses led to a

decrease in the displacements whereas an increase

in the accelerations.

change in displacements, 34.06% in accelerations

(Case 1-5), and for DUZCE/BOL090 record 12.89%

change in displacements and 12.52% in

Uncertainties in stiffness can be caused by many

reasons such as design assumptions, differences in

the behavior of the material (especially using non-

homogeneous materials such as concrete) or

manufacturing errors. Depending on the quality of

the control process during the construction of the

structure, these uncertainties can be minimized, but

it is not possible to completely eliminate.

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[10] Li, C. and Xiong, X. (2008). Estimation of

[13] Guclu, R., and Yazici, H., 2009a, Seismic-

[14] Guclu, R., and Yazici, H., 2009b, Self-tuning

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[27] Heidari, A. H., Etedali, S., and Javaheri-Tafti,

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