Yapıların optimal kontrolu
Optimal control of structures
- Tez No: 100686
- Danışmanlar: PROF.DR. MEHMET BAKİOĞLU
- Tez Türü: Doktora
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1999
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 124
Özet
YAPILARIN OPTIMAL KONTROLÜ ÖZET Yapıların aktif kontrolü ile ilgili yapılan çalışmaların büyük bir kısmı, optimalliğin gerekli koşullarından yararlanarak entegral formda tanımlanmış kuadratik amaç fonksiyonunun minimizasyonundan elde edilen ve lineer regülatör probleminin bir tür uygulaması olan klasik aktif kontrol algoritmalarına dayanmaktadır. Bu algoritmalardan sadece yaklaşık optimal olan kapalı-çevrim kontrolü yapılara uygulanabilmektedir. Kapalı-açık ve açık-çevrim kontrolleri ise depremin önceden bilinmesini gerektirdiklerinden yapı kontrolüne uygulanamamaktadırlar. Bu çalışmada yapı kontrolü için tanımlanan lineer regülatör probleminin analitik çözümü V. F. Krotov tarafından verilen optimalliğin yeterli koşullarından yararlanarak elde edilmiştir. Ayrıca kapalı-açık çevrim kontrol algoritmasının yaklaşık çözümü depremin yakın-gelecek ivme değerleri Kalman filtresi tekniği ile tahmin edilerek elde edilmiştir. Sayısal uygulama olarak sönümsüz üç ve sönümlü beş katlı iki binanın El Centro depremi altındaki davranışları incelenmiş ve depremin yakın gelecek ivme değerleri hassas olarak tahmin edilebildiği takdirde optimal çözüme yaklaşılabileceği gösterilmiştir. Daha sonra lineer regülatör problemi kararlılık mertebesi kavramı dahil edilerek çözülmüş ve kararlılık mertebesi ile tahmin edilen deprem ivme değerleri arasındaki ilişki sayısal olarak incelenmiştir. Klasik kontrol algoritmalarının mevcut eksikliğine ikinci bir alternatif olarak çok noktalı kuadratik ani amaç fonksiyonu önerilmiş ve Lagrange yöntemiyle elde edilen algoritma üç katlı sönümsüz yapıya uygulanarak sonuçlar karşılaştırılmıştır. Ayrıca, üzerine pasif ayarlı kütlesel sönümleyici yerleştirilmiş bir esnek deniz yapışma bir geminin yanaşma problemi Wilson- 0 yöntemiyle lineer ve lineer olmayan durumlar için sayısal olarak incelenmiş ve kütlesel sönümleyicinin sisteme olan etkisi enerji dağılımı hesaplanarak araştırılmıştır.
Özet (Çeviri)
OPTIMAL CONTROL OF STRUCTURES SUMMARY In recent decades, many advances have been made in modern control theory and their applications to engineering systems. Since the pioneer works of J. T. P. Yao based on the control theory, considerable progress has been made in the applications of the structural control. The optimal control problem for the structures which is given by T. T. Soong and the other authors can be solved by using the classical method (The method of calculus of variations), Pontryagin's maximum principle or the method of dynamic programming of R. Bellman. A great number of the researches presented previously are based on the classical active control algorithms, which are the applications of the regulator problem. These algorithms which are based on the minimization of a quadratic performance index lead to the Riccati type differential equations. Optimal regulator is derived generally based on the necessary conditions of optimality. Depending on whether the algorithm depends on the state of the system or directly on the forcing excitation it may be classified as closed-loop, open-loop or closed-open loop. Among these, only classical closed-loop control is applicable to structural control problems. However, since the Riccati equation is obtained by ignoring the earthquake excitation term classical closed-loop control is approximately optimal and does not satisfy the optimality condition. On the other hand, even though the classical closed-open loop and open- loop control algorithms are superior to the closed-loop control, since they require the whole knowledge of the earthquake acceleration history they are not applicable to earthquake-excited structures. Therefore, it is almost impossible to find the optimal control exactly for the structures under earthquake and wind forces and in terms of application in control of structures, none of these methods can be considered as optimal control. In an attempt to resolve these problems, in Sections 2-4 of this thesis analytical solution of the linear regulator problem for structural control is derived based on the sufficient conditions of optimality given by V. F. Krotov and then the solution of the closed-open loop control is carried out based on the numerical solution with the prediction of near-future earthquake excitation using the Kalman filtering technique. The summary of the work done in Sections 2-4 is given below. Introducing a 2N-dimensional state vector, Z(t), as followsthe equation of motion of a shear-beam lumped mass linear building structure under the one-dimensional earthquake ground acceleration and the control can be described in state-space form as in which X(Y)=( x\, X2,-, x“ )T is the «-dimensional response vector denoting the relative displacement of the each story unit with respect to the ground; M is the (nxn)-dimensional diagonal constant mass matrix with diagonal elements mt = mass of / th story (z-1, 2,..., n); C and K are (nxn)-dimensional viscous damping and stiffness matrices, respectively; V=(1,...,1)T is the «-dimensional vector; L is the (nxr)-dimensional location matrix of r controllers (V and L indicate the locations of the earthquake excitation terms and the controllers in the matrix equation, respectively); \J(t) is the r-dimensional active control force vector and scalar function fit) is the one-dimensional earthquake acceleration. In obtaining the optimal control law; the classical quadratic performance measure is minimized under the constraints imposed by Eq. 2, where [0, t{\ time interval is the control time and defined to be longer than that of the external excitation duration; Q is a (2nx2n) dimensional positive semidefinite symmetric weighting matrix and R is a (rxr) dimensional positive definite symmetric weighting matrix. Numerical values for the elements of Q and R matrices are assigned according to the relative importance of the state variables and the control forces in the minimization procedure in order to adjust the power requirements in the actuators. The sufficient conditions, which are used for the solution of the optimal control problem given by the Eqs. 2 and 4 are defined by using a definite function !f(/, Z) which is a generalization of Bellman function. For a given function n(t, Z)e Q(cr), a=[0, ?i]xR2”, the following functions can be defined: where XllIf (Z (0,U (/.)) is an admissible process and if there exists at least one function such that then we say that the process (Z (i),XJ (t)) satisfies the extended maximum principle. The function f{t,Z) in the definition of extended maximum principle is selected as where 2n-dimensional column vector q(t) and (2nx2n)-dimensional symmetric matrix P(/) are considered as unknowns. Since our performance index is quadratic, the function f{t,Z) is selected in this form. Using the given function ¥(t,Z) and the sufficient conditions given by Eqs. 7 and 8, the optimal control force is obtained as where P(t) and q(f) are the solutions of the following equations: and Upon substituting the vector function v* (t, Z) given by Eq. 10 into Eq. 2 in place of U, the equation of the structure under optimal control is obtained as Backward integration of Eq. 12 requires the complete knowledge of the earthquake excitation in the whole control interval. Since it is impossible to know the earthquake Xlllexcitation a priori the closed-open loop control can not be applied to the structural control. So, forward integration of Eq. 12, instead of backward, is calculated by using the few steps ahead predictions of the earthquake excitation. This prediction is called near-future prediction. Eqs. 11, 12 and Eq. 13 can be put into a similar form of the first-order matrix differential equation, which is given below: When D is constant, the expression of S* can be given by the following simple form: k I Here, Gj+i is given by As seen in Eq. 17, since i>j, Sj values at any pointy are dependent on the c, terms that are completely beyond the point j and include the unknown excitation terms. These terms will be predicted by using their known values in the past. Besides that, if the norm of the matrix G (j-i
Benzer Tezler
- Deprem etkisinde zeminle etkileşen yapıların optimal kontrolü
Optimal control of structures under earthquakes including soil-structure interaction
ALİ RUZİ ÖZUYGUR
Doktora
Türkçe
2011
İnşaat Mühendisliğiİstanbul Teknik Üniversitesiİnşaat Mühendisliği Ana Bilim Dalı
DOÇ. DR. A. NECMETTİN GÜNDÜZ
- Optimal structural control using Wavelet-based algorithm
Wavelet yaklaşımını içeren LGR tekniği ile yapıların optimal kontrolu
MAHDİ ABDOLLAHİRAD
Yüksek Lisans
İngilizce
2014
Deprem Mühendisliğiİstanbul Teknik Üniversitesiİnşaat Mühendisliği Ana Bilim Dalı
PROF. ÜNAL ALDEMİR
- Deprem etkisindeki yapıların optimal yarı-aktif kontrolü
Optimal semi-active control for the structures under the earthquake effects
MELİH ÖZDİLİM
Yüksek Lisans
Türkçe
2005
İnşaat Mühendisliğiİstanbul Teknik ÜniversitesiDeprem Mühendisliği Ana Bilim Dalı
DOÇ. DR. ÜNAL ALDEMİR
- Optimal control of physical systems governed by partial differential equations
Kısmi diferansiyel denklemler tarafından yönetilen fiziksel sistemlerin optimal kontrolü
SEDA GÖKTEPE KÖRPEOĞLU
Doktora
İngilizce
2019
MatematikYıldız Teknik ÜniversitesiMatematik Mühendisliği Ana Bilim Dalı
PROF. DR. İSMAİL KÜÇÜK
- Sismik yükler altında yapı davranış kontrolü
Structure behavior control under seismic loads
MÜRÜVVET BATI
Yüksek Lisans
Türkçe
2020
Deprem MühendisliğiKocaeli Üniversitesiİnşaat Mühendisliği Ana Bilim Dalı
PROF. DR. KEMAL BEYEN