Hamiltonian Sistemler İçin Dayanıklı Kontrolör Tasarımı
Hamiltonian Sistemler İçin Dayanıklı Kontrolör Tasarımı
Dosyalar
Tarih
2010-07-23
Yazarlar
Yalçın, Yaprak
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Institute of Science and Technology
Özet
Bu doktora çalısması kapsamında; Önce, toplu-parametreli Hamiltonian sistemlerin,doğrudan ayrık kontrollör tasarım yöntemleri gelistirmeye elverisli ayrık-zamanlı modelinin eldesi için, sistemin sürekli modelinin bilindiği varsayılarak gradyan temelli bir yöntem gelistirilmistir. Üç farklı yeni ayrık-gradyan ifadesi önerilmis ve bu gradyanlar kullanılarak elde edilen ayrık-zamanlı modeller verilmistir. Daha sonra, sürekli Hamiltonian sistemler için gelistirilmis olan PBC (Passivity Based Control)tekniğinin, doğrudan ayrık zaman karsılığı n-serbestlik dereceli mekanik sistemler için elde edilmistir. Ardından, n-serbestlik dereceli mekanik sistemler için ayrık zamanlı bozucu bastırma problemi ele alınmıs, sistemin ayrık zamanlı Hamiltonian modeli için problemin formulasyonu yapılmıs ve problemin çözüm kosulu bir teorem ile verilmistir. Ayrıca, parametrelerinde belirsizlik içeren n-serbestlik dereceli mekanik sistemler için ayrık zamanlı dayanıklı bozucu bastırma problemi de ele alınmıstır. n-serbestlik dereceli sistemlerin dayanıklı kontrol probleminin, özel bir kontrol yapısı kullanıldığında, bozucu bastırma problemine indirgenebildiği gösterilerek, dayanıklı bozucu bastırma probleminin doğrudan-ayrık tasarımla çözümü bir yeter kosulla verilmistir. Ek olarak, Navarro-Lopez (2002a) tarafından, genel doğrusal olmayan sistemlerin yerel kararlılık probleminin çözümü için sunulmus olan yöntem,Hamiltonian sistemlerin ayrık-zamanlı modelleri kullanılarak yeniden yazılmıstır. Ayrıca, Navarro-Lopez (2002a)’in sunmus olduğu kayıplı olma tanımı, bozucu bastırma probleminin çözümü için de kullanılmıs ve daha önce elde edilen yeter kosuldan daha kullanıslı bir kosul elde edilmistir. Son olarak, önerilen ayrık-zamanlı PBC yöntemi, bu çalısma kapsamında gerçeğine uygun olarak 1/20 oranında insa edilmis gezer köprülü vinç düzeneği üzerinde, konum kontrolü ve köprü hareketinden kaynaklanan yük salınımının azaltılması amacıyla uygulanmıstır.
The problem of discrete-time modelling of the lumped-parameter Hamiltonian systems is considered and a novel gradient-based method is presented under the assumption of the continuous Hamiltonian model is known. In order to provide alternate discrete time models, three different discrete-gradient definitions are given. After then the direct discrete time control of the Port Controlled Hamiltonian Systems in the sense of energy shaping and damping injection is considered. The discrete-time counterpart of PBC technique is developed for n-degree of freedom mechanical systems using this proposed discrete-time model. Next, the discrete-time disturbance attenuation problem for the considered class of Hamiltonian systems is considered. The disturbance attenuation problem characterised by means of L2 gain is redefined in the discrete-time setting and a sufficient condition for the solution of the considered problem is given. Besides, the discrete-time robust disturbance attenuation problem for n-dof mechanical system with uncertainty is considered. First, it is shown that the robust control problem of the n-dof mechanical systems can be reduced to the disturbance attenuation problem when a specific type of control rule is used. Then, the solution of robust disturbance attenuation problem via direct-discrete time design is given as a sufficient condition. In addition, the method presented by Navarro-Lopez (2002) for the solution on the stability problem of general nonlinear systems, is rewritten for the discrete-model of Hamiltonian systems. Furthermore, the dissipativity definition presented by Navarro-Lopez (2002) is utilized for the disturbance attenuation problem and a new result is obtained which gives the construction of the control rule by a simple algebraic computation. Finally, the proposed discrete-time PBC method is applied to an industrial overhead crane mechanism -which is built, in the context of this study, at the ratio of 1/20 according to industrial overhead crane system - to solve the problem of precise positioning of the load and reduce the oscillations arise from the movement of the bridge.
The problem of discrete-time modelling of the lumped-parameter Hamiltonian systems is considered and a novel gradient-based method is presented under the assumption of the continuous Hamiltonian model is known. In order to provide alternate discrete time models, three different discrete-gradient definitions are given. After then the direct discrete time control of the Port Controlled Hamiltonian Systems in the sense of energy shaping and damping injection is considered. The discrete-time counterpart of PBC technique is developed for n-degree of freedom mechanical systems using this proposed discrete-time model. Next, the discrete-time disturbance attenuation problem for the considered class of Hamiltonian systems is considered. The disturbance attenuation problem characterised by means of L2 gain is redefined in the discrete-time setting and a sufficient condition for the solution of the considered problem is given. Besides, the discrete-time robust disturbance attenuation problem for n-dof mechanical system with uncertainty is considered. First, it is shown that the robust control problem of the n-dof mechanical systems can be reduced to the disturbance attenuation problem when a specific type of control rule is used. Then, the solution of robust disturbance attenuation problem via direct-discrete time design is given as a sufficient condition. In addition, the method presented by Navarro-Lopez (2002) for the solution on the stability problem of general nonlinear systems, is rewritten for the discrete-model of Hamiltonian systems. Furthermore, the dissipativity definition presented by Navarro-Lopez (2002) is utilized for the disturbance attenuation problem and a new result is obtained which gives the construction of the control rule by a simple algebraic computation. Finally, the proposed discrete-time PBC method is applied to an industrial overhead crane mechanism -which is built, in the context of this study, at the ratio of 1/20 according to industrial overhead crane system - to solve the problem of precise positioning of the load and reduce the oscillations arise from the movement of the bridge.
Açıklama
Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2010
Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2010
Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2010
Anahtar kelimeler
Hamiltonian Sistemler,
Modelleme,
Dayanıklı Kontrol,
Hamiltonian Systems,
Modelling,
Robust Control