Etkileşimsiz kontrol problemi
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Bu çalışma, lineer, zamanla değişmeyen, sürekli sistemlerde etkileşimsız kontrol problemi üzerine bir 'survey' dir. Etkileşimsiz kontrol problemi, kontrol teorisinin en eski problemlerinden biridir. Problemin ilk ele alınışı 1936'lara kadar gitmekle birlikte, üzerine esaslı bir şekilde gidilmesi, Morgan (1964) ile problem durum uzayında tanımlandıktan sonra olmuştur. Morgan, problemi statik durum geribeslemesi ile satır satıra etkisizleştirme anlamında tanımlar. Buna göre, problem; verilen bir sistemin her bir çıkışının yalnız ve yalnız bir girişten kontrol edilecek sekile, statik durum geribeslemesi ile dönüştü rülüp dönüştürülemeyeceğinin araştırılmasıdır. Bu formülasyondan daha genel olanı blok etkisizleştirme problemi olarak adlandırılır. Blok etkisizleştirme problemi; giriş ve çıkışları, gruplararası etkileşimin olmadığı gruplara ayırma olarak tanımlanabilir. Bu tanımlamaların ışığında; satır satıra etkisizleştirmen bir sistem, bir giriş bir çıkışlı alt sistemlere, blok etkisizleştirilen bir sistem ise orijinalsisteme göre daha az giriş ve çıkışları olan altsistemlere indirgenmiş olur. Bu anlamda, pratikte daha küçük boyutlu sistemlerle uğraşmak gibi bir yaran olduğu düşünülebilir. Bu durum, hem kontrolör tasarımında kolaylık sağlaya cağı gibi hem de insanlar tarafindan yönetilen sistemler için önemli bir kolaylık sağlayabilir. Kare sistemlerin statik durum geribeslemesi ile etkisizleştirilmesi için Falb ve Wolovich (1967) ile ilk ciddi sonuç elde edilir. Daha sonra Wonham ve Morse (1970) ile blok etkisizleştirme tanımlanır. Statik durum geribeslemesi ile blok etkisizleştirme problemi; yapı algoritması kullanılarak Silverman ve Payne (1971) ve geometrik formülasyonla Morse ve Wonham (1971) ile çözülür. Descusse ve Dion (1982) ile satır satıra etkisizleştirme için ve Dion (1983) ile de blok etkisizleştirme için sistemin sonsuzdaki sıfir yapısı ile etkisizleştirme probleminin bağlantısı verilir. Dinamik durum geribeslemesi ile satır satıra etkisizleştirme Dion ve Commault (1988) ve blok etkisizleştirme de Commault, Dion ve Torres (1988) ile çözülür. Blok etkisizleştirmenin ilginç bir çözümü Özgüler ve Eldem (1989) ile verilmiştir. Bu çalışmada, etkileşimsiz kontrol problemi üzerine yapılan araştırmaların sonuçlan sistematik bir yapıda sunulmuştur. Etkisizleştirme problemine eklemlenebil en kararlılık v.b. gibi alt problemler çalışma kapsamı tutulmuştur.
The noninteraction control (or decoupling) problem is one of the oldest in the control literature. Originally, interest focused on the diagonal decoupling and the formulation was made in the transfer function setting (see for details Kucera (1991) and Morse and Wonham ( 197İİ). The state-space formulation was given much later bv Morgan (1964).' The diagonal decoupling problem, which is called as Morgan's problem, is finding a state feedback law such that each input influences only an output i.e., each output can be independently controlled by a corresponding input. When a system is diagonal decoupled, it reduces single-input single-output subsystems and its transfer matrix becomes diagonal. More general problem is block decoupling or block noninteraction. The block decoupling problem is to find a state feedback law and a partition on the inputs for a given partition on the outputs such that each portion of outputs can be independently controlled by a corresponding portion of inputs. Block decoupling splits the system into independent subsystems and results block diagonal transfer matrix. Considerable advantages may result of simplicity and reliability, especially when the system is large scale or controlled by sophisticated algorithms or a human operator. During the last 30 years, a great deal of interest has been brought to the theory of decoupling. The formulation of the noninteraction control problem, for block decoupling by dynamic state feedback case is below. VI Let a system which obeys the input-state-output equations *(t)= A M!)+ B u(t) y(t)= Cx(t)+ Du(t) x(t) e X~R», u(t) e U~Rm, y(t) e Y~W AeR***, BeRws, CeR***, I>eR**w and a set of positive integers {j\} satisfying *=1 be given. These integers define a partition of output vector into 1 subvectors. The problem of noninteraction, or the decoupling problem, is that of determining when there exists a dynamic feedback U(s) = F(s) X(s) + G V(s) F(s) e RBUfB(5) 9GeRw and a set of positive integers {rj satisfying <=1 Vll SUMMARY A SURREY ON THE PROBLEM OF NUN INTERACTION CUNTRUL The noninteraction control (or decoupling) problem is one of the oldest in the control literature. Originally, interest focused on the diagonal decoupling and the formulation was made in the transfer function setting (see for details Kucera (1991) and Morse and Wonham ( 197İİ). The state-space formulation was given much later bv Morgan (1964).' The diagonal decoupling problem, which is called as Morgan's problem, is finding a state feedback law such that each input influences only an output i.e., each output can be independently controlled by a corresponding input. When a system is diagonal decoupled, it reduces single-input single-output subsystems and its transfer matrix becomes diagonal. More general problem is block decoupling or block noninteraction. The block decoupling problem is to find a state feedback law and a partition on the inputs for a given partition on the outputs such that each portion of outputs can be independently controlled by a corresponding portion of inputs. Block decoupling splits the system into independent subsystems and results block diagonal transfer matrix. Considerable advantages may result of simplicity and reliability, especially when the system is large scale or controlled by sophisticated algorithms or a human operator. During the last 30 years, a great deal of interest has been brought to the theory of decoupling. The formulation of the noninteraction control problem, for block decoupling by dynamic state feedback case is below. VI Let a system which obeys the input-state-output equations *(t)= A M!)+ B u(t) y(t)= Cx(t)+ Du(t) x(t) e X~R», u(t) e U~Rm, y(t) e Y~W AeR***, BeRws, CeR***, I>eR**w and a set of positive integers {j\} satisfying *=1 be given. These integers define a partition of output vector into 1 subvectors. The problem of noninteraction, or the decoupling problem, is that of determining when there exists a dynamic feedback U(s) = F(s) X(s) + G V(s) F(s) e RBUfB(5) 9GeRw and a set of positive integers {rj satisfying <=1 Vll SUMMARY A SURREY ON THE PROBLEM OF NUN INTERACTION CUNTRUL The noninteraction control (or decoupling) problem is one of the oldest in the control literature. Originally, interest focused on the diagonal decoupling and the formulation was made in the transfer function setting (see for details Kucera (1991) and Morse and Wonham ( 197İİ). The state-space formulation was given much later bv Morgan (1964).' The diagonal decoupling problem, which is called as Morgan's problem, is finding a state feedback law such that each input influences only an output i.e., each output can be independently controlled by a corresponding input. When a system is diagonal decoupled, it reduces single-input single-output subsystems and its transfer matrix becomes diagonal. More general problem is block decoupling or block noninteraction. The block decoupling problem is to find a state feedback law and a partition on the inputs for a given partition on the outputs such that each portion of outputs can be independently controlled by a corresponding portion of inputs. Block decoupling splits the system into independent subsystems and results block diagonal transfer matrix. Considerable advantages may result of simplicity and reliability, especially when the system is large scale or controlled by sophisticated algorithms or a human operator. During the last 30 years, a great deal of interest has been brought to the theory of decoupling. The formulation of the noninteraction control problem, for block decoupling by dynamic state feedback case is below.
The noninteraction control (or decoupling) problem is one of the oldest in the control literature. Originally, interest focused on the diagonal decoupling and the formulation was made in the transfer function setting (see for details Kucera (1991) and Morse and Wonham ( 197İİ). The state-space formulation was given much later bv Morgan (1964).' The diagonal decoupling problem, which is called as Morgan's problem, is finding a state feedback law such that each input influences only an output i.e., each output can be independently controlled by a corresponding input. When a system is diagonal decoupled, it reduces single-input single-output subsystems and its transfer matrix becomes diagonal. More general problem is block decoupling or block noninteraction. The block decoupling problem is to find a state feedback law and a partition on the inputs for a given partition on the outputs such that each portion of outputs can be independently controlled by a corresponding portion of inputs. Block decoupling splits the system into independent subsystems and results block diagonal transfer matrix. Considerable advantages may result of simplicity and reliability, especially when the system is large scale or controlled by sophisticated algorithms or a human operator. During the last 30 years, a great deal of interest has been brought to the theory of decoupling. The formulation of the noninteraction control problem, for block decoupling by dynamic state feedback case is below. VI Let a system which obeys the input-state-output equations *(t)= A M!)+ B u(t) y(t)= Cx(t)+ Du(t) x(t) e X~R», u(t) e U~Rm, y(t) e Y~W AeR***, BeRws, CeR***, I>eR**w and a set of positive integers {j\} satisfying *=1 be given. These integers define a partition of output vector into 1 subvectors. The problem of noninteraction, or the decoupling problem, is that of determining when there exists a dynamic feedback U(s) = F(s) X(s) + G V(s) F(s) e RBUfB(5) 9GeRw and a set of positive integers {rj satisfying <=1 Vll SUMMARY A SURREY ON THE PROBLEM OF NUN INTERACTION CUNTRUL The noninteraction control (or decoupling) problem is one of the oldest in the control literature. Originally, interest focused on the diagonal decoupling and the formulation was made in the transfer function setting (see for details Kucera (1991) and Morse and Wonham ( 197İİ). The state-space formulation was given much later bv Morgan (1964).' The diagonal decoupling problem, which is called as Morgan's problem, is finding a state feedback law such that each input influences only an output i.e., each output can be independently controlled by a corresponding input. When a system is diagonal decoupled, it reduces single-input single-output subsystems and its transfer matrix becomes diagonal. More general problem is block decoupling or block noninteraction. The block decoupling problem is to find a state feedback law and a partition on the inputs for a given partition on the outputs such that each portion of outputs can be independently controlled by a corresponding portion of inputs. Block decoupling splits the system into independent subsystems and results block diagonal transfer matrix. Considerable advantages may result of simplicity and reliability, especially when the system is large scale or controlled by sophisticated algorithms or a human operator. During the last 30 years, a great deal of interest has been brought to the theory of decoupling. The formulation of the noninteraction control problem, for block decoupling by dynamic state feedback case is below. VI Let a system which obeys the input-state-output equations *(t)= A M!)+ B u(t) y(t)= Cx(t)+ Du(t) x(t) e X~R», u(t) e U~Rm, y(t) e Y~W AeR***, BeRws, CeR***, I>eR**w and a set of positive integers {j\} satisfying *=1 be given. These integers define a partition of output vector into 1 subvectors. The problem of noninteraction, or the decoupling problem, is that of determining when there exists a dynamic feedback U(s) = F(s) X(s) + G V(s) F(s) e RBUfB(5) 9GeRw and a set of positive integers {rj satisfying <=1 Vll SUMMARY A SURREY ON THE PROBLEM OF NUN INTERACTION CUNTRUL The noninteraction control (or decoupling) problem is one of the oldest in the control literature. Originally, interest focused on the diagonal decoupling and the formulation was made in the transfer function setting (see for details Kucera (1991) and Morse and Wonham ( 197İİ). The state-space formulation was given much later bv Morgan (1964).' The diagonal decoupling problem, which is called as Morgan's problem, is finding a state feedback law such that each input influences only an output i.e., each output can be independently controlled by a corresponding input. When a system is diagonal decoupled, it reduces single-input single-output subsystems and its transfer matrix becomes diagonal. More general problem is block decoupling or block noninteraction. The block decoupling problem is to find a state feedback law and a partition on the inputs for a given partition on the outputs such that each portion of outputs can be independently controlled by a corresponding portion of inputs. Block decoupling splits the system into independent subsystems and results block diagonal transfer matrix. Considerable advantages may result of simplicity and reliability, especially when the system is large scale or controlled by sophisticated algorithms or a human operator. During the last 30 years, a great deal of interest has been brought to the theory of decoupling. The formulation of the noninteraction control problem, for block decoupling by dynamic state feedback case is below.
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1994
Konusu
Bilgisayar ve Kontrol, Computer Science and Control