Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova
Non-Lyapunov stability of singular systems: Classical and modern approaches with application to automatic drug delivery
Апстракт
U ovom radu izvedeni su dovoljni uslovi praktične stabilnosti i stabilnosti na konačnom vremenskom intervalu za klasu linearnih vremenski neprekidnih singularnih sistema sa čistim vremenskim kašnjenjem. Singularni sistemi i singularni sistemi sa čistim vremenskim kašnjenjem mogu biti matematički opisani jednačinama tipa: Ex(t) = Ax(t) i Ex(t) = A0x(t) - A1x(t - ), sledstveno. Analizirajući stabilnost na konačnom vremenskom intervalu izvedeni su novi uslovi, i to zavisni i nezavisni od vremenskog kašnjenja. Predloženi prilaz se zasniva na upotrebi Ljapunovljevih funkcija i njihovim osobinama na potprostoru konzistentinh početnih funkcija ili uslova. Ove funkcije ne moraju biti pozitivno određene u celom prostoru stanja, niti negativno određene duž trajektorija sistema. Kada se razmatra praktična stabilnost, ovaj prilaz se kombinuje sa klasičnom ljapunovskom tehnikom koja garantuje osobinu privlačenja sistema. U cilju dobijanja manje konzervativnih rezultata, korišćena je i LMI metoda.... Predloženi metod primenjen je i testiran na jednom medicinskom robotskom sistemu. Sistem je dizajniran za različite namene, kao što su automatska isporuka medikamenata, biopsija ili isporuka radioaktivnih zrnaca unutar obolelog tkiva. Za takav sistem razvijena je posebna tehnika modeliranja, upravljanja i analize stabilnosti opisanog sistema. U svrhu matematičkog modeliranja, sistem je dekomponovan na mehanički deo i na radnu okolinu koja presudno utiče na dinamičko ponašanje. Ovakav pristup se pokazao adekvatnim u slučaju kada spoljašnje sile utiču na dinamiku sistema. Dobijen matematički model se analizira kao singularni sistem automatskog upravljanja. U slučaju kada se uticaj spoljašnjih sila može zanemariti, dinamičko ponašanje se analizira klasičnim metodama teorije upravljanja.
In this paper sufficient conditions for both practical and finite time stability of linear singular continuous time delay systems were introduced. The singular and singular time delay systems can be mathematically described as Ex (t) = Ax (t) and Ex (t) = A0x (t) + A1x (t-), respectively. Analyzing finite time stability, the new delay independent and delay dependent conditions were derived using the approaches based on Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to be positive on the whole state space and to have negative derivatives along the system trajectories. When the practical stability was analyzed, the approach was combined with classical Lyapunov technique to guarantee the attractivity property of the system behavior. Furthermore, an LMI approach was applied to obtain less conservative stability conditions. The proposed methodology was applied and tested on a medical robotic system. The system was ...designed for different insertion tasks playing important roles in automatic drug delivery, biopsy or radioactive seeds delivery. In this paper we have summarized different techniques for adequate modeling, control and stability analysis of the medical robots. The model of the robotic system, with the tasks described above, the entire system can be decomposed to the robotic subsystem and the environment subsystem. Modeling of the system by the method mentioned has been proved to be suitable when the force appears as a result of the interaction of the two subsystems. The mathematical model of the system has a singular characteristic. The singular system theory could be applied to the case described. It is well known that all mechanical systems have some delay. In that case a theory of singular systems with delayed states may be applied, as well. For the second phase in which there is no interaction, the dynamic behavior can be analyzed by the classic theory.
Кључне речи:
sistemi sa kašnjenjem / singularni sistemi / medicinski robot / time delay systems / singular systems / robotics in medicine.Извор:
Contemporary materials, 2013, 4, 1, 22-32Финансирање / пројекти:
- Динамика хибридних система сложених структура. Механика материјала (RS-MESTD-Basic Research (BR or ON)-174001)
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Debeljković, Dragutin Lj. AU - Buzurović, Ivan AU - Matija, Lidija AU - Koruga, Đuro PY - 2013 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1611 AB - U ovom radu izvedeni su dovoljni uslovi praktične stabilnosti i stabilnosti na konačnom vremenskom intervalu za klasu linearnih vremenski neprekidnih singularnih sistema sa čistim vremenskim kašnjenjem. Singularni sistemi i singularni sistemi sa čistim vremenskim kašnjenjem mogu biti matematički opisani jednačinama tipa: Ex(t) = Ax(t) i Ex(t) = A0x(t) - A1x(t - ), sledstveno. Analizirajući stabilnost na konačnom vremenskom intervalu izvedeni su novi uslovi, i to zavisni i nezavisni od vremenskog kašnjenja. Predloženi prilaz se zasniva na upotrebi Ljapunovljevih funkcija i njihovim osobinama na potprostoru konzistentinh početnih funkcija ili uslova. Ove funkcije ne moraju biti pozitivno određene u celom prostoru stanja, niti negativno određene duž trajektorija sistema. Kada se razmatra praktična stabilnost, ovaj prilaz se kombinuje sa klasičnom ljapunovskom tehnikom koja garantuje osobinu privlačenja sistema. U cilju dobijanja manje konzervativnih rezultata, korišćena je i LMI metoda. Predloženi metod primenjen je i testiran na jednom medicinskom robotskom sistemu. Sistem je dizajniran za različite namene, kao što su automatska isporuka medikamenata, biopsija ili isporuka radioaktivnih zrnaca unutar obolelog tkiva. Za takav sistem razvijena je posebna tehnika modeliranja, upravljanja i analize stabilnosti opisanog sistema. U svrhu matematičkog modeliranja, sistem je dekomponovan na mehanički deo i na radnu okolinu koja presudno utiče na dinamičko ponašanje. Ovakav pristup se pokazao adekvatnim u slučaju kada spoljašnje sile utiču na dinamiku sistema. Dobijen matematički model se analizira kao singularni sistem automatskog upravljanja. U slučaju kada se uticaj spoljašnjih sila može zanemariti, dinamičko ponašanje se analizira klasičnim metodama teorije upravljanja. AB - In this paper sufficient conditions for both practical and finite time stability of linear singular continuous time delay systems were introduced. The singular and singular time delay systems can be mathematically described as Ex (t) = Ax (t) and Ex (t) = A0x (t) + A1x (t-), respectively. Analyzing finite time stability, the new delay independent and delay dependent conditions were derived using the approaches based on Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to be positive on the whole state space and to have negative derivatives along the system trajectories. When the practical stability was analyzed, the approach was combined with classical Lyapunov technique to guarantee the attractivity property of the system behavior. Furthermore, an LMI approach was applied to obtain less conservative stability conditions. The proposed methodology was applied and tested on a medical robotic system. The system was designed for different insertion tasks playing important roles in automatic drug delivery, biopsy or radioactive seeds delivery. In this paper we have summarized different techniques for adequate modeling, control and stability analysis of the medical robots. The model of the robotic system, with the tasks described above, the entire system can be decomposed to the robotic subsystem and the environment subsystem. Modeling of the system by the method mentioned has been proved to be suitable when the force appears as a result of the interaction of the two subsystems. The mathematical model of the system has a singular characteristic. The singular system theory could be applied to the case described. It is well known that all mechanical systems have some delay. In that case a theory of singular systems with delayed states may be applied, as well. For the second phase in which there is no interaction, the dynamic behavior can be analyzed by the classic theory. T2 - Contemporary materials T1 - Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova T1 - Non-Lyapunov stability of singular systems: Classical and modern approaches with application to automatic drug delivery EP - 32 IS - 1 SP - 22 VL - 4 DO - 10.7251/COMEN1301022D ER -
@article{ author = "Debeljković, Dragutin Lj. and Buzurović, Ivan and Matija, Lidija and Koruga, Đuro", year = "2013", abstract = "U ovom radu izvedeni su dovoljni uslovi praktične stabilnosti i stabilnosti na konačnom vremenskom intervalu za klasu linearnih vremenski neprekidnih singularnih sistema sa čistim vremenskim kašnjenjem. Singularni sistemi i singularni sistemi sa čistim vremenskim kašnjenjem mogu biti matematički opisani jednačinama tipa: Ex(t) = Ax(t) i Ex(t) = A0x(t) - A1x(t - ), sledstveno. Analizirajući stabilnost na konačnom vremenskom intervalu izvedeni su novi uslovi, i to zavisni i nezavisni od vremenskog kašnjenja. Predloženi prilaz se zasniva na upotrebi Ljapunovljevih funkcija i njihovim osobinama na potprostoru konzistentinh početnih funkcija ili uslova. Ove funkcije ne moraju biti pozitivno određene u celom prostoru stanja, niti negativno određene duž trajektorija sistema. Kada se razmatra praktična stabilnost, ovaj prilaz se kombinuje sa klasičnom ljapunovskom tehnikom koja garantuje osobinu privlačenja sistema. U cilju dobijanja manje konzervativnih rezultata, korišćena je i LMI metoda. Predloženi metod primenjen je i testiran na jednom medicinskom robotskom sistemu. Sistem je dizajniran za različite namene, kao što su automatska isporuka medikamenata, biopsija ili isporuka radioaktivnih zrnaca unutar obolelog tkiva. Za takav sistem razvijena je posebna tehnika modeliranja, upravljanja i analize stabilnosti opisanog sistema. U svrhu matematičkog modeliranja, sistem je dekomponovan na mehanički deo i na radnu okolinu koja presudno utiče na dinamičko ponašanje. Ovakav pristup se pokazao adekvatnim u slučaju kada spoljašnje sile utiču na dinamiku sistema. Dobijen matematički model se analizira kao singularni sistem automatskog upravljanja. U slučaju kada se uticaj spoljašnjih sila može zanemariti, dinamičko ponašanje se analizira klasičnim metodama teorije upravljanja., In this paper sufficient conditions for both practical and finite time stability of linear singular continuous time delay systems were introduced. The singular and singular time delay systems can be mathematically described as Ex (t) = Ax (t) and Ex (t) = A0x (t) + A1x (t-), respectively. Analyzing finite time stability, the new delay independent and delay dependent conditions were derived using the approaches based on Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to be positive on the whole state space and to have negative derivatives along the system trajectories. When the practical stability was analyzed, the approach was combined with classical Lyapunov technique to guarantee the attractivity property of the system behavior. Furthermore, an LMI approach was applied to obtain less conservative stability conditions. The proposed methodology was applied and tested on a medical robotic system. The system was designed for different insertion tasks playing important roles in automatic drug delivery, biopsy or radioactive seeds delivery. In this paper we have summarized different techniques for adequate modeling, control and stability analysis of the medical robots. The model of the robotic system, with the tasks described above, the entire system can be decomposed to the robotic subsystem and the environment subsystem. Modeling of the system by the method mentioned has been proved to be suitable when the force appears as a result of the interaction of the two subsystems. The mathematical model of the system has a singular characteristic. The singular system theory could be applied to the case described. It is well known that all mechanical systems have some delay. In that case a theory of singular systems with delayed states may be applied, as well. For the second phase in which there is no interaction, the dynamic behavior can be analyzed by the classic theory.", journal = "Contemporary materials", title = "Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova, Non-Lyapunov stability of singular systems: Classical and modern approaches with application to automatic drug delivery", pages = "32-22", number = "1", volume = "4", doi = "10.7251/COMEN1301022D" }
Debeljković, D. Lj., Buzurović, I., Matija, L.,& Koruga, Đ.. (2013). Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova. in Contemporary materials, 4(1), 22-32. https://doi.org/10.7251/COMEN1301022D
Debeljković DL, Buzurović I, Matija L, Koruga Đ. Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova. in Contemporary materials. 2013;4(1):22-32. doi:10.7251/COMEN1301022D .
Debeljković, Dragutin Lj., Buzurović, Ivan, Matija, Lidija, Koruga, Đuro, "Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova" in Contemporary materials, 4, no. 1 (2013):22-32, https://doi.org/10.7251/COMEN1301022D . .