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Register a new userControllability and Observerability of Linear Continuous-Time Systems
قابلية التحكم و قابلية الرصد في الأنظمة الخطية المستمرة زمنيا
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Authors
محمود عثمان( باحث )
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تم في هذا البحث عرض دراسة مسألة قابلية التحكم و كذلك قابلية الرصد للأنظمة الخطية المستمرة الثابتة مع الزمن. و تم التوصل إلى إيجاد معايير لقابلية التحكم و قابلية الرصد. و كذلك تم استنتاج متجهة التحكم التي تنقل النظام من الحالة الابتدائية x(0) إلى الحالة النهائية x(tf) في زمن محدد tf>0 موضحا ذلك بمثال. و كذلك تم وضع خوارزمية جديدة لإيجاد متجهة التحكم و التي تمكننا من نقل النظام من الحالة الابتدائية إلى الحالة النهائية. كما تموضع برنامج لرسم مسار متجهة الحالة و متجهة الرصد.
In this research, we investigate a problem of controllable and observerable for linear Continuous-time systems. We have founded controllable and observerable conditions for the linear continuous-time system. Moreover, we put out a new algorithm for finding control vector of steps that can enable us to move the state vector from the initial stage x(0) into the final onex(tf) for finite time tf>0, the theoretical results is illustrated by an example. Finally,we put program to plot trajectory of state vector x(t) and observer vector y(t)
References used
GAJIC, Z. and LELIC, M., Modern Control Systems Engineering. Prentice Hall International, London, (1996), 241–247
HOU, M. and MÜLLER P. C., Design of Observers for Linear Systems With Unknown Inputs. IEEE Trans. Automat. Contr., Vol. AC-37, (1992), 871-875
DAVIS J. M., I. A. GRAVAGNE, B. J. JACKSON, R. J. MARKS II., Controllability, Observability, Realizability, And Stability of Dynamic Linear Systems,Electronic Journal of Differential Equations, Vol. 2009(2009), No. 37, pp. 1–32
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إن اختبار قابلية قسمة عدد صحيح موجب N أكبر من الواحد، على عدد صحيح موجب Q أكبر من الواحد، يتحدد تبعًا للعدد Q. فلكل عدد Q رائزه الخاص ( ١ ).
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