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Robust/Optimal Control of Minimum-Phase Nolinear Systems

Thesis Info

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Author

Zaffar, Salman

Program

PhD

Institute

National University of Sciences & Technology

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Electrical Engineering

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12026/1/SALMAN%20ZAFFAR%20electrical%20engg%202018%20NUST%20isb%20prr.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727828126

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This thesis proposes a framework that provides suboptimal control laws for a class of minimum-phase nonlinear systems. This class includes systems whose state dynamics are an algebraic sum of their linear and nonlinear sub-dynamics. We propose a systematic method of designing a robust and optimal control law which essentially consists of two components a linear and a nonlinear. It is shown that the proposed control scheme achieves stabilization while providing suboptimality for the class of systems under consideration. Furthermore, the framework provides for a mechanism which is suitable for handling tracking and regulation problems for the class of minimum-phase nonlinear systems by using the Internal Model Principle. Astrikingfeatureoftheproposedframeworkistheflexibilityofstartingwithsynthesizing a Linear-Quadratic-Regulator for linear sub-dynamics of the system and then including a nonlinear control component that stabilizes the nonlinear sub-dynamics of the system. The flexibility offered by the proposed framework is applied firstly to a general class of linear parameter-varying and linear time-varying systems. We extend the flexibility obtained for these two systems to the class of minimum-phase nonlinear systems which are decomposable through existence of an appropriate transformation into their linear and nonlinear sub dynamics. Moreover, we also propose a simplified approach to obtain an approximate yet practical solution to the nonlinear optimal control problem by replacing the requirement of solving Hamilton-Jacobi-Bellman equations with that of the Riccati partial differential equations,andthensynthesizingthenonlinearcomponentofthecontrollawtoachieverobust and suboptimal stabilization
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حقیقت کا اقرار

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استفہام کا ایک بلیغ موقع استعمال وہ بھی ہے جب مخاطب سے کسی ایسی بات کا اقرار کرانا ہو جس کی نوعیت ہو تو ایک بدیہی حقیقت کی لیکن مخاطب اس کو تسلیم کرنے کے باوجود عملاً اس سے منحرف ہو۔ جیسے آیت ذیل :
" هَلْ أَتَى عَلَى الْإِنْسَانِ حِينٌ مِنَ الدَّهْرِ لَمْ يَكُنْ شَيْئًا مَذْكُورًا" “[ ]
"انسان پر کبھی ایسا وقت آیاہے کہ نہیں جب وہ کوئی قابل چیز نہیں تھا" کی تفسیر میں مولانا امین اصلاحی کانقطہ نظر ہے یہ محض ایک سادہ خبریہ جملہ نہیں ہے بلکہ اس کے اندر بہت سے معانی مضمر ہیں۔ مثلاً:
۱۔ ایک عظیم حق کی یاددہانی ہے جو اس پر عائد ہوتا ہے اور جس سے اس کے لیے انکار کی گنجائش نہیں ہے لیکن اس کا رویہ اس کے منافی ہے۔
۲۔اس میں ملامت ‘ غصہ ‘ رنج اور اظہار حسرت کے بھی گوناگوں پہلو ہیں۔
۳۔اس میں نہایت مبنی برحقیقت گلہ و شکوہ بھی ہے اور نہایت موثر اپیل بھی۔
۴۔ استفہامیہ اسلوب نے اس حسن فکر کو بیدار کرنا چاہا ہے کہ انسان کی نظروں سے خدا اوجھل ہے تو اس کا اپنا وجود تو اوجھل نہیں ہے ‘ وہ خود اپنے اندر خدا کی قدرت و حکمت اور اس کے عدل و رحمت کی نشانیاں دیکھ سکتا ہے۔[ ]
" قُلْ لِمَنْ مَا فِي السَّمَاوَاتِ وَالْأَرْضِ قُلْ لِلَّهِ" “[ ]
"ان سے پوچھوکہ آسمانوں اور زمین میں جو کچھ ہے وہ کس کی ملکیت ہے(پھر اگر وہ جواب نہ دیں توخود ہی )کہہ دو کہ اللہ ہی کی ملکیت ہے"۔
مولانا امین احسن اصلاحی کی تحقیق کےمطابق قرآن مجید میں جہاں جہاں سوال کر کے مخاطب کے جواب کا انتظار کیے بغیر خود اس کا جواب دیا ہے۔ غور کرنے سے معلوم ہوتا ہے کہ...

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