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] | เปรม ติณสูลานนท์
พลเอกเปรม รับตำแหน่งรัฐมนตรีเป็นครั้งแรกในรัฐบาลพลเอกเกรียงศักดิ์ ชมะนันทน์ ในตำแหน่งรัฐมนตรีช่วยว่าการกระทรวงมหาดไทย และดำรงตำแหน่งรัฐมนตรีอย่างต่อเนื่องในรัฐบาลนั้น ในช่วงปลายรัฐบาลพลเอกเกรียงศักดิ์ ดำรงตำแหน่งรัฐมนตรีว่าการกระทรวงกลาโหม ควบคู่กับตำแหน่งผู้บัญชาการทหารบก |
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] | เปรม ติณสูลานนท์
ในช่วงนั้น พลเอกเปรมได้รับการยอมรับจากหลายฝ่าย หลังจากพลเอกเกรียงศักดิ์ ชมะนันทน์ ลาออกจากตำแหน่งนายกรัฐมนตรีเมื่อวันที่ 23 กุมภาพันธ์ พ.ศ. 2523 สภาผู้แทนราษฎรทำการหยั่งเสียงเพื่อหาตัวผู้ดำรงตำแหน่งนายกรัฐมนตรี และเลือกพลเอกเปรมเป็นนายกรัฐมนตรี โดยพระบาทสมเด็จพระปรมินทรมหาภูมิพลอดุลยเดชมีพระบรมราชโองการโปรดเกล้าฯ ให้พลเอกเปรมดำรงตำแหน่งนายกรัฐมนตรี เมื่อวันที่ 3 มีนาคม พ.ศ. 2523 เป็นนายกรัฐมนตรีคนที่ 16 ของไทย |
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พลเอก เปรม ติณสูลานนท์ เข้ารับตำแหน่งนายกรัฐมนตรีสืบต่อจากพลเอกเกรียงศักดิ์ ชมะนันทน์ เมื่อวันที่ 3 มีนาคม พ.ศ. 2523 ซึ่งตลอดระยะเวลาของพลเอกเปรมในการบริหารประเทศได้มีผลงานสำคัญมากมาย เช่น การปรับปรุงประมวลกฎหมายรัษฎากรและกฎหมายสรรพสินค้า เพื่อให้เกิดความเป็นธรรมแก่สังคม การสร้างงานตามโครงการสร้างงานในชนบท (กสช.) การจัดตั้งคณะกรรมการร่วมภาครัฐบาล และเอกชน (กรอ.) เพื่อส่งเสริมบทบาททางการค้าและการลงทุนของภาคเอกชนภายในประเทศ การดำเนินการปราบปรามผู้ก่อการร้ายคอมมิวนิสต์ในประเทศไทยอย่างได้ผล โดยนำนโยบายการใช้ "การเมืองนำการทหาร" ตามคำสั่งสำนักนายกรัฐมนตรีที่ 66/2523 เป็นผลให้พรรคคอมมิวนิสต์แห่งประเทศไทยอ่อนกำลังลงและสลายตัวไปในที่สุด |
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] | เปรม ติณสูลานนท์
คณะรัฐมนตรี คณะที่ 42: 3 มีนาคม พ.ศ. 2523 - 29 เมษายน พ.ศ. 2526 สิ้นสุดลงภายหลังการยุบสภา ในวันที่ 19 มีนาคม พ.ศ. 2526 เนื่องจากสภาผู้แทนราษฎรไม่เห็นชอบกับการเสนอให้ยืดอายุการใช้บทเฉพาะกาลของ รัฐธรรมนูญแห่งราชอาณาจักรไทย พุทธศักราช 2521 มีการเลือกตั้งในวันที่ 18 เมษายน พ.ศ. 2526 |
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] | เปรม ติณสูลานนท์
คณะรัฐมนตรี คณะที่ 43: 30 เมษายน พ.ศ. 2526 - 4 สิงหาคม พ.ศ. 2529 สิ้นสุดลงภายหลังการยุบสภา ในวันที่ 1 พฤษภาคม พ.ศ. 2529 เนื่องจากรัฐบาลแพ้เสียงในสภา ในการออกพระราชกำหนดการขนส่งทางบก มีการเลือกตั้งในวันที่ 27 กรกฎาคม พ.ศ. 2529 |
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คณะรัฐมนตรี คณะที่ 44: 5 สิงหาคม พ.ศ. 2529 - 3 สิงหาคม พ.ศ. 2531 สิ้นสุดลงภายหลังการยุบสภา ในวันที่ 29 เมษายน พ.ศ. 2531 เนื่องจากเกิดปัญหาขึ้นในพรรคประชาธิปัตย์ เกิดกลุ่ม 10 มกรา ดำเนินกิจกรรมทางการเมืองอย่างเป็นเอกเทศภายในพรรค กลุ่ม 10 มกรา นี้ลงมติไม่สนับสนุนพระราชบัญญัติลิขสิทธิ์ ที่รัฐบาลเสนอเข้าสู่การพิจารณาของสภา จนทำให้พระราชบัญญัติไม่ผ่านการเห็นชอบ พรรคประชาธิปัตย์แสดงความรับผิดชอบโดยการถอนตัวจากการเป็นพรรคร่วมรัฐบาล พลเอกเปรมจึงประกาศยุบสภา มีการเลือกตั้งในวันที่ 24 กรกฎาคม พ.ศ. 2531 |
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] | เปรม ติณสูลานนท์
ในช่วงปลายรัฐบาลพลเอกเปรม ขณะที่กำลังจะมีการเลือกตั้ง มีกระแสการคัดค้านการดำรงตำแหน่งนายกรัฐมนตรีเป็นสมัยที่ 4 จากกลุ่มนักวิชาการ |
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] | เปรม ติณสูลานนท์
ภายหลังการเลือกตั้ง ในคืนวันที่ 24 กรกฎาคม พ.ศ. 2531 หัวหน้าพรรคการเมืองที่จะร่วมกันจัดตั้งรัฐบาล โดยมีพรรคชาติไทยเป็นแกนนำ ได้เข้าพบพลเอกเปรมที่บ้านพัก เพื่อเชิญให้มาดำรงตำแหน่งนายกรัฐมนตรีเป็นสมัยที่ 4 แต่พลเอกเปรมปฏิเสธ ต่อมาในวันที่ 4 สิงหาคม พ.ศ. 2531 จึงได้มีพระบรมราชโองการ โปรดเกล้าฯ พลตรีชาติชาย ชุณหะวัณ (ยศขณะนั้น) ดำรงตำแหน่งนายกรัฐมนตรีคนที่ 17 |
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หลังพ้นจากตำแหน่งนายกรัฐมนตรี พระบาทสมเด็จพระปรมินทรมหาภูมิพลอดุลยเดช มีพระบรมราชโองการโปรดเกล้าฯ ให้พลเอกเปรม เป็นองคมนตรี ในวันที่ 23 สิงหาคม พ.ศ. 2531 จากนั้นในวันที่ 29 สิงหาคม พ.ศ. 2531 ได้รับโปรดเกล้าฯ ยกย่องให้เป็นรัฐบุรุษ และในวันที่ 4 สิงหาคม พ.ศ. 2541 มีพระบรมราชโองการ โปรดเกล้าฯ ให้เป็นประธานองคมนตรี |
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] | เปรม ติณสูลานนท์
1.การปรับปรุงประมวลกฎหมายรัษฎากรและกฎหมายสรรพสินค้า เพื่อให้เกิดความเป็นธรรมแก่สังคม |
1849#21 | [
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] | เปรม ติณสูลานนท์
2.การสร้างงานตามโครงการสร้างงานในชนบท (กสช.) โดยสานต่อจากนโยบายเงินผันที่ดำเนินการมาตั้งแต่สมัยรัฐบาลของหม่อมราชวงศ์คึกฤทธิ์ ปราโมช |
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] | เปรม ติณสูลานนท์
3.การจัดตั้งคณะกรรมการร่วมภาครัฐบาลและเอกชน (กรอ.) เพื่อส่งเสริมบทบาททางการค้าและการลงทุนของภาคเอกชนภายในประเทศ |
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] | เปรม ติณสูลานนท์
4.การแก้ปัญหาการตกต่ำทางเศรษฐกิจในช่วงแรกที่เข้าบริหารประเทศ รัฐบาลได้ดำเนินนโยบายประหยัดมุ่งเน้นในด้านการผลิตและการส่งออกของสินค้ากับประเทศสังคมนิยมตะวันออกอย่างได้ผล ทำให้รัฐบาลชุดนี้สามารถสร้างเสริมกำลังทางด้าน เงินทุนสำรองเงินตราต่างประเทศได้อย่างน่าภูมิใจ จึงนับว่ารัฐบาลสมัยพลเอกเปรม ติณสูลานนท์เป็นผู้สร้างฐานเศรษฐกิจของชาติที่สำคัญ ทำให้ประเทศไทยมีเงินทุนสำรองที่เป็นเงินตราต่างชาติมากขึ้น รัฐบาลได้สนับสนุนการส่งออก |
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] | เปรม ติณสูลานนท์
5.การเข้าร่วมประชุมองค์การสหประชาชาติที่สหรัฐอเมริกา ทั้งพลเอกเปรม ติณสูลานนท์ ยังได้เป็นผู้กล่าวปราศรัยสุนทรพจน์ในที่ประชุมด้วย ทำให้ภาพลักษณ์ของประเทศไทยดีขึ้นต่อสายตาต่างชาติ มุมมองทางด้านการลงทุนจากนักลงทุนทั้งหลายต่อท่าทีของภาวะทั่วไปของเศรษฐกิจไทยในด้านการผลิตและการอุตสาหกรรมนั้นแจ่มใสและชัดเจนมากขึ้น |
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] | เปรม ติณสูลานนท์
ผลงานสำคัญชิ้นหนึ่ง ของพลเอกเปรม คือการผลักดันนโยบาย “การเมืองนำการทหาร” ซึ่งปรากฏออกมาในรูป คำสั่งสำนักนายกรัฐมนตรีที่ 66/2523 65/2525 เพื่อยุติการทำสงครามสู้รบ ระหว่างพรรคคอมมิวนิสต์แห่งประเทศไทย กับ ฝ่ายรัฐบาล ผลพวงจากนโยบายดังกล่าว ทำให้นักศึกษา ที่หนีเข้าป่าภายหลังเหตุการณ์ 6 ตค. พ.ศ. 2519 เพื่อจับอาวุธต่อสู้กับรัฐบาล มีโอกาสหวนมาเดินบนหนทางแห่งสันติภาพได้ นโยบายดังกล่าว ช่วยลด กระทั่งดับเชื้อไฟสงครามกลางเมืองในช่วงนั้นลง เพื่อให้รัฐบาลสามารถทุ่มเทกำลัง มาฟื้นฟูเศรษฐกิจของประเทศต่อไป |
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] | เปรม ติณสูลานนท์
ในช่วงปี พ.ศ. 2524 การส่งออกของไทย โดยเฉพาะพืชผลเกษตรประสบปัญหา ขณะเดียวกัน มีปัญหาการขาดดุลการค้า การขาดดุลบัญชีเดินสะพัด และขาดดุลงบประมาณอย่างต่อเนื่อง เงินบาทของไทย ผูกติดกับดอลลาร์ของสหรัฐฯ ซึ่งแข็งตัวอย่างรวดเร็ว ส่งผลให้การส่งออกของไทยได้รับผลกระทบ
พลเอกเปรม ได้ตัดสินร่วมกับทีม รมต.เศรษฐกิจ ที่จะลดค่าเงินบาทถึงสามครั้ง โดยเฉพาะครั้งที่สาม ในวันที่ 2 พ.ย. พ.ศ. 2523 ซึ่งมีการปรับลดถึงร้อยละ 15 |
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นอกจากนั้น รัฐบาลพลเอกเปรมยังได้ปรับระบบอัตราแลกเปลี่ยนจาก “อัตราแลกเปลี่ยนคงที่ “ระหว่างเงินบาทกับเงินดอลลาร์สหรัฐ มาเป็น “ระบบตะกร้าเงิน” ซึ่งทำให้มีความยืดหยุ่นมากขึ้น |
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โครงการสำคัญ เช่น การพัฒนาชายฝั่งทะเลตะวันออก การสร้างท่าเรือน้ำลึกมาบตาพุด และ แหลมฉบัง ล้วนตัดสินดำเนินโครงการ ในช่วงรัฐบาลพลเอกเปรมทั้งสิ้น |
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หลังรัฐประหาร พ.ศ. 2549 มีนักวิชาการกล่าวหาพลเอกเปรมว่ามีความเกี่ยวข้องกับวิกฤตการณ์การเมืองในประเทศไทย พ.ศ. 2548-2549 ที่นำไปสู่รัฐประหาร ซึ่งในเวลาพลบค่ำวันที่ 19 กันยายน ช่วงเดียวกับที่กำลังทหารหน่วยรบพิเศษจากจังหวัดลพบุรีเคลื่อนกำลังเข้ากรุงเทพมหานคร พลเอกเปรมเข้าเฝ้าฯ พระบาทสมเด็จพระเจ้าอยู่หัว สุริยะใส กตะศิลา ผู้ประสานงานเครือข่ายพันธมิตรประชาชนเพื่อประชาธิปไตย กล่าวว่า พลเอกเปรมเป็นผู้สั่งการรัฐประหารโดยนั่งบัญชาการอยู่ที่บ้านสี่เสาร์เทเวศร์ มีบทวิเคราะห์จากสำนักข่าว XFN-ASIA ระบุในเว็บไซต์นิตยสารฟอร์บ ว่า พลเอกเปรมเป็นบุคคลที่มีบทบาทสำคัญในการเมืองไทย พร้อมทั้งสนับสนุนให้คณะปฏิรูปการปกครองในระบอบประชาธิปไตย อันมีพระมหากษัตริย์ทรงเป็นประมุข (คปค.) รัฐประหารรัฐบาลพันตำรวจโท ทักษิณ ชินวัตร ฝ่ายรัฐบาลทหารว่า พลเอกเปรมไม่เคยมีบทบาททางการเมือง |
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] | เปรม ติณสูลานนท์
ในเวลาต่อมา มีการอ้างว่า พลเอกเปรมอาจมีบทบาทสำคัญในการเชิญพลเอก สุรยุทธ์ จุลานนท์ อดีตผู้บัญชาการทหารบก และอดีตลูกน้อง มาดำรงตำแหน่งนายกรัฐมนตรี รวมทั้งการแต่งตั้งคณะรัฐมนตรี และสภานิติบัญญัติแห่งชาติด้วย จนนักวิจารณ์บางคน กล่าวว่า สภาฯ ชุดนี้เต็มไปด้วย "ลูกป๋า" |
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] | เปรม ติณสูลานนท์
วันที่ 22 กรกฎาคม 2550 นปก. นับพันรวมตัวประท้วงหน้าบ้านของพลเอกเปรมเพื่อเรียกร้องให้ลาออกจากตำแหน่งประธานองคมนตรี เพราะเชื่อว่ามีบทบาททางการเมือง เจ้าหน้าที่ตำรวจได้เข้าสลายการชุมนุม มีการยิงแก๊สพริกไทยแล้วล้อมรถบรรทุก 6 ล้อติดเครื่องขยายเสียงของแกนนำ ผู้ชุมนุมขว้างปาขวดพลาสติกและขวดแก้วใส่เจ้าหน้าที่ตำรวจ เกิดการปะทะกันชุลมุนวุ่นวาย เจ้าหน้าที่และผู้ชุมนุมได้รับบาดเจ็บหลายคน ด้านแยกสี่เสาเทเวศร์ กลุ่ม นปก.ส่วนหนึ่งทุบทำลายซุ้มตำรวจจราจรและทุบรถส่องไฟและกระจายเสียงของตำรวจที่จอดไว้ รวมทั้งปล่อยลมยางรถยนต์ ในวันต่อมา พลเอกสนธิ พลเอกสุรยุทธ์ และคณะรัฐมนตรีไปเยี่ยมพลเอกเปรมเพื่อขอโทษที่ยอมให้มีการประท้วง |
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] | เปรม ติณสูลานนท์
บางกอกพันดิท (Bangkok Pundit) เขียนในเอเชียคอร์เรสปอนเดนท์ว่า พลเอกเปรมเป็นผู้เล่นสำคัญในการเมืองไทยในหลายทศวรรษหลัง เจมส์ อ็อกคีย์ (James Ockey) ว่า "ก่อนรัฐบาลไทยรักไทยกำเนิดในปี พ.ศ. 2544 ผู้บัญชาการทหารสูงสุดและผู้บัญชาการทหารบกแทบทุกคนในทศวรรษที่ผ่านมาเป็นอดีตผู้ช่วยของเปรม" แต่ "แน่นอนว่ายิ่งเปรมเกษียณนานเท่าไร อิทธิพลของเขาในกองทัพก็ยิ่งอ่อนลงเท่านั้น" เขามีอำนาจและอิทธิพลสูงสุดเมื่อรัฐประหารปี พ.ศ. 2549 และยังเป็นสะพานเชื่อมระหว่างกองทัพและพระราชวัง ทว่า นับแต่ปี พ.ศ. 2549 อำนาจของเขาและความสามารถมีอิทธิพลจางลงเมื่อพลเอก ประยุทธ์ จันทร์โอชาและบูรพาพยัคฆ์มีเส้นสายของตัวและสามารถเลี่ยงพลเอกเปรมได้แล้ว Marwaan Macan-Markar เขียนว่า "ต่างกับสนธิ ประยุทธ์ยังไม่เป็นหนี้บุญคุณเครือข่ายอิทธิพลซึ่งเป็นผู้รักษาประตูสู่พระมหากษัตริย์แต่เดิม อันเป็นที่สถิตของอำนาจสูงสุดในราชอาณาจักร" และ "บูรพาพยัคฆ์คืนชีพโดยทำลายสายการบังคับบัญชาเดิมซึ่งเป็นหนี้บุญคุณต่อพลเอกเปรม เขามีสามัคคีจิตของเขาเอง" |
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พลเอกเปรม ชื่นชอบดูการแข่งขันกีฬา โดยเฉพาะกีฬามวยและฟุตบอล มักเปิดโอกาสให้นักกีฬาเข้าพบเพื่อคารวะ และให้กำลังใจ ก่อนจะเดินทางไปแข่งขันในต่างประเทศอยู่เสมอ นอกจากนี้ยังชื่นชอบการร้องเพลง ระยะหลังได้ฝึกหัดเล่นเปียโนกับ ณัฐ ยนตรรักษ์ และประพันธ์เพลงเป็นงานอดิเรก พลเอกเปรมมีผลงานเพลงบันทึกเสียงจำหน่าย บรรเลงดนตรีโดย กองดุริยางค์ทหารบก |
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] | เปรม ติณสูลานนท์
พลเอก พลเรือเอก พลอากาศเอก เปรม ติณสูลานนท์ ได้รับพระราชทานยศ "นายกองใหญ่แห่งกองอาสารักษาดินแดน" เป็น พลเอก พลเรือเอก พลอากาศเอก นายกองใหญ่ เปรม ติณสูลานนท์ เมื่อ พ.ศ. 2528 |
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] | เปรม ติณสูลานนท์
พลเอกเปรม ติณสูลานนท์ ได้รับพระราชทานเครื่องราชอิสริยาภรณ์สูงสุดต่าง ๆ ดังนี้ |
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อุนสุยอัน นักเขียนนิยายจีนกำลังภายใน, นามแฝง อุนเลี้ยงเง็ก |
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] | ทฤษฎีระบบควบคุม
ทฤษฎีระบบควบคุม () เป็นสาขาหนึ่งของคณิตศาสตร์และวิศวกรรมศาสตร์ ในที่นี้ การควบคุมหมายถึง การควบคุมระบบพลศาสตร์ ให้มีค่าเอาต์พุตที่ต้องการ โดยการป้อนค่าอินพุตที่เหมาะสมให้กับระบบ ตัวอย่างที่เห็นได้ทั่วไป เช่น ระบบควบคุมอุณหภูมิห้องของเครื่องปรับอากาศ หรือ แม้แต่ลูกลอยในโถส้วม ที่เปิดน้ำปิดน้ำโดยอัตโนมัติเมื่อน้ำหมดและน้ำเต็ม |
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] | ทฤษฎีระบบควบคุม
การควบคุมการขับเคลื่อนยานพาหนะ เช่น รถยนต์ ก็ถือเป็นการควบคุมชนิดหนึ่ง โดยผู้ขับขี่เป็นผู้ควบคุมทิศทางและความเร็ว ซึ่งระบบควบคุมประเภทที่ต้องมีคนเข้ามาเกี่ยวข้องนี้ถือว่าเป็น ระบบควบคุมไม่อัตโนมัติ (manual control) แต่ทฤษฎีระบบควบคุมจะครอบคลุมเฉพาะการวิเคราะห์และออกแบบ ระบบควบคุมอัตโนมัติ (automatic control) เท่านั้น เช่น ระบบขับเคลื่อนอัตโนมัติ (cruise control) |
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] | ทฤษฎีระบบควบคุม
ระบบควบคุมยังอาจแบ่งออกได้เป็นระบบควบคุมวงเปิด (open-loop control) คือ ระบบควบคุมที่ไม่ได้ใช้สัญญาณจากเอาต์พุต มาบ่งชี้ถึงลักษณะการควบคุม ส่วนระบบควบคุมวงปิด (closed-loop control) หรือ ระบบป้อนกลับ (feedback control) นั้นจะใช้ค่าที่วัดจากเอาต์พุต มาคำนวณค่าการควบคุม นอกจากนี้ยังอาจแบ่งได้ตามคุณลักษณะของระบบ เช่น เป็นเชิงเส้น (linear) / ไม่เป็นเชิงเส้น (nonlinear) , แปรเปลี่ยนตามเวลา (time-varying) / ไม่เปลี่ยนแปลงตามเวลา (time-invariant) และเวลาต่อเนื่อง (Continuous time) / เวลาไม่ต่อเนื่อง (Discontinuous time) |
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การใช้ระบบควบคุมวงปิด นั้นมีมาแต่โบราณกาล ตัวอย่างเช่น นาฬิกาน้ำของกรีก ซึ่งมีการใช้ลูกลอยในการควบคุมระดับน้ำในถัง อุปกรณ์ที่ถือว่าเป็นจุดเริ่มต้น ของการใช้ระบบควบคุมป้อนกลับในวงการอุตสาหกรรม ก็คือ ลูกเหวี่ยงหนีศูนย์กลาง ( หรือเรียก fly-ball governor) ในการควบคุมความเร็วในการหมุน เครื่องจักรไอน้ำที่ประดิษฐ์ขึ้นโดย เจมส์ วัตต์ ในปี ค.ศ. 1788 |
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] | ทฤษฎีระบบควบคุม
ในยุคก่อนหน้านี้ การออกแบบระบบควบคุมต่าง ๆ นั้น เป็นไปในลักษณะลองผิดลองถูก ไม่ได้มีการใช้คณิตศาสตร์ในการวิเคราะห์ ออกแบบแต่อย่างใด จนกระทั่งในปี ค.ศ. 1840 นักดาราศาสตร์ชาวอังกฤษ จอร์จ แอรี ได้ประดิษฐ์อุปกรณ์ควบคุมทิศทางของกล้องดูดาว โดยอุปกรณ์นี้จะหมุนกล้องดูดาว เพื่อชดเชยกับการหมุนของโลกโดยอัตโนมัติ ในระหว่างการออกแบบ แอรีได้สังเกตถึงความไม่เสถียร (instability) ของระบบป้อนกลับ จึงใช้สมการเชิงอนุพันธ์ในการจำลองและวิเคราะห์พฤติกรรมของระบบ การวิเคราะห์เสถียรภาพของระบบนี้เป็นหัวใจสำคัญของทฤษฎีระบบควบคุม |
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] | ทฤษฎีระบบควบคุม
ในปี ค.ศ. 1868 เจมส์ เคลิร์ก แมกซ์เวลล์ เป็นบุคคลแรก ที่ทำการศึกษาถึงเสถียรภาพของ ลูกเหวี่ยงหนีศูนย์กลางของ เจมส์ วัตต์ โดยใช้แบบจำลองสมการเชิงอนุพันธ์เชิงเส้น ทฤษฎีเสถียรภาพของระบบเชิงเส้นของแมกซ์เวลล์นี้ พิจารณาเสถียรภาพของระบบจาก รากของสมการคุณลักษณะ () ของระบบ ต่อมาในปี ค.ศ. 1892 เลียปูนอฟได้ทำการศึกษาถึงเสถียรภาพของระบบไม่เป็นเขิงเส้น และสร้างทฤษฎีเสถียรภาพของเลียปูนอฟ () แต่ทฤษฎีของเลียปูนอฟนี้เป็นทฤษฎีที่สำคัญที่ไม่ได้รับความสนใจ จนกระทั่งหลายสิบปีต่อมา |
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พัฒนาการของทฤษฎีระบบควบคุมในช่วงนี้นั้น ส่วนใหญ่พัฒนาขึ้นเพื่อประยุกต์ใช้งานในทางทหารและทางระบบสื่อสาร อันเนื่องมาจากสงครามโลกครั้งที่สอง และ การขยายตัวของโครงข่ายสื่อสารโทรศัพท์ |
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] | ทฤษฎีระบบควบคุม
ในช่วงยุคที่มีการขยายตัวของระบบสื่อสารโทรศัพท์นั้น ระบบสื่อสารทางไกลมีความจำเป็นต้องใช้อุปกรณ์ขยายสัญญาณด้วยหลอดสุญญากาศ ในปี ค.ศ. 1927 แนวความคิดและประโยชน์ของระบบป้อนกลับแบบลบ ได้ถูกนำเสนอในรูปของ อุปกรณ์ขยายสัญญาณป้อนกลับแบบลบ (negative feedback amplifier) โดย เอช. เอส. แบล็ก แต่การวิเคราะห์เสถียรภาพของระบบขยายสัญญาณตามทฤษฎีของแมกซ์เวลล์ โดยใช้วิธีของ เราท์-ฮิวรวิทซ์ (Routh-Hurwitz) นั้นเป็นไปได้ยาก เนื่องจากความซับซ้อนของระบบ วิศวกรสื่อสารของ Bell Telephone Laboratories จึงได้นำเสนอการวิเคราะห์บนโดเมนความถี่ โดยในปี ค.ศ. 1932 แฮร์รี่ ไนควิสต์นำเสนอ เกณฑ์เสถียรภาพของไนควิสต์ () ซึ่งใช้วิธีการพล็อตกราฟเชิงขั้ว ของผลตอบสนองความถี่ตลอดวงรอบ (loop frequency response) ของระบบ ต่อมาในปี ค.ศ. 1940 เฮนดริค โบดีได้นำเสนอวิธีการวิเคราะห์เสถียรภาพโดยขอบเขตอัตราขยาย (gain margin) และขอบเขตมุม (phase margin) จากกราฟระหว่างขนาดและมุม () ของผลตอบสนองความถี่ เรียกว่า โบดีพล็อต () |
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] | ทฤษฎีระบบควบคุม
ปัญหาหลายปํญหาในทางหทาร เช่น ปัญหาการนำร่องการเดินเรืออัตโนมัติ ปัญหาการเล็งเป้าโดยอัตโนมัติ นั้นเป็นแรงผลักดันสำคัญให้เกิดการพัฒนาการทางทฤษฎีระบบควบคุมที่สำคัญหลายอย่าง ในปี ค.ศ. 1922 มินอร์สกี () ได้กำหนดและวิเคราะห์กฎของ ระบบควบคุมพีไอดี หรือ สัดส่วน-ปริพันธ์-อนุพันธ์ (proportional-integral-derivative) ซึ่งยังเป็นที่นิยมใช้อย่างกว้างขวางในปัจจุบัน เพื่อใช้ในการนำร่องการเดินเรือ ปัญหาที่สำคัญในช่วงนั้นคือ การเล็งเป้าของปืนจากเรือหรือเครื่องบิน ซึ่งในปี ค.ศ. 1934 ฮาเซน (H.L. Házen) ได้บัญญัติคำสำหรับประเภทปัญหาการควบคุมกลไกนี้ว่า กลไกเซอร์โว () การวิเคราะห์และออกแบบนั้นก็ใช้วิธีการบนโดเมนความถี่ จนกระทั่งในปีค.ศ. 1948 อีแวนส์ (W. R. Evans) ซึ่งทำงานกับปัญหาทางด้านการนำร่องและควบคุมเส้นทางบิน ซึ่งส่วนใหญ่นั้นเป็นระบบที่ไม่เสถียร ได้ประสบกับปํญหาการวิเคราะห์เสถียรภาพบนโดเมนของความถี่ จึงได้หันกลับไปศึกษาถึงรากของสมการคุณลักษณะ ซึ่งเป็นวิธีการวิเคราะห์บนโดเมนการแปลงลาปลาส และได้พัฒนาวิธี ทางเดินราก (root locus) ในการออกแบบระบบ |
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ข้อจำกัดของระบบควบคุมแบบดั้งเดิมต่องานด้านอวกาศยาน :
จากความสำเร็จในการส่งดาวเทียมสปุตนิก 1 ของสหภาพโซเวียตในปี ค.ศ. 1957 นั้นกระตุ้นให้เกิดความตื่นตัวของการประยุกต์ใช้งานทางด้านอวกาศยาน ความสำเร็จของโซเวียตนั้นเนื่องมาจากพัฒนาการทางด้านทฤษฎีระบบควบคุมแบบไม่เป็นเชิงเส้น ซึ่งไม่ได้รับความสนใจมากนักจากประเทศตะวันตก เนื่องจากความล้มเหลวในการใช้เทคนิคต่าง ๆ ของระบบควบคุมแบบดั้งเดิม กับงานด้านอวกาศยาน ซึ่งระบบส่วนใหญ่นั้น เป็นระบบหลายตัวแปรแบบไม่เป็นเชิงเส้น (nonlinear multivariable system) จึงมีการหันกลับมาพิจารณาการวิเคราะห์จากปัญหาดั้งเดิม ในรูปของแบบจำลองสมการอนุพันธ์ของระบบ |
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พัฒนาการของคอมพิวเตอร์ มีส่วนสำคัญในการพัฒนาทฤษฎีต่าง ๆ ของระบบควบคุม เนื่องจากทำให้สามารถสร้างอุปกรณ์ควบคุมที่สามารถทำงานซับซ้อนได้ รวมทั้งการใช้คอมพิวเตอร์ช่วยคำนวณในการออกแบบกฎของการควบคุม ดังนั้นจึงมีการพัฒนาระบบควบคุมแบบต่าง ๆ ขึ้นอย่างมากมาย |
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ด้วยเหตุดังกล่าว จึงมีการพัฒนาทฤษฎีระบบควบคุม จากหลายแง่มุม |
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] | ทฤษฎีระบบควบคุม
จากความพยายามในการใช้คอมพิวเตอร์ซึ่งเป็นดิจิทัล เพื่อการควบคุมระบบซึ่งโดยส่วนใหญ่จะเป็นระบบอนาล็อก จึงส่งผลให้มีการพัฒนาทางทฤษฎีระบบควบคุมดิจิทัล () โดยในปี ค.ศ. 1952 จอห์น รากัซซินี (J.R. Ragazzini) , แฟรงคลิน (G Franklin) และ ซาเดห์ () ที่มหาวิทยาลัยโคลัมเบีย ได้พัฒนาทฤษฎีระบบแบบชักข้อมูล (sampled data systems) ขึ้น การใช้คอมพิวเตอร์ในการควบคุมกระบวนการในอุตสาหกรรมนั้น ครั้งแรกในปี ค.ศ. 1959 ที่ โรงกลั่นน้ำมัน พอร์ต อาเธอร์ (Port Arthur) ในรัฐเทกซัส |
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นอกจากนั้นแล้วแนวความคิดของการควบคุมที่ซับซ้อนขึ้นโดยมีการรวม ข้อกำหนดความต้องการทางด้านประสิทธิภาพ (performance) ในการออกแบบระบบควบคุม ซึ่งเรียกว่า ระบบควบคุมแบบเหมาะสมที่สุด () รากฐานของทฤษฎีระบบควบคุมแบบเหมาะสมที่สุดนี้มีมายาวนานตั้งแต่ปี ค.ศ. 1696 จาก "หลักของความเหมาะสมที่สุด" (principle of optimality) ในปัญหา บราคิสโตโครน () และ แคลคูลัสของการแปรผัน () ในปีค.ศ. 1957 ริชาร์ด เบลแมน ได้ประยุกต์ใช้วิธีการกำหนดการพลวัตของเขาในการแก้ปัญหาระบบควบคุมแบบเหมาะสมที่สุด แบบเวลาไม่ต่อเนื่อง ต่อมาในปีค.ศ. 1958 พอนเทรียกิน () ได้พัฒนา "หลักการมากที่สุด" () สำหรับแก้ปัญหาในรูปของแคลคูลัสของการแปรผัน แบบเวลาต่อเนื่อง |
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] | ทฤษฎีระบบควบคุม
การสังเกตถึงผลกระทบของสัญญาณรบกวนต่อประสิทธิภาพของระบบควบคุมนั้นมีมาตั้งแต่ในช่วงระบบควบคุมยุคดั้งเดิม เช่นในช่วงสงครามโลกครั้งที่สอง ในการพัฒนาระบบควบคุมสำหรับเรดาร์ติดเครื่องบิน เพื่อควบคุมการยิง ที่ ห้องทดลองเรดิเอชัน (Radiation Lab) ที่ เอ็มไอที, ฮอลล์ (A.C. Hall) ได้ประสบปัญหาในการออกแบบ เขาได้สังเกตถึงผลกระทบจากการออกแบบที่ไม่ได้คำนึงถึงสัญญาณรบกวนต่อประสิทธิภาพของระบบ ถึงแม้ว่าจะมีการคำนึงถึงผลกระทบของสัญญาณรบกวน แต่ก็ไม่ได้มีการใช้แบบจำลองทางคณิตศาสตร์ของสัญญาณรบกวนในการวิเคราะห์แต่อย่างใด จนกระทั่ง นอร์เบิร์ต วีนเนอร์ ได้จำลองสัญญาณรบกวน โดยใช้แบบจำลองกระบวนการสตอแคสติก หรือ แบบจำลองทางสถิติ แบบเวลาต่อเนื่อง ในการพัฒนาระบบเล็งเป้าและควบคุมการยิงปืนต่อต้านอากาศยาน โดยใช้ข้อมูลจากเรดาร์ ซึ่งงานของเขาได้ถูกเก็บเป็นความลับ จนถึงปี ค.ศ. 1949 ในช่วงเดียวกันในปี ค.ศ. 1941 คอลโมโกรอฟ ก็ได้ทำการพัฒนาแบบจำลองสำหรับระบบเวลาไม่ต่อเนื่องขึ้น ระบบควบคุมที่ใช้แบบจำลองสคอแคสติกนี้ในการวิเคราะห์ จะเรียกว่า ระบบควบคุมสตอแคสติก () |
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การวิเคราะห์และควบคุมระบบบนโดเมนเวลา โดยใช้แบบจำลองตัวแปรสถานะ หรือ แบบจำลองปริภูมิสถานะ () นั้นเป็นหัวใจของทฤษฎีระบบควบคุมสมัยใหม่ รูดอล์ฟ อีมิว คาลมาน และ Bellman นั้นถือได้ว่าเป็นบุคคลที่มีส่วนสำคัญในการพัฒนาทฤษฎีระบบควบคุมโดยใช้แบบจำลองตัวแปรสถานะนี้ โดยที่ในปี ค.ศ. 1960 คาลมานได้นำมาใช้ในการออกแบบระบบ ซึ่งเป็นผลให้ผลงานของเลียปูนอฟกลับมาได้รับความสนใจ นอกจากนี้แนวทางใหม่นี้ยังสามารถตอบคำถามเกี่ยวกับลักษณะเฉพาะของตัวระบบได้ ได้แก่ สภาพควบคุมได้ (controllability) สภาพสังเกตได้ (observability) ผลสัมฤทธิ์เล็กสุดเฉพาะกลุ่ม (minimal realization) และยังนำไปสู่การออกแบบตัวควบคุมแบบใหม่ เช่น การวางขั้ว (pole placement) ตัวควบคุมอิงตัวสังเกต (observer-based controller) และตัวควบคุมกำลังสองเชิงเส้นเหมาะที่สุด (optimal linear quadratic regulator) คาลมานได้พัฒนาวิธีการออกแบบระบบควบคุมแบบเหมาะสมที่สุด จากแบบจำลองปริภูมิสถานะ ในรูปของปัญหาระบบเชิงเส้นคงค่าแบบเหมาะสมที่สุดตามสมการกำลังสอง หรือ LQR () ในปีเดียวกันนี้ คาลมานได้นำเสนอผลงานของเขาในการประยุกต์ใช้แบบจำลองตัวแปรสถานะนี้เข้ากับแนวความคิดทางด้านสตอแคสติกของวีนเนอร์ และคิดค้นสิ่งที่เรารู้จักกันในชื่อ ตัวกรองคาลมาน () ขึ้นมา โดยการใช้งานจริงครั้งแรกของตัวกรองคาลมาน นั้นได้ถูกประยุกต์เป็นส่วนหนึ่งของระบบนำร่องในโครงการอพอลโล ตั้งแต่นั้นมาตัวกรองคาลมานก็ได้ถูกประยุกต์ใช้งานอย่างกว้างขวางในปัจจุบัน |
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ในปัจจุบันแนวทางการวิเคราะห์และควบคุมระบบบนโดเมนเวลา โดยใช้แบบจำลองตัวแปรสถานะสามารถประยุกต์ใช้ได้กับงานวิศวกรรมห้วงอากาศอวกาศ (aerospace engineering) การควบคุมกระบวนการ (process control) และเศษฐมิติ () |
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] | ทฤษฎีระบบควบคุม
ปัญหาของทฤษฎีระบบควบคุมนั้น สามารถแยกออกได้เป็นประเภทใหญ่ 2 ประเภท คือ |
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] | ทฤษฎีระบบควบคุม
เราอาจจะสามารถจำแนกประเภทของระบบได้หลายแบบตามแต่เงื่อนไขในการจำแนกระบบที่ใช้ แต่ในบริบทของทฤษฎีระบบควบคุมนั้น เรามักจำแนกระบบตามภาวะเชิงเส้น, การแปรเปลี่ยนตามเวลา และความต่อเนื่องโดเมนเวลา ดังต่อไปนี้ คือ |
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] | ทฤษฎีระบบควบคุม
ระบบเชิงเส้น (Linear Systems) คือระบบที่มีภาวะเชิงเส้น (Linearity) กล่าวคือ ถ้าให้ formula_1 เป็นสัญญาณขาเข้าของระบบ และ formula_2 โดยที่ formula_3เป็นสัญญาณขาออก ถ้าระบบมีภาวะเชิงเส้นแล้วจะต้องสอดคล้องกับคุณสมบัติดังนี้
formula_5 |
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] | ทฤษฎีระบบควบคุม
ระบบไม่เชิงเส้น (Nonlinear Systems) คือระบบที่ไม่มีสมบัติภาวะเชิงเส้นดังกล่าว |
1853#24 | [
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] | ทฤษฎีระบบควบคุม
ระบบไม่แปรเปลี่ยนตามเวลา (Time-invariant system) คือระบบที่คุณสมบัติของระบบไม่เปลี่ยนไปเมื่อเวลาเปลี่ยนไป กล่าวคือ สมมุติว่าไม่มีความล่าช้าเกิดขึ้นในระบบ (ระบบรับสัญญาณขาเข้าแล้วสามารถให้สัญญาณขาออกได้ในทันที) ถ้าป้อนสัญญาณขาเข้า formula_6 ที่เวลา formula_7 จะได้สัญญาณขาออกเป็น formula_8 ที่เวลา formula_7 ดังนั้นหากป้อนสัญญาณขาเข้าเดิมที่เวลา formula_10 นั้นคือ formula_11 สัญญาญาณขาออกผลลัพธ์ก็ต้องเป็น ค่าเดิม คือ formula_12เพียงแต่จะปรากฏที่เวลา formula_10 ตามเวลาที่ป้อนสัญญาณขาเข้า formula_11 |
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] | ทฤษฎีระบบควบคุม
ระบบแปรเปลี่ยนตามเวลา (Time-variant system) คือระบบที่จะปลี่ยนแปลงคุณสมบัติไปตามเวลา กล่าวคือ ถ้าป้อนสัญญาณขาเข้า formula_6 ที่เวลา formula_7 แล้วจะได้สัญญาณขาออกเป็น formula_8 ที่เวลา formula_7 ดังนั้นหากป้อนสัญญาณขาเข้าเดิมที่เวลา formula_10 นั้นคือ formula_11 สัญญาญาณขาออกผลลัพธ์ จะไม่ได้ค่าเดิม คือ formula_12 แต่จะเป็นค่าอื่นเพราะในช่วงเวลา formula_22 นั้นระบบได้เปลี่ยนคุณสมบัติไปแล้ว |
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] | ทฤษฎีระบบควบคุม
ระบบเวลาต่อเนื่อง (Continuous time systems) คือระบบที่มีโดเมนเวลาเป็นสมาชิกเซตของจำนวนจริง กล่าวคือ formula_23 |
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] | ทฤษฎีระบบควบคุม
ระบบเวลาวิยุต หรือ ระบบเวลาไม่ต่อเนื่อง (Discontinuous time systems) คือระบบที่มีโดเมนเวลาเป็นสมาชิกเซตของจำนวนเต็ม (แม้ในบางครั้ง อาจจะไม่ใช้จำนวนเต็ม แต่ ถ้ากล่าวโดยไม่เสียนัยยะความเป็นทั่วไป เราสามารถแทนจำนวนเหล่านั้นที่แม้ไม่ใช้จำนวนเต็มได้ด้วย ดัชนีเวลา (time index) ที่เป็นจำนวนเต็มได้เสมอ) กล่าวคือ formula_24 |
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] | ทฤษฎีระบบควบคุม
ระบบผสม (Hybrid systems) คือระบบที่โดเมนของเวลาต่อเนื่องเป็นช่วง ๆ กล่าวคือ มีทั้งช่วงที่ต่อเนื่องและไม่ต่อเนื่องในโดเมนของเวลา ตัวอย่างของระบบที่ศึกษากันคือ ระบบเชิงเส้นกระโดดแบบมาร์คอฟ (Markovian jump linear system : MJLS) |
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ในกรณีที่เป็น ระบบเชิงเส้นกระโดดแบบมาร์คอฟและเวลาไม่ต่อเนื่อง ระบบจะมีแบบจำลองดังต่อไปนี้ |
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formula_27 เป็นตัวแปรสถานะของกระบวนการมาร์คอฟ (Markov process) ที่มีความน่าจะเป็นในการเปลี่ยนสถานะเป็น formula_28
และเมทริกซ์ของระบบแปรเปลี่ยนขึ้นกับ formula_29 |
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formula_30 เป็นสัญญาณรบกวนที่มีต่อตัวระบบ |
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formula_31 เป็นสัญญาณรบกวนที่มีการสังเกต (สัญญาณขาออก) |
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ส่วน formula_32 จะนิยามในส่วนของแบบจำลองปริภูมิสถานะ ต่อไป |
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เนื่องจากระบบควบคุมแบบวงเปิดมีปัญหาด้านเสถียรภาพของระบบเพราะไม่มีการป้อนกลับของสัญญาณขาออก ซึ่งไม่เหมาะกับการใช้งานหลายอย่าง จึงมีความต้องการที่จะออกแบบระบบควบคุมที่สามารถตรวจจับความคลาด |
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] | ทฤษฎีระบบควบคุม
เคลื่อนระหว่างสัญญาณขาออกและสัญญาณอ้างอิงได้ จึงได้มีการคิดค้นระบบควบคุมแบบป้อนกลับ (Feedback control systems) หรือระบบควบคุมแบบวงปิด (Closed loop control systems) ขึ้นมาเพื่อหลีกเลี่ยงปัญหาที่เกิด |
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ขึ้นกับระบบควบคุมแบบวงเปิด โดยมีโครงสร้างดังในรูป |
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ระบบควบคุมแบบป้อนกลับมีความได้เปรียบเหนือกว่าระบบควบคุมแบบวงเปิด ดังต่อไปนี้ |
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ในบางระบบ ระบบควบคุมแบบวงปิดและวงเปิดจะใช้ควบคู่กัน โดยที่ในกรณีนี้ระบบวงเปิดจะเรียกว่า |
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] | ทฤษฎีระบบควบคุม
ฟังก์ชันส่งผ่าน (transfer function) คือความสัมพันธ์ทางคณิตศาสตร์ที่ใช้แสดงถึงความสัมพันธ์ระหว่างสัญญาณขาออก (output signal) ต่อสัญญาณขาเข้า (input signal)
โดยฟังก์ชันส่งผ่านสามารถหาได้จากความสัมพันธ์ดังต่อไปนี้
สมมุติให้ ตัวควบคุม formula_33, ระบบพลวัต formula_34, ตัวตรวจจับ formula_35 เป็นเชิงเส้น และ ไม่เปลี่ยนแปลงตามเวลา (ฟังก์ชันส่งผ่านของ formula_36, formula_37, and formula_38 ไม่เปลี่ยนแปลงตามเวลา) และในที่นี้เราจะพิจารณาผลการแปลงการแปลงลาปลาสของฟังก์ชันส่งผ่านย่อย ๆ กล่าวคือ ฟังก์ชันส่งผ่านของ formula_36, formula_37, and formula_38 ซึ่งการหาฟังก์ชันส่งผ่านหาได้ดังนี้ |
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แก้หา formula_45 ในรูปของ formula_46 จะได้ว่า: |
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] | ทฤษฎีระบบควบคุม
โดยที่ formula_48 เราจะเรียกว่า ฟังก์ชันส่งผ่านของระบบวงปิดของระบบ (closed-loop transfer function) |
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ตัวควบคุมพีไอดี หรือ ตัวควบคุมแบบสัดส่วน-ปริพันธ์-อนุพันธ์ เป็นตัวควบคุมที่ได้รับความนิยมเป็นอย่างสูงและใช้งานอย่างแพร่หลาย โดยในปัจจุบันยังมีการใช้งานในแวดวงอุตสาหกรรม จนไปถึงยานอวกาศ ทั้งนี้เพราะเป็นตัวคบคุมที่มีใช้งานกันมานานและจนได้รับความไว้วางในแง่ของประสิทธิภาพ อีกทั้งแบบจำลองทางคณิตศาสตร์ของมันก็เรียบง่ายและง่ายต่อการนำไปติดตั้ง
ตัวควบคุมพีไอดีมีแบบจำลองทางคณิตศาสตร์ดังต่อไปนี้ |
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กำหนดให้ formula_49 คือสัญญาณควบคุมที่จะส่งให้ตัวระบบ |
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และ formula_8 คือสัญญาณขาออกที่ถูกวัดมาได้ |
1853#47 | [
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และ formula_51 คือสัญญาณอ้างอิง |
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สัญญาณความคลาดเคลื่อนคือ formula_52 ดังนั้น |
1853#49 | [
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] | ทฤษฎีระบบควบคุม
สมรรถนะและเสถียรถาพของระบบจะถูกกำหนดโดยการปรับแต่งค่าพารามิเตอร์สามตัว คือ formula_54, formula_55 และ formula_56 นอกเหนือจากการปรับแต่งค่าเหล่านี้หลังจากการวิเคราะห์ทางคณิตศาสตร์ของตัวระบบแล้ว ในทางปฏิบัติ ยังนิยมปรับแต่งค่าโดยใช้หลักการของ หรือใช้ประสบการณ์ของวิศวกร โดยที่เสถียรภาพของระบบมักขึ้นอยู่กับพารามิเตอร์ formula_54 แต่เพียงอย่างเดียว ส่วน formula_55 มักส่งผลในแง่ของความคงทนต่อการเปลี่ยนแปลงฉับพลันต่อตัวระบบ และ formula_56 มักเกี่ยวกับรูปร่างของผลตอบสนอง
เมื่อพิจารณาบนโดเมนการแปลงลาปลาส จะได้ว่า
โดยจะเห็นได้ว่าฟังกชั่นส่งผ่านของตัวควบคุมพีไอดีคือ
แม้ระบบควบคุมแบบดั้งเดิมที่ใช้ตัวควบคุมพีไอดีจะมีความสามารถที่ถูกปรับปรุงดีขึ้นมากกว่าระบบควบคุมแบบเปิดมาก แต่ก็ยังเหมาะแค่กับระบบที่มีสัญญาณเข้าทางเดียวและสัญญาณขาออกทางเดียว ( or SISO) และยังไม่สามารถใช้ควบคุมระบบที่มีความซับซ้อนสูงได้ โดยเฉพาะอย่างยิ่งระบบที่มีสัญญาณขาเข้าหลายทางและสัญญาณขาออกหลายทาง ( or MIMO) |
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] | ทฤษฎีระบบควบคุม
ระบบพลวัตส่วนใหญ่มักมีพฤติกรรมที่สามารถใช้สมการอนุพันธ์อันดับใด ๆ มาอธิบายได้ ในขณะเดียวกันสมการเชิงอนุพันธ์อันดับใด ๆ ก็สามารถลดอันดับให้เหลือเพียงสมการเชิงอนุพันธ์อันดับหนึ่งได้ จากความจริงตรงนี้จึงได้มีการเสนอวิธีการใหม่ในการวิเคราะห์และควบคุมระบบ ซึ่งจะวิเคราะห์บนโดเมนเวลาและได้มีการนำแบบจำลองปริภูมิสถานะ () มาใช้ซึ่งจะอยู่ในรูปของสมการอนุพันธ์อันดับหนึ่งและแตกต่างจากระบบควบคุมแบบดั้งเดิมที่นิยมวิเคราะห์พฤติกรรมของระบบบนโดเมนความถี่ นอกจากนี้การนำแบบจำลองปริภูมิสถานะมาใช้ทำให้เราสามารถสร้างแบบจำลองทางคณิตศาสตร์สำหรับระบบแบบสัญญาณขาเข้าหลายทางสัญญาณขาออกหลายทาง (MIMO) ได้โดยการกำหนดมิติของตัวแปรในสมการปริภูมิสถานะอย่างเหมาะสม |
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] | ทฤษฎีระบบควบคุม
กำหนดให้ระบบพลวัตมี formula_63 สัญญาณขาเข้า formula_64 สัญญาณขาออก และ formula_65 ตัวแปรสถานะ |
1853#52 | [
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สมการปริภูมิสถานะคือ:
โดยที่: |
1853#53 | [
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] | ทฤษฎีระบบควบคุม
โดยทั่วไปแล้ว เมทริกซ์ข้างต้นจะเป็นเมทริกซ์แปรผันตามเวลาได้ แต่ในกรณีเฉพาะที่ระบบไม่แปรผันตามเวลา () มักจะถูกนำมาศึกษาอยางแพร่หลายเพราะมีความซับซ้อนน้อยกว่าและเหมาะต่อการศึกษาในระดับพื้นฐาน นอกจากนี้ตัวแปรเวลาสามารถมีได้ทั้งแบบเวลาต่อเนื่อง (continuous time : formula_84) และแบบเวลาวิยุต (ไม่ต่อเนื่อง) (discrete time : formula_85) โดยในกรณีของเวลาไม่ต่อเนื่องมักนิยมใช้ตัวแปร formula_86 นอกเหนื่อจากระบบแบบที่กล่าวมาแล้วยังมีระบบผสมซึ่งเป็นระบบที่มีโดเมนของเวลาอยู่ทั้งบนแกนเวลาต่อเนื่องและไม่ต่อเนื่อง |
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สมการปริภูมิสถานะ()ข้างต้นหากพิจารณาตามโดเมนของเวลาจะมีรูปแบบต่าง ๆ กันดังต่อไปนี้ : |
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] | ทฤษฎีระบบควบคุม
สภาพควบคุมได้ () จะบ่งบอกถึงความสามารถที่สัญญาณขาเข้าที่เป็นไปได้ (admissible inputs) จะสามารถขับเคลื่อนตัวแปรสถานะให้ไปถึงค่าใด ๆ ได้ในช่วงเวลาจำกัด (เวลาอันตะ) ไม่ว่าค่าเริ่มต้น (initial value) ของตัวแปรสถานะนั้น ๆ จะเป็นค่าอะไร ในกรณีระบบพลวัตเชิงเส้นเวลาต่อเนื่องไม่แปรผันตามเวลานั้นเงื่อนไขที่จะทำให้มีสภาพควบคุมได้ ก็ต่อเมื่อ
สภาพสังเกตได้ () เป็นสภาพที่บ่งบอกว่าระบบพลวัตมีความสามารถที่จะส่งผ่านข้อมูลของตัวแปรสถานะได้ดีแค่ไหนเมื่อพิจารณาจากสัญญาณขาออก สภาพควบคุมได้ และ สภาพสังเกตได้ เป็นสภาพคู่กันทางคณิตศาสตร์ () กล่าวคือ ในขณะที่ สภาพควบคุมได้ หมายถึง สภาพที่แสดงออกว่าสัญญาณขาเข้าสามารถขับเคลื่อนตัวแปรสถานะไปที่ค่าใด ๆ ที่ต้องการได้ แต่ สภาพสังเกตได้ จะเป็นสภาพที่แสดงออกถึงสัญญาณขาออก (output trajectory) จะให้ข้อมูลเพียงพอต่อการคาดคะเนค่าเริ่มต้นของตัวแปรสถานะของระบบได้
ในกรณีระบบพลวัตเชิงเส้นเวลาต่อเนื่องไม่แปรผันตามเวลานั้น เงื่อนไขที่จะทำให้มีสภาพสังเกตได้ได้ ก็ต่อเมื่อ |
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การแยกตัวประกอบคาลมาน () เป็นกระบวนการแยกส่วนประกอบของเมทริกซ์ในสมการปริภูมิสถานะของระบบเชิงเส้นไม่เปลี่ยนตามเวลา ให้อยู่ในรูปแบบที่สามารถจำแนกได้ว่าส่วนใดในเมทริกซ์ของระบบ มีผลต่อ สภาพสังเกตได้ และสภาพควบคุมได้ ทำให้ง่ายต่อการวิเคราะห์คุณลักษณะของระบบ |
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] | ทฤษฎีระบบควบคุม
จากสมการปริภูมิสถานะของระบบข้างต้น จะเห็นได้ว่าพารามิเตอร์ที่กำหนดลักษณะของระบบ LTI สามารถเขียนโดยย่อได้เป็นเวกเตอร์ formula_91 ในที่นี้จะสมมุติว่าระบบมีมิติเป็น formula_92. |
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] | ทฤษฎีระบบควบคุม
การแยกตัวประกอบคาลมาน ถูกนิยามว่า คือ การแปลงเวกเตอร์ formula_91 ให้เป็น formula_94 โดยคูณเมทริกซ์การแปลง formula_95 ดังต่อไปนี้ |
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โดยเมทริกซ์การแปลง formula_95 มีมิติ formula_101 เป็นเมทริกซ์ผกผันได้ ถูกนิยามดังต่อไปนี้ ดังต่อไปนี้: |
1853#60 | [
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] | ทฤษฎีระบบควบคุม
โดยที่
จะเห็นได้ว่าโดยการสร้งเมทริกซ์ formula_95 ในลักษณะข้างต้น เมทริกซ์ formula_95 จึงผกผันได้ เป็นที่น่าสังเกตว่าเมทริกซ์ย่อยในเมทริกซ์ formula_95 นั้นสามารถเป็นเมทริกซ์ศูนย์ได้ ยกตัวอย่างเช่น กรณีที่ระบบมีสภาพสังเกตได้และควบคุมได้ เมทริกซ์ formula_95 ลดรูปเหลือ formula_114 โดยที่ เมทริกซ์ย่อยอื่นเป็นเมทริกซ์ศูนย์ |
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ระบบที่ได้รับการแปลงแล้ว formula_94 จะมีรูปแบบดังต่อไปนี้: |
1853#62 | [
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โดยที่ |
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อักษรย่อ STP อาจหมายถึง: |
1860#0 | [
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] | มังกรอหังการหมาป่าคะนองศึก
มังกรอหังการหมาป่าคะนองศึก () เป็นการ์ตูนญี่ปุ่นแนวแฟนตาซีอิงประวัติศาสตร์ เกี่ยวกับเด็กมัธยมญี่ปุ่นสองคน ที่หลุดย้อนเวลาเข้าไปอยู่ในสมัยสามก๊กของจีน ในปี 2540 การ์ตูนเรื่องนี้ได้ชนะเลิศรางวัลโคดันชะมังงะ สำหรับโชเน็ง |
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ตัวเอกชื่อ "อามาจิ ชิโร่" หรือชื่อเรียกในสมัยของสามก๊กว่า "บุตรมังกร" และเพื่อนสมัยเด็กของเขา "มาซึมิ" ซึ่งถูกเรียกว่า"ธิดามังกร" ได้เป็นจุดเปลี่ยนของประวัติศาสตร์ครั้งสำคัญของสงครามครั้งนี้ โดยจุดประสงค์ในการเปลี่ยนแปลงนั้นคือการต่อกรกับเพชรฆาตหน้าหยกเพื่อช่วยมนุษย์จากการทำลายล้างให้หมดสิ้นไป |
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เรื่องและภาพ โดย โยชิโตะ ยามาฮาระ แปลเป็นไทยและจัดพิมพ์ในประเทศไทยโดยสำนักพิมพ์วิบูลย์กิจ |
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] | ประเทศทาจิกิสถาน
ทาจิกิสถาน (; ) หรือชื่อทางการว่า สาธารณรัฐทาจิกิสถาน (; ) เป็นประเทศที่ไม่มีทางออกสู่ทะเลในภูมิภาคเอเชียกลาง มีอาณาเขตติดต่อกับอัฟกานิสถาน จีน คีร์กีซสถาน และอุซเบกิสถาน ทาจิกิสถานเคยเป็นส่วนหนึ่งของสหภาพโซเวียต |
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] | ประเทศทาจิกิสถาน
ทาจิกิสถานหมายถึง "ดินแดนแห่งชาวทาจิก" (Tajiks) คำทาจิกถูกใช้โดยยุคกลาง เพื่ออ้างถึงคนที่พูดภาษาอิหร่าน จากศตวรรษที่ 11 ระยะที่อ้างถึงประเทศอิหร่านตะวันออก แต่โดยศตวรรษที่ 15 มาจะนำไปใช้กับลำโพงเปอร์เซีย ในวรรณคดีเปอร์เซียยุคกลาง ทาจิกจะปรากฏเป็นความหมายของ "เปอร์เซีย" |
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] | ประเทศทาจิกิสถาน
ขณะที่การกำหนดตัวเองระยะทาจิก ได้กลายเป็นที่ยอมรับเฉพาะในช่วงทศวรรษสุดท้ายของศตวรรษที่ 20 โดยเฉพาะอย่างยิ่งเป็นผลของการบริหารงานของสหภาพโซเวียตในเอเชียกลาง ไม่แสดงว่ากลุ่มชาติพันธุ์ในความหมายแคบ แต่ยังคงกำหนดทั่วไปของความหลากหลายของคนที่พูดภาษาเปอร์เซียในเอเชียกลาง |
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] | ประเทศทาจิกิสถาน
บ่อยครั้งทาจิกิสถานถูกสะกดเป็นอักษรละตินว่า Tadjikistan หรือ Tadzhikistan เป็นภาษาอังกฤษทับศัพท์จากภาษารัสเซีย Tadzhikistan คือการสะกดแบบอื่นที่พบมากที่สุดและมีการใช้กันอย่างแพร่หลายในวรรณคดีอังกฤษ มาจากแหล่งรัสเซีย "Tadjikistan" คือการสะกดคำจากภาษาฝรั่งเศสและบางครั้งสามารถพบได้ในตำราภาษาอังกฤษ |
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ทาจิกิสถานจะไม่มีทางออกสู่ทะเลและเป็นประเทศที่เล็กที่สุดในเอเชียกลางโดยพื้นที่ มันถูกปกคลุมด้วยภูเขา และมากกว่าร้อยละห้าสิบของประเทศเป็นกว่า 3,000 เมตร (9,800 ฟุต) เหนือระดับน้ำทะเล เฉพาะพื้นที่ที่สำคัญของที่ดินที่ต่ำในภาคเหนือ และในภาคใต้ |
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] | ประเทศทาจิกิสถาน
ทาจิกิสถานได้ได้รับเอกราชในปีค.ศ. 1990 ภายหลังการล่มสลายของสหภาพโซเวียต แต่ในช่วงแรก การเมืองภายในประเทศขาดเสถียรภาพเนื่องจากเกิดความขัดแย้งภายในอย่างรุนแรงระหว่างกลุ่มชาตินิยม กลุ่ม Neo-communist และกลุ่มอิสลามหัวรุนแรง และมีผู้เสียชีวิตจากเหตุการณ์ดังกล่าว 60,000 คน ต่อมากลุ่มอิสลามหัวรุนแรงได้อพยพออกนอกประเทศพร้อมด้วยประชาชนหลายหมื่นคน ไปตั้งมั่นอยู่ทางภาคเหนือของอัฟกานิสถาน และกลับเข้ามาปฏิบัติการแบบกองโจรในทาจิกิสถาน ทำให้รัฐบาลทาจิกิสถานต้องพึ่งกองกำลังรัสเซียดูแลแนวชายแดนทาจิกิสถาน-อัฟกานิสถาน และมีการสู้รบยืดเยื้อเป็นเวลาหลายปี จนในปี 1997 จึงมีการลงนามสนธิสัญญาสันติภาพระหว่างประธานาธิบดี Emomali Rahmonov กับนาย Sayed Abdulla Nuri ผู้นำกลุ่มแนวร่วมต่อต้านรัฐบาล (United Tajik Opposition - UTO) |
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] | ประเทศทาจิกิสถาน
เกือบจะทันทีหลังจากเป็นอิสระ ทาจิกิสถานได้ตกลงไปอยู่ในสงครามกลางเมืองที่เห็นฝ่ายต่าง ๆ การสนับสนุนที่ถูกกล่าวหาว่าโดยรัสเซียและอิหร่านที่ต่อสู้กัน แต่ทั้งหมด 25,000 ของรัสเซียชนกลุ่มน้อยกว่า 400,000 คนซึ่งได้มีงานทำส่วนใหญ่ในอุตสาหกรรมการหลบหนีไปยังรัสเซีย โดยปี 1997 สงครามได้เย็นลงและรัฐบาลกลางเริ่มที่จะอยู่ในรูปแบบที่มีการเลือกตั้งในปี 1999 ที่เงียบสงบ |
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