july 2004 2009 lecture side lecture by suradet tantrairatn instructor and researcher chapter twelve...
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![Page 1: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/1.jpg)
July 20042009 Lecture Side
Lecture by
Suradet Tantrairatn
Instructor and Researcher
Chapter Twelve
week3
January 2009
Design of Control System in State Space
![Page 2: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/2.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Introduction
This Chapter we will learn about state-space design
methods based on the pole-placement method and the quadratic optimal regulator method.
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Review
First Order:
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Review
Second Order:
Back to review Chapter4 Transient Response Analysis( Ogata Book )
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Pole Placement
Pole Placement ( วิ�ธี�การวิางโพล ) คื�อ ตั้��งข้�อก�าหนดสำ�าหร�บตั้�าแหน�ง
โพลทั้��งหมดข้องระบบวิงปิ!ด และออกแบบตั้�วิคืวิบคื"มทั้�#จะได�ตั้�าแหน�งโพลตั้ามข้�อก�าหนดน��น เง�#อนไข้จ�าเปิ'นข้องระบบหร�อพลานตั้(ทั้�#ทั้�าให�สำามารถทั้�าการเคืล�#อนย้�าย้โพลทั้��งหมดไปิย้�งตั้�าแหน�งทั้�#ตั้�องการได�
ในการออกแบบทั้�#วิไปิจะไม�ได�ตั้�องการให�ระบบม�เสำถ�ย้รภาพอย้�างเด�ย้วิ แตั้�ย้�งตั้�องการสำมรรถนะหร�อผลตั้อบสำนองตั้ามตั้�องการด�วิย้ ด�งน��นการก�าหนดตั้�าแหน�งข้องโพลระบบวิงปิ!ดจ.งม�ใช่�เพ�ย้งแตั้�วิ�าตั้�องการอย้0�บนด�านซ้�าย้ข้องระนาบเช่�งซ้�อนเทั้�าน��น แตั้�อาจจะตั้�องอย้0�ในพ��นทั้�#ทั้�#จะให�ผลตั้อบสำนองทั้�#ด�ด�วิย้ เช่�น ถ�าตั้�าแหน�งโพลอย้0�ใกล�แกนจ�นตั้ภาพมากเก�นไปิ ผลตั้อบสำนองจะม�ล�กษณะแกวิ�ง
ในระบบอ�นด�ล n ทั้�#วิ ๆ ไปิ คืวิามสำ�มพ�นธี(ผลตั้อบสำนองทั้างเวิลาข้องระบบก�บตั้�าแหน�งข้องโพล ม�กม�คืวิามซ้�บซ้�อน จ.งเปิ'นการย้ากทั้�#จะก�าหนดตั้�าแหน�งโพลเพ�#อให�ได�ผลตั้อบสำนองทั้�#ด� ด�งน��นวิ�ธี�การออกแบบน��โดย้ทั้�#วิไปิอาศั�ย้หล�กการข้องระบบทั้�#ม�ลั�กษณะเด่นเป็�นอั�นด่�บสอัง
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Design By Pole Placement
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Design By Pole Placement
(a) Open-loop control system; (b) Closed-loop control sysytem
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Design By Pole Placement
Control signal
The Solution is
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K using Transformation Matrix T.
ai are coefficients of the characteristic polynomial
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K using Transformation Matrix T. (2)
where
![Page 11: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/11.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K using Transformation Matrix T. (3)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K using Transformation Matrix T. (4)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K using Transformation Matrix T. (5)
![Page 14: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/14.jpg)
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Summary to Find Matrix K Using Transformation Matrix T
Step1: Check the controllability condition Step2: From the characteristic polynomial for matrix A
Step3: Determine the transformation Matrix T
Step4: Using the desired eigenvalues
Final Step : Calculate K from
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Example
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Example
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K Using Direct Substitution Method.
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Example
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K Using Ackerman’s Formula.
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K Using Ackerman’s Formula. (2)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K Using Ackerman’s Formula. (3)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of Matrix K Using Ackerman’s Formula. (4)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Example
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Solving Pole-Placement Problems with MATLAB
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Ackermann’s Formula
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Ackermann’s Formula
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Ackermann’s Formula
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
MATLAB Program (Produce The Feedback Gain Matrix K by Using Ackermann’s Formula)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
MATLAB Program (Produce The Feedback Gain Matrix K by Using Ackermann’s Formula)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
MATLAB Program (Produce The Feedback Gain Matrix K by Using Ackermann’s Formula)
![Page 38: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/38.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
MATLAB Program (Produce The Feedback Gain Matrix K by Using Ackermann’s Formula)
![Page 39: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/39.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Design of Regulator-type Systems by Pole Placement
![Page 40: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/40.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 41: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/41.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
We assume that the moment of inertia of the pendulum about its center of gravity is zero
![Page 42: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/42.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 43: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/43.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 44: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/44.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 45: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/45.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
Define state variables
![Page 46: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/46.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 47: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/47.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 48: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/48.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
In terms of vector-matrix equations.
![Page 49: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/49.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
By substituting the given numerical values
![Page 50: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/50.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 51: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/51.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
Use state-feedback control
![Page 52: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/52.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 53: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/53.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 54: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/54.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 55: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/55.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 56: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/56.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
The desired characteristic equation
![Page 57: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/57.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 58: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/58.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 59: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/59.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 60: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/60.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 61: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/61.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 62: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/62.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
Inverted-pendulum system with state-feedback control
![Page 63: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/63.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 64: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/64.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Mathematical Modeling
![Page 65: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/65.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of state-feedback gain matrix K with MATLAB
![Page 66: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/66.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of state-feedback gain matrix K with MATLAB
![Page 67: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/67.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Determination of state-feedback gain matrix K with MATLAB
![Page 68: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/68.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
State equation
![Page 69: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/69.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
Control equation
![Page 70: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/70.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
![Page 71: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/71.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
Substitute the numerical values.
![Page 72: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/72.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
![Page 73: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/73.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
![Page 74: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/74.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
Initial condition
![Page 75: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/75.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
![Page 76: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/76.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
![Page 77: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/77.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Obtaining System Response To Initial Condition
![Page 78: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/78.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
MATLAB Program
![Page 79: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/79.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
MATLAB Program
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
Response Of Inverted Pendulum System Subjected To Initial Condition
![Page 81: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/81.jpg)
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
![Page 82: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/82.jpg)
© A
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righ
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fide
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Month 200X 2009 Subject Name Automotive Automatic Control Page 2
![Page 83: July 2004 2009 Lecture Side Lecture by Suradet Tantrairatn Instructor and Researcher Chapter Twelve week3 January 2009 Design of Control System in State](https://reader035.vdocuments.net/reader035/viewer/2022062404/551b1df75503462e578b6171/html5/thumbnails/83.jpg)
© A
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US
UK
LT
D 2
002.
All
righ
ts r
ese
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. Con
fide
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l and
pro
prie
tary
do
cum
ent.
Month 200X 2009 Subject Name Automotive Automatic Control Page 2