Saturday, October 23, 2010

Inverted pendulum state feedback control

พอดีทาง FIBO ได้มอบหมายงานชิ้นแรกให้ผม คือ ออกแบบ Control low เพื่อ ควบคุม Inverted pendulum หลังจากทำได้สองอาทิตย์ก็ทำสามารถให้มันตั้งได้แล้วแต่ state ของ cart ยังคง oscillate อยู่เพราะการปรับค่า gain ของระบบที่มีความเป็น Nonlinear และ Unstable มันไม่ใช่เรื่องง่าย และ Mechanic ก็ยังไม่ค่อยดีเท่าไหร่ แต่นี้เป็นแค่การทดสอบ Algorithm ว่า Micro controller รุ่น PIC18f4431 สามารถเขียน Control law u=-k1*(x1-reference)-k2*x2-k3*(x3-reference)-k4*x4-k5*z-k6*z1 ได้หรือเปล่าวโดยที่ x1 คือ Angle ของ pendulum x2 คือ Angular velocity ของ pendulum โดยติดตั้ง Potentiometer ไว้ที่จุดหมุนของ pendulum ส่วน x3 คือ Cart position และ x4 คือ linear velocity ของ cart มี Encoder ติดไว้ที่ motor z1 และ z2 คือ Integral error ของ Pendulum และ Cart x1 to x4 เราเรียกมันว่า State variable จะเห็นว่า x1 และ x3 สามารถวัดได้โดยตรง ส่วน x2 และ x4 ผมนำมันมา Derivative เทียบกับเวลาซึ่งไม่ใช่วิธีการที่ดีเท่าไหร่ แต่คิดไว้แล้วว่าจะใช้ Reduce order observer  หรือ อาจจะใช้ Kalman filter มาประมาณหาความเร็วแต่ทั้งสองวิธีนี้จะต้องมีแบบจำลองทางคณิตศาสตร์ของระบบก่อนวันนี้พอเท่านี้ก่อนแล้วกันครับ ครั้งหน้าจะมาดูว่า
1. หาแบบจำลองอย่างไร
2.หาสัมประสิทธิ์คงที่ ของ Model
3.ออกแบบ Observer 
4.หา Gain K โดยวิธี Lqr  
5.เขียน Code ลงใน PIC18F

อันนี้เป็น VDO ลองดูเล่นๆก่อน มันยังไม่สมบูรณ์เท่าที่ควรเพราะยังขาด Algorithm บางตัวอยู่ 





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