本文通過拉格朗日方程推導(dǎo)出環(huán)形一級倒立擺系統(tǒng)的數(shù)學(xué)模型，用能量方法對該模型進行擺起控制；在倒立擺成功擺起后，在倒立平衡點對系統(tǒng)模型進行線性化，并用線性二次型最優(yōu)控制（LQR）算法對倒立擺線性化模型進行穩(wěn)定控制。仿真結(jié)果表明本文給出的控制方法是有效的。
關(guān)鍵詞：環(huán)形倒立擺；擺起控制；穩(wěn)定控制；線性二次型最優(yōu)控制

Abstract: This paper derives the mathematical model for system of single link rotary inverted
pendulum from Lagrange Equation, and through this model the rotary inverted pendulum is
swung up by energy methods. After the success of the inverted pendulum swung up, the mathematical model is made linear on the inverted balance point and through the linear model
the inverted pendulum is kept stable on the inverted point by linear quadratic optimal control.
Simulation experiments show that the control methods are effective.
Key words: rotary inverted pendulum; swing-up control; stability control; LQR