CAJ | 학술논문

为了实现导轨受限情况下二级倒立摆非线性系统的自动摆起控制，提出了基于变增益LQR控制方法的自动摆起控制方案．首先，基于Lyapunov函数，设计了变参数切换控制器，通过限制小车运动的最大速度，将小车位移控制在一定的范围内，并将第一级摆杆从下垂位置摆起到倒立位置；其次，采用变增益LQR控制方法将第一级摆杆稳定在倒立位置，同时，采用等效小车法将第二级摆杆摆起到倒立位置；最后，采用变增益LQR控制方法将两摆杆同时稳定在倒立平衡点．变增益LQR控制器的鲁棒性较强，避免了由于摆杆状态变化而引起小车位移的冲击．仿真和实物实验均验证了该控制方案的有效性．
위료실현도궤수한정황하이급도립파비선성계통적자동파기공제，제출료기우변증익LQR공제방법적자동파기공제방안．수선，기우Lyapunov함수，설계료변삼수절환공제기，통과한제소차운동적최대속도，장소차위이공제재일정적범위내，병장제일급파간종하수위치파기도도립위치；기차，채용변증익LQR공제방법장제일급파간은정재도립위치，동시，채용등효소차법장제이급파간파기도도립위치；최후，채용변증익LQR공제방법장량파간동시은정재도립평형점．변증익LQR공제기적로봉성교강，피면료유우파간상태변화이인기소차위이적충격．방진화실물실험균험증료해공제방안적유효성．
A control scheme based on variable gain LQR technique is proposed in order to realize the swing-up control of nonlinear double inverted pendulum under restricted rail length. Firstly, a variable- parameter switching controller is designed to swing up the first rod to the upright position based on Lyapunov function; and the displacement of cart is restricted via limiting the maximum velocity of cart. Secondly, the first rod is stabilized at upright position by utilizing variable gain LQR technique; and at the same time the second rod is swung up by using control strategy of ＂equivalent cart＂. Finally, the both rods are stabilized around the unstable equilibrium point by using variable gain LQR technique. Because of the good robustness of the variable gain LQR controller, the displacement impact of cart which is caused by the change of rods＇s statement is avoided. The simulation and experiments demonstrate the effectiveness of the proposed control scheme.