Abstract: The rotary inverted pendulum is a strong coupling, nonlinear and unstable system which has one input and two outputs. In order to realize the effective control of the system in the stable stage, fractional order PID, PI^γD^μ, and FOPID are used in the pendulum angle and rotation angle's position and speed closed-loop control, respectively. Because of the large number of FOPID controllers and parameters, manual setting of the controller parameters is very complicated and not easy to achieve. Therefore, this paper uses the improved multi-objective particle swarm algorithm (IMOPSO) to adjust FOPID controller parameters. The effectiveness of the IMOPSO-FOPID algorithm is verified by the QUBE-Servo the rotary inverted pendulum. The inverted pendulum obtains good dynamic quality and stability, better than PID.

Key words: Multi-objective particle swarm optimization, rotational inverted-pendulum, parameter setting, FOPID controller, PID

摘要： 来旋转式倒立摆是一种单输入双输出、强耦合、非线性不稳定系统。为实现对该系统在稳定阶段进行有效控制，采用分数阶PID(PI^γD^μ，FOPID)分别对倒立摆摆角、转角的位置和速度进行闭环控制。因为FOPID控制器数目和参数较多，手动调节各控制器参数极为繁琐且不易实现，故采用改进多目标粒子群(IMOPSO)算法整定各个FOPID控制器参数。通过QUBE-Servo旋转式倒立摆上验证了IMOPSO-FOPID算法的有效性，并使倒立摆获得优于PID控制系统的良好的动态品质，同时具备良好的稳定性和鲁棒性。

关键词: 多目标粒子群优化算法, 旋转式倒立摆, 参数整定, 分数阶PID, PID