基于粒子群算法的LQR直线二级倒立摆的控制研究

发布时间：2019-06-03 22:25

【摘要】：倒立摆系统具有非线性、高阶次、多变量、强耦合等特点,是绝不稳定欠驱动系统的典型代表。倒立摆系统可以抽象的表示多种应用领域控制对象的基本模型,可以作为理想的多智能控制理论验证控制应用平台,从而实现倒立摆系统在航空航天领域、智能机器领域的广泛应用,因此倒立摆稳定性控制研究是非常重要的。本文以直线二级倒立摆控制系统作为研究对象,首先对直线二级倒立摆进行物理机理分析并建立数学模型,然后对直线二级倒立摆的数学模型线性化分析,得到系统的线性状态空间表达式。其次,对比分析了PID控制器和LQR控制器实现直线二级倒立摆的控制仿真实验,结果表明,PID实现的控制器数量多、控制效果差,而LQR控制器实现的直线二级倒立摆控制准确性优于PID控制,但LQR控制器参数选取过程偏经验化,可优化参数数量少,造成控制精度不高。最后,针对LQR控制器参数选取问题,采用粒子群算法对LQR控制器参数进行优化,通过一个LQR控制实现对小车位移、小车速度、摆杆1角度和角速度、摆杆2角度和角速度进行参数优化。在实验设备平台上进行验证,粒子群算法优化后的LQR控制器提高了直线二级倒立摆控制的稳定性和准确性,实现了摆杆偏离平衡后自恢复状态,并维持在平衡稳定状态。实验结果表明,粒子群优化算法实现了对LQR直线二级倒立摆控制系统的优化,对改善直线二级倒立摆控制系统稳定性能具有极其重要的理论意义,为倒立摆系统的实际应用奠定了理论基础,具有一定的应用价值。
[Abstract]:Inverted pendulum system is a typical representative of unstable underdriven system because of its nonlinear, high order, multivariable, strong coupling and so on. Inverted pendulum system can represent the basic model of control objects in various application fields abstractly, and can be used as an ideal multi-intelligent control theory to verify control application platform, so as to realize inverted pendulum system in the field of aerospace. The research on stability control of inverted pendulum is very important because of its wide application in the field of intelligent machine. In this paper, the control system of linear two-stage inverted pendulum is taken as the research object. Firstly, the physical mechanism of the straight-line two-stage inverted pendulum is analyzed and the mathematical model is established, and then the linear analysis of the mathematical model of the straight-line two-stage inverted pendulum is carried out. The linear state space expression of the system is obtained. Secondly, the control simulation experiment of PID controller and LQR controller to realize linear two-stage inverted pendulum is compared and analyzed. The results show that the number of controllers realized by PID is large and the control effect is poor. However, the accuracy of linear two-stage inverted pendulum control realized by LQR controller is better than that of PID control, but the parameter selection process of LQR controller is empirical, and the number of optimized parameters is small, resulting in low control accuracy. Finally, aiming at the parameter selection of LQR controller, particle swarm optimization algorithm is used to optimize the parameters of LQR controller, and a LQR control is used to realize the displacement of trolley, the speed of trolley, the angle and angular velocity of swinging rod 1. The parameters of swing rod 2 angle and angular velocity are optimized. It is verified on the experimental equipment platform that the LQR controller optimized by particle swarm optimization improves the stability and accuracy of the linear two-stage inverted pendulum control, realizes the self-recovery state of the swinging rod after deviating from equilibrium, and maintains it in a balanced and stable state. The experimental results show that the particle swarm optimization algorithm realizes the optimization of LQR linear two-stage inverted pendulum control system, which is of great theoretical significance to improve the stability of linear two-stage inverted pendulum control system. It lays a theoretical foundation for the practical application of inverted pendulum system and has certain application value.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH112

【参考文献】