【作者】 段学超；

【导师】 仇原鹰；

【作者基本信息】 西安电子科技大学 ， 机械电子工程， 2006， 硕士

【摘要】 倒立摆是典型的非线性、高阶次、强耦合、不稳定、欠驱动系统,研究倒立摆的精确控制对工业生产中复杂对象的控制有着重要的应用价值,因此倒立摆仿真或实物控制实验是控制领域中用来检验某种控制理论或方法的典型方案。目前直线型倒立摆作为一种实验仪器以其结构相对简单、形象直观、构件参数易于改变和价格低廉等优点,已经广泛运用于教学。环形倒立摆和平面倒立摆尚处于实验室研究阶段。平面倒立摆的基座可以在二维平面内运动,基础运动具有两个自由度。由于系统变量的增多、阶次的增高和基座运动、控制的耦合特性,与基座只有一个自由度的直线型或环形倒立摆相比其控制更具有挑战性。本文以固高GPIP2002型平面运动倒立摆为研究对象,采用拉格朗日方程建立了平面一级、二级倒立摆的数学模型,通过将其在平衡位置附近进行泰勒级数展开并线性化,得到了系统在两个正交方向解耦的线性化模型。基于所建立的倒立摆线性化模型,根据最优控制理论,设计了平面一级、二级倒立摆的线性二次最优控制器,同时实现了摆杆平衡控制和基座运动的定位控制,通过仿真结果说明了线性二级最优控制在平面倒立摆控制中的有效性。模糊滑模控制是典型的智能变结构控制方法,它综合了模糊控制不依赖于系统精确模型的优点和滑模控制的完全鲁棒性。自适应滑模模糊控制则是将自适应思想融入模糊滑模控制,通过适应性地调整滑模函数的斜率以提高控制性能。本文在平面一、二级倒立摆的X、Y方向分别设计了自适应滑模模糊控制算法,通过仿真实现了摆杆平衡情况下的小车定位控制。根据设计的线性二次最优控制和自适应滑模模糊控制算法进行了平面一级倒立摆实验,实现了摆杆平衡控制和基座小车的定位控制,并进行了基座小车的圆轨迹跟踪实验。实验结果验证了所建立的平面倒立摆数学模型的正确性和所设计的两类控制算法在平面倒立摆控制中的有效性。更多还原

【Abstract】 The inverted pendulum is characterized as a typical nonlinear, high order, unstable and underactuated system. Research on precise control of the inverted pendulum has great value for control problems of complicated plant in industrial production process, as a result, the inverted pendulum simulation and physical experiments are representative project for verifying a certain control theory or approach in the fields of control science and technology. At present, linear inverted pendulum has found wide use in instruction due to the advantages of simplicity, intuition, easy to change the components parameters and low price. Rotary and planar inverted pendulums remain the research stage so far.The base cart of a planar inverted pendulum moves in the 2D plane, i.e. the base motion has two degrees-of-freedom (DOF). As a result of the number of system parameters increase and coupling characteristic of motion and control, the control problem of the planar inverted pendulum is more challenging compared with linear or rotary inverted pendulums, which base has only one DOF.The GPIP2002 planar inverted pendulum is considered as a plant in this paper. The mathematical models of the planar single and double inverted pendulums are established by using the Lagrange equations. Taloy series expansion of the mathematical models around the balance postion and linearation result in the decoupled linear models in two orthogonal directions of the planar single and double inverted pendulums respectively.Based on optimal control theory, linear quadratic optimal regulator (LQR) is designed for linear model of the inverted pendulum. Balancing and positioning control goals are achived at the same time, furthermore, simulation results shows the validity of the linear quadratic optimal control strategy in the control of planar inverted pendulums.A typical intelligent variable structure control approach, fuzzy sliding mode control (FSMC) combines robustness of sliding mode (SMC) control and independence of system model of fuzzy logical control (FLC). Adaptive FSMC incorporates the adaption into SMC and improves the control performance by adjusting the slopes of the sliding mode functions adptively. An adaptive sliding mode fuzzy controller is designed in each direction of the planar inverted pendulum, and positing control is realized under the condition of pole balace.更多还原