【作者】 顾宇杰；

【导师】 涂源钊；

【作者基本信息】 四川大学 ， 控制理论与控制工程， 2004， 硕士

【摘要】 H₂控制和H_∞控制在现代控制理论中占有极其重要的地位，在众多领域内受到了广泛的关注，并取得了不少研究成果。上世纪80年代末期提出的H₂／H_∞混合控制问题作为一种多目标控制问题，则是将H₂性能设计与H_∞性能设计相结合，使整个系统既可以获得优良的调节性能，又可以保持鲁棒稳定性。而变结构控制则以其在滑动模态上对参数摄动和外干扰在一定条件下的完全鲁棒性而受到研究者的重视，研究也覆盖了飞行器控制、机器人控制、电机与电力系统控制等诸多领域。 本文结合了H₂／H_∞混合优化的方法和变结构控制的方法，利用变结构控制的不变性，使得在滑动模态面上系统在鲁棒性能和动态、稳态性能之间达到混合优化，从而提出了基于H₂／H_∞混合优化的变结构控制的概念。本文采用运动分解法和干扰重定义法描述了系统在滑模面上的运动方程，通过定义辅助被控信号得到广义被控对象，采用基于状态反馈的凸优化方法求解滑模面上的H₂／H_∞混合优化控制器从而确定终端滑模面的表达式，最后给出保证滑模可达的控制律并给予稳定性证明。最后，针对一类具有不满足匹配条件干扰的线性不确定系统进行了仿真研究，结果证明了所提方法的有效性。动态、稳态性能较好，又不失鲁棒性，本文提出的方法在工程领域应该有较好的应用前景。更多还原

【Abstract】 H2 control and H_∞ control occupy the most significant status inthe modern control theory. They have been received comprehensive attentions in many fields, and some research results have been acquired. As a kind of multitarget control problems, mixed H2/H_∞ control problempresented in the late eighties of the 20th century integrates H2 performance design with H_∞’ s, then the whole system can not only attainan excellent regulative performance, but also keep the robust stability. On the other hand, variable structure control (VSC) got researchers’ attentions because of its absolute robustness for the parameter uncertainty and the exterior disturbances on the sliding mode. The research fields of VSC also embrace aerocraft control robot control electric & electrician system control, etc.This paper integrated mixed H2/H_∞ optimization with VSC, makinguse of VSC invariability, so that the system could achieve mixed optimization between robust performance and the dynamic and stable performance in the sliding mode, then the concept of variable structure control based on mixed H2/H_∞ optimization was presented. Afterintroducing the methods of states transformation and the disturbance redefinition, this paper described the system’ s dynamics equation on the sliding mode. By means of defining the assistant controlled signals, this paper gained the generalized plant, and then made certain the terminal sliding mode’ s expression through solving the mixed H2/H_∞optimization controller by way of using the convex approach based on state feedback. Last, the control law, which ensured the existence of sliding mode, was given and the stability was proved. The simulation results for a class of linear uncertainty systems with mismatching disturbance show the effective of this method. Not only have good dynamic and stable performance but also without loss robustness, the approach proposed in this paper should have preferable application foreground in the engineering fields.更多还原