【作者】 乔军丽；

【导师】 贾新春；

【作者基本信息】 山西大学 ， 应用数学， 2006， 硕士

【摘要】 众所周知,在实际应用的过程中,执行器的通道经常会出现一些故障,因此,对于所研究的控制系统来说,可靠性就是一个非常重要的要求,即所设计的控制器在可以容忍执行器故障的同时,还要保证系统的稳定性和一些基本的性能要求。也就是说,无论在系统正常运行还是执行器发生故障的情况下,都可以保证系统的稳定性和对控制系统的性能要求。因此,研究可靠控制理论无论在理论上还是实际应用中都是非常有意义的。 本文的主要工作如下: (1)介绍了可靠控制的理论意义和实用价值,并概括了国内外研究现状。 (2)针对带有执行器故障的非线性离散时间系统,本文给出了其可靠的区域保性能模糊控制器设计方法。用T-S模糊模型来表示该非线性系统,文中采用了一种更实际的执行器故障模型,可以用理想执行器的函数来表示,它体现出执行器的平均执行程度和故障程度。这种故障模型使用范围更广,包含了执行器正常、部分故障、完全故障等情形。当初始状态已知时,以线性矩阵不等式的形式给出了可靠保性能模糊控制器存在的充分判据以及控制器的参数化设计方法。所设计的控制器不仅保证闭环模糊系统是渐近稳定的,而且给出了系统的二次性能函数的可保性能值。当初始状态为不确定,但属于一个有界的闭区域时,针对两类常见的有界闭区域:凸包区域和椭圆区域,分别给出了系统的可靠区域可保性能的有效计算公式。为了降低系统的区域可保性能的保守性,又提出了最优可靠的区域可保性能控制问题,即最小化可靠区域可保性能的上界,这一最小化过程通过LMI的优化方法来实现,我们可以用任何凸优化算法来解决这一问题。最后,通过一个数值例子说明了本文所给设计方法的有效性。 (3)总结本文的研究成果,提出今后的研究方向。更多还原

【Abstract】 As is well known, in practical applications, since failures of actuator components often occur in real world, an important reliability requirement for the design of control systems is to guarantee the stability and basic performance of the plant by the designed controller which can tolerate actuator failures. That is, the stability and performance requirements for the closed-loop control systems can be ensured, not only when the systems is operating properly, but also in the presence of actuator failures. So it is significant to research reliable control problem in both theory and practical applications.The main results in the thesis are as follows.(1) The significance of reliable control issue is introduced, both in theory and in applications. And the related development abroad and at home is retrospected briefly.(2) The design method of a reliable fuzzy controller with domain guaranteed cost for nonlinear discrete-time systems with actuator failures is proposed. The Takagi and Sugeno (T-S) fuzzy model is employed to represent the nonlinear systems. A more general failure model is adopted for such actuator failures, which is a function of ideal actuator and consists of the average factor and the failure degree of such actuator. This failure model is more practical, which includes the ideal actuator, the partial failure case and the outage model, respectively. When the initial state of such systems is known, a sufficient criterion for the existence of the reliable fuzzy controller with domain guaranteed cost is derived in the linear matrix inequality (LMI) form, and a parameterized design procedure of such controllers is presented. The designed fuzzy controller not only guarantees the stability of the closed-loop fuzzy system, but also provides a guaranteed cost in the sense of quadratic cost function. Moreover, when the initial state of such systems is unknown, but belongs to a known bounded closed domain (called initial statedomain), polygon domain or ellipsoid domain are considered here, some formulas for the reliable domain guaranteed costs are presented. To decrease the conservatism of the value of the reliable domain guaranteed cost, a design problem of the optimal reliable domain guaranteed cost fuzzy controller is addressed in the sense of minimizing a bound on the reliable domain guaranteed cost via an LMI optimization procedure, which can be solved efficiently using any convex optimization algorithms. A numeric example is given to illustrate the effectiveness of the proposed design methods.(3) The main results of the thesis are concluded, and the subjects of future investigation are proposed.更多还原