【作者】 宗广灯；

【导师】 武玉强；

【作者基本信息】 曲阜师范大学 ， 运筹学与控制论， 2002， 硕士

【摘要】 本文主要利用Backstepping方法与变结构控制方法，研究了有未建模动态及不确定非线性项的线性时不变系统，以及输入通道带有干扰的线性时变系统的控制器设计问题．同时，本文还考虑了一类动态不确定系统的变结构鲁棒观测器设计问题．主要内容有三部分： 第一部分研究已建模部分为最小相位，但系统线性部分参数未知的被控对象．苏联学者Emelyanov．S．V(1998)通过采用降阶观测器，研究了带有精确线性建模的不确定系统的输出反馈问题，并设计了鲁棒变结构控制器．Yuqiang Wu和Xinghuo Yu(1998)针对相同的控制模型但假设系统线性建模部分参数未知，利用输入输出信号给出了一种新的鲁棒自适应变结构控制器设计策略．其不足之处是，当系统相对阶大于2时，控制器的设计方案将会极为复杂． 众所周知，Backstepping方法彻底解决了参数严格反馈结构非线性系统的控制器设计问题．针对一大类线性时不变系统，线性时变系统及非线性系统，许多学者利用Backstpping方法提出了一系列新的非线性控制器设计方案．考虑了其输出跟踪问题及调节问题．另外，有些学者将Backstpping方法与变结构控制策略相结合，给出了一类新的全局稳定控制器设计方案． 本文针对一类动态不确定系统，基于Backstepping设计策略，结合变结构控制与非线性Damping方法，充分考虑了系统的未建模动态与输入输出通道有干扰的情况．仅利用输入输出可测信号给出了一种新的全 局稳定的非线性控制器设计方案，保证了系统的所有信号有界．通过适当 选择控制器和中间控制函数的参数，系统输出可以被驱动到原点的任意小 0 邻域．本文结果与现有的文献相比，优点在于：1）控制器的设计思路简 单，易实现；2）系统线性建模部分可以具有任意的相对阶而不增加控制 器设计的复杂性；3）系统关于不确定项的假设条件可以减弱．本章仿真 验证了本文的结论． 第二部分考虑了一类传递函数描述的线性时变不确定系统，研究了其 输出跟踪问题．对于最小相位线性连续系，Narendra（1978 1980）提出了 全局稳定的模型参考自适应控制策略，其控制方案成为设计鲁棒自适应控 制器的一般方法．在其设计基础上，许多抑制未建模动态和外部干扰的鲁 棒自适应控制方法被提出．在选取控制系统结构方面，Morse＊990，1992） 等人提出了一种参数自适应控制的统一方法．并且证明了对于线性被控 对象，一个适当设计的确定性等价控制可导致一个可调的闭环参数化系 统，对于可调的系统，闭环参数化系统可被稳定化．基于可调性理论，＠M盯％＊992）提出了一种切换的参数自适应控制，并证明当闭环参数系统 可调时整个系统全局稳定并且跟踪误差趋于零。为了保证可调性，被控 对象必须是最小相位的，对于线性时变系统，Tskalis与Ioannou＊992， 1989）给出了模型参考自适应控制器的设计方法．以上研究均是基于线 性控制结构，当系统相对阶大于1时，控制器设计和闭环系统的稳定性 分析复杂而困难。 BackstePPing方法对于解决参数严格反馈结构的非线性系统控制器 设计问题，给出了一种强有力的工具．Xinghuo Yu和Yuqiang Wu（1998） 针对一类线性时变系统的输出跟踪问题，基于Back飞tepping设计机制， 将带有非线性DallPIPg项的设计方法与变结构控制方法相结合，给出了 一种新的非线性控制器设计方法．本文基于同样的研究模型，并充分考 虑了系统输入通道的干扰因素，不论被控对象己建模部分的相对阶等于巴1还是大于乙通过选择合适的控制器设计参数，跟踪误差可以趋于原点 的任意一个小邻域，且闭环系统的所有信号一致有界，保证了系统的全 局稳定性．最后通过实例仿真验证了本文结果的正确性． 一 第三部分针对一类带有动态不确定项和干扰项的不确定系统，给出 了其变结构鲁棒观测器的设计．由于实际控制系统的设计中系统状态一 ． 般并非可知，从而迫使我们利用系统的可测量（输入输出）去构造估计 状态来设计控制器．本文所设计的观测器，充分考虑了系统不确定因素 满足匹配条件和不满足匹配条件但具有小的慢变脉冲干扰的情况，保证 了观测误差一致最终有界．实例仿真验证了本文结果的正确性．更多还原

【Abstract】 In this dissertation, a kind of linear time invariant systems with unmodeled dynamics and nonlinear uncertainties are considered by using backstepping approach and variable structure control algorithm. Also another kind of linear time varying systems are studied based on the same method. Meanwhile, the problem of variable structure robust observer design for a kind of uncertain systems is also considered in this paper. The main contents include three parts:In the first part, the minimum phase systems with unmodeled dynamics and disturbances in the input-output channel are studied . Emelyanov. S. V (1998) studied the output feedback problem for the uncertain systems with exact linear model and constructed robust variable structure observer using descending-order observer method. For the same model but assuming that the parameters of the linear parts unknown, Wu yuqiang and Xinghuo Yu(1998) proposed a kind of new robust adaptive variable structure controller design algorithm. Its defect is the algorithm becomes very complex when the relative degree exceeds two.As we all know, backstepping approach completely solves the controller design problem of parametric-strict-feedback systems. For a large scale of linear time- invariant systems, linear time-varying systems and nonlinear systems, many scholars proposed a series of new schemes. In addition, there are many people presented a kind of new control design scheme by the combination of backstepping approach and softied-variable control scheme.For a kind of dynamic uncertain systems, basing on backstepping scheme and combining variable structure and nonlinear damping approach, this paper sufficiently considers unmodeled dynamics and disturbances in the input-output channel. And presents a kind of new globally stabilizing nonlinear controller design scheme only using input and output signals, which guarantees the boundness of all the signals in the closed system. The output can be made sufficiently small by properly choosing the controller parameters and the intermediate control functions. The controller is easy to be carried out, and the assumptions can be weaker compared to other works.The second part deals with the problem of output tracking for a kind of linear time-varying uncertain systems described by transfer functions. For the continuous minimum phase system, Narendra (1978, 1980) presented globally stabilized model reference adaptive control scheme, which later became a kind of generic design method of robust adaptive control. On the base of Narendra’ s work, in order to suppress the unmodeled dynamics and external disturbances, many robust adaptive control schemes are proposed. In choosing control structures, Morse (1990, 1992) proposed a kind of unifying method of theparameter adaptive control. For the linear plants, he also proved that a designed well equivalent controller could lead to a tunable closed loop parametric system that can be stabilized. Basing on the tuning theory, Morse (1992) proposed a kind of switching parametric adaptive control scheme and proved that a tunable closed loop system can be globally stabilized. What’ s more, the tracking error can be driven to zero. In addition, Morse proved that tenable system must be a minimum phase system. For linear time varying systems, Tskalis and loannou (1992,1989) proposed MRAC design method. However all these design schemes based on the linear control structure. When the relative degree exceeds one, the controller’ s design and the stability analysis of the closed system becomes very difficult.Using the cogent validity of backstepping’ s solving parametric-strict-feedback nonlinear systems, Xinghuo Yu and Wu Yuqiang (1998) solved the output-tracking problem of a kind of linear time varying system by combining nonlinear damping method and variable structure scheme. In this dissertation, we sufficiently consider the effect of disturbances in the input channel basing on the same model. By the proper choices of the controller parameters and the intermediate control fu更多还原