现代控制理论考试卷及答案(2).doc

Leaders: provincial agricultural work Conference held in XX, which is our concern and love, will greatly promote XX agricultural and rural economic development. First of all, I am representing XX municipal party Committee and Government, extend a warm welcome to the attending leaders! XX has been given support and assistance to the province of agriculture, provincial agricultural Office, and expressed heartfelt thanks to all the friends! below, I XX with a brief report. A basic XX of XX municipality located (cities, omitted). One is the superior ecological environment. XX blue, clear, green, water, air, 70% of land in the territory is covered with forests, grasslands, wetlands and waters, built 7 thousands of square kilometers of the total area of nature reserves. Within major industrial pollution sources, air quality at the national level, national levels, water quality, soil pollution, pure land reputation, was heralded by the United Nations environmental officials the most suitable place for human survival. Second, the enrichment of natural resources. A total area of more than 5 million mu of arable land (which owned 1.53 million acres), the annual grain output of more than 2 million tons and is located in the internationally recognized gold cattle, there should be more than 400,000 acres of grazing grassland, developing animal husbandry conditions; a total area of 4.1 million acres of forest land, rich in precious wood such as pine, ash, yellow pineapple, standing timber volume of more than 26 million cubic meters. Forest Xia has hundreds of species precious wildlife, more than 200 more species precious herbs, annual Super thousand tons of wild mushroom and reserves Super 100,000 tons of mountain dish; nectar plant throughout, can bee 100,000 group, is China bee of Xiang, and national Northeast black bee reserves and important of bee products production base; can using water 2.5 billion cubic metres, should be fishing water 460,000 acres, rich big salmon, and three spent five Luo, North cold water specialty fish; found and proved reserves of mineral resources has 36 species. Third, geopolitical advantages. XX open midpoint is located in the eastern part of the province along the border, 264 km long border, with national road passenger and freight transport port, built on the border between China and Russia has the largest permanent boundary River Bridge, running at full capacity the annual cargo capacity of up to 2.6 million tons. Russia two (HABA and Marina), two cities (Iman and Lesozavodsk) is the Russian Far East in developed areas. Lesozavodsk is only 8 km from XX port corresponding to the port of markovo, Lu Rinuo station is one of three railway marshalling yards in the far East, the far East-Siberian railway and a parallel road runs through the pass. By rail and road, to the North by HABA capital Khabarovsk, the Russian hinterland, radiation in the CIS and Eastern European countries; to the South through the port of Vladivostok and the nahuo card on the sea, to reach South Korea, Japan and other Pacific Rim countries and regions. Four is rich in tourism resources. XX tourist resources types, many attractions, beautiful scenery of the Sino-Russian border-river-wusuli River, a famous treasure island, known as the Oriental Maginot line of the Japanese invading army Tiger underground fortress ruins, General Chi 西北工业大学考试试题（卷）2008 2009 学年第 2 学期开课学院 自动化学院 课程 现代控制理论 学时 32 一、 简答题（对或错，10分）（1） 描述系统的状态方程不是唯一的。（2） 用独立变量描述的系统状态向量的维数不是唯一的。（3） 对单输入单输出系统，如果存在零极点对消，则系统一定不可控或者不可观测。（4） 对多输入多数出系统，如果存在零极点对消，则系统一定不可控。（5） 李雅普诺夫直接法的四个判定定理中所述的条件都是充分条件。（6） 李雅普诺夫函数是正定函数，李雅普诺夫稳定性是关于系统平衡状态的稳定性。（7） 线性定常系统经过非奇异线性变换后，系统的可控性不变。（8） 用状态反馈进行系统极点配置可能会改变系统的可观测性。（9） 通过全维状态观测器引入状态反馈来任意配置系统的闭环极点时，要求系统必须同时可控和可观测。（10） 对一个线性定常的单输入单输出5阶系统，假定系统可控可观测，通过设计输出至输入的反馈矩阵H的参数能任意配置系统的闭环极点。二、 试求下述系统的状态转移矩阵和系统状态方程的解x1(t)和x2(t)。（15分） 三、 设系统的传递函数为 。试用状态反馈方法，将闭环极点配置在2，1j，1j处，并写出闭环系统的动态方程和传递函数。（15分）四、 已知系统传递函数，试求系统可观标准型和对角标准型，并画出系统可观标准型的状态变量图。（15分）五、 已知系统的动态方程为，试确定a，b值，使系统完全可控、完全可观。（15分）六、 确定下述系统的平衡状态，并用李雅普诺夫稳定性理论判别其稳定性。（15分）七、以下两题任选一题（15分）(1) 证明状态转移矩阵性质：。(2) 证明：非奇异性变换后，线性定常系统S（A,B,C,D）的可观测性不变。拉氏变换H(s)时间函数拉氏变换H(s)时间函数教务处印制 共 2页第2页2009年现代控制理论试卷A评分标准及答案第一题（10分，每个小题答对1分，答错0分）（1）对 （2）错 （3）对 （4）错 （5）对 （6）对 （7）对 （8）对 （9）对 （10）错第二题（15分）（1）（7分）：公式正确3分，计算过程及结果正确4分（2） 状态方程有两种解法（8分）：公式正确4分，计算过程及结果正确4分第三题（15分，答案不唯一，这里仅给出可控标准型的结果）（1） 系统动态方程（3分）（2） 状态反馈矩阵（5分，公式正确3分） 由闭环极点和闭环系统特征多项式有比较，。（3）闭环系统的动态方程（3分）：（4）闭环系统的传递函数（4分）：第四题（15分）已知系统传递函数，试求系统可观标准型和对角标准型，并画出相应的系统状态图。答：（1）可观标准型及状态图（5分）（2）系统可观测标准型状态变量图如下：（5分）（3）对角标准型（5分，答案不唯一，两种常见形式如下）第五题（15分）已知，试确定a，b值，使系统完全可控、完全可观。可控部分正确7分：公式正确4分，可控性矩阵计算正确2分，a值正确1分；可观部分正确7分：公式正确4分，可观性矩阵计算正确2分，b值正确1分；总结论正确1分。第六题（15分）（1）（5分） 原点是系统唯一的平衡状态（2）（6分） （答案不唯一，仅供参考）（3）（4分）K0 时系统大范围一致渐近稳定；K=0时 系统是李雅普诺夫意义下稳定的(或系统一致稳定)；K0时 系统不稳定。写对平衡状态表达式2分；求出原点是系统的平衡状态2分；说明唯一性1分。写对李雅普诺夫函数3分；求导正确3分；正确分析出上述（3）中的3种情况分别为2分、1分、1分，其中K0时未说明大范围和一致性稳定各扣0.5分。第七题（15分，（1）和（2）小题任选一题）（1）小题：证明过程引用的公式正确7分，证明过程严谨正确8分。证明：由，有 所以证毕。(2)小题：写对变换后的可观测性矩阵8分，仅写对非奇异变换公式4分；证明过程正确严谨7分。证明：怒发冲冠凭栏处，潇潇两歇，抬眼望仰天长啸，壮怀激烈，三十功名尘与土，八千里路云和月，莫等闲白了少年头，空悲切，靖廉耻，犹末雪，臣子恨，何时灭!驾长车，塌破贺兰山缺。