1/27作业第二章：2-6某水槽如题图2-1所示。其中A1为槽的截面积，R1、R2均为线性水阻，Qi为流入量，Q1和Q2为流出量要求：(1)写出以水位h1为输出量，Qi为输入量的对象动态方程；(2)写出对象的传递函数G(s)并指出其增益K和时间常数T的数值。图2-1解：1）平衡状态：02010QQQi2）当非平衡时：iiiQQQ0；1011QQQ；2022QQQ质量守恒：211QQQdthdAi对应每个阀门，线性水阻：11RhQ；22RhQ动态方程：iQRhRhdthdA2113)传递函数：)()()11(211sQsHRRSAi1)11(1)()()(211TsKRRSAsQsHsGi这里：21121212111111RRATRRRRRRK；R2h1QiQ1R1A1Q22/272-7建立三容体系统h3与控制量u之间的动态方程和传递数,见题图2-2。h2UR1R2Q2Q1Qih1h3Q3R3解：如图为三个单链单容对像模型。被控参考△h3的动态方程：3233QQdthdc；22RhQ；33RhQ；2122QQdthdc；11RhQ111QQdthdciuKQi得多容体动态方程：uKRhdthdcRcRcRdthdccRRccRRccRRdthdcccRRR333332211232313132322121333321321)()(传递函数：322133)()()(asasasKsUsHsG；这里：32132133213213321321332211232132131313232212111;cccRRRkRKcccRRRacccRRRcRcRcRacccRRRccRRccRRccRRa题图2-23/272-8已知题图2-3中气罐的容积为V，入口处气体压力，P1和气罐内气体温度T均为常数。假设罐内气体密度在压力变化不大的情况下，可视为常数，并等于入口处气体的密度；R1在进气量Q1变化不大时可近似看作线性气阻。求以用气量Q2为输入量、气罐压力P为输出量对象的动态方程。解：根据题意：假设：1)ρ在P变化不大时为常数2)R1近似线性气阻；3）气罐温度不变，压力的变化是进出流量的变化引起；平衡时：211QQpp非平衡时：21GQQdtdC气容：容器内气体变化量量容器内气体重量的变化CdtdGdtpdCpddGC111)(1RppPPRG动态方程：211pQRpdtdC；2-10有一复杂液位对象，其液位阶跃响应实验结果为:t／S01020406080100140180250300400500600h／Cm000.20.82.03.65.48.8l1.814.416.618.419.219.6(1)画出液位的阶跃响应曲线；TR2P、V、ρR1Q1Q2题图2-34/27(2)若该对象用带纯延迟的一阶惯性环节近似，试用作图法确定纯延迟时间τ和时间常数Ｔ。(3)定出该对象，增益K和响应速度ε设阶跃扰动量△μ=20%。解：1）画出液位动态曲线：20cmy0PBTτAt2)切线近似解：τ=40sT=180-40=140(s)1002.020)0()(uyyKsseseTsKsG4011401001)(3）采用两点法：取【t1,y*(t1)】,【t2,y*(t2)】无量纲化：)(201)()(*tyytyy则：TtTtTtty)exp(10)(*取两点：)exp(18.0)exp(14.021TtTt解得：TtTt61.151.0211.151.061.11.12112ttttT5/272-12知矩阵脉冲宽度为1s，幅值为0.3，测得某对象的脉冲响应曲线数据如下表：t(s)0123456789y03.757.209.009.359.158.407.657.056.45t(s)10111213141516171819y5.855.104.954.504.053.603.303.002.702.40t(s)20212223242526272829y2.252.101.951.801.651.501.351.201.050.90t(s)30313233343536373839y0.750.600.450.400.360.300.200.150.100.08试求阶跃响应曲线。解：设脉冲响应y(t)，阶跃输入R(t);1)列关系式：122111()()()()()()()()utututututtutututt1211()()()()()ytytytytytt即11()()()ytytytt从题意知：△t=1秒一拍;可列表格：2）表格计算：t(s)0123456789y03.757.209.009.359.158.407.657.056.45y103.7510.9519.9529.338.4546.8554.5061.5568.00t(s)10111213141516171819y5.855.104.954.504.053.603.303.002.702.40y173.8578.9583.9088.4092.0596.0599.35102.35105.05107.45t(s)20212223242526272829y2.252.101.951.801.651.501.351.201.050.90109.70111.8113.75115.55117.20118.70120.05121.25122.30123.20t(s)30313233343536373839y0.750.600.450.400.360.300.200.150.100.08typ0tu0tt00t0tt0ut0)(ty)(1ty)(1tu)(1ttu)(1tty6/27y1123.20124.55125.00175.40175.76176.06176.26176.41176.51176.593)做图：2-14已知被控对象的单位阶跃响应曲线试验数据如下表所示：t(s)0153045607590105120135y00.020.0450.0650.0900.1350.1750.2330.2850.330t(s)150165180195210225240255270285y0.3790.4300.4850.5400.5950.6500.7100.7800.8300.885t(s)300315330340360375y0.9510.9800.9980.9991.001.000分别用切...
