自控2011期中考试试题及答案.doc

学院 班级 学号 姓名 -装 -订-线- 北京交通大学 2011 -2012学年 第一学期考试试题课程名称：自动控制理论 班级： 出题人： 题 号一二三四五总分满 分2020202020100得 分签 字1. The schematic diagram of a temperature control system of an electric furnace is shown in figure 1. Applying basic concepts of control theory, (20 points)1) block the diagram of the temperature control system. (6 points)2) Point out input, plant, feedback variable, output, error, controller(s), actuator(s), and sensor of the system. Please show them on the diagram. (6 points)3) Tell how the temperature control system work. (8 points) HeaterVoltage amplifierK1220VVoltage regulatoruguf+- -+-ReducerReversible motoruiThermometerRiuPower amplifierK2Figure 1.答：1）和2）的解答如图所示。3) 假设电炉炉温低于给定的炉温，给定电压ui，经过Ri分压获得给定电压ug，其对应希望的电炉炉温（假定是300C），经过热电偶检测电炉内实际的炉温（假定是285 C）并变换为电压值，反馈到输入端与给定电压ug比较获得炉温对应电压的偏差u，此时u0，经过电压放大和功率放大，得到使可逆电机旋转的电压ua，经过减速装置驱动调压器触头使其向上滑动，提高电炉内电加热器两端的电压，从而使炉内温度升高，当炉内温度达到300C时，电炉内电加热器停止加热。反之亦然。- 7 -ErrorActuatorControllerPlantuInputPower amplifierK2Voltage amplifierK1OutputHeaterVoltage regulatorReducerReversible motoruguiRiFeedbackTemperaturefCFeedback variableDesiredTemperaturedCSensorThermometerActualTemperature0Cuf2. Obtain the transfer function C(s)/R(s) of the op-amp circuit shown in figure 2, and determine the output steady-state value css(t) and the steady-state error ess(t). Assume that (20 points)Figure 2答： (6 points) (10 points) (4 points)3. Consider the system shown in figure 3,(20points) Figure 31) Write the open-loop transfer function of the system;(5 points) 2) Write the closed-loop transfer function of the transfer;（5 points）3) If the Maximum overshoot (Mp) of the system is 16.3%,Peak time (tp) is 1s,Determine the gain K and velocity-feedback constant （5 points）4) If , determine the steady-state error ess.(5 points)答：（1） （2） （3）由 联立解出 由（2） ，得出 。（4） 4. Consider the system shown in figure 4, determine the range of K for stability. (20 points)Figure 4答：由结构图，系统开环传递函数为： (4分) (3分)Routh： S5 1 4 2K S4 1 4K K S3 K S2 K S S0 K 使系统稳定的K值范围是： 。(13分)5. Consider the system which open-loop transfer function is, (20 points)1) Sketch the root loci for the system. (5 points)2) Determine the range of gain K corresponding to underdamped system for closedloop system. (5 points)3) Giving K=1, determine the closedloop poles of the system, and calculate the damping ration , maximum overshoot Mp and settling time ts. (5 points)4) Giving K=1, design a compensator to make damping ration =0.5, Calculate the maximum overshoot Mp and settling time ts of compensated system. Determine what kind of the compensator is used by you. (5 points)答：1)如图.2) 计算分离点.N(s)D(s)-N(s)D(s)=0(s+2)(2s+1)-(s*s+s)=0s*s+4s+2=0s12=(-,-)或者(-3.41, -0.59)闭环特征方程: s*s+