2011北交大自动控制期中考试试题及答案

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

总分 100 课程名称：自动控制理论 班级： 出题人：

题 号 满 分 得 分 签 字 一 20 二 20 三 20 四 20 五 20 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) Thermometer ui - + R iug Voltage - + + uf Δu amplifier - K1 θo Reversible motor Power amplifier K2 - Reducer Heater ~220V Voltage regulator

Figure 1.

答：1）和2）的解答如图所示。（给分标准：画错两个环节扣一分，包括节点和比较节点和6个方框。2）中8个量，错一个扣1分。）

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300oC），经过热电偶检测电炉内实际的炉温（假定是285 oC）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Δu，此时Δu〉0，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300oC时，电炉内电加热器停止加热。反之亦然。（给分标准：错两个环节叙述扣一分。）

- 1 -

Controller Error InputPower Δu Voltage ui ug amplifier amplifier Ri K1 K2 Desired Temperature θdoC uf Feedback Feedback Temperature variable θfoC

Actuator Reversible motor Reducer Plant Voltage regulator Heater Output Actual Temperature θ0oC Thermometer Sensor - 2 -

2. 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 R?1M?,C?0.1?F,r(t)?5sin5t (20 points)

Figure 2

答：?(s)?C?s?11?222?R?s?sCR?sCR?10.01s2?0.1s?1(6 points)

?(j?)?110.1????arctg?0.01?2?0.1?j?11?0.01?2(1?0.01?2)2?(0.1?)2

424??arctg??33.7?31313

20(10 points) sin?5t?33.7??,?t?0?13

20(4 points) sin?5t?33.7??,?t?0?13

?(j5)??css?t???ess?t??r?t??css?t??5sin5t?3. Consider the system shown in figure 3,(20points)

Figure 3

- 3 -

1) Write the open-loop transfer function of the system;(5 points) 2) Write the closed-loop transfer function of the transfer;（5points）

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 τ（5 points） 4) If

r(t)?1.5t(?/s), determine the steady-state error ess.(5 points)

1010Ks(s?1)?答：（1） G(s)?K 5points

10?ss(s?10??1)1?s(s?1)（2）

?n2G(s)10K?(s)??2?21?G(s)s?(10??1)s?10Ks?2??ns??n2???0.5???3.63 ?n????0.263 5points

??o?e???1??2?16.3oo?o?（3）由 ? 联立解出

tp??1??n1??2?2由（2） 10K??n?3.632?13.18，得出 K?1.318。5points

（4）

Kv?limsG(s)?s?010K13.18??3.63 3points

10??110?0.263?1

ess?A1.5??0.413 5points Kv3.634. 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 -