1、Four short words sum up what has lifted most successful individuals above the crowd: a little bit more.-author-dateProcess-Control-2011-05-11-A-with-Solution(Basic-theory)重庆大学计算机软件技术基础(理)课程试题 (A 卷)命题人： 组题人： 审题人： 命题时间： 教务处制学院 专业、班 年级 学号 姓名 公平竞争、诚实守信、严肃考纪、拒绝作弊封线密重庆大学Process Control课程试卷20092010学年 第一学期开
2、课学院：自动化学院 课程号：17001825考试日期：2009-05-18 考试时间：120分钟题 号一二三四五六七八九十总 分得 分一、 Basic Concepts (30 points） You are designing controls for the CSTR in the figure. What are some of the disturbances that the control system should compensate? (4 points）. Feed composition (Yes or No)Yes,(the control system should
3、compensate for changes in feed composition. Corrective actions could affect the temperature or residence time in the reactor.) Lack of perfect mixing (Yes or No)No, (lack of perfect mixing will usually lead to very irregular behavior that would be difficult to control. The tank should have a properl
4、y designed stirrer - which can be designed by a chemical engineer who knows about fluid mechanics!) Error in the level sensor (Yes or No)Yes, (small errors in the level affect the conversion. These errors could be compensated by changes to the temperature.Note that large errors in level could lead t
5、o overflowing the vessel and hazards to people.) Feed temperature (Yes or No)Yes,(changes in feed temperature affect the conversion. These disturbances can be compensated by changes to heating or cooling to the tank.) Poor understanding of reaction engineering by the engineers (Yes or No)No, (contro
6、l does not compensate for ignorance, only for lack of exact information. Every graduate engineer understands the basics of reaction engineering!) The tank level control system is analytically modeled by a nonlinear function and approximated by a Taylor expansion in linear fashion. The figure shows t
7、hat level response for a large step input. What can you describe for the analytical model and the Taylor linearized model（3 points） From the figure, when in the region from the step change to 1.5 hours, the linearization serves as a very good representation of the physical system. After approximatel
8、y 2.5, the linearized curve indicates a negative level hours. This certainly defies the physical properties of a tank.At this point, the linearized model is no longer able to predict the behavior. the gain and time constant for the overall dynamic model of a series of first order systems can be calc
9、ulated in terms of following equations (3 points). The overall gain Koverall = K1 K2Kn (true or false)True, (this equation can derived from standard series capacity process) The overall time constant toverall = t1+t2+tn (true or false)False, (the systems with larger numbers of first order systems ex
10、perience some degree of apparent dead time, thus the overall time constant is usually estimated by toverall = t63% (t1+td1)+(t2+td2)+(tn +tdn) using the Sigmoidal shaped curve of a step response)4. Find two methods to reject the reset windup in integral action (3 points). The Jacketing rule that sim
11、ple limits the controller output in the range of the actuator (e.g., valve) Velocity form of PID controller that only uses the current error for the current calculation of controller output.5. In common chemical process, we usually take the sample time Dt according to the process time constant t as
12、follow (2 points) Dt 10t Dt 0.1t (correct choice) Dt 0.1t Dt 10t6. To obtain the transfer functions of a process, you can either use mathematical modelling that follows the process mass balance, or data modelling that is obtained from system identification. (3 points)7. When evaluate the control per
13、formance from the view of error, we can certainly say that the minimum error results in the best performance (2 points)(True or False) False, (because the response time and the stability of the system should also be considered) 8. Give some tuning relations that are of aggressive, moderate and conse
14、rvative when you tune the controllers based on PRC (3 points). a. Cohn-Coon is of aggressive tuning relation b. Ziegler-Nichols is of moderate tuning relation c. Ciancone-Marlin is of conservative tuning relation 9. Describe your procedure considerations when you design a control system for a proces
15、s (5 points) a. investigate the background of the process, b. select the control instruments and process instruments for the plantc. model the process using either mathematic or empirical approaches d. select and tune the controller parameter based on the viewpoints of error, stability and time resp
16、onse (e.g., empirical tuning relations, step and impulse and sinusoidal response of the system， model error, sample time) e. reconsider the facts that impact the performance of the control system, such as, where there is the possibilities to construct the cascade control, feedforward and feedback co
17、ntrol, ratio control, MIMO and decoupling control. f. synthesize the above steps until the performance of the control system is acceptable for the design specification 10. For a process that takes x1 and x2 as manipulated variables, y1 and y2 as the controlled variables, interpret the RGA and pair t
18、he input-output variables while (2 points) a. paring y2 with x1, and y1 with x2, since the strong interaction among the respective pairs due to the value of 0.91 b. avoiding the paring of y1 with x1, and y2 with x2 since the weak interaction among the respective pairs due to the value of 0.09 二、 Bas
19、ic Theory (40 points)In this part, we consider the temperature control of a stirred-tank heater,The mathematic model of this process is:1.Use a feedback Control structure for the stirred-tank heater as the following diagram，:1) Derive the closed-loop transfer function equation(8 points)Solution:At t
20、he summing point：For the process: Substituting E into C, we have: Rearranging the equation above: 2) What is the offset if we consider the servo problem with (8 points)Solution:The difference between controlled variable and set pointSuppose then If (P-controller), we have If (PI-controller), we have
21、 If (PD-controller), we have 3) Build a P-only controller and a PI controller for the regulatory problem with (10 points) Solution:a. the P-controller can be design as time domaincontroller: where es =0 at t=0 is the steady state error. s-domain controller: We have the transfer function for the p-on
22、ly control system using the block diagram: b. the PI controller can be as time domain controller: s-domain controller We have the transfer function for the PI controller using the block diagram: We can solve for this nonlinear system using Pader approximation or Taylor series for linearization (not
23、required for the exam).4) Describe General qualitative features of PI control From Practical Perspective(6 points).Solution: a. Using PI controller when offset is unacceptably bigb. Offset elimination results a more underdamped processc. Lowering the proportional gain Kc while integral used2. With r
24、espect to the Feedforward-Feedback (FF-FB) Control structure as the following block diagram(a): What affect the system stability (why?), why the feedforward control doesnt affect the system stability? (10 points)Solution:According to the block diagram (a),we can get the following algebraic equation:
25、Substitution of E leads toRearranging the equation above:The closed-loop characteristic equation isFrom the closed-loop characteristic equation we know: the feedback controller (GmGc) and the cascade controller (GV*) affect the closed-loop system stability, but the feedforward controller GFF does no
26、t affect the system stability 三、 Basic Application (30 points) When the controller is placed in service, what should be performed as part of the initialization? Also interpret what is the bumpless transfer (10 point) Solution: a. Before you put the controller into action, the following system parame
27、ters should be properly initialized in order to have a better bumpless transfer controller output: p (controlled variable CO) process variable: PV (controlled variable CV) set point: SP disturbance D b. the bumpless transfer means that the process to be changed from auto to manual without upsetting
28、the process. For example, in a PLC, in the auto mode, loading the controller output register value into a spare register will call register value, resulting in a smooth running fine of the system. When switched to manual mode, the register value is loaded into the controller output register, keeping
29、 the same vale for the auto-manual switch. That is, the auto-manual modes start their control from the same output value2. Given a PI controller Gc(s)=Kc1+1/(tIs) for a process, Derive its magnitude and phase lag (5 points) Solution: One of the simple ways to find the magnitude and phase lag is to s
30、ubstitute directly s=jw into the transfer function, resulting in: and Therefore, we can consider which is a product of an integrator and a first order lead. Consequently, the magnitude and phase lag are Make a Matlab program for the Bode and Nyquist plots (5 points) The required code in Matlab is: 3
31、 Given below are the transient responses y(t) of two different processes to changes in their inputs x(t): Which process has the larger gain? Explain your answer.Solution: Based on the plots, two process gains can be estimated as, For process A: Kp 4/2 = 2.0For process B: Kp 2.5/1 = 2.5Therefore, pr
32、ocess B has the larger gain. What type of the function the processes belong to? Which process has the larger time constant? Justify your answer. Solution: We can obviously see that Process A is the first order process with the time constant tp 1.5, Process B is the first order process with dead time td 1.5 and the time constant tp 0.5Therefore, process A has the larger time constant -
