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Faculty of Science and EngineeringDepartment of Electronic and ComputerEngineeringEnd of Semester Assessment PaperModule Code: EE4218 / EE4216Module Title: Control 2Semester: Spring 2018Duration of Exam: 21Grading Scheme: Final Exam : 80%Coursework : 20%Instructions to Candidates:Answer any FOUR questions. All questions carry equal marks.A University Standard Calculator may be used.Module Code & Title: EE4218 / EE4216 Control 2 Page 2 of 6MARKS1. (a) Consider the system�You may assume that β is a parameter that is allowed to vary in the rangeβ ∈ [0.25, . . . , 1.5]i. Determine the natural frequency of oscillation ωn for this system. 2ii. Write a MATLAB script (.m file) that will illustrate the effect of variationin the parameter β in the region [0.25, . . . , 1.5] on a system stepresponse.Your answer should briefly sketch the typical step responses that youwould expect to observe. 7(b) This question concerns the locus of the roots of the characteristic equationfor the closed loop system described by Figure 1.i. Determine equations for the asymptotes to the locus as K → ∞. 2ii. What are the departure angles for the locus as it leaves the complexopen loop poles? 3iii. Assume that one feasible multiple root (accurate to 1 decimal place)exists for this locus at s = ?4.8 and that two infeasible multiple rootsexist at s = ?1.8 ± ?1.3.Determine the other feasible multiple root location for this locus. 8iv. Sketch the root locus for this system. 3�Figure 1:Module Code & Title: EE4218 / EE4216 Control 2 Page 3 of 6MARKS2. This question considers the D.C Motor�System performance is to be improved using the following controller.K(s) = 50(s + 3)(s + 7)(a) Derive a bound on the Phase Margin of a system in terms of its worst casesystem sensitivity kSk∞. 6(b) Draw a system sensitivity plot, S(?ω), for this combination of plant andcontroller.Your answer should compute S(?ω) atω = [0, 14, 23, 50,∞] radsYou may assume that kSk∞ = ks(?23)k. 8(c) Describe how bounds on Phase Margin, Steady state error, 5% settlingtime and Bandwidth can be read from the S(?ω) you have computed inPart (b) of this question. 6(d) Estimate the 5% settling time for this design to a step input demand.Briefly describe how you would use MATLAB to construct S(?ω) and toobserve the step response for this particular design.Your answer should sketch an indicative step response for this system. 5Module Code & Title: EE4218 / EE4216 Control 2 Page 4 of 6MARKS3. This questions considers Nyquist based tuning for the following system :-2s + 8(s + 1)(s + 3)((s + 2)2 + 5)(a) Using the following frequency vectorω ∈ [0, 1.25, 3.3, . . . ,∞]draw a Nyquist diagram for this system. 10(b) Use your diagram to estimate the system phase and gain margins. 3(c) Using your Nyquist diagram, design a PID controller, K(s), for this systemthat is tuned for good low frequency performance. You may assume thatthe following tuning rules are appropriate :-KP = 0.4 × Kuwhere Ku is the limit cycle gain with the application of proportional onlycontrol andTI = 1.0 × TuTD = 0.25 × Tuwhere Tu is the corresponding limit cycle period. 7(d) How would you improve the speed of response of your design using PhaseLead methods?Please note that an exact design is NOT required, it is sufficient to providethe design steps that you would take. 5Module Code & Title: EE4218 / EE4216 Control 2 Page 5 of 6MARKS4. This question considers the system shown in Figure 3. Denote the state variablesfor this system as x1 = VC(t) x2 = iL(t). The following describing equationsfor the system may be useful.Vin(t) = u(t) = LdiL(t)dt + VC(t) ; Vout(t) = Vin(t) ?VC(t)VC(t)R1+ CdVC(t)dt = iL(t) + LR2diL(t)Figure 2:(a) Briefly list TWO reasons for a state space approach to Control SystemsDesign 2(b) For the case whereL = 2H, R1 = 1?, R2 = 3?, C = 0.5FComplete the continuous A state matrix for this system and hence writethe continuous state and output equation. 8(c) Design a State feedback controller that will place the closed loop poles forthis system at ?2 ± 0.2?.Your answer should provide a diagram illustrating how this design can beimplemented in practice. 8(d) Determine the feasibility of an Observer based controller design strategyfor this system. 2(e) Describe one advantage and one disadvantage of such an Observer basedstrategy over a more traditional state feedback approach. 2(f) Explain how such an Observer based strategy might be implemented inpractice 3Module Code & Title: EE4218 / EE4216 Control 2 Page 6 of 6MARKS5. This question concerns the following system that you have studied extensivelyduring your Laboratory work this semester�(a) What type of problem does this system model and why is it such a difficultproblem to control? 3(b) Determine the values of Proportional gain K that will stabilise this system.Why is the proportional control that is suggested by Figure 3 unsuitablefor this system? 8(c) Discuss the various approaches that you used to control this system overthe course of the semester. For each different strategy that you consideryour answer should describei. How you implemented the design in MATLAB.ii. The frequency domain analysis tools that you used to assess the design.iii. The steps that you took to improve the time domain performance ofyour design. 14本团队核心人员组成主要包括BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：[email protected] 微信：codehelp