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1、1 Chapter 8 Compensator Design 8.1 Introduction 8.2 Cascade compensation 8.3 Summary 2 8.1 Introduction Necessities of compensation nStability. nSpeed of response. nSteady-state error. 3 The design of a control system is concerned with the arrangement, or the plan, of the system structure and the se
2、lection of suitable components and parameters. A compensator is an additional component or circuit that is inserted into a control system to compensate for a deficient performance. 4 Performance measures in the time domain: Peak time; Overshoot; Settling time; Steady-state error. 理硕教育专注北理工考研辅导 n本资料由
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4、t frequency ; Peak value at ; Bandwidth ; For open-loop: Gain margin ; Phase margin ; Crossover frequency . 7 Notes: nHigh performance means high cost. nRequired performance specifications may be contradictory (矛盾)to each other. 8 Cascade Compensation. nFeatures: Simple; Additional amplifier. nCompe
5、nsator types: Lag compensator (raise steady state accuracy); Lead compensator (improve transient response); Lag-lead compensator (raise steady state accuracy and response speed ) 9 Frequency response approach The common specifications used are represents the damping ratio. represents the speediness.
6、 10 Relations between the frequency response and system performance at: Lower frequency Middle frequency Higher frequency 11 Unsatisfactory performances (1) Stable but ess is too big The magnitude of the response at lower frequency is too low. 12 (2) Stable but time response is too slow The middle f
7、requency response ensures the stability. But wc is not high enough. 13 (3) Stable but ess is too big and time response is too slow 14 8.2 Cascade compensation phase-lead compensation phase-lag compensation lead-lag compensation 15 1. Phase-lead compensation 16 17 Phase-lead compensator The phase-lea
8、d compensator is a differential-type network. 18 19 Fig. jm vs. a for a phase lead network jm is not much greater than 70, so if more phase lead is needed, two cascade networks would be used. 20 Improvements of the performance seen from the Bode diagrams. nRelative stability nSpeed of response 21 步骤
9、： 1、确定开环增益和型别，使满足稳态指标； 2、绘制未校正系统开环Bode图，确定原系统频域 参数：wc0、g0 3、确定要补偿的超前相角度数 判断 是否能够用超前补偿； 4、根据 ，计算a 和10lga； 5、由 确定wm； 6、计算T 和Gc(s) ； 7、验证校正后系统是否满足指标。 22 Example 8.1 The specifications 23 Conclusion: Phase-lead network increases the phase margin of feedback systems. When the design specifications includ
10、e an error constant requirement, the Bode diagram method is more suitable. The root locus method often results in an iterative design procedure. For overshoot and settling time specifications, the root locus method is better. As the lead network extends the bandwidth, it may be objectionable for sys
11、tems subjected to large amount of noise. 24 直流电机实验 25 2. Phase-lag compensator nPhase-lag network 26 27 Phase-lag compensator The phase-lag compensator is an integration-type network. 28 29 Phase-lag compensation by using Bode diagram 30 31 Example 8.2 Given Design a cascade compensator such that th
12、e compensated system has 32 Solution: (i) Determine K (ii) Gain-compensated system analysis The closed-loop system is unstable. 33 34 (iii) Selection of new crossover frequency wc (iv) Let (v) Calculate a 35 (vi) Compensated system check 36 37 Procedures (for reference only) (1) Determine the desire
13、d open-loop gain according to the steady-state error coefficient. (2) Draw the Bode diagrams of the gain-compensated system and obtain the gain margin and phase margin of the system with K included. (3) Choose a new wc such that 38 (4) Let (5) Calculate a (6) Compensated system check and analysis. 3
14、9 例、 要求： 画Bode图： 得： 取： 40 3. Lead-lag compensator Lead-lag network 41 42 Characteristics nPole-Zero allocation nThe two sets of one pole and one zero: nsimilar to a lead comp. + a lag comp. 43 Bode diagrams 44 Lag-lead comp. = Lag comp+Lead comp Alternate form 45 Lead-lag compensation by Bode diagram 46 Design methods (1) Method A: design the lead part firstly, then design the lag part. *(2) Method B: design the lag part firstly, then design the lead part. 47 Home Work E10.14, P10.1(a) 知识回顾知识回顾 Knowledge Knowledge ReviewReview
