Chapter 9: Controller design


 Darcy Singleton
 3 years ago
 Views:
Transcription
1 Chapter 9. Controller Design 9.1. Introduction 9.2. Effect of negative feedback on the network transfer functions Feedback reduces the transfer function from disturbances to the output Feedback causes the transfer function from the reference input to the output to be insensitive to variations in the gains in the forward path of the loop 9.3. Construction of the important quantities 1/(1T) and T/(1T) and the closedloop transfer functions 1
2 Controller design 9.4. Stability The phase margin test The relation between phase margin and closedloop damping factor Transient response vs. damping factor 9.5. Regulator design Lead (PD) compensator Lag (PI) compensator Combined (PID) compensator Design example 2
3 Controller design 9.6. Measurement of loop gains Voltage injection Current injection Measurement of unstable systems 9.7. Summary of key points 3
4 9.1. Introduction v g (t) Switching converter v(t) Load i load (t) Output voltage of a switching converter depends on duty cycle d, input voltage v g, and load current i load. δ(t) δ(t) Transistor gate driver Pulsewidth modulator v c (t) v g (t) Switching converter v(t) = f(v g, i load, d) dt s T s t v(t) Disturbances i load (t) } d(t) } Control input 4
5 The dc regulator application Switching converter Objective: maintain constant output voltage v(t) = V, in spite of disturbances in v g (t) and i load (t). v g (t) i load (t) v(t) = f(v g, i load, d) } Disturbances v(t) Typical variation in v g (t): 100Hz or 120Hz ripple, produced by rectifier circuit. d(t) } Control input Load current variations: a significant stepchange in load current, such as from 50% to 100% of rated value, may be applied. A typical output voltage regulation specification: 5V ± 0.1V. Circuit elements are constructed to some specified tolerance. In high volume manufacturing of converters, all output voltages must meet specifications. 5
6 The dc regulator application So we cannot expect to set the duty cycle to a single value, and obtain a given constant output voltage under all conditions. Negative feedback: build a circuit that automatically adjusts the duty cycle as necessary, to obtain the specified output voltage with high accuracy, regardless of disturbances or component tolerances. 6
7 Negative feedback: a switching regulator system Power input Switching converter Load i load v g v H Sensor gain Transistor gate driver δ Pulsewidth modulator v c G c Compensator Error signal v e Hv Reference input v ref 7
8 Negative feedback Switching converter v g (t) v(t) = f(v g, i load, d) v ref Reference input Error signal v e (t) v c Compensator Pulsewidth modulator i load (t) d(t) } Disturbances } Control input v(t) Sensor gain 8
9 9.2. Effect of negative feedback on the network transfer functions Small signal model: openloop converter e d 1 : M(D) L e v g jd C v R i load Output voltage can be expressed as where v=g vd dg vg v g Z out i load G vd = v d v g =0 i load =0 G vg = v v g d =0 i load =0 Z out = v i load d =0 v g =0 9
10 Voltage regulator system smallsignal model Use smallsignal converter model Perturb and linearize remainder of feedback loop: v ref (t)=v ref v ref (t) v e (t)=v e v e (t) etc. v g v ref Reference input ed jd Error signal v e G c v c Compensator 1 : M(D) 1 V M Pulsewidth modulator L e d C v R i load Hv H Sensor gain 10
11 Regulator system smallsignal block diagram i load Load current variation ac line variation Pulsewidth Compensator modulator 1 v ref v e v c d G c Reference input Error signal V M v g Duty cycle variation Z out G vg G vd Converter power stage v Output voltage variation H v H Sensor gain 11
12 Solution of block diagram Manipulate block diagram to solve for v. Result is v = v ref G c G vd / V M 1HG c G vd / V M v g G vg 1HG c G vd / V M i load Z out 1HG c G vd / V M which is of the form v = v ref 1 H T 1T v g G vg 1T i load Z out 1T with T=H G c G vd /V M ="loop gain" Loop gain T = products of the gains around the negative feedback loop. 12
13 Feedback reduces the transfer functions from disturbances to the output Original (openloop) linetooutput transfer function: G vg = v v g d =0 i load =0 With addition of negative feedback, the linetooutput transfer function becomes: v v g v ref =0 i load =0 = G vg 1T Feedback reduces the linetooutput transfer function by a factor of 1 1T If T is large in magnitude, then the linetooutput transfer function becomes small. 13
14 Closedloop output impedance Original (openloop) output impedance: Z out = With addition of negative feedback, the output impedance becomes: v i load v ref =0 v g =0 Feedback reduces the output impedance by a factor of 1 1T v i load d =0 v g =0 = Z out 1T If T is large in magnitude, then the output impedance is greatly reduced in magnitude. 14
15 Feedback causes the transfer function from the reference input to the output to be insensitive to variations in the gains in the forward path of the loop Closedloop transfer function from to v is: v ref v v ref v g =0 i load =0 = 1 H T 1T If the loop gain is large in magnitude, i.e., T >> 1, then (1T) T and T/(1T) T/T = 1. The transfer function then becomes v v ref 1 H which is independent of the gains in the forward path of the loop. This result applies equally well to dc values: V V ref = 1 H(0) T(0) 1T(0) 1 H(0) 15
16 9.3. Construction of the important quantities 1/(1T) and T/(1T) Example T 80 db 60 db T 0 db Q db T=T 0 1 s Qω p1 1 s ω z s ω p1 2 1 s ω p2 40 db f p1 40 db/decade 20 db 0 db f z 20 db/decade 20 db f c Crossover frequency f p2 40 db/decade 40 db 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz At the crossover frequency f c, T = 1 f 16
17 Approximating 1/(1T) and T/(1T) T 1T 1 for T >> 1 T for T << 1 1 1T 1 for T >> 1 T 1 for T << 1 17
18 Example: construction of T/(1T) 80 db 60 db T 1T 1 for T >> 1 T for T << 1 40 db f p1 T 20 db 0 db 20 db T 1T f z 20 db/decade Crossover frequency f c f p2 40 db/decade 40 db 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 18
19 Example: analytical expressions for approximate reference to output transfer function At frequencies sufficiently less that the crossover frequency, the loop gain T has large magnitude. The transfer function from the reference to the output becomes v v ref = 1 H v v ref = 1 H 19 T 1T 1 H This is the desired behavior: the output follows the reference according to the ideal gain 1/H. The feedback loop works well at frequencies where the loop gain T has large magnitude. At frequencies above the crossover frequency, T < 1. The quantity T/(1T) then has magnitude approximately equal to 1, and we obtain T 1T T H = G cg vd V M This coincides with the openloop transfer function from the reference to the output. At frequencies where T < 1, the loop has essentially no effect on the transfer function from the reference to the output.
20 Same example: construction of 1/(1T) 80 db 60 db 40 db 20 db 0 db 20 db 40 db 60 db T 0 db f p1 40 db/decade 40 db/decade T 0 db f p1 Q db T f z 20 db/decade 20 db/decade f z Q db f c Crossover frequency 1 1T 1 1T f p2 1 for T >> 1 T 1 for T << 1 40 db/decade 80 db 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 20
21 Interpretation: how the loop rejects disturbances Below the crossover frequency: f < f c and T > 1 Then 1/(1T) 1/T, and disturbances are reduced in magnitude by 1/ T 1 1T 1 for T >> 1 T 1 for T << 1 Above the crossover frequency: f > f c and T < 1 Then 1/(1T) 1, and the feedback loop has essentially no effect on disturbances 21
22 Terminology: openloop vs. closedloop Original transfer functions, before introduction of feedback ( openloop transfer functions ): G vd G vg Z out Upon introduction of feedback, these transfer functions become ( closedloop transfer functions ): 1 H T 1T G vg 1T Z out 1T The loop gain: T 22
23 9.4. Stability Even though the original openloop system is stable, the closedloop transfer functions can be unstable and contain right halfplane poles. Even when the closedloop system is stable, the transient response can exhibit undesirable ringing and overshoot, due to the high Q factor of the closedloop poles in the vicinity of the crossover frequency. When feedback destabilizes the system, the denominator (1T) terms in the closedloop transfer functions contain roots in the right halfplane (i.e., with positive real parts). If T is a rational fraction of the form N / D, where N and D are polynomials, then we can write T 1T = N D 1 N D 1 1T = 1 1 N D = = N ND D ND Could evaluate stability by evaluating N D, then factoring to evaluate roots. This is a lot of work, and is not very illuminating. 23
24 Determination of stability directly from T Nyquist stability theorem: general result. A special case of the Nyquist stability theorem: the phase margin test Allows determination of closedloop stability (i.e., whether 1/(1T) contains RHP poles) directly from the magnitude and phase of T. A good design tool: yields insight into how T should be shaped, to obtain good performance in transfer functions containing 1/(1T) terms. 24
25 The phase margin test A test on T, to determine whether 1/(1T) contains RHP poles. The crossover frequency f c is defined as the frequency where T(j2πf c ) = 1 0dB The phase margin ϕ m is determined from the phase of T at f c, as follows: ϕ m = 180 T(j2πf c ) If there is exactly one crossover frequency, and if T contains no RHP poles, then the quantities T/(1T) and 1/(1T) contain no RHP poles whenever the phase margin ϕ m is positive. 25
26 Example: a loop gain leading to a stable closedloop system T 60 db 40 db T T 20 db f p1 f z Crossover frequency 0 db T f c 0 20 db db ϕ m Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz T(j2πf c ) = 112 ϕ m = = 68 f 26
27 Example: a loop gain leading to an unstable closedloop system T 60 db 40 db T T 20 db f p1 Crossover frequency 0 db T f p2 f c 0 20 db db ϕ m (< 0) Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz T(j2πf c ) = 230 ϕ m = = 50 f 27
28 The relation between phase margin and closedloop damping factor How much phase margin is required? A small positive phase margin leads to a stable closedloop system having complex poles near the crossover frequency with high Q. The transient response exhibits overshoot and ringing. Increasing the phase margin reduces the Q. Obtaining real poles, with no overshoot and ringing, requires a large phase margin. The relation between phase margin and closedloop Q is quantified in this section. 28
29 A simple secondorder system Consider the case where T can be wellapproximated in the vicinity of the crossover frequency as T = 1 s ω 0 1 s ω 2 40 db T f 0 T T f 20 db 0 db 20 db 40 db 20 db/decade T 90 f 0 f 2 /10 f f 2 ϕ m f 2 f 0 f 2 f 2 40 db/decade 10f
30 Closedloop response If Then or, T = 1 s ω 0 1 s ω 2 T 1T = T T 1T = 1 1 s Qω c = 1 1 s ω 0 s2 ω 0 ω 2 s ω c 2 where ω c = ω 0 ω 2 =2π f c Q = ω 0 ω c = ω 0 ω 2 30
31 LowQ case Q = ω 0 ω c = 40 db 20 db 0 db 20 db ω 0 ω 2 lowq approximation: Q ω c = ω ω c 0 Q = ω 2 T 20 db/decade T 1T f 0 f f 0 f c = f 0 f 2 Q = f0 / fc f 2 40 db f 0 f 2 f 2 40 db/decade f 31
32 HighQ case ω c = ω 0 ω 2 =2π f c Q = ω 0 ω c = ω 0 ω 2 60 db 40 db T 20 db/decade f 0 f 20 db f 2 0 db 20 db 40 db T 1T f c = f 0 f 2 f f 0 f 2 f 2 f 0 Q = f 0 /f c 40 db/decade 32
33 Q vs. ϕ m Solve for exact crossover frequency, evaluate phase margin, express as function of ϕ m. Result is: Q = cos ϕ m sin ϕ m ϕ m =tan Q 4 2Q 4 33
34 Q vs. ϕ m Q 20 db 15 db 10 db 5 db 0 db 5 db Q = 1 0 db ϕ m = 52 Q = db 10 db ϕ m = db 20 db ϕ m 34
35 Transient response vs. damping factor Unitstep response of secondorder system T/(1T) v(t)=1 2Qeω c t/2q 4Q 2 1 sin 4Q 2 1 2Q ω c t tan 1 4Q 2 1 Q > 0.5 v(t)=1 ω 2 ω ω 2 ω e ω 1 t 1 1 ω 1 ω e ω 2 t 2 Q < 0.5 ω 1, ω 2 = ω c 2Q 1 ± 1 4Q2 For Q > 0.5, the peak value is peak v(t)=1e π / 4Q2 1 35
36 Transient response vs. damping factor v(t) Q = 50 Q = 10 Q = 4 Q = Q = 1 Q = 0.75 Q = 0.5 Q = 0.3 Q = 0.2 Q = 0.1 Q = 0.05 Q = ω c t, radians 36
37 9.5. Regulator design Typical specifications: Effect of load current variations on output voltage regulation This is a limit on the maximum allowable output impedance Effect of input voltage variations on the output voltage regulation This limits the maximum allowable linetooutput transfer function Transient response time This requires a sufficiently high crossover frequency Overshoot and ringing An adequate phase margin must be obtained The regulator design problem: add compensator network G c to modify T such that all specifications are met. 37
38 Lead (PD) compensator G c =G c0 1 s ω z 1 s ω p G c G c0 G c0 f p f z f p f ϕmax Improves phase margin 0 45 /decade f z /10 f z = f z f p f p /10 10f z 45 /decade G c f 38
39 Lead compensator: maximum phase lead Maximum phase lead f ϕmax = f z f p G c ( f ϕmax )=tan f p / f z f p f z 2 f p = 1sin θ f z 1 sin θ f z f p 39
40 Lead compensator design To optimally obtain a compensator phase lead of θ at frequency f c, the pole and zero frequencies should be chosen as follows: f z = f c f p = f c 1 sin θ 1sin θ 1sin θ 1 sin θ If it is desired that the magnitude of the compensator gain at f c be unity, then G c0 should be chosen as f G c0 = z f p G c 0 G c G c0 G c0 f z 45 /decade f z /10 f f p f z f p /10 f ϕmax = f z f p f p 10f z 45 /decade 40
41 Example: lead compensation 60 db 40 db T T 0 G c0 Original gain T T 20 db T 0 Compensated gain f 0 0 db f z f c 20 db 40 db T 0 Compensated phase asymptotes f p 0 Original phase asymptotes 90 ϕ m f 41
42 Lag (PI) compensation G c =G c 1 ω L s G c 20 db /decade G c Improves lowfrequency loop gain and regulation f L 10f L 0 G c 90 f L /10 45 /decade f 42
43 Example: lag compensation original (uncompensated) loop gain is T T u = u0 1 ω s 0 compensator: G c =G c 1 ω L s Design strategy: choose G c to obtain desired crossover frequency ω L sufficiently low to maintain adequate phase margin 40 db 20 db 0 db 20 db 40 db T u T u T T T u0 f L f 0 f 0 f G c T u0 10f L 10f 0 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f c ϕ m
44 Example, continued Construction of 1/(1T), lag compensator example: 40 db T 20 db f L f 0 G c T u0 0 db f c 20 db 40 db 1 1T f L f 0 1 G c T u0 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 44
45 Combined (PID) compensator 40 db 20 db 0 db G c =G cm 1 ω L s 1 ω s z 1 ω s p1 1 ω s p2 G c G G c c G cm f L f z f c f p1 f p2 20 db 45 /decade 10f L 10f z f p2 / db G c 90 f L /10 f z /10 f p1 /10 90 /decade 90 /decade 10f p f 45
46 Design example L 50 µh i load v g (t) 28 V Transistor gate driver δ Pulsewidth modulator C 500 µf f s = 100 khz V M = 4 V v c G c v(t) Compensator Error signal v e R 3 Ω v ref 5 V Hv H Sensor gain 46
47 Quiescent operating point Input voltage V g = 28V Output V = 15V, I load = 5A, R = 3Ω Quiescent duty cycle D = 15/28 = Reference voltage V ref = 5V Quiescent value of control voltage V c = DV M = 2.14V Gain H H = V ref /V = 5/15 = 1/3 47
48 Smallsignal model V D 2 d 1 : D L v g V R d C v R i load v ref (= 0) Error signal v e G c v c Compensator 1 V M V M = 4 V d T H v H H =
49 Openloop controltooutput transfer function G vd G vd = V D standard form: 1 1s L R s2 LC G vd =G 1 d0 1 s Q 0 ω s 0 ω 0 salient features: 2 60 dbv G vd G vd 40 dbv 20 dbv 0 dbv 20 dbv 40 dbv G vd G vd G d0 = 28 V 29 dbv f /2Q 0 f 0 = 900 Hz 10 1/2Q 0 f 0 = 1.1 khz Q 0 = db G d0 = D V =28V f 0 = ω 0 2π = 1 2π LC = 1kHz Q 0 = R C = dB L 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 49
50 Openloop linetooutput transfer function and output impedance G vg =D 1 1s L R s2 LC same poles as controltooutput transfer function standard form: G vg =G 1 g0 1 s Q 0 ω s 0 ω 0 Output impedance: Z out =R 1 sc sl = 2 sl 1s L R s2 LC 50
51 System block diagram T=G c 1 VM G vd H T= G c H V 1 V M D 1 s Q 0 ω s 0 ω 0 2 v g ac line variation G vg i load Z out Load current variation v ref (=0) v e G c T v c V M = 4 V 1 V M H = 1 3 d Duty cycle variation G vd Converter power stage v H 51
52 Uncompensated loop gain (with G c = 1) With G c = 1, the loop gain is T u =T 1 u0 1 s Q 0 ω s 0 ω 0 T u0 = HV DV M = dB 2 40 db T u T u 20 db 0 db 20 db 40 db T u T u T u db f c = 1.8 khz, ϕ m = 5 f f 0 1 khz Q f 0 = 900 Hz Q f 0 = 1.1 khz Q 0 = db 40 db/decade 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz
53 Lead compensator design Obtain a crossover frequency of 5 khz, with phase margin of 52 T u has phase of approximately 180 at 5 khz, hence lead (PD) compensator is needed to increase phase margin. Lead compensator should have phase of 52 at 5 khz T u has magnitude of 20.6 db at 5 khz Lead compensator gain should have magnitude of 20.6 db at 5 khz Lead compensator pole and zero frequencies should be f z =(5kHz) f p =(5kHz) 1 sin (52 ) 1sin (52 ) = 1.7kHz 1sin (52 ) 1 sin (52 ) = 14.5kHz Compensator dc gain should be G c0 = f c f T u0 f z f p = dB 53
54 Lead compensator Bode plot 40 db G c G G c c0 f f G c z p 20 db 0 db G c0 fz f p f c = f z f p 20 db 40 db 0 f z /10 f p /10 10f z 90 0 G c Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 54
55 Loop gain, with lead compensator 40 db 20 db T=T u0 G c0 1 s ω p 1 1 s ω z s Q 0 ω 0 s ω 0 T T T T 0 = db Q 0 = db 2 0 db 20 db 40 db T Hz f 0 f z 1 khz 1.7 khz f c 5 khz f p 900 Hz 14 khz khz 17 khz 1.1 khz ϕ m = Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 55
56 1/(1T), with lead compensator 40 db 20 db T T 0 = db f 0 Q 0 = db need more lowfrequency loop gain 0 db 20 db 1 1T 1/T 0 = db f z Q 0 f c f p hence, add inverted zero (PID controller) 40 db 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 56
57 Improved compensator (PID) 1 ω s 1 ω L z s G c =G cm 40 db 20 db 0 db 20 db 40 db f 1 s ω p G c G c G c G c 90 f z /10 f L /10 G f cm c f L f z 10f 90 L 10f z 45 /decade 45 /dec 0 f p /10 90 /decade Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f p add inverted zero to PD compensator, without changing dc gain or corner frequencies choose f L to be f c /10, so that phase margin is unchanged 57
58 T and 1/(1T), with PID compensator 60 db 40 db T 20 db Q 0 0 db f L f 0 fz f c 20 db 40 db 1 1T Q 0 f p 60 db 80 db 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 58
59 Linetooutput transfer function v v g 20 db 0 db G vg (0) = D Q 0 20 db 40 db 60 db Openloop G vg 20 db/decade D T u0 G cm f L f 0 f z f c 80 db Closedloop G vg 1T 40 db/decade 100 db 1 Hz 10 Hz 100 Hz 1 khz 10 khz 100 khz f 59
60 9.6. Measurement of loop gains Block 1 Block 2 A Z 1 v ref v e G 1 v e v x Z 2 G 2 v x = v T H Objective: experimentally determine loop gain T, by making measurements at point A Correct result is Z T=G 1 2 G 2 H Z 1 Z 2 60
61 Conventional approach: break loop, measure T as conventional transfer function V CC 0 Block 1 Block 2 dc bias Z 1 v ref v e G 1 v e v y v z v x Z 2 G 2 v x = v T m H measured gain is T m = v y v x v ref =0 v g =0 T m =G 1 G 2 H 61
62 Measured vs. actual loop gain Actual loop gain: T=G 1 Measured loop gain: Z 2 Z 1 Z 2 G 2 H T m =G 1 G 2 H Express T m as function of T: T m =T 1 Z 1 Z 2 T m T provided that Z 2 >> Z 1 62
63 Discussion Breaking the loop disrupts the loading of block 2 on block 1. A suitable injection point must be found, where loading is not significant. Breaking the loop disrupts the dc biasing and quiescent operating point. A potentiometer must be used, to correctly bias the input to block 2. In the common case where the dc loop gain is large, it is very difficult to correctly set the dc bias. It would be desirable to avoid breaking the loop, such that the biasing circuits of the system itself set the quiescent operating point. 63
64 Voltage injection 0 Block 1 Block 2 i Z 1 Z s v z v ref v e G 1 v e v y v x Z 2 G 2 v x = v T v H Ac injection source v z is connected between blocks 1 and 2 Dc bias is determined by biasing circuits of the system itself Injection source does modify loading of block 2 on block 1 64
65 Voltage injection: measured transfer function T v Network analyzer measures T v = v y v x v ref =0 v g =0 v ref 0 v e G 1 v e Block 1 v z Block 2 i Z 1 Z s v y T v v x Z 2 G 2 v x = v Solve block diagram: v e = H G 2 v x v y =G 1 v e i Z 1 Hence v y = v x G 2 H G 1 i Z 1 with i= v x Z 2 H Substitute: v y =v x G 1 G 2 H Z 1 Z 2 which leads to the measured gain T v =G 1 G 2 H Z 1 Z 2 65
66 Comparison of T v with T Actual loop gain is T=G 1 Z 2 Z 1 Z 2 G 2 H Gain measured via voltage injection: T v =G 1 G 2 H Z 1 Z 2 Express Tv in terms of T: T v =T 1 Z 1 Z 2 Z 1 Z 2 Condition for accurate measurement: T v T provided (i) Z 1 << Z 2, and (ii) T >> Z 1 Z 2 66
67 Example: voltage injection Block 1 Block 2 50 Ω v y v z v x 500 Ω Z 1 =50Ω Z 2 =500Ω Z 1 = dB Z 2 1 Z 1 Z 2 = dB suppose actual T= 1 s 2π 10Hz s 2π 100kHz 67
68 Example: measured T v and actual T 100 db 80 db T v =T 1 Z 1 Z 2 Z 1 Z 2 60 db 40 db T T v 20 db 0 db 20 db Z 1 Z 2 20dB T v 40 db 10 Hz 100 Hz 1 khz 10 khz 100 khz 1 MHz f T 68
69 Current injection T i = i y i x v ref =0 v g =0 0 Block 1 Block 2 i y i x Z 1 i z v ref v e G 1 v e Z s Z 2 G 2 v x = v T i H 69
70 Current injection It can be shown that T i =T 1 Z 2 Z 1 Z 2 Z 1 Injection source impedance Z s is irrelevant. We could inject using a Theveninequivalent voltage source: Conditions for obtaining accurate measurement: i y C b i z i x (i) Z 2 << Z 1, and R s (ii) T >> Z 2 Z 1 v z 70
71 Measurement of unstable systems Injection source impedance Z s does not affect measurement Increasing Z s reduces loop gain of circuit, tending to stabilize system Original (unstable) loop gain is measured (not including Z s ), while circuit operates stabily Block 1 Block 2 v z 0 Z 1 R ext Z s v ref v e G 1 v e v y L ext v x Z 2 G 2 v x = v T v H 71
72 9.7. Summary of key points 1. Negative feedback causes the system output to closely follow the reference input, according to the gain 1/H. The influence on the output of disturbances and variation of gains in the forward path is reduced. 2. The loop gain T is equal to the products of the gains in the forward and feedback paths. The loop gain is a measure of how well the feedback system works: a large loop gain leads to better regulation of the output. The crossover frequency f c is the frequency at which the loop gain T has unity magnitude, and is a measure of the bandwidth of the control system. 72
73 Summary of key points 3. The introduction of feedback causes the transfer functions from disturbances to the output to be multiplied by the factor 1/(1T). At frequencies where T is large in magnitude (i.e., below the crossover frequency), this factor is approximately equal to 1/T. Hence, the influence of lowfrequency disturbances on the output is reduced by a factor of 1/T. At frequencies where T is small in magnitude (i.e., above the crossover frequency), the factor is approximately equal to 1. The feedback loop then has no effect. Closedloop disturbancetooutput transfer functions, such as the linetooutput transfer function or the output impedance, can easily be constructed using the algebraonthegraph method. 4. Stability can be assessed using the phase margin test. The phase of T is evaluated at the crossover frequency, and the stability of the important closedloop quantities T/(1T) and 1/(1T) is then deduced. Inadequate phase margin leads to ringing and overshoot in the system transient response, and peaking in the closedloop transfer functions. 73
74 Summary of key points 5. Compensators are added in the forward paths of feedback loops to shape the loop gain, such that desired performance is obtained. Lead compensators, or PD controllers, are added to improve the phase margin and extend the control system bandwidth. PI controllers are used to increase the lowfrequency loop gain, to improve the rejection of lowfrequency disturbances and reduce the steadystate error. 6. Loop gains can be experimentally measured by use of voltage or current injection. This approach avoids the problem of establishing the correct quiescent operating conditions in the system, a common difficulty in systems having a large dc loop gain. An injection point must be found where interstage loading is not significant. Unstable loop gains can also be measured. 74
Chapter 9: Controller design. Controller design. Controller design
Chapter 9. Controller Deign 9.. Introduction 9.2. Eect o negative eedback on the network traner unction 9.2.. Feedback reduce the traner unction rom diturbance to the output 9.2.2. Feedback caue the traner
More informationChapter 8: Converter Transfer Functions
Chapter 8. Converter Transfer Functions 8.1. Review of Bode plots 8.1.1. Single pole response 8.1.2. Single zero response 8.1.3. Right halfplane zero 8.1.4. Frequency inversion 8.1.5. Combinations 8.1.6.
More informationFeedback design for the Buck Converter
Feedback design for the Buck Converter Portland State University Department of Electrical and Computer Engineering Portland, Oregon, USA December 30, 2009 Abstract In this paper we explore two compensation
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder 8.1.7. The lowq approximation Given a secondorder denominator polynomial, of the form G(s)= 1
More informationConverter System Modeling via MATLAB/Simulink
Converter System Modeling via MATLAB/Simulink A powerful environment for system modeling and simulation MATLAB: programming and scripting environment Simulink: block diagram modeling environment that runs
More informationLecture 50 Changing Closed Loop Dynamic Response with Feedback and Compensation
Lecture 50 Changing Closed Loop Dynamic Response with Feedback and Compensation 1 A. Closed Loop Transient Response Waveforms 1. Standard Quadratic T(s) Step Response a. Q > 1/2 Oscillatory decay to a
More informationB. T(s) Modification Design Example 1. DC Conditions 2. Open Loop AC Conditions 3. Closed Loop Conditions
Lecture 51 Tailoring Dynamic Response with Compensation A. Compensation Networks 1. Overview of G c (Alterations and Tailoring) a. Crude Single Pole G C Tailoring b. Elegant Double Pole/Double Zero G C
More informationChapter 11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode
Chapter 11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode Introduction 11.1. DCM Averaged Switch Model 11.2. SmallSignal AC Modeling of the DCM Switch Network 11.3. HighFrequency
More informationChapter 8: Converter Transfer Functions
Chapter 8. Converter Transer Functions 8.1. Review o Bode plots 8.1.1. Single pole response 8.1.2. Single zero response 8.1.3. Right halplane zero 8.1.4. Frequency inversion 8.1.5. Combinations 8.1.6.
More informationHomework Assignment 08
Homework Assignment 08 Question 1 (Short Takes) Two points each unless otherwise indicated. 1. Give one phrase/sentence that describes the primary advantage of an active load. Answer: Large effective resistance
More informationELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques
CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques [] For the following system, Design a compensator such
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder 8.1. Review of Bode plots Decibels Table 8.1. Expressing magnitudes in decibels G db = 0 log 10
More informationLecture 46 Bode Plots of Transfer Functions:II A. Low Q Approximation for Two Poles w o
Lecture 46 Bode Plots of Transfer Functions:II A. Low Q Approximation for Two Poles w o   w L =Q  w o πf o w h =Qw o w L ~ RC w h w L f(l) w h f(c) B. Construction from T(s) Asymptotes
More information(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications:
1. (a) The open loop transfer function of a unity feedback control system is given by G(S) = K/S(1+0.1S)(1+S) (i) Determine the value of K so that the resonance peak M r of the system is equal to 1.4.
More informationTransient response via gain adjustment. Consider a unity feedback system, where G(s) = 2. The closed loop transfer function is. s 2 + 2ζωs + ω 2 n
Design via frequency response Transient response via gain adjustment Consider a unity feedback system, where G(s) = ωn 2. The closed loop transfer function is s(s+2ζω n ) T(s) = ω 2 n s 2 + 2ζωs + ω 2
More informationR a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Forcecurrent and ForceVoltage analogies.
SET  1 II B. Tech II Semester Supplementary Examinations Dec 01 1. a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Forcecurrent and ForceVoltage analogies..
More informationHomework 7  Solutions
Homework 7  Solutions Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s) = K s(s + 5)(s + 11) do the following: (c) Find the
More informationEE C128 / ME C134 Fall 2014 HW 8  Solutions. HW 8  Solutions
EE C28 / ME C34 Fall 24 HW 8  Solutions HW 8  Solutions. Transient Response Design via Gain Adjustment For a transfer function G(s) = in negative feedback, find the gain to yield a 5% s(s+2)(s+85) overshoot
More informationDr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review
Week Date Content Notes 1 6 Mar Introduction 2 13 Mar Frequency Domain Modelling 3 20 Mar Transient Performance and the splane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Part II" Converter Dynamics and Control! 7.!AC equivalent circuit modeling! 8.!Converter transfer
More informationPart II Converter Dynamics and Control
Part II Converter Dynamics and Control 7. AC equivalent circuit modeling 8. Converter transfer functions 9. Controller design 10. Ac and dc equivalent circuit modeling of the discontinuous conduction mode
More informationCHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION
CHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION Objectives Students should be able to: Draw the bode plots for first order and second order system. Determine the stability through the bode plots.
More informationSection 5 Dynamics and Control of DCDC Converters
Section 5 Dynamics and ontrol of DD onverters 5.2. Recap on StateSpace Theory x Ax Bu () (2) yxdu u v d ; y v x2 sx () s Ax() s Bu() s ignoring x (0) (3) ( si A) X( s) Bu( s) (4) X s si A BU s () ( )
More informationDESIGN MICROELECTRONICS ELCT 703 (W17) LECTURE 3: OPAMP CMOS CIRCUIT. Dr. Eman Azab Assistant Professor Office: C
MICROELECTRONICS ELCT 703 (W17) LECTURE 3: OPAMP CMOS CIRCUIT DESIGN Dr. Eman Azab Assistant Professor Office: C3.315 Email: eman.azab@guc.edu.eg 1 TWO STAGE CMOS OPAMP It consists of two stages: First
More informationLecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science  Bangalore
Lecture 6 Classical Control Overview IV Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science  Bangalore Lead Lag Compensator Design Dr. Radhakant Padhi Asst.
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Sampleddata response: i L /i c Sampleddata transfer function : î L (s) î c (s) = (1 ) 1 e st
More informationLecture 17 Date:
Lecture 17 Date: 27.10.2016 Feedback and Properties, Types of Feedback Amplifier Stability Gain and Phase Margin Modification Elements of Feedback System: (a) The feed forward amplifier [H(s)] ; (b) A
More informationFREQUENCYRESPONSE DESIGN
ECE45/55: Feedback Control Systems. 9 FREQUENCYRESPONSE DESIGN 9.: PD and lead compensation networks The frequencyresponse methods we have seen so far largely tell us about stability and stability margins
More informationESE319 Introduction to Microelectronics. Feedback Basics
Feedback Basics Stability Feedback concept Feedback in emitter follower Onepole feedback and root locus Frequency dependent feedback and root locus Gain and phase margins Conditions for closed loop stability
More informationTable of Laplacetransform
Appendix Table of Laplacetransform pairs 1(t) f(s) oct), unit impulse at t = 0 a, a constant or step of magnitude a at t = 0 a s t, a ramp function e at, an exponential function s + a sin wt, a sine fun
More informationECEN 607 (ESS) OpAmps Stability and Frequency Compensation Techniques. Analog & MixedSignal Center Texas A&M University
ECEN 67 (ESS) OpAmps Stability and Frequency Compensation Techniques Analog & MixedSignal Center Texas A&M University Stability of Linear Systems Harold S. Black, 97 Negative feedback concept Negative
More informationECE1750, Spring Week 11 Power Electronics
ECE1750, Spring 2017 Week 11 Power Electronics Control 1 Power Electronic Circuits Control In most power electronic applications we need to control some variable, such as the put voltage of a dcdc converter,
More informationUnit 8: Part 2: PD, PID, and Feedback Compensation
Ideal Derivative Compensation (PD) Lead Compensation PID Controller Design Feedback Compensation Physical Realization of Compensation Unit 8: Part 2: PD, PID, and Feedback Compensation Engineering 5821:
More informationEC CONTROL SYSTEM UNIT I CONTROL SYSTEM MODELING
EC 2255  CONTROL SYSTEM UNIT I CONTROL SYSTEM MODELING 1. What is meant by a system? It is an arrangement of physical components related in such a manner as to form an entire unit. 2. List the two types
More informationECE3050 Assignment 7
ECE3050 Assignment 7. Sketch and label the Bode magnitude and phase plots for the transfer functions given. Use loglog scales for the magnitude plots and linearlog scales for the phase plots. On the magnitude
More informationFrequency Dependent Aspects of Opamps
Frequency Dependent Aspects of Opamps Frequency dependent feedback circuits The arguments that lead to expressions describing the circuit gain of inverting and noninverting amplifier circuits with resistive
More informationStudio 9 Review Operational Amplifier Stability Compensation Miller Effect Phase Margin Unity Gain Frequency Slew Rate Limiting Reading: Text sec 5.
Studio 9 Review Operational Amplifier Stability Compensation Miller Effect Phase Margin Unity Gain Frequency Slew Rate Limiting Reading: Text sec 5.2 pp. 232242 Twostage opamp Analysis Strategy Recognize
More informationToday (10/23/01) Today. Reading Assignment: 6.3. Gain/phase margin lead/lag compensator Ref. 6.4, 6.7, 6.10
Today Today (10/23/01) Gain/phase margin lead/lag compensator Ref. 6.4, 6.7, 6.10 Reading Assignment: 6.3 Last Time In the last lecture, we discussed control design through shaping of the loop gain GK:
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 OpenLoop Process The study of dynamics was limited to openloop systems Observe process behavior as a result of specific input signals
More informationFinal Exam. 55:041 Electronic Circuits. The University of Iowa. Fall 2013.
Final Exam Name: Max: 130 Points Question 1 In the circuit shown, the opamp is ideal, except for an input bias current I b = 1 na. Further, R F = 10K, R 1 = 100 Ω and C = 1 μf. The switch is opened at
More informationLecture 47 Switch Mode Converter Transfer Functions: Tvd(s) and Tvg(s) A. Guesstimating Roots of Complex Polynomials( this section is optional)
Lecture 47 Switch Mode Converter Transfer Functions: T vd (s) and T vg (s) A. Guesstimating Roots of Complex Polynomials( this section is optional). Quick Insight n=. n th order case. Cuk example 4. Forth
More informationElectronic Circuits Summary
Electronic Circuits Summary Andreas Biri, DITET 6.06.4 Constants (@300K) ε 0 = 8.854 0 F m m 0 = 9. 0 3 kg k =.38 0 3 J K = 8.67 0 5 ev/k kt q = 0.059 V, q kt = 38.6, kt = 5.9 mev V Small Signal Equivalent
More informationThe output voltage is given by,
71 The output voltage is given by, = (3.1) The inductor and capacitor values of the Boost converter are derived by having the same assumption as that of the Buck converter. Now the critical value of the
More informationStability of CL System
Stability of CL System Consider an open loop stable system that becomes unstable with large gain: At the point of instability, K( j) G( j) = 1 0dB K( j) G( j) K( j) G( j) K( j) G( j) =± 180 o 180 o Closed
More informationRegulated DCDC Converter
Regulated DCDC Converter Zabir Ahmed Lecturer, BUET Jewel Mohajan Lecturer, BUET M A Awal Graduate Research Assistant NSF FREEDM Systems Center NC State University Former Lecturer, BUET 1 Problem Statement
More informationExercises for lectures 13 Design using frequency methods
Exercises for lectures 13 Design using frequency methods Michael Šebek Automatic control 2016 31317 Setting of the closed loop bandwidth At the transition frequency in the open loop is (from definition)
More informationEE 422G  Signals and Systems Laboratory
EE 4G  Signals and Systems Laboratory Lab 9 PID Control Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 April, 04 Objectives: Identify the
More informationAutomatic Control 2. Loop shaping. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Loop shaping Prof. Alberto Bemporad University of Trento Academic year 21211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21211 1 / 39 Feedback
More informationChapter 2. Classical Control System Design. Dutch Institute of Systems and Control
Chapter 2 Classical Control System Design Overview Ch. 2. 2. Classical control system design Introduction Introduction Steadystate Steadystate errors errors Type Type k k systems systems Integral Integral
More informationThe requirements of a plant may be expressed in terms of (a) settling time (b) damping ratio (c) peak overshoot  in time domain
Compensators To improve the performance of a given plant or system G f(s) it may be necessary to use a compensator or controller G c(s). Compensator Plant G c (s) G f (s) The requirements of a plant may
More informationFEEDBACK CONTROL SYSTEMS
FEEDBAC CONTROL SYSTEMS. Control System Design. Open and ClosedLoop Control Systems 3. Why ClosedLoop Control? 4. Case Study  Speed Control of a DC Motor 5. SteadyState Errors in Unity Feedback Control
More informationECE137B Final Exam. Wednesday 6/8/2016, 7:3010:30PM.
ECE137B Final Exam Wednesday 6/8/2016, 7:3010:30PM. There are7 problems on this exam and you have 3 hours There are pages 132 in the exam: please make sure all are there. Do not open this exam until
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : CONTROL SYSTEMS BRANCH : ECE YEAR : II SEMESTER: IV 1. What is control system? 2. Define open
More informationSteady State Frequency Response Using Bode Plots
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 3 Steady State Frequency Response Using Bode Plots 1 Introduction
More informationControl Systems. EC / EE / IN. For
Control Systems For EC / EE / IN By www.thegateacademy.com Syllabus Syllabus for Control Systems Basic Control System Components; Block Diagrammatic Description, Reduction of Block Diagrams. Open Loop
More informationCYBER EXPLORATION LABORATORY EXPERIMENTS
CYBER EXPLORATION LABORATORY EXPERIMENTS 1 2 Cyber Exploration oratory Experiments Chapter 2 Experiment 1 Objectives To learn to use MATLAB to: (1) generate polynomial, (2) manipulate polynomials, (3)
More informationIC6501 CONTROL SYSTEMS
DHANALAKSHMI COLLEGE OF ENGINEERING CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEMESTER: II/IV IC6501 CONTROL SYSTEMS UNIT I SYSTEMS AND THEIR REPRESENTATION 1. What is the mathematical
More informationESE319 Introduction to Microelectronics Bode Plot Review High Frequency BJT Model
Bode Plot Review High Frequency BJT Model 1 Logarithmic Frequency Response Plots (Bode Plots) Generic form of frequency response rational polynomial, where we substitute jω for s: H s=k sm a m 1 s m 1
More informationCourse Summary. The course cannot be summarized in one lecture.
Course Summary Unit 1: Introduction Unit 2: Modeling in the Frequency Domain Unit 3: Time Response Unit 4: Block Diagram Reduction Unit 5: Stability Unit 6: SteadyState Error Unit 7: Root Locus Techniques
More informationCDS 101/110a: Lecture 81 Frequency Domain Design
CDS 11/11a: Lecture 81 Frequency Domain Design Richard M. Murray 17 November 28 Goals: Describe canonical control design problem and standard performance measures Show how to use loop shaping to achieve
More informationActive Control? Contact : Website : Teaching
Active Control? Contact : bmokrani@ulb.ac.be Website : http://scmero.ulb.ac.be Teaching Active Control? Disturbances System Measurement Control Controler. Regulator.,,, Aims of an Active Control Disturbances
More informationENGN3227 Analogue Electronics. Problem Sets V1.0. Dr. Salman Durrani
ENGN3227 Analogue Electronics Problem Sets V1.0 Dr. Salman Durrani November 2006 Copyright c 2006 by Salman Durrani. Problem Set List 1. Opamp Circuits 2. Differential Amplifiers 3. Comparator Circuits
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 21: Stability Margins and Closing the Loop Overview In this Lecture, you will learn: Closing the Loop Effect on Bode Plot Effect
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Objective of Part II! Develop tools for modeling, analysis, and design of converter control systems!
More information8.1.6 Quadratic pole response: resonance
8.1.6 Quadratic pole response: resonance Example G(s)= v (s) v 1 (s) = 1 1+s L R + s LC L + Secondorder denominator, of the form 1+a 1 s + a s v 1 (s) + C R Twopole lowpass filter example v (s) with
More informationECE 486 Control Systems
ECE 486 Control Systems Spring 208 Midterm #2 Information Issued: April 5, 208 Updated: April 8, 208 ˆ This document is an info sheet about the second exam of ECE 486, Spring 208. ˆ Please read the following
More informationMAS107 Control Theory Exam Solutions 2008
MAS07 CONTROL THEORY. HOVLAND: EXAM SOLUTION 2008 MAS07 Control Theory Exam Solutions 2008 Geir Hovland, Mechatronics Group, Grimstad, Norway June 30, 2008 C. Repeat question B, but plot the phase curve
More informationElectronic Circuits. Prof. Dr. Qiuting Huang Integrated Systems Laboratory
Electronic Circuits Prof. Dr. Qiuting Huang 6. Transimpedance Amplifiers, Voltage Regulators, Logarithmic Amplifiers, AntiLogarithmic Amplifiers Transimpedance Amplifiers Sensing an input current ii in
More informationDEPARTMENT OF ECE UNIT VII BIASING & STABILIZATION AMPLIFIER:
UNIT VII IASING & STAILIZATION AMPLIFIE:  A circuit that increases the amplitude of given signal is an amplifier  Small ac signal applied to an amplifier is obtained as large a.c. signal of same frequency
More informationSECTION 2: BLOCK DIAGRAMS & SIGNAL FLOW GRAPHS
SECTION 2: BLOCK DIAGRAMS & SIGNAL FLOW GRAPHS MAE 4421 Control of Aerospace & Mechanical Systems 2 Block Diagram Manipulation Block Diagrams 3 In the introductory section we saw examples of block diagrams
More informationR10 JNTUWORLD B 1 M 1 K 2 M 2. f(t) Figure 1
Code No: R06 R0 SET  II B. Tech II Semester Regular Examinations April/May 03 CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry
More informationMAE143a: Signals & Systems (& Control) Final Exam (2011) solutions
MAE143a: Signals & Systems (& Control) Final Exam (2011) solutions Question 1. SIGNALS: Design of a noisecancelling headphone system. 1a. Based on the lowpass filter given, design a highpass filter,
More informationThe loop shaping paradigm. Lecture 7. Loop analysis of feedback systems (2) Essential specifications (2)
Lecture 7. Loop analysis of feedback systems (2). Loop shaping 2. Performance limitations The loop shaping paradigm. Estimate performance and robustness of the feedback system from the loop transfer L(jω)
More informationEstimation of Circuit Component Values in Buck Converter using Efficiency Curve
ISPACS2017 Paper 2017 ID 21 Nov. 9 NQL5 Paper ID 21, Estimation of Circuit Component Values in Buck Converter using Efficiency Curve S. Sakurai, N. Tsukiji, Y. Kobori, H. Kobayashi Gunma University 1/36
More informationVALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year
More informationContents. PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations... 42
Contents Preface.............................................. xiii 1. Introduction......................................... 1 1.1 Continuous and Discrete Control Systems................. 4 1.2 OpenLoop
More informationTransient Response of a SecondOrder System
Transient Response of a SecondOrder System ECEN 830 Spring 01 1. Introduction In connection with this experiment, you are selecting the gains in your feedback loop to obtain a wellbehaved closedloop
More informationFrequency Response Techniques
4th Edition T E N Frequency Response Techniques SOLUTION TO CASE STUDY CHALLENGE Antenna Control: Stability Design and Transient Performance First find the forward transfer function, G(s). Pot: K 1 = 10
More informationA LDO Regulator with Weighted Current Feedback Technique for 0.47nF10nF Capacitive Load
A LDO Regulator with Weighted Current Feedback Technique for 0.47nF10nF Capacitive Load Presented by Tan Xiao Liang Supervisor: A/P Chan Pak Kwong School of Electrical and Electronic Engineering 1 Outline
More informationFEEDBACK AND STABILITY
FEEDBCK ND STBILITY THE NEGTIVEFEEDBCK LOOP x IN X OUT x S + x IN x OUT Σ Signal source _ β Open loop Closed loop x F Feedback network Output x S input signal x OUT x IN x F feedback signal x IN x S x
More informationESE319 Introduction to Microelectronics. Feedback Basics
Feedback Basics Feedback concept Feedback in emitter follower Stability Onepole feedback and root locus Frequency dependent feedback and root locus Gain and phase margins Conditions for closed loop stability
More informationIntro to Frequency Domain Design
Intro to Frequency Domain Design MEM 355 Performance Enhancement of Dynamical Systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline Closed Loop Transfer Functions
More informationControl Systems. University Questions
University Questions UNIT1 1. Distinguish between open loop and closed loop control system. Describe two examples for each. (10 Marks), Jan 2009, June 12, Dec 11,July 08, July 2009, Dec 2010 2. Write
More informationChemical Process Dynamics and Control. Aisha Osman Mohamed Ahmed Department of Chemical Engineering Faculty of Engineering, Red Sea University
Chemical Process Dynamics and Control Aisha Osman Mohamed Ahmed Department of Chemical Engineering Faculty of Engineering, Red Sea University 1 Chapter 4 System Stability 2 Chapter Objectives End of this
More informationLaplace Transform Analysis of Signals and Systems
Laplace Transform Analysis of Signals and Systems Transfer Functions Transfer functions of CT systems can be found from analysis of Differential Equations Block Diagrams Circuit Diagrams 5/10/04 M. J.
More informationDESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD
206 Spring Semester ELEC733 Digital Control System LECTURE 7: DESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD For a unit ramp input Tz Ez ( ) 2 ( z ) D( z) G( z) Tz e( ) lim( z) z 2 ( z ) D( z)
More informationCross Regulation Mechanisms in MultipleOutput Forward and Flyback Converters
Cross Regulation Mechanisms in MultipleOutput Forward and Flyback Converters Bob Erickson and Dragan Maksimovic Colorado Power Electronics Center (CoPEC) University of Colorado, Boulder 803090425 http://ecewww.colorado.edu/~pwrelect
More informationRefinements to Incremental Transistor Model
Refinements to Incremental Transistor Model This section presents modifications to the incremental models that account for nonideal transistor behavior Incremental output port resistance Incremental changes
More informationControls Problems for Qualifying Exam  Spring 2014
Controls Problems for Qualifying Exam  Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function
More informationFrequency Response. Re ve jφ e jωt ( ) where v is the amplitude and φ is the phase of the sinusoidal signal v(t). ve jφ
27 Frequency Response Before starting, review phasor analysis, Bode plots... Key concept: smallsignal models for amplifiers are linear and therefore, cosines and sines are solutions of the linear differential
More information6.302 Feedback Systems
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.302 Feedback Systems Fall Term 2005 Issued : November 18, 2005 Lab 2 Series Compensation in Practice Due
More information34 Control Methods for Switching Power Converters
4 Control Methods for Switching Power Converters J. Fernando Silva, Ph.D. and Sónia Ferreira Pinto, Ph.D. Instituto Superior Técnico, DEEC, CAUTL, Laboratório Máquinas Eléctricas e Electrónica de Potência,
More informationPID Control. Objectives
PID Control Objectives The objective of this lab is to study basic design issues for proportionalintegralderivative control laws. Emphasis is placed on transient responses and steadystate errors. The
More informationLecture 120 Compensation of Op AmpsI (1/30/02) Page ECE Analog Integrated Circuit Design  II P.E. Allen
Lecture 20 Compensation of Op AmpsI (/30/02) Page 20 LECTURE 20 COMPENSATION OF OP AMPS I (READING: GHLM 425434 and 624638, AH 249260) INTRODUCTION The objective of this presentation is to present the
More informationIndex. Index. More information. in this web service Cambridge University Press
Atype elements, 4 7, 18, 31, 168, 198, 202, 219, 220, 222, 225 Atype variables. See Across variable ac current, 172, 251 ac induction motor, 251 Acceleration rotational, 30 translational, 16 Accumulator,
More information1 (20 pts) Nyquist Exercise
EE C128 / ME134 Problem Set 6 Solution Fall 2011 1 (20 pts) Nyquist Exercise Consider a close loop system with unity feedback. For each G(s), hand sketch the Nyquist diagram, determine Z = P N, algebraically
More informationECE137B Final Exam. There are 5 problems on this exam and you have 3 hours There are pages 119 in the exam: please make sure all are there.
ECE37B Final Exam There are 5 problems on this exam and you have 3 hours There are pages 9 in the exam: please make sure all are there. Do not open this exam until told to do so Show all work: Credit
More informationReview: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control
Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Goal: understand the difference between openloop and closedloop (feedback)
More informationRoot Locus Methods. The root locus procedure
Root Locus Methods Design of a position control system using the root locus method Design of a phase lag compensator using the root locus method The root locus procedure To determine the value of the gain
More informationMEM 355 Performance Enhancement of Dynamical Systems
MEM 355 Performance Enhancement of Dynamical Systems Frequency Domain Design Intro Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University /5/27 Outline Closed Loop Transfer
More information