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Control System Analysis

by: Robb McCullough

Control System Analysis AAE 36400

Robb McCullough
GPA 3.65


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Class Notes
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This 53 page Class Notes was uploaded by Robb McCullough on Saturday September 19, 2015. The Class Notes belongs to AAE 36400 at Purdue University taught by Staff in Fall. Since its upload, it has received 163 views. For similar materials see /class/207861/aae-36400-purdue-university in Aerospace Engineering at Purdue University.

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Date Created: 09/19/15
Three of the infinite possible lead compensator solutions Dcxlrud pol luczmon punu Improving Steady State Time Response Improving transient response Adding poles atjnear the origin l Plcontroller 15 Kp 21 Sr3 2 Lag compensator VIA Vszlr 39 I U 1xsa Zr gt Pt 722 130 Improving SteadyState Response PIcontroller megral I Ks RS 4 Icontroller m1 Pmch m n a zwlymr m PIController fnpmmu tm a E IE 71 I PIEI l qt J 3955 39 715i 0 Di in i 1ampm iii39 an E 5 2 m a lm I H H mm Lag Compensator Type 1 Plum I 39 E l quot5quot pl 3 39 C H if Lag Co mpensator Ks Z5 gt PC m2 Improving Transient and SteadyState Responses PIDController 12 r I r I X 432 r KS A LeadLag compensator inf5A Kc 5ZIpm quotZlaz 39spzead spzagj n a mr1 Meaa leadw 39vvwag piag Improving Transient and SteadyState Responses K8 Ks K1 K3s PIDController Design Rs ES Ks 8 CS 7T s3s6s10 39 Uncompensated feedback control system Performance spec 39 Peak time two thirds that of the uncompensated system 20 max overshoot zero steadystate error wrt a step input PIDController Design Uncompensated dominantpoles s 75415 i j1057 7 W 0297 quot M w 77W 21587 d t 0297 M mnO A rD n 4 Mp Lwo g u rau gt 03 813 Unwmpcnwu Mum pnk vphlm Angle deficiency w 18370 I I 7 Im X r L Insullonp pnh X r penhum lwlc Predicted characteristics of uncompensated PD and PID compensated systems pn nln Plum and cmnpcnsmm39 Dominant pnlcs up llmr poles urns Comments KIN 4 8 a 39 Sltx lh4 l0 54I5 11057 Sccnmlmnlur rnx K le t ux P 5592 i lly A ultx Iquot 813 flSkl I 534 0456 Sucumlunlcr approx KIN r Kin i 5592ltx 4 05 x i 3l39 9 lly le 39 7516 fl1lv7 46 456 I049 It 532 Lllv l 1 X099 7 0546 8 i5392 05 um ill 5593 and 05 um canceled Design PDcontroller Calculating the PD compensator zero angle deficiency 13960 PDcompensated dominant pole j1587 tan18370 7553813 S plane 39 2 5592 C 7813 X Closed loop pole Note This gure is not drawn to scale Root locus for PDcompensated system I39D cnmpclv39alcd uummum mh39 78 KPDSGS x u 39 1537 pm y Mm 7559 mer 7x n X Clowdrluuppulc X 39 Unawhxun mlc Vn x a J Root locus for PIDcgmpensate system KPDSGS 7 5m yHlv7 K 4 n lt11ch mm 1 n rum 755quot rHvrxrn 71f 0 J x mmmpuk x upmmp M Vn l 8 05 XFJ quotfJ S Step responses for uncompensated PD compensated and PIDcompensated systems 1 r h PD Uncumpensnlcd I 4 i 0 04 08 l2 L6 21 Time seconds LeadLag Compensator Design Rs 8 ES K CS SS 6S 10 Uncompensated system Performance spec 39 d 0456 wnd 7869 Reduce the steadystate error by 10 times for a ramp input LeadLag Compensator Design IeadKL7 rl I E y L s K13 where K KZKL Root locus for uncompensated system In sd 73588 j 17003 quotAmie HowLI A qu humm H l 49m x r x x mosmw pole x ownmp pun Angle deficiency 4 55430 4 Uncmupuh ulvd dmnluzml mn Characteristics of uncompensated lead compensated and laglead compensated systems Uncompemud Laidcnmnanialad Lagludcumpensaled Plum and mmpmmum Dumumm pm K 4 ml was 1 7 7mm pole Zn 1 Cmumem m A mm nn mm 29 I 7 L794 733m 73588 17003 192 I I077 0450 045 3 934 7859 20 20 1 210 115 0 m7 144 32m 0704 I 2 quot147 r I 41 H 91 Mme None Secmldrmdcr SecmuLurdur uppmx 0s ppm on K mm up um 29 um mm 71574 116976 V971 0 n3 a 73191 450474 700471 Secundrm um appnvx DK Evaluating the compensator pole Lead 15lt I 7291 Compensator 74 6 x Clusedloop pole X OperHoop pnlc flu 5543 7 on 3588 KldeS KisfrTg a Root locus for leadcompensated system by j m g madam Kleadg 19778 459601 i 7I IHTTJ3EEISEI IEQ dmmmmt pale 15 a lms 79 1395 J JH 1 7 1 I l I j 7 M r x I 7 J 7 7 4 i n F sH g2 734 21 EMS 15 EIE ail 3EJ1 i l dul np EHImgp F g 93 Kzeadltsgt9ltsgt 13 1291gt KO 3202 gt ngad 6794 gt 2122 2112 4713 2 11 4713 PL Root locus for lagleadCompensated g 9459 3574 mlmng m d mnmnf lame 31112 m K KZKL 1392 El 739quot l3 n if 1 mtgl 394394 NJ 39 qli39 i39il iiquotIILHJF Faun Mme Thi quottizigure is um drawn m 31919 79693 Kfjf f KL 2 0997 17 Improvement in step response for laglead compensated system Lead and LagIeadcompensaled Uncompensaled CU Improvement in ramp response error for the system mm 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31359 39 53an903 3 AWL g i S3 mus Hm amp wu 4ny Kim 3 vicar its mt 0 Hawk egg 2 zwk l cmsjf 2 4 e ad 39 m m CW Kvsgteafm 4 lnervezv M wtky Brow 4W1 warm w W amt Control Systems Analysis AAE 364 PURDUE Instructor Prof Inseok Hwang Simplified description of a control system Input stimulus Desired response Control system Output response b Actual response PURD UE Examples Elevator a b Photos courtesy of United Technologies Otis Elevator gt HUUQD 6m mxm3omm 21830 Emmmmm ami muonszmao mi 0 mmwmzmmm L Ooovmqm zm 8422 0 3 wme 8 co m E g Q lt36 om Sommzsm 1er Z 2 ma Historical Review Centrifugal governor forthe speed control of a steam engine James Watt 18th century Stability analysis Routh Lyapunov Nyquist Classical Control Frequencyresponse methods 1940s 1950s 1 Singleinput Singleoutput SISO linear systems 2 Bode Plot Nyquist Plot and Rootlocus 3 Complex variables and functions Modern Control Time domain methods 1960s present Multipleinput Multipleoutput MIMO nonlinear systems State space method linear algebra differential geometry Optimal control adaptive and learning control robust control P URDUE Floor InputOutput Relation Input stimulus Control Output response SYStem Actual response Desired response Input command Transient gt response Steadystate Steadystate response error Elevator response Time PURDUE Block diagrams of control systems Disturbance l Disturbance Z 1 t i Output I Input Controller Process or Rc rcncc transducer or Plum commum Summing Summing vu ri 21b lc junction junction Openloop system Error 01 D l39 l t r w Acnmting Ihtlll 7vquotCL Tl1 1xHCL A Input hlgmi Output or or Controlled Rc L HCL unimng miltblc S Summing motion junction 0139 Sensor Closedloop system Antenna azimuth position control system r R aw n J sun Am nu nngi at my J m six nu ffvmw um Differential ampli er n pnwei ampli el Vlnhur Pnrcittinwtclcr b a system concept b detailed layout Angular input Mathematical description Angular output Equivalent block diagram Response of a position control system 0 utp ut with high gain Input Output with low gain Response Time PURD UE Control system design process Given physical system and specs Control system Design synthesis Mathematical Modeling Control System Analysis Penman RDUE Air Traffic Control Con ict Resolution ProtocolBased Conflict Resolution x v 39 I 4 3939 h N 1 i J x7 v lt v 39 39 14quot t H i M 1 i l s i jh a 41 i r i i 39 I I 2 3 7 x x 7 x 2 K v k 7 zquot x 1 x kr x quot i Using ETMS data Safety is guaranteed Unmanned Aerial Vehicle UAV o x Fligh ynamics and Con rolIHybrid Systems Lab PURDUE PURDUE nmlvrns l39xv n ma ai mg anw Luna39uw maunm 1mm Euummen mm Debug Help Flight Test Flight Movies Visualized Flight Data Autonomous navigation of a helicogter UAV Autonomous navi ation of a unmanned round vehicle UGV PURDUE W


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