Lecture 8. PID control. Industrial process control ( today) PID control. Insights about PID actions

Size: px
Start display at page:

Download "Lecture 8. PID control. Industrial process control ( today) PID control. Insights about PID actions"

Transcription

1 Lecture 8. PID control. The role of P, I, and D action 2. PID tuning Indutrial proce control (92... today) Feedback control i ued to improve the proce performance: tatic performance: for contant reference, the output aymptotically converge to the deired value, regardle of load diturbance. dynamic performance: enure proper tranient behavior during tep change Proportional control i not ufficient: feedback gain mut be frequency dependent! controller i itelf a dynamical ytem C() Syt3 lecture 8 Syt3 lecture 8 2 PID control Inight about PID action The magical three-term controller (99% of indutrial controller): u = K P e }{{} proportional Frequency interpretation: e + }{{} K D ė }{{} derivative integral +K I C() = K P + K I + K D K I dominate at low frequencie while K D dominate at high frequencie P I D Syt3 lecture 8 3 Syt3 lecture 8 4

2 Proportional control Frequency domain interpretation: 2 log H Suppoe P() = τ+ and C() = K. Cloed-loop tranfer function: Y R = K +K + +K τ The tatic error and the time contant are divided by ( + K) Feedback modifie the location of the pole. More generally: rlocu how how cloed-loop pole move with K. 2 log( + K) τ τ ( + K) Feedback ditribute the loop tranfer from u to y: trading gain for bandwidth... ω Increaing the bandwidth typically reduce the phae margin. Proportional control uually increae ocillation and overhoot in tep repone. Syt3 lecture 8 5 Syt3 lecture 8 6 Feedback to reduce tatic error r - Y = d e C() u + CP + CP R + P + CP D P() Aymptotic value of tep repone i given by lim t y(t) = lim Y () if ROC(Y ()) include the imaginary axi. For tep input R() = r and D() = d, we obtain y( ) = C()G() + C()G() r G() + + C()G() d r if + C()G() = S() >> y The role of integral feedback Integral action C() ha a pole at =. y( ) = r + d!! a general feature in feedback loop with contant external ignal: modulo tability (tatic regime may not exit!), block that contain a pole at = aymptotically force their input to zero. the property i independent of ytem parameter and linearity aumption! Syt3 lecture 8 7 Syt3 lecture 8 8

3 Integral feedback Internal model principle: for perfect tracking (rejection), the controller mut include a model of the reference (diturbance) ignal. For tep ignal, the model i. the controller pole at = caue a phae lag of 9deg in the loop tranfer integral action uually reduce the phae margin and increae overhoot Integral feedback a automatic bia adjutment compenate for tatic error if u(t) = Ke(t) + u ff u ff = + KP() With a PI control u(t) = Ke(t) + K I e, the bia i automatically adjuted. Syt3 lecture 8 9 Syt3 lecture 8 Derivative feedback PD control anticipate future error: u(t) = ke(t) + k d ė(t) = k(e(t) + T d ė(t)) ke(t + T d ) Think of pendulum model: u i a torque, y i a poition derivative feedback act a velocity feedback, i.e. a a friction force derivative control add a phae lead of +9deg in the loop tranfer uually increae the phae margin and damp the ocillation of the tep repone Derivative feedback amplifie noie the derivative action act a a noie amplifier require good enor the derivative i uually filtered: T d i replaced by limit the high-frequency gain amplification T d +T d /N to in a digital implementation, dicretizing the derivative feedback can be interpreted a filtering the derivative action i often not ued in proce control Syt3 lecture 8 Syt3 lecture 8 2

4 PI controller : + T i Set-point weighting G db G PID control i often implemented in the form T i -9 log ω log ω t u(t) = k(βr(t) y(t)) + k i (r y)(τ)dτ + k d (γṙ(t) ẏ(t)) Good for tatic performance but phae lag chooe T i ω B PD controller : + T d G db T d G +9 log ω log ω which correpond to a controller with two degree of freedom: U() = C()(R Y ) + F()R C() i tuned for diturbance rejection and F() i adjuted for reference tracking Phae lead i beneficial to tability margin but the cloed-loop bandwidth i increaed limit T d Syt3 lecture 8 3 Syt3 lecture 8 4 Antiwindup Due to actuator limitation, integral action i never implemented without an antiwindup mechanim. A general tructure for PID control The antiwindup reet the integral action when the input aturate. Syt3 lecture 8 5 Syt3 lecture 8 6

5 PID tuning control parameter tuning can be interpreted a pole placement for low-order model control parameter tuning can be interpreted a loop haping Special tuning method are model-free: the tuning i intead baed on a few open-loop experiment Many indutrial controller are mituned becaue they are tuned once forever adaptive control or auto-tuning method PI control of a firt order ytem Proce tranfer function Controller tranfer function P() = K τ + C() = k P + k I Cloed loop tranfer function from reference r to output y: Y () R() = CP + CP = K(k P + k I ) τ 2 + ( + Kk P ) + Kk I Cloed loop ytem of econd order; two parameter allow to place the pole of the cloed loop ytem Syt3 lecture 8 7 Syt3 lecture 8 8 PI control of a firt order ytem Example of deign: cancel the (low) proce pole, i.e. k I = τk P and place the cloed loop pole no overhoot, aignment of time contant, no tatic error. Perhap not the bet choice: one hould alo pay attention to the cloed loop tranfer function from the diturbance d to the output y: Y () D() = P + CP = K τ 2 + ( + Kk P ) + Kk I PD control of a econd order ytem Proce tranfer function Controller tranfer function b P() = 2 + a + a 2 C() = k P + k D Cloed loop tranfer function from reference r to output y: Y () R() = CP + CP = b(k D + k P ) 2 + (a + bk D ) + a 2 + bk P Cloed loop ytem of econd order; two parameter allow to place the pole of the cloed loop ytem. Syt3 lecture 8 9 Syt3 lecture 8 2

6 PD control of a econd order ytem The derivative action will damp the ocillation ( ζ) bk The cloed loop tatic gain i P bk P +a 2. But increaing k P may be harmful to bandwidth. The zero = k P /k D may caue coniderable overhoot if it i cloer to the origin than the dominant pole. PID control of a econd order ytem Proce tranfer function Controller tranfer function b G() = 2 + a + a 2 C() = k P + k D + k I Cloed loop tranfer function from reference r to output y: Y () R() = CG + CG = b(k D 2 + k P + k I ) 3 + (a + bk D ) 2 + (a 2 + bk P ) + bk I Cloed loop ytem of third order; three parameter allow to place the pole of the cloed loop ytem. Intability may occur for bad choice of control parameter! Syt3 lecture 8 2 Syt3 lecture 8 22 A zero in the tranfer function affect the tep repone H new = (z + )H old The location of a zero i NOT affected by feedback. In contrat, feedforward action change the location of zero. Interet of controller with two degree of freedom new (t) = old (t) + d old z dt (t) zero in left half plane: increae the overhoot a it approache imaginary axi. zero in right-half plane: reponible for invere repone phenomenon. Syt3 lecture 8 23 Syt3 lecture 8 24

7 Loop haping with PI control Two parameter allow to fix one point on the Nyquit curve. C() = K + T i Chooe K to aign the croover frequency ω c with ufficient phae margin. Maximize T i under the contraint φ m φ min m. Note: A larger T i low down the diturbance rejection. Phae-lag compenation K T i+, > T i + = K T i + T i + = K ( + z), z p + p G db -6-9 ωt i ωt i Static gain i increaed by factor. Phae lag will not affect the phae margin if T i ω C. Synthei guideline: adjut K to aign ω C with ufficient phae margin. Evaluate the neceary reduction of tatic error to chooe ; Maximize T i without degrading the phae margin. Syt3 lecture 8 25 Syt3 lecture 8 26 Loop haping with phae-lead compenator C() = K(T d + ) T d +, < = PD control Low-pa filter = K +z +p, p z G db K K +9 ωt d φ max Limitation of derivative action at high frequency. ωt d Phae-lead compenation Ueful formula: log ω max = 2 φ max = arcin ω max = z p ( log ( )) + log T d T d ( ) + Synthei guideline: Chooe ω c to aign cloed-loop bandwidth. Evaluate the neceary phae lead at ω c (not more than 6 = 6) and adjut T d to place the maximal phae lead at ω C. Chooe K to have L(jω c ) =. Syt3 lecture 8 27 Syt3 lecture 8 28

8 Summary of lecture PID i widely ued in the indutry. Three parameter roughly correpond to three performance criteria: tatic performance (I), cloed-loop bandwidth (P), and tability margin (D). Implementation of PID control include antiwindup, filtering of the derivative action, and et-point weighting. Syt3 lecture 8 29

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004 METR4200 Advanced Control Lecture 4 Chapter Nie Controller Deign via Frequency Repone G. Hovland 2004 Deign Goal Tranient repone via imple gain adjutment Cacade compenator to improve teady-tate error Cacade

More information

Lecture 5 Introduction to control

Lecture 5 Introduction to control Lecture 5 Introduction to control Tranfer function reviited (Laplace tranform notation: ~jω) () i the Laplace tranform of v(t). Some rule: ) Proportionality: ()/ in () 0log log() v (t) *v in (t) () * in

More information

Lecture 8 - SISO Loop Design

Lecture 8 - SISO Loop Design Lecture 8 - SISO Loop Deign Deign approache, given pec Loophaping: in-band and out-of-band pec Fundamental deign limitation for the loop Gorinevky Control Engineering 8-1 Modern Control Theory Appy reult

More information

ECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances

ECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances ECE 350 Root Locu Deign Example Recall the imple crude ervo from lab G( ) 0 6.64 53.78 σ = = 3 23.473 PI To eliminate teady-tate error (for contant input) & perfect reection of contant diturbance Note:

More information

MM1: Basic Concept (I): System and its Variables

MM1: Basic Concept (I): System and its Variables MM1: Baic Concept (I): Sytem and it Variable A ytem i a collection of component which are coordinated together to perform a function Sytem interact with their environment. The interaction i defined in

More information

ME 375 FINAL EXAM Wednesday, May 6, 2009

ME 375 FINAL EXAM Wednesday, May 6, 2009 ME 375 FINAL EXAM Wedneday, May 6, 9 Diviion Meckl :3 / Adam :3 (circle one) Name_ Intruction () Thi i a cloed book examination, but you are allowed three ingle-ided 8.5 crib heet. A calculator i NOT allowed.

More information

Digital Control System

Digital Control System Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital

More information

Wolfgang Hofle. CERN CAS Darmstadt, October W. Hofle feedback systems

Wolfgang Hofle. CERN CAS Darmstadt, October W. Hofle feedback systems Wolfgang Hofle Wolfgang.Hofle@cern.ch CERN CAS Darmtadt, October 9 Feedback i a mechanim that influence a ytem by looping back an output to the input a concept which i found in abundance in nature and

More information

Chapter 9: Controller design. Controller design. Controller design

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 information

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples Root Locu Content Root locu, ketching algorithm Root locu, example Root locu, proof Root locu, control example Root locu, influence of zero and pole Root locu, lead lag controller deign 9 Spring ME45 -

More information

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with :

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with : 376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD Therefore by applying the lead compenator with ome gain adjutment : D() =.12 4.5 +1 9 +1 we get the compenated ytem with : PM =65, ω c = 22 rad/ec, o

More information

ME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004

ME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004 ME 375 FINAL EXAM SOLUTIONS Friday December 7, 004 Diviion Adam 0:30 / Yao :30 (circle one) Name Intruction () Thi i a cloed book eamination, but you are allowed three 8.5 crib heet. () You have two hour

More information

Control Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax:

Control Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax: Control Sytem Engineering ( Chapter 7. Steady-State Error Prof. Kwang-Chun Ho kwangho@hanung.ac.kr Tel: 0-760-453 Fax:0-760-4435 Introduction In thi leon, you will learn the following : How to find the

More information

G(s) = 1 s by hand for! = 1, 2, 5, 10, 20, 50, and 100 rad/sec.

G(s) = 1 s by hand for! = 1, 2, 5, 10, 20, 50, and 100 rad/sec. 6003 where A = jg(j!)j ; = tan Im [G(j!)] Re [G(j!)] = \G(j!) 2. (a) Calculate the magnitude and phae of G() = + 0 by hand for! =, 2, 5, 0, 20, 50, and 00 rad/ec. (b) ketch the aymptote for G() according

More information

EE Control Systems LECTURE 14

EE Control Systems LECTURE 14 Updated: Tueday, March 3, 999 EE 434 - Control Sytem LECTURE 4 Copyright FL Lewi 999 All right reerved ROOT LOCUS DESIGN TECHNIQUE Suppoe the cloed-loop tranfer function depend on a deign parameter k We

More information

Department of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002

Department of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002 Department of Mechanical Engineering Maachuett Intitute of Technology 2.010 Modeling, Dynamic and Control III Spring 2002 SOLUTIONS: Problem Set # 10 Problem 1 Etimating tranfer function from Bode Plot.

More information

Homework 12 Solution - AME30315, Spring 2013

Homework 12 Solution - AME30315, Spring 2013 Homework 2 Solution - AME335, Spring 23 Problem :[2 pt] The Aerotech AGS 5 i a linear motor driven XY poitioning ytem (ee attached product heet). A friend of mine, through careful experimentation, identified

More information

Gain and Phase Margins Based Delay Dependent Stability Analysis of Two- Area LFC System with Communication Delays

Gain and Phase Margins Based Delay Dependent Stability Analysis of Two- Area LFC System with Communication Delays Gain and Phae Margin Baed Delay Dependent Stability Analyi of Two- Area LFC Sytem with Communication Delay Şahin Sönmez and Saffet Ayaun Department of Electrical Engineering, Niğde Ömer Halidemir Univerity,

More information

Module 4: Time Response of discrete time systems Lecture Note 1

Module 4: Time Response of discrete time systems Lecture Note 1 Digital Control Module 4 Lecture Module 4: ime Repone of dicrete time ytem Lecture Note ime Repone of dicrete time ytem Abolute tability i a baic requirement of all control ytem. Apart from that, good

More information

MODERN CONTROL SYSTEMS

MODERN CONTROL SYSTEMS MODERN CONTROL SYSTEMS Lecture 1 Root Locu Emam Fathy Department of Electrical and Control Engineering email: emfmz@aat.edu http://www.aat.edu/cv.php?dip_unit=346&er=68525 1 Introduction What i root locu?

More information

CHAPTER 4 DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL

CHAPTER 4 DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL 98 CHAPTER DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL INTRODUCTION The deign of ytem uing tate pace model for the deign i called a modern control deign and it i

More information

SKEE 3143 CONTROL SYSTEM DESIGN. CHAPTER 3 Compensator Design Using the Bode Plot

SKEE 3143 CONTROL SYSTEM DESIGN. CHAPTER 3 Compensator Design Using the Bode Plot SKEE 3143 CONTROL SYSTEM DESIGN CHAPTER 3 Compenator Deign Uing the Bode Plot 1 Chapter Outline 3.1 Introduc4on Re- viit to Frequency Repone, ploang frequency repone, bode plot tability analyi. 3.2 Gain

More information

Lecture 10 Filtering: Applied Concepts

Lecture 10 Filtering: Applied Concepts Lecture Filtering: Applied Concept In the previou two lecture, you have learned about finite-impule-repone (FIR) and infinite-impule-repone (IIR) filter. In thee lecture, we introduced the concept of filtering

More information

Compensation Techniques

Compensation Techniques D Compenation ehnique Performane peifiation for the loed-loop ytem Stability ranient repone Æ, M (ettling time, overhoot) or phae and gain margin Steady-tate repone Æ e (teady tate error) rial and error

More information

ECEN620: Network Theory Broadband Circuit Design Fall 2018

ECEN620: Network Theory Broadband Circuit Design Fall 2018 ECEN60: Network Theory Broadband Circuit Deign Fall 08 Lecture 6: Loop Filter Circuit Sam Palermo Analog & Mixed-Signal Center Texa A&M Univerity Announcement HW i due Oct Require tranitor-level deign

More information

Solutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam

Solutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam BSc - Sample Examination Digital Control Sytem (5-588-) Prof. L. Guzzella Solution Exam Duration: Number of Quetion: Rating: Permitted aid: minute examination time + 5 minute reading time at the beginning

More information

S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS

S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS by Michelle Gretzinger, Daniel Zyngier and Thoma Marlin INTRODUCTION One of the challenge to the engineer learning proce control i relating theoretical

More information

The Root Locus Method

The Root Locus Method The Root Locu Method MEM 355 Performance Enhancement of Dynamical Sytem Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Outline The root locu method wa introduced by Evan

More information

MEM 355 Performance Enhancement of Dynamical Systems Root Locus Analysis

MEM 355 Performance Enhancement of Dynamical Systems Root Locus Analysis MEM 355 Performance Enhancement of Dynamical Sytem Root Locu Analyi Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Outline The root locu method wa introduced by Evan in

More information

Lecture 6: Resonance II. Announcements

Lecture 6: Resonance II. Announcements EES 5 Spring 4, Lecture 6 Lecture 6: Reonance II EES 5 Spring 4, Lecture 6 Announcement The lab tart thi week You mut how up for lab to tay enrolled in the coure. The firt lab i available on the web ite,

More information

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}

More information

Design of Digital Filters

Design of Digital Filters Deign of Digital Filter Paley-Wiener Theorem [ ] ( ) If h n i a caual energy ignal, then ln H e dω< B where B i a finite upper bound. One implication of the Paley-Wiener theorem i that a tranfer function

More information

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005.

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005. SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2005. Initial Condition Source 0 V battery witch flip at t 0 find i 3 (t) Component value:

More information

March 18, 2014 Academic Year 2013/14

March 18, 2014 Academic Year 2013/14 POLITONG - SHANGHAI BASIC AUTOMATIC CONTROL Exam grade March 8, 4 Academic Year 3/4 NAME (Pinyin/Italian)... STUDENT ID Ue only thee page (including the back) for anwer. Do not ue additional heet. Ue of

More information

Given the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is

Given the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is EE 4G Note: Chapter 6 Intructor: Cheung More about ZSR and ZIR. Finding unknown initial condition: Given the following circuit with unknown initial capacitor voltage v0: F v0/ / Input xt 0Ω Output yt -

More information

ECE-320 Linear Control Systems. Spring 2014, Exam 1. No calculators or computers allowed, you may leave your answers as fractions.

ECE-320 Linear Control Systems. Spring 2014, Exam 1. No calculators or computers allowed, you may leave your answers as fractions. ECE-0 Linear Control Sytem Spring 04, Exam No calculator or computer allowed, you may leave your anwer a fraction. All problem are worth point unle noted otherwie. Total /00 Problem - refer to the unit

More information

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web:     Ph: Serial :. PT_EE_A+C_Control Sytem_798 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubanewar olkata Patna Web: E-mail: info@madeeay.in Ph: -4546 CLASS TEST 8-9 ELECTRICAL ENGINEERING Subject

More information

Design By Emulation (Indirect Method)

Design By Emulation (Indirect Method) Deign By Emulation (Indirect Method he baic trategy here i, that Given a continuou tranfer function, it i required to find the bet dicrete equivalent uch that the ignal produced by paing an input ignal

More information

Control Systems Analysis and Design by the Root-Locus Method

Control Systems Analysis and Design by the Root-Locus Method 6 Control Sytem Analyi and Deign by the Root-Locu Method 6 1 INTRODUCTION The baic characteritic of the tranient repone of a cloed-loop ytem i cloely related to the location of the cloed-loop pole. If

More information

THE PARAMETERIZATION OF ALL TWO-DEGREES-OF-FREEDOM SEMISTRONGLY STABILIZING CONTROLLERS. Tatsuya Hoshikawa, Kou Yamada and Yuko Tatsumi

THE PARAMETERIZATION OF ALL TWO-DEGREES-OF-FREEDOM SEMISTRONGLY STABILIZING CONTROLLERS. Tatsuya Hoshikawa, Kou Yamada and Yuko Tatsumi International Journal of Innovative Computing, Information Control ICIC International c 206 ISSN 349-498 Volume 2, Number 2, April 206 pp. 357 370 THE PARAMETERIZATION OF ALL TWO-DEGREES-OF-FREEDOM SEMISTRONGLY

More information

Analysis of Stability &

Analysis of Stability & INC 34 Feedback Control Sytem Analyi of Stability & Steady-State Error S Wonga arawan.won@kmutt.ac.th Summary from previou cla Firt-order & econd order ytem repone τ ωn ζω ω n n.8.6.4. ζ ζ. ζ.5 ζ ζ.5 ct.8.6.4...4.6.8..4.6.8

More information

Exercises for lectures 19 Polynomial methods

Exercises for lectures 19 Polynomial methods Exercie for lecture 19 Polynomial method Michael Šebek Automatic control 016 15-4-17 Diviion of polynomial with and without remainder Polynomial form a circle, but not a body. (Circle alo form integer,

More information

The state variable description of an LTI system is given by 3 1O. Statement for Linked Answer Questions 3 and 4 :

The state variable description of an LTI system is given by 3 1O. Statement for Linked Answer Questions 3 and 4 : CHAPTER 6 CONTROL SYSTEMS YEAR TO MARKS MCQ 6. The tate variable decription of an LTI ytem i given by Jxo N J a NJx N JN K O K OK O K O xo a x + u Kxo O K 3 a3 OKx O K 3 O L P L J PL P L P x N K O y _

More information

Then C pid (s) S h -stabilizes G(s) if and only if Ĉpid(ŝ) S 0 - stabilizes Ĝ(ŝ). For any ρ R +, an RCF of Ĉ pid (ŝ) is given by

Then C pid (s) S h -stabilizes G(s) if and only if Ĉpid(ŝ) S 0 - stabilizes Ĝ(ŝ). For any ρ R +, an RCF of Ĉ pid (ŝ) is given by 9 American Control Conference Hyatt Regency Riverfront, St. Loui, MO, USA June -, 9 WeC5.5 PID Controller Synthei with Shifted Axi Pole Aignment for a Cla of MIMO Sytem A. N. Gündeş and T. S. Chang Abtract

More information

Root Locus Diagram. Root loci: The portion of root locus when k assume positive values: that is 0

Root Locus Diagram. Root loci: The portion of root locus when k assume positive values: that is 0 Objective Root Locu Diagram Upon completion of thi chapter you will be able to: Plot the Root Locu for a given Tranfer Function by varying gain of the ytem, Analye the tability of the ytem from the root

More information

6.447 rad/sec and ln (% OS /100) tan Thus pc. the testing point is s 3.33 j5.519

6.447 rad/sec and ln (% OS /100) tan Thus pc. the testing point is s 3.33 j5.519 9. a. 3.33, n T ln(% OS /100) 2 2 ln (% OS /100) 0.517. Thu n 6.7 rad/ec and the teting point i 3.33 j5.519. b. Summation of angle including the compenating zero i -106.691, The compenator pole mut contribute

More information

Multivariable Control Systems

Multivariable Control Systems Lecture Multivariable Control Sytem Ali Karimpour Aociate Profeor Ferdowi Univerity of Mahhad Lecture Reference are appeared in the lat lide. Dr. Ali Karimpour May 6 Uncertainty in Multivariable Sytem

More information

MM7. PID Control Design

MM7. PID Control Design MM7. PD Control Deign Reading Material: FC: p.79-200, DC: p.66-68. Propertie of PD control 2. uning Method of PD Control 3. Antiwindup echnique 4. A real cae tudy BO9000 0/9/2004 Proce Control . PD Feedback

More information

EE105 - Fall 2005 Microelectronic Devices and Circuits

EE105 - Fall 2005 Microelectronic Devices and Circuits EE5 - Fall 5 Microelectronic Device and ircuit Lecture 9 Second-Order ircuit Amplifier Frequency Repone Announcement Homework 8 due tomorrow noon Lab 7 next week Reading: hapter.,.3. Lecture Material Lat

More information

NAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE

NAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE POLITONG SHANGHAI BASIC AUTOMATIC CONTROL June Academic Year / Exam grade NAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE Ue only thee page (including the bac) for anwer. Do not ue additional

More information

5.5 Application of Frequency Response: Signal Filters

5.5 Application of Frequency Response: Signal Filters 44 Dynamic Sytem Second order lowpa filter having tranfer function H()=H ()H () u H () H () y Firt order lowpa filter Figure 5.5: Contruction of a econd order low-pa filter by combining two firt order

More information

arxiv: v1 [cs.sy] 24 May 2018

arxiv: v1 [cs.sy] 24 May 2018 No More Differentiator in : Development of Nonlinear Lead for Preciion Mechatronic Arun Palanikumar, Niranjan Saikumar, S. Haan HoeinNia arxiv:5.973v [c.sy] May Abtract Indutrial conit of three element:

More information

CONTROL OF INTEGRATING PROCESS WITH DEAD TIME USING AUTO-TUNING APPROACH

CONTROL OF INTEGRATING PROCESS WITH DEAD TIME USING AUTO-TUNING APPROACH Brazilian Journal of Chemical Engineering ISSN 004-6632 Printed in Brazil www.abeq.org.br/bjche Vol. 26, No. 0, pp. 89-98, January - March, 2009 CONROL OF INEGRAING PROCESS WIH DEAD IME USING AUO-UNING

More information

Lecture #9 Continuous time filter

Lecture #9 Continuous time filter Lecture #9 Continuou time filter Oliver Faut December 5, 2006 Content Review. Motivation......................................... 2 2 Filter pecification 2 2. Low pa..........................................

More information

Chapter 7. Root Locus Analysis

Chapter 7. Root Locus Analysis Chapter 7 Root Locu Analyi jw + KGH ( ) GH ( ) - K 0 z O 4 p 2 p 3 p Root Locu Analyi The root of the cloed-loop characteritic equation define the ytem characteritic repone. Their location in the complex

More information

16.400/453J Human Factors Engineering. Manual Control II

16.400/453J Human Factors Engineering. Manual Control II 16.4/453J Human Factor Engineering Manual Control II Pilot Input 16.4/453 Pitch attitude Actual pitch error 8 e attitude 8 Deired pitch attitude 8 c Digital flight control computer Cockpit inceptor Fly-by-wire

More information

R. 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 R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder Cloed-loop buck converter example: Section 9.5.4 In ECEN 5797, we ued the CCM mall ignal model to

More information

The loop shaping paradigm. Lecture 7. Loop analysis of feedback systems (2) Essential specifications (2)

The 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 information

A Simple Approach to Synthesizing Naïve Quantized Control for Reference Tracking

A Simple Approach to Synthesizing Naïve Quantized Control for Reference Tracking A Simple Approach to Syntheizing Naïve Quantized Control for Reference Tracking SHIANG-HUA YU Department of Electrical Engineering National Sun Yat-Sen Univerity 70 Lien-Hai Road, Kaohiung 804 TAIAN Abtract:

More information

EE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis

EE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis EE/ME/AE34: Dynamical Sytem Chapter 8: Tranfer Function Analyi The Sytem Tranfer Function Conider the ytem decribed by the nth-order I/O eqn.: ( n) ( n 1) ( m) y + a y + + a y = b u + + bu n 1 0 m 0 Taking

More information

1 Routh Array: 15 points

1 Routh Array: 15 points EE C28 / ME34 Problem Set 3 Solution Fall 2 Routh Array: 5 point Conider the ytem below, with D() k(+), w(t), G() +2, and H y() 2 ++2 2(+). Find the cloed loop tranfer function Y () R(), and range of k

More information

Chapter 13. Root Locus Introduction

Chapter 13. Root Locus Introduction Chapter 13 Root Locu 13.1 Introduction In the previou chapter we had a glimpe of controller deign iue through ome imple example. Obviouly when we have higher order ytem, uch imple deign technique will

More information

Stability. ME 344/144L Prof. R.G. Longoria Dynamic Systems and Controls/Lab. Department of Mechanical Engineering The University of Texas at Austin

Stability. ME 344/144L Prof. R.G. Longoria Dynamic Systems and Controls/Lab. Department of Mechanical Engineering The University of Texas at Austin Stability The tability of a ytem refer to it ability or tendency to eek a condition of tatic equilibrium after it ha been diturbed. If given a mall perturbation from the equilibrium, it i table if it return.

More information

What lies between Δx E, which represents the steam valve, and ΔP M, which is the mechanical power into the synchronous machine?

What lies between Δx E, which represents the steam valve, and ΔP M, which is the mechanical power into the synchronous machine? A 2.0 Introduction In the lat et of note, we developed a model of the peed governing mechanim, which i given below: xˆ K ( Pˆ ˆ) E () In thee note, we want to extend thi model o that it relate the actual

More information

CONTROL SYSTEMS. Chapter 2 : Block Diagram & Signal Flow Graphs GATE Objective & Numerical Type Questions

CONTROL SYSTEMS. Chapter 2 : Block Diagram & Signal Flow Graphs GATE Objective & Numerical Type Questions ONTOL SYSTEMS hapter : Bloc Diagram & Signal Flow Graph GATE Objective & Numerical Type Quetion Quetion 6 [Practice Boo] [GATE E 994 IIT-Kharagpur : 5 Mar] educe the ignal flow graph hown in figure below,

More information

Fractional-Order PI Speed Control of a Two-Mass Drive System with Elastic Coupling

Fractional-Order PI Speed Control of a Two-Mass Drive System with Elastic Coupling Fractional-Order PI Speed Control of a Two-Ma Drive Sytem with Elatic Coupling Mohammad Amin Rahimian, Mohammad Saleh Tavazoei, and Farzad Tahami Electrical Engineering Department, Sharif Univerity of

More information

J. Electrical Systems 8-1 (2012): Regular paper

J. Electrical Systems 8-1 (2012): Regular paper K.R.M. Vijaya Chandrakala S. Balamurugan K. Sankaranarayanan J. Electrical Sytem 8- (22): 85-94 Regular paper Damping of Tie-Line Power Ocillation in Interconnected Power Sytem uing Variable Structure

More information

ECE382/ME482 Spring 2004 Homework 4 Solution November 14,

ECE382/ME482 Spring 2004 Homework 4 Solution November 14, ECE382/ME482 Spring 2004 Homework 4 Solution November 14, 2005 1 Solution to HW4 AP4.3 Intead of a contant or tep reference input, we are given, in thi problem, a more complicated reference path, r(t)

More information

POWER SYSTEM SMALL SIGNAL STABILITY ANALYSIS BASED ON TEST SIGNAL

POWER SYSTEM SMALL SIGNAL STABILITY ANALYSIS BASED ON TEST SIGNAL POWE YEM MALL INAL ABILIY ANALYI BAE ON E INAL Zheng Xu, Wei hao, Changchun Zhou Zheang Univerity, Hangzhou, 37 PChina Email: hvdc@ceezueducn Abtract - In thi paper, a method baed on ome tet ignal (et

More information

ME2142/ME2142E Feedback Control Systems

ME2142/ME2142E Feedback Control Systems Root Locu Analyi Root Locu Analyi Conider the cloed-loop ytem R + E - G C B H The tranient repone, and tability, of the cloed-loop ytem i determined by the value of the root of the characteritic equation

More information

LOW ORDER MIMO CONTROLLER DESIGN FOR AN ENGINE DISTURBANCE REJECTION PROBLEM. P.Dickinson, A.T.Shenton

LOW ORDER MIMO CONTROLLER DESIGN FOR AN ENGINE DISTURBANCE REJECTION PROBLEM. P.Dickinson, A.T.Shenton LOW ORDER MIMO CONTROLLER DESIGN FOR AN ENGINE DISTURBANCE REJECTION PROBLEM P.Dickinon, A.T.Shenton Department of Engineering, The Univerity of Liverpool, Liverpool L69 3GH, UK Abtract: Thi paper compare

More information

Behavioral thermal modeling for quad-core microprocessors

Behavioral thermal modeling for quad-core microprocessors Behavioral thermal modeling for quad-core microproceor Duo Li and Sheldon X.-D. Tan Department of Electrical Engineering Univerity of California, Riveride, CA Murli Tirumala Intel Corporation Outline Introduction

More information

A Simplified Methodology for the Synthesis of Adaptive Flight Control Systems

A Simplified Methodology for the Synthesis of Adaptive Flight Control Systems A Simplified Methodology for the Synthei of Adaptive Flight Control Sytem J.ROUSHANIAN, F.NADJAFI Department of Mechanical Engineering KNT Univerity of Technology 3Mirdamad St. Tehran IRAN Abtract- A implified

More information

FRTN10 Exercise 3. Specifications and Disturbance Models

FRTN10 Exercise 3. Specifications and Disturbance Models FRTN0 Exercie 3. Specification and Diturbance Model 3. A feedback ytem i hown in Figure 3., in which a firt-order proce if controlled by an I controller. d v r u 2 z C() P() y n Figure 3. Sytem in Problem

More information

Massachusetts Institute of Technology Dynamics and Control II

Massachusetts Institute of Technology Dynamics and Control II I E Maachuett Intitute of Technology Department of Mechanical Engineering 2.004 Dynamic and Control II Laboratory Seion 5: Elimination of Steady-State Error Uing Integral Control Action 1 Laboratory Objective:

More information

( 1) EE 313 Linear Signals & Systems (Fall 2018) Solution Set for Homework #10 on Laplace Transforms

( 1) EE 313 Linear Signals & Systems (Fall 2018) Solution Set for Homework #10 on Laplace Transforms EE 33 Linear Signal & Sytem (Fall 08) Solution Set for Homework #0 on Laplace Tranform By: Mr. Houhang Salimian & Prof. Brian L. Evan Problem. a) xt () = ut () ut ( ) From lecture Lut { ()} = and { } t

More information

USING NONLINEAR CONTROL ALGORITHMS TO IMPROVE THE QUALITY OF SHAKING TABLE TESTS

USING NONLINEAR CONTROL ALGORITHMS TO IMPROVE THE QUALITY OF SHAKING TABLE TESTS October 12-17, 28, Beijing, China USING NONLINEAR CONTR ALGORITHMS TO IMPROVE THE QUALITY OF SHAKING TABLE TESTS T.Y. Yang 1 and A. Schellenberg 2 1 Pot Doctoral Scholar, Dept. of Civil and Env. Eng.,

More information

Chapter 10. Closed-Loop Control Systems

Chapter 10. Closed-Loop Control Systems hapter 0 loed-loop ontrol Sytem ontrol Diagram of a Typical ontrol Loop Actuator Sytem F F 2 T T 2 ontroller T Senor Sytem T TT omponent and Signal of a Typical ontrol Loop F F 2 T Air 3-5 pig 4-20 ma

More information

Chapter 2: Problem Solutions

Chapter 2: Problem Solutions Chapter 2: Solution Dicrete Time Proceing of Continuou Time Signal Sampling à 2.. : Conider a inuoidal ignal and let u ample it at a frequency F 2kHz. xt 3co000t 0. a) Determine and expreion for the ampled

More information

Chapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog

Chapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog Chapter Sampling and Quantization.1 Analog and Digital Signal In order to invetigate ampling and quantization, the difference between analog and digital ignal mut be undertood. Analog ignal conit of continuou

More information

Contents lecture 4. Automatic Control III. Summary of lecture 3 (II/II) Summary of lecture 3 (I/II) Lecture 4 Controller structures and control design

Contents lecture 4. Automatic Control III. Summary of lecture 3 (II/II) Summary of lecture 3 (I/II) Lecture 4 Controller structures and control design Content lecture 4 Automatic Control III Lecture 4 Controller tructure and control deign Thoma Schön Diviion of Sytem and Control Department of Information Technology Uppala Univerity. Email: thoma.chon@it.uu.e,

More information

Analysis and Design of a Third Order Phase-Lock Loop

Analysis and Design of a Third Order Phase-Lock Loop Analyi Deign of a Third Order Phae-Lock Loop DANIEL Y. ABRAMOVITCH Ford Aeropace Corporation 3939 Fabian Way, MS: X- Palo Alto, CA 94303 Abtract Typical implementation of a phae-lock loop (PLL) are econd

More information

Evolutionary Algorithms Based Fixed Order Robust Controller Design and Robustness Performance Analysis

Evolutionary Algorithms Based Fixed Order Robust Controller Design and Robustness Performance Analysis Proceeding of 01 4th International Conference on Machine Learning and Computing IPCSIT vol. 5 (01) (01) IACSIT Pre, Singapore Evolutionary Algorithm Baed Fixed Order Robut Controller Deign and Robutne

More information

6.302 Feedback Systems Recitation 6: Steady-State Errors Prof. Joel L. Dawson S -

6.302 Feedback Systems Recitation 6: Steady-State Errors Prof. Joel L. Dawson S - 6302 Feedback ytem Recitation 6: teadytate Error Prof Joel L Dawon A valid performance metric for any control ytem center around the final error when the ytem reache teadytate That i, after all initial

More information

Today s Lecture. Block Diagrams. Block Diagrams: Examples. Block Diagrams: Examples. Closed Loop System 06/03/2017

Today s Lecture. Block Diagrams. Block Diagrams: Examples. Block Diagrams: Examples. Closed Loop System 06/03/2017 06/0/07 UW Britol Indutrial ontrol UFMF6W-0- ontrol Sytem ngineering UFMUY-0- Lecture 5: Block Diagram and Steady State rror Today Lecture Block diagram to repreent control ytem Block diagram manipulation

More information

A Comparative Study on Control Techniques of Non-square Matrix Distillation Column

A Comparative Study on Control Techniques of Non-square Matrix Distillation Column IJCTA, 8(3), 215, pp 1129-1136 International Science Pre A Comparative Study on Control Technique of Non-quare Matrix Ditillation Column 1 S Bhat Vinayambika, 2 S Shanmuga Priya, and 3 I Thirunavukkarau*

More information

Feedback Control of Dynamic Systems. Yves Briere

Feedback Control of Dynamic Systems. Yves Briere Feedback Control of Dynamic Sytem Yve Briere yve.briere@iae.fr I. Introduction Introduction Aim of the coure Give a general overview of claical and modern control theory Give a general overview of modern

More information

RaneNote BESSEL FILTER CROSSOVER

RaneNote BESSEL FILTER CROSSOVER RaneNote BESSEL FILTER CROSSOVER A Beel Filter Croover, and It Relation to Other Croover Beel Function Phae Shift Group Delay Beel, 3dB Down Introduction One of the way that a croover may be contructed

More information

Resonant Load Control Methods for Industrial Servo Drives

Resonant Load Control Methods for Industrial Servo Drives IEEE Indutry Application Society Annual Meeting Rome, Italy, October 8 2, 2000 Reonant Load Control Method for Indutrial Servo Drive George Elli Kollmorgen Corporation 20 Rock Road Radford, VA 24060 T:

More information

MAHALAKSHMI ENGINEERING COLLEGE-TRICHY

MAHALAKSHMI ENGINEERING COLLEGE-TRICHY DIGITAL SIGNAL PROCESSING DEPT./SEM.: CSE /VII DIGITAL FILTER DESIGN-IIR & FIR FILTER DESIGN PART-A. Lit the different type of tructure for realiation of IIR ytem? AUC APR 09 The different type of tructure

More information

Function and Impulse Response

Function and Impulse Response Tranfer Function and Impule Repone Solution of Selected Unolved Example. Tranfer Function Q.8 Solution : The -domain network i hown in the Fig... Applying VL to the two loop, R R R I () I () L I () L V()

More information

Assessment of Performance for Single Loop Control Systems

Assessment of Performance for Single Loop Control Systems Aement of Performance for Single Loop Control Sytem Hiao-Ping Huang and Jyh-Cheng Jeng Department of Chemical Engineering National Taiwan Univerity Taipei 1617, Taiwan Abtract Aement of performance in

More information

Linear-Quadratic Control System Design

Linear-Quadratic Control System Design Linear-Quadratic Control Sytem Deign Robert Stengel Optimal Control and Etimation MAE 546 Princeton Univerity, 218! Control ytem configuration! Proportional-integral! Proportional-integral-filtering! Model

More information

PI control system design for Electromagnetic Molding Machine based on Linear Programing

PI control system design for Electromagnetic Molding Machine based on Linear Programing PI control ytem deign for Electromagnetic Molding Machine baed on Linear Programing Takayuki Ihizaki, Kenji Kahima, Jun-ichi Imura*, Atuhi Katoh and Hirohi Morita** Abtract In thi paper, we deign a PI

More information

Stability regions in controller parameter space of DC motor speed control system with communication delays

Stability regions in controller parameter space of DC motor speed control system with communication delays Stability region in controller parameter pace of DC motor peed control ytem with communication delay Şahin Sönmez, Saffet Ayaun Department of Electrical and Electronic Engineering, Nigde Univerity, 5124,

More information

CHAPTER 13 FILTERS AND TUNED AMPLIFIERS

CHAPTER 13 FILTERS AND TUNED AMPLIFIERS HAPTE FILTES AND TUNED AMPLIFIES hapter Outline. Filter Traniion, Type and Specification. The Filter Tranfer Function. Butterworth and hebyhev Filter. Firt Order and Second Order Filter Function.5 The

More information

A PLC BASED MIMO PID CONTROLLER FOR MULTIVARIABLE INDUSTRIAL PROCESSES

A PLC BASED MIMO PID CONTROLLER FOR MULTIVARIABLE INDUSTRIAL PROCESSES ABCM Sympoium Serie in Mechatronic - Vol. 3 - pp.87-96 Copyright c 8 by ABCM A PLC BASE MIMO PI CONOLLE FO MULIVAIABLE INUSIAL POCESSES Joé Maria Galvez, jmgalvez@ufmg.br epartment of Mechanical Engineering

More information

On Stability of Electronic Circuits

On Stability of Electronic Circuits roceeding of the th WSAS International Conference on CIUITS On Stability of lectronic Circuit HASSAN FATHABADI lectrical ngineering Department Azad Univerity (South Tehran Branch) Tehran, IAN h4477@hotmailcom

More information

Homework Assignment No. 3 - Solutions

Homework Assignment No. 3 - Solutions ECE 6440 Summer 2003 Page 1 Homework Aignment o. 3 Problem 1 (10 point) Aume an LPLL ha F() 1 and the PLL parameter are 0.8V/radian, K o 100 MHz/V, and the ocillation frequency, f oc 500MHz. Sketch the

More information

Feedback Control Systems (FCS)

Feedback Control Systems (FCS) Feedback Control Sytem (FCS) Lecture19-20 Routh-Herwitz Stability Criterion Dr. Imtiaz Huain email: imtiaz.huain@faculty.muet.edu.pk URL :http://imtiazhuainkalwar.weebly.com/ Stability of Higher Order

More information