Control System Design
|
|
- Delphia Parker
- 6 years ago
- Views:
Transcription
1 ELEC ENG 4CL4: Control System Design Notes for Lecture #1 Monday, January 6, 2003
2 Instructor: Dr. Ian C. Bruce Room CRL-229, Ext Office Hours: TBA Teaching Assistants: Kamran Mustafa Jennifer Ko Room CRL-205, Ext Office Hours: TBA Web Site:
3 Proposed Course Content: Introduction to the Principles of Feedback (1 hour) Continuous-Time Signals and Systems (1 hour) Review of the Laplace Transform, and the evaluation of time and frequency responses from poles and zeros Analysis of Single-Input Single-Output (SISO) Control Loops (2 hrs) Sensitivity Functions Root Locus, Frequency Response Techniques Relative Stability Robustness Classical Proportional-Integral-Derivative (PID) Control (5 hours) Ziegler-Nichols Methods Lead-Lag compensators Industrial application: Control of a distillation column
4 Course Content (cont.): Performance Limitations (4 hours) Sensors and actuators Bode's integral constraints Examples of design trade-offs Models for Sampled-Data Control Systems (2 hours) Advanced SISO Control Open loop inversion and affine parameterization of stabilizing controllers (2 hours) Optimization based designs (2 hours) Linear state space models (4 hours) Controller synthesis via state space methods (3 hours) Introduction to non-linear control (4 hours)
5 Course Content (cont.): Multi-Input Multi-Output (MIMO) Control (8 hours) Models for multivariable systems Stability, Frequency response, robustness Decentralized control Optimal multivariable control systems State-estimate feedback Linear Quadratic Regulator (LQR) Achieving integral action in LQR synthesis Industrial Applications (Total Course = 39 hours)
6 Textbook: G. C. Goodwin, S. F. Graebe, and M. E. Salgado, "Control System Design," Prentice Hall, (New and used copies available at Titles Bookstore.) Chapters 2 and 3 will only be covered briefly in lectures, but you should read these chapters thoroughly.
7 Prerequisites: Courses: ELEC ENG 3TP4 Competencies: Linear signals and systems analysis, esp. Laplace transform, differential equations, state-space models Matrix algebra Matlab/Simulink
8 Proposed Assessment: Weekly Homework (10%) Labs (15%) Project (15%) Midterm (20%) Final (40%) You will be notified in advance if any changes are to be made to this assessment scheme.
9 Lectures: There will be 39 one-hour lectures (3 per week) in BSB-B103 on: Mondays 11:30am-12:30pm, Wednesdays 11:30am-12:30pm, and Fridays 1:30-2:30pm. Lecture notes in PDF format will be posted on the course web site before each lecture.
10 Tutorials: There will be 1 one-hour tutorial per week. The class is split into two sections for tutorials: Section T1 is in LS-B130A on Wednesdays 10:30-11:30am Section T2 is in ABB-270 on Fridays 10:30-11:30am
11 Labs: There will be 5 three-hour labs in T every second week on Mondays 2:30-5:30pm. The two tutorial sections (T1 and T2) will alternate weeks for labs. Lab descriptions will be made available on this web site the week before the lab, and lab reports are to be submitted at the tutorial the week after the lab. The majority of the labs will be Matlab/Simulink based simulations that can also be performed outside of lab hours, but the TAs will only provide assistance during lab hours.
12 Weekly Homework: There will be 10 weekly homework assignments. Homework assignments will be given out at the end of the tutorial each week, and homework reports are to be submitted at the start of the tutorial the following week. TBA Project:
13 Policy Reminders: The Faculty of Engineering is concerned with ensuring an environment that is free of all adverse discrimination. If there is a problem, that cannot be resolved by discussion among the persons concerned, individuals are reminded they should contact the Departmental Chair, the Sexual Harassment Officer or the Human Rights Consultant, as soon as possible. Students are reminded that they should read and comply with the Statement on Academic Ethics and the Senate Resolutions on Academic Dishonesty as found in the Senate Policy Statements distributed at registration and available at the senate office.
14 Chapter 2 Introduction to the Principles of Feedback Topics to be covered include: An industrial motivational example; A statement of the fundamental nature of the control problem; The idea of inversion as the central ingredient in solving control problems; Evolution from open loop inversion to closed loop feedback solutions.
15 We will see that feedback is a key tool that can be used to modify the behaviour of a system. This behaviour altering effect of feedback is a key mechanism that control engineers exploit deliberately to achieve the objective of acting on a system to ensure that the desired performance specifications are achieved.
16 A motivating industrial example We first present a simplified, yet essentially authentic, example of an industrial control problem. The example, taken from the steel industry, is of a particular nature, however the principal elements of specifying a desired behaviour, modeling and the necessity for trade-off decisions are generic.
17 Photograph of Bloom Caster
18 Process schematic of an Industrial Bloom Caster
19 Continuous caster. Typical bloom (left) and simplified diagram (right) tundish with molten steel t l control valve mould primary cooling w continuously withdrawn, semi-solid strand
20 Operators viewing the mould
21 The cast strip in the secondary cooling chamber
22 Performance specifications The key performance goals for this problem are: Safety: Clearly, the mould level must never be in danger of overflowing or emptying as either case would result in molten metal spilling with disastrous consequences. Profitability: Aspects which contribute to this requirement include: Product quality Maintenance Throughput
23 Modeling To make progress on the control system design problem, it is first necessary to gain an understanding of how the process operates. This understanding is typically expressed in the form of a mathematical model. q h* h( t) v( t) σ ( t) q in out ( t) ( t) : : : : : : commanded level of steel in mould actual level of steel in mould valve position casting speed inflow of matter into the mould outflow of matter from the mould
24 Model as simple tank Molten Steel Tundish Valve Mould Level Cooling Water
25 Block diagram of the simplified mould level dynamics, sensors and actuators These variables are related as shown below: Casting speed measurement Inflow from control valve + Outflow due to casting speed Measured mould level + Mould level + Meas. noise
26 Feedback and Feedforward We will find later that the core idea in control is that of inversion. Moreover, inversion can be conveniently achieved by the use of two key mechanisms (namely, feedback and feedforward).
27 Figure 2.4: Model of the simplified mould level control with feedforward compensation for casting speed Suggested Control Strategy: Commanded mould level + K 1 Casting speed measurement K Inflow from control valve Outflow due to casting speed + Mould level Meas. noise Measured mould level + Note that this controller features joint feedback and a preemptive action (feedforward).
28 A first indication of trade-offs On simulating the performance of the above control loop for K=1 and K=5, see Figure 2.5, we find that the smaller controller gain (K=1) results in a slower response to a change in the mould level set-point. On the other hand, the larger controller gain (K=5), results in a faster response but also increases the effects of measurement noise as seen by the less steady level control and by the significantly more aggressive valve movements.
29 Figure 2.5: A first indication of trade-offs: Increased responsiveness to set-point changes also increases sensitivity to measurement noise and actuator wear. 1.4 Mould level K=5 K= Valve command K=1 0 K= Time [s]
30 Question We may ask if these trade-offs are unavoidable or whether we could improve on the situation by such measures as: better modelling more sophisticated control system design This will be the subject of the rest of our deliberations. (Aside: Actually the trade-off is fundamental as we shall see presently).
31 Definition of the control problem Abstracting from the above particular problem, we can introduce: Definition 2.1: The central problem in control is to find a technically feasible way to act on a given process so that the process behaves, as closely as possible, to some desired behaviour. Furthermore, this approximate behaviour should be achieved in the face of uncertainty of the process and in the presence of uncontrollable external disturbances acting on the process.
32 Prototype solution to the control problem via inversion One particularly simple, yet insightful way of thinking about control problems is via inversion. To describe this idea we argue as follows: say that we know what effect an action at the input of a system produces at the output, and say that we have a desired behaviour for the system output, then one simply needs to invert the relationship between input and output to determine what input action is necessary to achieve the desired output behaviour.
33 Figure 2.6: Conceptual controller The above idea is captured in the following diagram: d r + f 1 u f + + y Conceptual controller Plant
34 We will actually find that the inverse solution given on the last slide holds very generally. Thus, all controllers implicitly generate an inverse of the process, in so far that this is feasible. However, the details of controllers will differ with respect to the mechanism used to generate the required approximate inverse.
35 High gain feedback and inversion We next observe that there is a rather intriguing property of feedback, namely that it implicitly generates an approximate inverse of dynamic transformations, without the inversion having to be carried out explicitly. r u y h Plant + z f Figure 2.7: Realisation of conceptual controller The loop implements an approximate inverse of f ο, i.e. u = f r, if r - h -1 u r
36 Chapter 2 Specifically, u f r h z r h u = = or u f r u h = 1 Hence r f u h r f u = Provided is small, i.e. is high gain. u h 1 h
37 The above equation is satisfied if h -1 u is large. We conclude that an approximate inverse is generated provided we place the model of the system in a high gain feedback loop.
38 Example 2.3 Assume that a plant can be described by the model dy( t) + 2 dt y( t) = u( t) and that a control law is required to ensure that y(t) follows a slowly varying reference. One way to solve this problem is to construct an inverse for the model which is valid in the low frequency region. Using the architecture in Figure 2.7, we obtain an approximate inverse, provided that h ο has large gain in the low frequency region.
39 Figure 2.8: Tank level control using approximate inversion Simulating the resultant controller gives the results below: 2 Ref. and plant output r(t) y(t) Time [s]
40 From open to closed loop architectures Unfortunately, the above methodology will not lead to a satisfactory solution to the control problem unless: the model on which the design of the controller has been based is a very good representation of the plant, the model and its inverse are stable, and disturbances and initial conditions are negligible. We are thus motivated to find an alternative solution to the problem which retains the key features but which does not suffer from the above drawbacks.
41 Figure 2.9: Open loop control with built-in inverse r(t) + Feedback gain A u(t) Plant y(t) Model Open loop controller Figure 2.10: Closed loop control r(t) + e(t) u(t) A y(t) Feedback gain Plant
42 The first thing to note is that, provided the model represents the plant exactly, and that all signals are bounded (i.e. the loop is stable), then both schemes are equivalent, regarding the relation between r(t) and y(t). The key differences are due to disturbances and different initial conditions. In the open loop control scheme the controller incorporates feedback internally, i.e. a signal at point A is fed back.
43 In the closed loop scheme, the feedback signal depends on what is actually happening in the plant since the true plant output is used. We will see later that this modified architecture has many advantages including: insensitivity to modelling errors; insensitivity to disturbances in the plant (that are not reflected in the model).
44 For example, if a plant disturbance leads to a non-zero error e(t), in Figure 2.10, then high gain feedback will result in a very large control action u(t). This may lie outside the available input range and thus invalidate the solution. Chapter 2 Trade-offs involved in choosing the feedback gain The preliminary insights of the previous two sections would seem to imply that all that is needed to generate a controller is to put high gain feedback around the plant. This is true in so far that it goes. However, nothing in life is cost free and this also applies to the use of high gain feedback.
45 Another potential problem with high gain feedback is that it is often accompanied by the very substantial risk of instability. Instability is characterised by self sustaining (or growing) oscillations. As an illustration, the reader will probably have witnessed the high pitch whistling sound that is heard when a loudspeaker is placed too close to a microphone. This is a manifestation of instability resulting from excessive feedback gain. Tragic manifestations of instability include aircraft crashes and the Chernobyl disaster in which a runaway condition occurred.
46 Yet another potential disadvantage of high loop gain was hinted at in the mould level example. There we saw that increasing the controller gain lead to increased sensitivity to measurement noise. (Actually, this turns out to be generically true).
47 In summary, high loop gain is desirable from many perspectives but it is also undesirable when viewed from other perspectives. Thus, when choosing the feedback gain one needs to make a conscious tradeoff between competing issues.
48 The previous discussion can be summarised in the following statement: High loop gain gives approximate inversion which is the essence of control. However, in practice, the choice of feedback gain is part of a complex web of design trade-offs. Understanding and balancing these trade-offs is the essence of control system design.
49 Measurements Finally, we discuss the issue of measurements (i.e. what it is we use to generate the feedback signal). A more accurate description of the feedback control loop including sensors is shown in Figure 2.11.
50 Figure 2.11: Closed loop control with sensors r(t) + Controller u(t) Plant A y(t) y m (t) Measurement and signal transmission system
51 Desirable attributes of sensors Reliability. It should operate within the necessary range. Accuracy. For a variable with a constant value, the measurement should settle to the correct value. Responsiveness. If the variable changes, the measurement should be able to follow the changes. Slow responding measurements can, not only affect the quality of control but can actually make the feedback loop unstable. Loop instability may arise even though the loop has been designed to be stable assuming an exact measurement of the process variable.
52 Noise immunity. The measurement system, including the transmission path, should not be significantly affected by exogenous signals such as measurement noise. Linearity. If the measurement system is not linear, then at least the nonlinearity should be known so that it can be compensated. Non intrusive. The measuring device should not significantly affect the behaviour of the plant.
53 Figure 2.12: Typical feedback loop In summary, a typical feedback loop (including sensor issues) is shown below. Referenceof Desired value output Controller Control signal Actuators Disturbances System Actual output Measurements Sensors Measurement noise
Control System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #36 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Friday, April 4, 2003 3. Cascade Control Next we turn to an
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #24 Wednesday, March 10, 2004 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Remedies We next turn to the question
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #13 Monday, February 3, 2003 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca (3) Cohen-Coon Reaction Curve Method
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 s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationControl Systems Design
ELEC4410 Control Systems Design Lecture 3, Part 2: Introduction to Affine Parametrisation School of Electrical Engineering and Computer Science Lecture 3, Part 2: Affine Parametrisation p. 1/29 Outline
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #15 Friday, February 6, 2004 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca (3) Cohen-Coon Reaction Curve Method
More informationTopic # Feedback Control Systems
Topic #1 16.31 Feedback Control Systems Motivation Basic Linear System Response Fall 2007 16.31 1 1 16.31: Introduction r(t) e(t) d(t) y(t) G c (s) G(s) u(t) Goal: Design a controller G c (s) so that the
More informationLecture 12. Upcoming labs: Final Exam on 12/21/2015 (Monday)10:30-12:30
289 Upcoming labs: Lecture 12 Lab 20: Internal model control (finish up) Lab 22: Force or Torque control experiments [Integrative] (2-3 sessions) Final Exam on 12/21/2015 (Monday)10:30-12:30 Today: Recap
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #11 Wednesday, January 28, 2004 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Relative Stability: Stability
More informationCHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER
114 CHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER 5.1 INTRODUCTION Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. It also refers
More informationChapter 13 Digital Control
Chapter 13 Digital Control Chapter 12 was concerned with building models for systems acting under digital control. We next turn to the question of control itself. Topics to be covered include: why one
More informationControl Systems I. Lecture 1: Introduction. Suggested Readings: Åström & Murray Ch. 1, Guzzella Ch. 1. Emilio Frazzoli
Control Systems I Lecture 1: Introduction Suggested Readings: Åström & Murray Ch. 1, Guzzella Ch. 1 Emilio Frazzoli Institute for Dynamic Systems and Control D-MAVT ETH Zürich September 22, 2017 E. Frazzoli
More informationAutonomous Mobile Robot Design
Autonomous Mobile Robot Design Topic: Guidance and Control Introduction and PID Loops Dr. Kostas Alexis (CSE) Autonomous Robot Challenges How do I control where to go? Autonomous Mobile Robot Design Topic:
More informationControl of MIMO processes. 1. Introduction. Control of MIMO processes. Control of Multiple-Input, Multiple Output (MIMO) Processes
Control of MIMO processes Control of Multiple-Input, Multiple Output (MIMO) Processes Statistical Process Control Feedforward and ratio control Cascade control Split range and selective control Control
More information(Refer Slide Time: 1:42)
Control Engineering Prof. Madan Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 21 Basic Principles of Feedback Control (Contd..) Friends, let me get started
More informationLinear State Feedback Controller Design
Assignment For EE5101 - Linear Systems Sem I AY2010/2011 Linear State Feedback Controller Design Phang Swee King A0033585A Email: king@nus.edu.sg NGS/ECE Dept. Faculty of Engineering National University
More informationEECE 460. Decentralized Control of MIMO Systems. Guy A. Dumont. Department of Electrical and Computer Engineering University of British Columbia
EECE 460 Decentralized Control of MIMO Systems Guy A. Dumont Department of Electrical and Computer Engineering University of British Columbia January 2011 Guy A. Dumont (UBC EECE) EECE 460 - Decentralized
More informationClassify a transfer function to see which order or ramp it can follow and with which expected error.
Dr. J. Tani, Prof. Dr. E. Frazzoli 5-059-00 Control Systems I (Autumn 208) Exercise Set 0 Topic: Specifications for Feedback Systems Discussion: 30.. 208 Learning objectives: The student can grizzi@ethz.ch,
More informationCHEE 319 Process Dynamics and Control
CHEE 319 Process Dynamics and Control Winter 2012 Instructor: M.Guay TAs: S. Dougherty, D. Park and E. Moshksar 1 Organization Instructor: Dr. Martin Guay Office: Dupuis 406 Phone: 533-2788 Email: guaym@chee.queensu.ca
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #14 Wednesday, February 5, 2003 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Chapter 7 Synthesis of SISO Controllers
More informationD(s) G(s) A control system design definition
R E Compensation D(s) U Plant G(s) Y Figure 7. A control system design definition x x x 2 x 2 U 2 s s 7 2 Y Figure 7.2 A block diagram representing Eq. (7.) in control form z U 2 s z Y 4 z 2 s z 2 3 Figure
More informationRELAY CONTROL WITH PARALLEL COMPENSATOR FOR NONMINIMUM PHASE PLANTS. Ryszard Gessing
RELAY CONTROL WITH PARALLEL COMPENSATOR FOR NONMINIMUM PHASE PLANTS Ryszard Gessing Politechnika Śl aska Instytut Automatyki, ul. Akademicka 16, 44-101 Gliwice, Poland, fax: +4832 372127, email: gessing@ia.gliwice.edu.pl
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals
More informationDesign of Decentralised PI Controller using Model Reference Adaptive Control for Quadruple Tank Process
Design of Decentralised PI Controller using Model Reference Adaptive Control for Quadruple Tank Process D.Angeline Vijula #, Dr.N.Devarajan * # Electronics and Instrumentation Engineering Sri Ramakrishna
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #22 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Friday, March 5, 24 More General Effects of Open Loop Poles
More informationCM 3310 Process Control, Spring Lecture 21
CM 331 Process Control, Spring 217 Instructor: Dr. om Co Lecture 21 (Back to Process Control opics ) General Control Configurations and Schemes. a) Basic Single-Input/Single-Output (SISO) Feedback Figure
More informationLinear Control Systems General Informations. Guillaume Drion Academic year
Linear Control Systems General Informations Guillaume Drion Academic year 2017-2018 1 SYST0003 - General informations Website: http://sites.google.com/site/gdrion25/teaching/syst0003 Contacts: Guillaume
More informationFall 線性系統 Linear Systems. Chapter 08 State Feedback & State Estimators (SISO) Feng-Li Lian. NTU-EE Sep07 Jan08
Fall 2007 線性系統 Linear Systems Chapter 08 State Feedback & State Estimators (SISO) Feng-Li Lian NTU-EE Sep07 Jan08 Materials used in these lecture notes are adopted from Linear System Theory & Design, 3rd.
More informationAdvanced Aerospace Control. Marco Lovera Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano
Advanced Aerospace Control Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano ICT for control systems engineering School of Industrial and Information Engineering Aeronautical Engineering
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 open-loop and closed-loop (feedback)
More informationModeling and Analysis of Dynamic Systems
Modeling and Analysis of Dynamic Systems by Dr. Guillaume Ducard Fall 2016 Institute for Dynamic Systems and Control ETH Zurich, Switzerland based on script from: Prof. Dr. Lino Guzzella 1/33 Outline 1
More informationLecture 9. Introduction to Kalman Filtering. Linear Quadratic Gaussian Control (LQG) G. Hovland 2004
MER42 Advanced Control Lecture 9 Introduction to Kalman Filtering Linear Quadratic Gaussian Control (LQG) G. Hovland 24 Announcement No tutorials on hursday mornings 8-9am I will be present in all practical
More informationCHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING. Professor Dae Ryook Yang
CHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 11-1 Road Map of the Lecture XI Controller Design and PID
More informationCopyright. SRS, U DuE, rof. Söffker. Course Control Theory WiSe 2014/15
Course Theory WiSe 2014/15 Room: SG 135 Time: Fr 3.00 6.30 pm (lecture and exercise) Practical exercise: 2nd part of semester Assistants: Xi Nowak, M.Sc.; WEB: http://www.uni-due.de/srs Manuscript Note
More informationDr Ian R. Manchester
Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the s-plane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus 7 Root Locus 2 Assign
More informationPlan of the Lecture. Review: 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 Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic:
More informationOutline. Classical Control. Lecture 1
Outline Outline Outline 1 Introduction 2 Prerequisites Block diagram for system modeling Modeling Mechanical Electrical Outline Introduction Background Basic Systems Models/Transfers functions 1 Introduction
More informationCascade Control of a Continuous Stirred Tank Reactor (CSTR)
Journal of Applied and Industrial Sciences, 213, 1 (4): 16-23, ISSN: 2328-4595 (PRINT), ISSN: 2328-469 (ONLINE) Research Article Cascade Control of a Continuous Stirred Tank Reactor (CSTR) 16 A. O. Ahmed
More informationProcess Solutions. Process Dynamics. The Fundamental Principle of Process Control. APC Techniques Dynamics 2-1. Page 2-1
Process Dynamics The Fundamental Principle of Process Control APC Techniques Dynamics 2-1 Page 2-1 Process Dynamics (1) All Processes are dynamic i.e. they change with time. If a plant were totally static
More informationCDS 101/110a: Lecture 8-1 Frequency Domain Design
CDS 11/11a: Lecture 8-1 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 informationControl Systems I. Lecture 7: Feedback and the Root Locus method. Readings: Jacopo Tani. Institute for Dynamic Systems and Control D-MAVT ETH Zürich
Control Systems I Lecture 7: Feedback and the Root Locus method Readings: Jacopo Tani Institute for Dynamic Systems and Control D-MAVT ETH Zürich November 2, 2018 J. Tani, E. Frazzoli (ETH) Lecture 7:
More informationOverview of the Seminar Topic
Overview of the Seminar Topic Simo Särkkä Laboratory of Computational Engineering Helsinki University of Technology September 17, 2007 Contents 1 What is Control Theory? 2 History
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013 Problem Set #4 Posted: Thursday, Mar. 7, 13 Due: Thursday, Mar. 14, 13 1. Sketch the Root
More informationA FEEDBACK STRUCTURE WITH HIGHER ORDER DERIVATIVES IN REGULATOR. Ryszard Gessing
A FEEDBACK STRUCTURE WITH HIGHER ORDER DERIVATIVES IN REGULATOR Ryszard Gessing Politechnika Śl aska Instytut Automatyki, ul. Akademicka 16, 44-101 Gliwice, Poland, fax: +4832 372127, email: gessing@ia.gliwice.edu.pl
More information2018 SPRING PHYS 8011 Classical mechanics I (as of Apr. 19/2018) The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary. A FRIENDLY REMINDER:
More informationAE 200 Engineering Analysis and Control of Aerospace Systems
Instructor Info Credit Class Days / Time Office Location: ENG 272C Office Hours: Monday 4:00pm 6:30pm Email: kamran.turkoglu@sjsu.edu 3 units Tuesday, 6:00pm 8:45pm Classroom CL 222 Prerequisites TA: Contact
More informationPhysics 18, Introductory Physics I for Biological Sciences Spring 2010
Physics 18 page 1/6 Physics 18, Introductory Physics I for Biological Sciences Spring 2010 - Course Description - Instructor: Dr. Derrick Kiley Office: AOB 176; Office Phone 209 228-3076 E-mail Address:
More informationTradeoffs and Limits of Performance
Chapter 9 Tradeoffs and Limits of Performance 9. Introduction Fundamental limits of feedback systems will be investigated in this chapter. We begin in Section 9.2 by discussing the basic feedback loop
More informationYTÜ Mechanical Engineering Department
YTÜ Mechanical Engineering Department Lecture of Special Laboratory of Machine Theory, System Dynamics and Control Division Coupled Tank 1 Level Control with using Feedforward PI Controller Lab Date: Lab
More information6.1 Sketch the z-domain root locus and find the critical gain for the following systems K., the closed-loop characteristic equation is K + z 0.
6. Sketch the z-domain root locus and find the critical gain for the following systems K (i) Gz () z 4. (ii) Gz K () ( z+ 9. )( z 9. ) (iii) Gz () Kz ( z. )( z ) (iv) Gz () Kz ( + 9. ) ( z. )( z 8. ) (i)
More informationIntermediate Process Control CHE576 Lecture Notes # 2
Intermediate Process Control CHE576 Lecture Notes # 2 B. Huang Department of Chemical & Materials Engineering University of Alberta, Edmonton, Alberta, Canada February 4, 2008 2 Chapter 2 Introduction
More informationChapter 7 Interconnected Systems and Feedback: Well-Posedness, Stability, and Performance 7. Introduction Feedback control is a powerful approach to o
Lectures on Dynamic Systems and Control Mohammed Dahleh Munther A. Dahleh George Verghese Department of Electrical Engineering and Computer Science Massachuasetts Institute of Technology c Chapter 7 Interconnected
More informationEG4321/EG7040. Nonlinear Control. Dr. Matt Turner
EG4321/EG7040 Nonlinear Control Dr. Matt Turner EG4321/EG7040 [An introduction to] Nonlinear Control Dr. Matt Turner EG4321/EG7040 [An introduction to] Nonlinear [System Analysis] and Control Dr. Matt
More informationEECE Adaptive Control
EECE 574 - Adaptive Control Overview Guy Dumont Department of Electrical and Computer Engineering University of British Columbia Lectures: Thursday 09h00-12h00 Location: PPC 101 Guy Dumont (UBC) EECE 574
More informationDesign and Comparative Analysis of Controller for Non Linear Tank System
Design and Comparative Analysis of for Non Linear Tank System Janaki.M 1, Soniya.V 2, Arunkumar.E 3 12 Assistant professor, Department of EIE, Karpagam College of Engineering, Coimbatore, India 3 Associate
More informationLecture 5 Classical Control Overview III. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore
Lecture 5 Classical Control Overview III Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore A Fundamental Problem in Control Systems Poles of open
More informationLinear System Theory. Wonhee Kim Lecture 1. March 7, 2018
Linear System Theory Wonhee Kim Lecture 1 March 7, 2018 1 / 22 Overview Course Information Prerequisites Course Outline What is Control Engineering? Examples of Control Systems Structure of Control Systems
More informationIntroduction to Feedback Control
Introduction to Feedback Control Control System Design Why Control? Open-Loop vs Closed-Loop (Feedback) Why Use Feedback Control? Closed-Loop Control System Structure Elements of a Feedback Control System
More informationAMME3500: System Dynamics & Control
Stefan B. Williams May, 211 AMME35: System Dynamics & Control Assignment 4 Note: This assignment contributes 15% towards your final mark. This assignment is due at 4pm on Monday, May 3 th during Week 13
More informationERTH2104 Winter Igneous Systems, Geochemistry and Processes. Instructor: Brian Cousens
ERTH2104 Winter 2019 Igneous Systems, Geochemistry and Processes Instructor: Brian Cousens Igneous Petrology is the study of processes that produce melts (magmas) within the Earth, how these melts then
More informationUnit 11 - Week 7: Quantitative feedback theory (Part 1/2)
X reviewer3@nptel.iitm.ac.in Courses» Control System Design Announcements Course Ask a Question Progress Mentor FAQ Unit 11 - Week 7: Quantitative feedback theory (Part 1/2) Course outline How to access
More informationProfessional Portfolio Selection Techniques: From Markowitz to Innovative Engineering
Massachusetts Institute of Technology Sponsor: Electrical Engineering and Computer Science Cosponsor: Science Engineering and Business Club Professional Portfolio Selection Techniques: From Markowitz to
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 Open-Loop
More information6.302 Feedback Systems Recitation 16: Compensation Prof. Joel L. Dawson
Bode Obstacle Course is one technique for doing compensation, or designing a feedback system to make the closed-loop behavior what we want it to be. To review: - G c (s) G(s) H(s) you are here! plant For
More informationME 475/591 Control Systems Final Exam Fall '99
ME 475/591 Control Systems Final Exam Fall '99 Closed book closed notes portion of exam. Answer 5 of the 6 questions below (20 points total) 1) What is a phase margin? Under ideal circumstances, what does
More informationEET 3212 Control Systems. Control Systems Engineering, 6th Edition, Norman S. Nise December 2010, A. Goykadosh and M.
NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York 300 Jay Street Brooklyn, NY 11201-2983 Department of Electrical and Telecommunications Engineering Technology TEL (718) 260-5300 - FAX:
More informationReturn Difference Function and Closed-Loop Roots Single-Input/Single-Output Control Systems
Spectral Properties of Linear- Quadratic Regulators Robert Stengel Optimal Control and Estimation MAE 546 Princeton University, 2018! Stability margins of single-input/singleoutput (SISO) systems! Characterizations
More informationCourse Outline. Higher Order Poles: Example. Higher Order Poles. Amme 3500 : System Dynamics & Control. State Space Design. 1 G(s) = s(s + 2)(s +10)
Amme 35 : System Dynamics Control State Space Design Course Outline Week Date Content Assignment Notes 1 1 Mar Introduction 2 8 Mar Frequency Domain Modelling 3 15 Mar Transient Performance and the s-plane
More informationPole placement control: state space and polynomial approaches Lecture 2
: state space and polynomial approaches Lecture 2 : a state O. Sename 1 1 Gipsa-lab, CNRS-INPG, FRANCE Olivier.Sename@gipsa-lab.fr www.gipsa-lab.fr/ o.sename -based November 21, 2017 Outline : a state
More informationCDS 110b: Lecture 2-1 Linear Quadratic Regulators
CDS 110b: Lecture 2-1 Linear Quadratic Regulators Richard M. Murray 11 January 2006 Goals: Derive the linear quadratic regulator and demonstrate its use Reading: Friedland, Chapter 9 (different derivation,
More informationGoodwin, Graebe, Salgado, Prentice Hall Chapter 11. Chapter 11. Dealing with Constraints
Chapter 11 Dealing with Constraints Topics to be covered An ubiquitous problem in control is that all real actuators have limited authority. This implies that they are constrained in amplitude and/or rate
More informationState Regulator. Advanced Control. design of controllers using pole placement and LQ design rules
Advanced Control State Regulator Scope design of controllers using pole placement and LQ design rules Keywords pole placement, optimal control, LQ regulator, weighting matrixes Prerequisites Contact state
More informationAnalysis and Synthesis of Single-Input Single-Output Control Systems
Lino Guzzella Analysis and Synthesis of Single-Input Single-Output Control Systems l+kja» \Uja>)W2(ja»\ um Contents 1 Definitions and Problem Formulations 1 1.1 Introduction 1 1.2 Definitions 1 1.2.1 Systems
More informationControl Systems Lab - SC4070 Control techniques
Control Systems Lab - SC4070 Control techniques Dr. Manuel Mazo Jr. Delft Center for Systems and Control (TU Delft) m.mazo@tudelft.nl Tel.:015-2788131 TU Delft, February 16, 2015 (slides modified from
More informationRobust Control. 2nd class. Spring, 2018 Instructor: Prof. Masayuki Fujita (S5-303B) Tue., 17th April, 2018, 10:45~12:15, S423 Lecture Room
Robust Control Spring, 2018 Instructor: Prof. Masayuki Fujita (S5-303B) 2nd class Tue., 17th April, 2018, 10:45~12:15, S423 Lecture Room 2. Nominal Performance 2.1 Weighted Sensitivity [SP05, Sec. 2.8,
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 Steady-state Steady-state errors errors Type Type k k systems systems Integral Integral
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 informationECSE 4962 Control Systems Design. A Brief Tutorial on Control Design
ECSE 4962 Control Systems Design A Brief Tutorial on Control Design Instructor: Professor John T. Wen TA: Ben Potsaid http://www.cat.rpi.edu/~wen/ecse4962s04/ Don t Wait Until The Last Minute! You got
More informationChemistry 14C: Structure of Organic Molecules - Winter 2017 Version 56
Chemistry 14C: Structure of Organic Molecules - Winter 2017 Version 56 Instructor: Dr. Steven A. Hardinger Office: Young Hall 3077C harding@chem.ucla.edu Office hours: Monday and Tuesday 2:00-2:50 PM Teaching
More informationCONTROL OF MULTIVARIABLE PROCESSES
Process plants ( or complex experiments) have many variables that must be controlled. The engineer must. Provide the needed sensors 2. Provide adequate manipulated variables 3. Decide how the CVs and MVs
More informationIntroduction to Process Control
Introduction to Process Control For more visit :- www.mpgirnari.in By: M. P. Girnari (SSEC, Bhavnagar) For more visit:- www.mpgirnari.in 1 Contents: Introduction Process control Dynamics Stability The
More informationReglerteknik, TNG028. Lecture 1. Anna Lombardi
Reglerteknik, TNG028 Lecture 1 Anna Lombardi Today lecture We will try to answer the following questions: What is automatic control? Where can we nd automatic control? Why do we need automatic control?
More informationEECS C128/ ME C134 Final Wed. Dec. 15, am. Closed book. Two pages of formula sheets. No calculators.
Name: SID: EECS C28/ ME C34 Final Wed. Dec. 5, 2 8- am Closed book. Two pages of formula sheets. No calculators. There are 8 problems worth points total. Problem Points Score 2 2 6 3 4 4 5 6 6 7 8 2 Total
More informationSchool of Mechanical Engineering Purdue University. ME375 Feedback Control - 1
Introduction to Feedback Control Control System Design Why Control? Open-Loop vs Closed-Loop (Feedback) Why Use Feedback Control? Closed-Loop Control System Structure Elements of a Feedback Control System
More informationAircraft Stability & Control
Aircraft Stability & Control Textbook Automatic control of Aircraft and missiles 2 nd Edition by John H Blakelock References Aircraft Dynamics and Automatic Control - McRuler & Ashkenas Aerodynamics, Aeronautics
More informationME 132, Dynamic Systems and Feedback. Class Notes. Spring Instructor: Prof. A Packard
ME 132, Dynamic Systems and Feedback Class Notes by Andrew Packard, Kameshwar Poolla & Roberto Horowitz Spring 2005 Instructor: Prof. A Packard Department of Mechanical Engineering University of California
More informationEE 4443/5329. LAB 3: Control of Industrial Systems. Simulation and Hardware Control (PID Design) The Torsion Disks. (ECP Systems-Model: 205)
EE 4443/539 LAB 3: Control of Industrial Systems Simulation and Hardware Control (PID Design) The Torsion Disks (ECP Systems-Model: 05) Compiled by: Nitin Swamy Email: nswamy@lakeshore.uta.edu Email: okuljaca@lakeshore.uta.edu
More informationCHAPTER 13: FEEDBACK PERFORMANCE
When I complete this chapter, I want to be able to do the following. Apply two methods for evaluating control performance: simulation and frequency response Apply general guidelines for the effect of -
More informationSolutions for Tutorial 10 Stability Analysis
Solutions for Tutorial 1 Stability Analysis 1.1 In this question, you will analyze the series of three isothermal CSTR s show in Figure 1.1. The model for each reactor is the same at presented in Textbook
More informationVideo 5.1 Vijay Kumar and Ani Hsieh
Video 5.1 Vijay Kumar and Ani Hsieh Robo3x-1.1 1 The Purpose of Control Input/Stimulus/ Disturbance System or Plant Output/ Response Understand the Black Box Evaluate the Performance Change the Behavior
More informationLecture 25: Tue Nov 27, 2018
Lecture 25: Tue Nov 27, 2018 Reminder: Lab 3 moved to Tuesday Dec 4 Lecture: review time-domain characteristics of 2nd-order systems intro to control: feedback open-loop vs closed-loop control intro to
More informationWhat is flight dynamics? AE540: Flight Dynamics and Control I. What is flight control? Is the study of aircraft motion and its characteristics.
KING FAHD UNIVERSITY Department of Aerospace Engineering AE540: Flight Dynamics and Control I Instructor Dr. Ayman Hamdy Kassem What is flight dynamics? Is the study of aircraft motion and its characteristics.
More informationECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : Steady-state error Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling Analysis Design Laplace
More informationControl Systems I. Lecture 7: Feedback and the Root Locus method. Readings: Guzzella 9.1-3, Emilio Frazzoli
Control Systems I Lecture 7: Feedback and the Root Locus method Readings: Guzzella 9.1-3, 13.3 Emilio Frazzoli Institute for Dynamic Systems and Control D-MAVT ETH Zürich November 3, 2017 E. Frazzoli (ETH)
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 informationModeling and Control Overview
Modeling and Control Overview D R. T A R E K A. T U T U N J I A D V A N C E D C O N T R O L S Y S T E M S M E C H A T R O N I C S E N G I N E E R I N G D E P A R T M E N T P H I L A D E L P H I A U N I
More information1 Loop Control. 1.1 Open-loop. ISS0065 Control Instrumentation
Lecture 4 ISS0065 Control Instrumentation 1 Loop Control System has a continuous signal (analog) basic notions: open-loop control, close-loop control. 1.1 Open-loop Open-loop / avatud süsteem / открытая
More informationFeedback Basics. David M. Auslander Mechanical Engineering University of California at Berkeley. copyright 1998, D.M. Auslander
Feedback Basics David M. Auslander Mechanical Engineering University of California at Berkeley copyright 1998, D.M. Auslander 1 I. Feedback Control Context 2 What is Feedback Control? Measure desired behavior
More informationLecture 9. Welcome back! Coming week labs: Today: Lab 16 System Identification (2 sessions)
232 Welcome back! Coming week labs: Lecture 9 Lab 16 System Identification (2 sessions) Today: Review of Lab 15 System identification (ala ME4232) Time domain Frequency domain 1 Future Labs To develop
More informationCBE507 LECTURE III Controller Design Using State-space Methods. Professor Dae Ryook Yang
CBE507 LECTURE III Controller Design Using State-space Methods Professor Dae Ryook Yang Fall 2013 Dept. of Chemical and Biological Engineering Korea University Korea University III -1 Overview States What
More information