modelling and simulation 6. februar 2008 / dr. –ing naveed ramzan # process control and dynamics...
TRANSCRIPT
![Page 1: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/1.jpg)
Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Process Control and dynamics
Department of Chemical Engineering, U.E.T. Lahore Pakistan
Dr. –Ing. Naveed Ramzan
Lecture 1: Introduction to Process Control
![Page 2: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/2.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Course Books
Ch.E-411 PROCESS DYNAMICS AND CONTROLIntroduction & significance of control; Feedback& feed forward control; Design & Hardware elements of control; Dynamics of first & second order systems; Overall transfer function testability; Controllers (P, PI, PID etc) & final control elements; Representation of control systems; Multiple control loops; cascade, ratio, over-riding etc. Introduction to stability of chemical processes; introduction to frequency response techniques; Routh's criteria, Bode plots, Nyquit method; Computer control, Introduction to Distributed Control Systems; Case study: Development of control scheme of complete plant.
![Page 3: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/3.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Tentative Schedule
Ch.E-411 PROCESS DYNAMICS AND CONTROL Weeks Book Chapter
• Introduction & significance of control;
• Feedback& feed forward control; 1-2 1 1,2,3,13
• Design & Hardware elements of control;
• Dynamics of first & second order systems; 2-3 1(2) 10,11(5,6,8)
• Overall transfer function testability;
• Controllers (P, PI, PID etc) & 3-4 1(2) 14,15,16 (9.10.11.14.22)
• Final control elements
• Representation of control systems;
• Multiple control loops;cascade,ratio,over-riding etc. 1
• Introduction to stability of chemical processes;
• introduction to frequency response techniques; 2-3 1 15,17,18
• Routh's criteria,
• Bode plots, Nyquit method;
• Computer control, 1
• Introduction to Distributed Control Systems; 1
• Case study: Development of control scheme of complete plant. 1
![Page 4: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/4.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Contact Hours
Section A
Monday : 3-4Thursday : 2
Section B
Tuesday 3-4, 5
KSK Campus
Friday 1-3
![Page 5: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/5.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Introduction to Process Control
![Page 6: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/6.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Introduction to Process Control
![Page 7: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/7.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Introduction to Process Control
![Page 8: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/8.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
What does a feedback system do?
![Page 9: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/9.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
What does a feedback system do?
![Page 10: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/10.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
What does a feedback system do?
![Page 11: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/11.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
What does a feedback system do?
![Page 12: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/12.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
What does a feedback system do?
![Page 13: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/13.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Basic Concept feedback system
![Page 14: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/14.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Examples of feedback system
![Page 15: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/15.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Examples of feedback system
![Page 16: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/16.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Examples of feedback system
![Page 17: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/17.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Examples of feedback system
![Page 18: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/18.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Examples of feedback system
![Page 19: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/19.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
What does a feedback system do?
![Page 20: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/20.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Suppressing the influence of external disturbances
Ensuring the stability of a chemical process
Optimizing the performance of a chemical process
Incentives for Chemical Process Control
![Page 21: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/21.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Suppressing the influence of external disturbances
Incentives for Chemical Process Control
![Page 22: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/22.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Suppressing the influence of external disturbances
Incentives for Chemical Process Control
Disturbances?
![Page 23: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/23.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Suppressing the influence of external disturbances
Incentives for Chemical Process Control
![Page 24: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/24.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Ensuring the stability of a chemical process
Incentives for Chemical Process Control
![Page 25: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/25.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Ensuring the stability of a chemical process
Incentives for Chemical Process Control
![Page 26: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/26.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Ensuring the stability of a chemical process
Incentives for Chemical Process Control
![Page 27: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/27.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Why is Control Necessary?
Optimizing the performance of a chemical process
Incentives for Chemical Process Control
![Page 28: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/28.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Home Work-1
![Page 29: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/29.jpg)
Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
![Page 30: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/30.jpg)
Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Instrumentation and Process Control
Department of Chemical Engineering, U.E.T. Lahore Pakistan
Dr. –Ing. Naveed Ramzan
Lecture 2: Design Aspects of a Process Control System
![Page 31: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/31.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Classification of Variables in a Chemical Process
![Page 32: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/32.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Example
Classification of Variables in a Chemical Process
![Page 33: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/33.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
![Page 34: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/34.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
![Page 35: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/35.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
Primary Measurements
![Page 36: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/36.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
Secondary MeasurementsUnmeasured output=ƒ(Secondary measurements)
![Page 37: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/37.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
Direct Measurements of external disturbances
![Page 38: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/38.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
![Page 39: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/39.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
A control configuration is the information structure that is used to connect the available measurements to the available manipulated variables.
![Page 40: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/40.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
Same information flows to different manipulated variables
![Page 41: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/41.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
Same manipulated variables but different measurements
![Page 42: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/42.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
General Control Configurations
Feedback control configuration Feedforward control configuration
![Page 43: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/43.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
General Control Configurations
Inferential control configuration
![Page 44: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/44.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
General Control Configurations
--- Single input , Single output (SISO)
--- Multiple input , Multiple output (MIMO)
![Page 45: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/45.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Design Elements of a Control System
--- Proportional Control
--- Integral Control
--- Proportional Integral Control
--- Derivative Control
--- Proportional Integral Derivative Control
![Page 46: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/46.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Hardware for a process Control System
--- Chemical Process
--- Measurement Instruments or sensors
--- Transducers
--- Transmission lines
--- The Controller
--- The Final Control Element
--- Recording Elements
![Page 47: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/47.jpg)
6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Hardware for a process Control System
![Page 48: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/48.jpg)
Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
![Page 49: Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan # Process Control and dynamics Department of Chemical Engineering, U.E.T. Lahore Pakistan](https://reader036.vdocuments.us/reader036/viewer/2022081504/5515f4cc550346a2308b4660/html5/thumbnails/49.jpg)
Modelling and Simulation 6. Februar 2008 / Dr. –Ing Naveed Ramzan ‹#›
Instrumentation and Process Control
Department of Chemical Engineering, U.E.T. Lahore Pakistan
Dr. –Ing. Naveed Ramzan
Lecture 3: Dynamic behaviour of first order system