LINEAR CONTROL SYSTEMS

Transcription

1 LINEAR CONTROL SYSTEMS Ali Karimpour Associate Professor Ferdowsi Uniersity of Mashhad

2 Prerequisite English Knowledge Primary Mathematics MATLAB Software 2

3 Syllabus An Introduction to Linear Control Systems.(Lecture 1) Different Representations of Control Systems. (Lecture 2) Linearization. (Lecture 3) Internal and External Description. (Tf and SS Description). (Lecture 4) Stability Analysis. (Lecture 5) Time Domain Analysis of Control Systems. (Lecture 6) Root Locus Criteria. (Lecture 7) Controller Design in the Time Domain. (Lecture 8) Frequency Domain Analysis of Control Systems.(Lecture 9) Nyquist Stability Criteria. (Lecture 10) Controller Design in the Frequency Domain. (Lecture 11) 3

4 Grading No delay policy. Bonus(on your participation) up to 5% Exercises (1-2, 3-4, 6, 7, 9 and10 each 2%) 12% Midterm1 (Lectures 1, till 5) 18% Midterm2 (Lectures 6, 7 and 8) 20% Final 50% 4

5 References Modern Control Systems (12th Edition) By Richard C. Dorf, Robert H. Bishop. Automatic Control Systems (9th Edition) By Farid Golnaraghi, Benjamin C. Kuo. Control Systems Engineering (Wiley 2000) By Norman S. Nise 5

6 Lecture 1 An Introduction to Linear Control Systems Topics to be coered include: Introduction. Some Adanced Control System. Different Parts of Control Systems. Modelling of Systems. Systems With Time Delay. 6

7 Introduction Control System An interconnection of components forming a system configuration that will proide a desired response. 7

8 Introduction - History of Control Engineering Water-leel float regulator (before BC) RQ-170 unmanned plane (Nowadays) 8

9 Introduction - History of Control Engineering 18th Century James Watt s centrifugal goernor for the speed control of a steam engine. 9

10 Introduction - Earliest Control Systems? Human System i. Pancreas ii. Regulates blood glucose leel Adrenaline iii. Eye i. Automatically generated to increase the heart rate and oxygen in times of flight Follow moing object Hand Pick up an object and place it at a predetermined location. Temperature Regulated temperature of 36 C to 37 C 10

11 Introduction Some Control benefits Enhanced Product Quality. Waste Minimization. Enironmental Protection. Greater Throughput for a Gien Installed Capacity. Higher Safety Margins. 11

12 Adanced Control Systems A Manual Leel Control An Automatic Control System 12

13 Adanced Control Systems A Modern High Voltage Transformer 13

14 An Introduction to Linear Control Systems Introduction. Some Adanced Control System. Different Parts of Control Systems. Modelling of Systems. Systems With Time Delay. 14

15 Different Parts of Control Systems 15

16 Different Parts of Control Systems Success in control engineering depends on some of the issues: Plant Objecties Sensors Actuators Computing Disturbance & noises Set points Uncertainties 16

17 Different Part of a Control Systems Plant Objecties Sensors Actuators Computing Disturbance & noises دهانه مايع قيف Set points Uncertainties پوسته جامد مايع خنک کننده نورد مايع خنک کننده ثانويه نورد نگهدارنده 17

18 In summary: Sensors proide the eyes and actuators the muscle but control science proides the finesse. Better Sensors Different Parts of Control Systems Proide better Vision Better Actuators Proide more Muscle Better Control(Computing) Proides more finesse by combining sensors and actuators in more intelligent ways 18

19 Control System Examples Inerted Pendulum. Ball & Beam. Ball and plate. Segway. Donkey. 19

20 An Introduction to Linear Control Systems Introduction. Some Adanced Control System. Different Parts of Control Systems. Modelling of Systems. Systems With Time Delay. 20

21 Modeling of Systems Model: Relationship among obsered signals. Split up system into subsystems, 1- Modeling Joined subsystems mathematically, Building models 2- System identification 3- Combined Does not necessarily inole any experimentation on the actual system. It is directly based on experimentation. Input and output signals from the system are recorded. 21

22 Modeling Example 1: Dynamics of a mechanical system خروجی ورودی u bx Mx b x x M 1 u M 22

23 Modeling Example 2: Dynamics of a electromechanical system Position control system 23

24 Modeling Example 2: Continue خروجی ورودی 24

25 Modeling A simplified aeroplane Position control system 25

26 System Identification مثال 3 : یک سيستم حرارتی Example 3: A thermal system 1 Input signal k Output signal Input signal is an step function so: t (Time) u( t) y( t) 1 0 k 0 ke t t t 0 0 t 0 t 0 u( s) y( s) 1 s k s k s 1/ y( s) k g( s)? u( s) s 1 26

27 Exercises خروجی system. 1-1 Specify actuator and disturbance in the following ورودی 1-2 Specify actuator, sensor and disturbance in the following system. 27

28 Exercises 1-3 Derie the output of following system if it is excited by u=sint خروجی ورودی 1-4 Derie model of following system, but neglect the inductance of the motor. 1-5 Repeat exercise 1-4, but consider the motor as a series motor. 28

29 Exercises 1-6 Find the mathematical model of the system. Final answer is: m 2y by k2y bx k2x x bx ( k k x by k y k u m1 1 2)

30 Exercises 1-7 In a control system of an industrial composition process, it is ery important to control the chemical composition of the output. There is an infrared analyzer for measurement and the ale of additie stream is controllable. Complete the feedback loop and find the block diagram of the process. 30