1. LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad

2. lecture 2 Ali Karimpour Oct 2009 2 Lecture 2 Topics to be covered include: v An industrial example v Modeling of systems v Systems with time delay. Modeling of Control Systems

3. lecture 2 Ali Karimpour Oct 2009 3 Example 1: An industrial plant 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. مثال 1 : يک سيستم صنعتی

4. lecture 2 Ali Karimpour Oct 2009 4 Process schematic of a steel industry نمای شماتيک صنعت فولاد قيف دهانه مايع مايع خنک کننده پوسته جامد نورد نورد نگهدارنده مايع خنک کننده ثانويه

5. lecture 2 Ali Karimpour Oct 2009 5 Process schematic of a steel industry (continue) يک نمونه شمش قيف حاوی مواد مذاب شير کنترل قالب گيری خنک سازی اوليه

6. lecture 2 Ali Karimpour Oct 2009 6 The cast strip in the secondary cooling chamber نوار ريخته گری در دومين بخش خنک سازی

7. lecture 2 Ali Karimpour Oct 2009 7 Performance specifications مشخصه های عملکردی The key performance goals for this problem are: v 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. v Profitability: Aspects which contribute to this requirement include: u Product quality u Maintenance u Throughput

8. lecture 2 Ali Karimpour Oct 2009 8 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.

9. lecture 2 Ali Karimpour Oct 2009 9 Models Model: Relationship among observed signals. Model types 1- Mental models 2- Graphical models 3- Mathematical (analytical) models 4- Software models Split up system into subsystems, Joined subsystems mathematically, 1- Modeling 2- System identification Does not necessarily involve any experimentation on the actual system. Building models It is directly based on experimentation. Input and output signals from the system are recorded. 3- Combined

10. lecture 2 Ali Karimpour Oct 2009 10 Modeling مدلسازی 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

11. lecture 2 Ali Karimpour Oct 2009 11 Modelling a simple tank مدلسازی يک منبع ساده Tundish Valve Molten Steel Mould Level Cooling Water قيف سطح قالب گيری شير آب خنک کننده

12. lecture 2 Ali Karimpour Oct 2009 12 Simplified block diagram for modeling بلوک دياگرام ساده شده برای مدلسازی Block diagram of the simplified mould level dynamics, sensors and actuators سطح قالب گيری خروجی با توجه به سرعت ريخته گری ورودی با توجه به شير کنترل سطح قالب گيری اندازه گيری شده نويز اندازه گيری

13. lecture 2 Ali Karimpour Oct 2009 13 Suggested Control Strategy استراتژی پيشنهادی برای کنترل

14. lecture 2 Ali Karimpour Oct 2009 14 Result of simulation shows a trade off نتايج شبيه سازی نياز به مصالحه با توجه به

15. lecture 2 Ali Karimpour Oct 2009 15 Level of compromise سطح مصالحه We may ask if these trade-offs are unavoidable or whether we could improve on the situation by such measures as: v better modelling v more sophisticated control system design (Aside: Actually the trade-off is fundamental as we shall see presently).

16. lecture 2 Ali Karimpour Oct 2009 16 Example 2: Dynamics of a mechanical system مثال 2 : ديناميک يک سيستم مکانيکی ورودی خروجی

17. lecture 2 Ali Karimpour Oct 2009 17 A simplified aeroplane يک هواپيمای ساده شده Position control system

18. lecture 2 Ali Karimpour Oct 2009 18 Example 3:Dynamics of a electromechanical system مثال 3 : ديناميک يک سيستم الکترومکانيکی Position control system

19. lecture 2 Ali Karimpour Oct 2009 19 Example 3: Continue مثال 3 : ادامه خروجی ورودی

20. lecture 2 Ali Karimpour Oct 2009 20 Example 4: Dynamics of a liquid level system مثال 4 : ديناميک يک سيستم سطح مايعات ورودی خروجی کنترلی مایع خروجی

21. lecture 2 Ali Karimpour Oct 2009 21 Systems with delay سيستمهای دارای تاخير سيگنال ورودی سنسوردما جريان هوا دمای سنجش شده زمان تاخیر

22. lecture 2 Ali Karimpour Oct 2009 22 2-1 Derive the output of example 2 excited by following input u=sint 2-2 Repeat example 3, but neglect the inductance of the motor. 2-3 Repeat example 3, but consider the motor as a series motor. Exercises

23. lecture 2 Ali Karimpour Oct 2009 23 Exercises (Continue) 2-4 Find the mathematical model of the following system. Final answer is: