Introduction to Control (034040) lecture no. 1

Transcription

1 Introdction to Control (034040) lectre no. 1 Leonid Mirkin Faclt of Mechanical Engineering Technion IIT

2 Otline Corse info Introdction Block diagrams

3 Otline Corse info Introdction Block diagrams

4 General info Corse web site: Prereqisite (mst): Linear Sstems M (034032) Msts from LS: linearization Laplace transform and signals in s-domain, initial and final vale theorems, etc transfer fnctions and their properties (poles, zeros, static gain, etc) stabilit and Roth test freqenc response and freqenc-response plots (Bode and polar) 1st and 2nd order dnamical sstems (definitions, step/freqenc responses, etc) Grading polic: Project with lab parts (provided the final exam grade 55): 30% Final exam: % The se of books / lectre notes is not permitted dring exams.

5 Topics 1. Block diagrams 2. Modeling, DC motors 3. Signals and sstems in freqenc domain 4. Stead-state and transient reqirements 5. Open-loop control, plant inversion 6. Closed-loop control 7. Internal stabilit 8. Root locs method 9. Nqist stabilit criterion 10. Basic loop shaping and stabilit margins 11. PID controllers and their tning

6 Otline Corse info Introdction Block diagrams

7 What is control? Roghl, control is the discipline stding how to change behavior of sstems (mechanical, electrical, chemical, biological, economical, etc) so that the behave in a desirable manner. Control is relativel ong field (as separate discipline since 40s), et control sstems appear nowadas practicall everwhere, in homes, in indstr, in commnications sstems, in vehicles, in scientific instrments, etc. Natre also offers a plent of examples of sophisticated and sccessfl control sstems (biological sstems, ecosstems, etc).

8 What is control? Roghl, control is the discipline stding how to change behavior of sstems (mechanical, electrical, chemical, biological, economical, etc) so that the behave in a desirable manner. Control is relativel ong field (as separate discipline since 40s), et control sstems appear nowadas practicall everwhere, in homes, in indstr, in commnications sstems, in vehicles, in scientific instrments, etc. Natre also offers a plent of examples of sophisticated and sccessfl control sstems (biological sstems, ecosstems, etc).

9 Example 1: steam engine Boiler Steam Otpt shaft Engine Problem: maintain rotation speed at a constant predetermined level Actator: throttle valve can reglate the admission of steam into clinders Obstacles: npredictable changes (ncertainties), like load steam pressre engine / valve aging...

10 Example 1: steam engine Boiler Steam Valve Otpt shaft Engine Problem: maintain rotation speed at a constant predetermined level Actator: throttle valve can reglate the admission of steam into clinders Obstacles: npredictable changes (ncertainties), like load steam pressre engine / valve aging...

11 Example 1: steam engine Boiler Steam Valve Otpt shaft Engine Problem: maintain rotation speed at a constant predetermined level Actator: throttle valve can reglate the admission of steam into clinders Obstacles: npredictable changes (ncertainties), like load steam pressre engine / valve aging...

12 Steam engine: centrifgal governor Metal sphere Boiler Steam Valve Governor Otpt shaft Engine Soltion adapted 1 b James Watt in 1788 did the trick: if properl tned, the governor maintains a near constant speed whatever the load or fel sppl conditions are. 1 It was not Watt s invention: centrifgal governors were sed to reglate the distance and pressre between millstones in windmills since the 17th centr.

13 Centrifgal governor: idea When rotation speed increases, balls move otwards, redcing the valve apertre and steam admission When rotation speed falls, balls move inwards, increasing the valve apertre and steam admission This operation principle called feedback control.

14 Centrifgal governor: idea When rotation speed increases, balls move otwards, redcing the valve apertre and steam admission When rotation speed falls, balls move inwards, increasing the valve apertre and steam admission This operation principle called feedback control.

15 Steam engine: the neverending stor The first atomatic control sstem sed in indstrial processes Watt s governor tamed steam engine and made the Indstrial Revoltion possible Tning centrifgal governors trned ot to be not simple at all Too enthsiastic governor cold case oscillator motion of steam engine (hnting phenomenon). This catalzed the development of rigoros theor (b J. C. Maxwell) The problem redces to the qestion abot stabilit of differential eqations Verifing stabilit trned ot to be not qite simple This catalzed frther development of mathematical tools (b Roth, Hrwitz, et alii)...

16 Steam engine: the neverending stor The first atomatic control sstem sed in indstrial processes Watt s governor tamed steam engine and made the Indstrial Revoltion possible Tning centrifgal governors trned ot to be not simple at all Too enthsiastic governor cold case oscillator motion of steam engine (hnting phenomenon). This catalzed the development of rigoros theor (b J. C. Maxwell) The problem redces to the qestion abot stabilit of differential eqations Verifing stabilit trned ot to be not qite simple This catalzed frther development of mathematical tools (b Roth, Hrwitz, et alii)...

17 Steam engine: the neverending stor The first atomatic control sstem sed in indstrial processes Watt s governor tamed steam engine and made the Indstrial Revoltion possible Tning centrifgal governors trned ot to be not simple at all Too enthsiastic governor cold case oscillator motion of steam engine (hnting phenomenon). This catalzed the development of rigoros theor (b J. C. Maxwell) The problem redces to the qestion abot stabilit of differential eqations Verifing stabilit trned ot to be not qite simple This catalzed frther development of mathematical tools (b Roth, Hrwitz, et alii)...

18 Steam engine: the neverending stor The first atomatic control sstem sed in indstrial processes Watt s governor tamed steam engine and made the Indstrial Revoltion possible Tning centrifgal governors trned ot to be not simple at all Too enthsiastic governor cold case oscillator motion of steam engine (hnting phenomenon). This catalzed the development of rigoros theor (b J. C. Maxwell) The problem redces to the qestion abot stabilit of differential eqations Verifing stabilit trned ot to be not qite simple This catalzed frther development of mathematical tools (b Roth, Hrwitz, et alii)...

19 Steam engine: the neverending stor The first atomatic control sstem sed in indstrial processes Watt s governor tamed steam engine and made the Indstrial Revoltion possible Tning centrifgal governors trned ot to be not simple at all Too enthsiastic governor cold case oscillator motion of steam engine (hnting phenomenon). This catalzed the development of rigoros theor (b J. C. Maxwell) The problem redces to the qestion abot stabilit of differential eqations Verifing stabilit trned ot to be not qite simple This catalzed frther development of mathematical tools (b Roth, Hrwitz, et alii)...

20 Example 2: blood glcose reglation Glcose, transported via the bloodstream, is Its the primar sorce of energ for bod s cells. concentration mst be kept within a narrow level arond 90 mg/dl (normall, mg/dl, might be higher after meals). Failre to maintain this range consistentl (hperglcemia 2 or hpoglcemia) is ver dangeros. 2 Chronic hperglcemia (even in fasting states) most commonl cased b diabetes.

21 Blood glcose reglation mechanisms Glcose stocked in the form of glcogen, which is prodced, stored, and cleaved in the liver. When blood glcose levels are in excess, glcose can be stored in the liver as glcogen (glcogenesis). When glcose levels in the blood stream are low, the glcogen can be catabolised and glcose ma re-enter the blood stream. Blood glcose level monitored b cells in the pancreas. If blood glcose level falls, -cells of the pancreas release glcagon, a hormone casing liver cells to release glcose from glcogen. If blood glcose level rises, ˇ-cells of the pancreas release inslin, a hormone casing liver cells to convert more glcose into glcogen, ths decreasing blood sgar levels.

22 Blood glcose reglation mechanisms Glcose stocked in the form of glcogen, which is prodced, stored, and cleaved in the liver. When blood glcose levels are in excess, glcose can be stored in the liver as glcogen (glcogenesis). When glcose levels in the blood stream are low, the glcogen can be catabolised and glcose ma re-enter the blood stream. Blood glcose level monitored b cells in the pancreas. If blood glcose level falls, -cells of the pancreas release glcagon, a hormone casing liver cells to release glcose from glcogen. If blood glcose level rises, ˇ-cells of the pancreas release inslin, a hormone casing liver cells to convert more glcose into glcogen, ths decreasing blood sgar levels.

23 Blood glcose reglation Problem: maintain blood glcose level constant Actator: liver (via glcogen) Obstacles: npredictable changes (ncertainties), like irreglar meals irreglar phsical exertions stress... Sensor: pancreas cells Controller: pancreas cells (via glcagon / inslin) This is nothing bt a feedback control sstem

24 Blood glcose reglation Problem: maintain blood glcose level constant Actator: liver (via glcogen) Obstacles: npredictable changes (ncertainties), like irreglar meals irreglar phsical exertions stress... Sensor: pancreas cells Controller: pancreas cells (via glcagon / inslin) This is nothing bt a feedback control sstem

25 Example 3: breakwater Breakwater is a barrier bilt ot into a bod of water to protect a coast or harbor from the force of waves. The idea is to dissipate the energ of waves b properl designed offshore constrctions.

26 Example 3: breakwater Breakwater is a barrier bilt ot into a bod of water to protect a coast or harbor from the force of waves. The idea is to dissipate the energ of waves b properl designed offshore constrctions 3. 3 Althogh there is no feedback (even no inpts / otpts) involved, this sstem can still be considered control sstem (et not of the tpe we ll std) we change behavior of the sstem to achieve or goals.

27 What this corse is abot? This corse aims at providing primar insight into the principles of atomatic control sstems as well as at introdcing some basic theoretical methods of control sstems analsis and design. We ll confine orselves to continos-time sstems inpt / otpt approach LTI (linear time-invariant) SISO (single-inpt / single-otpt) models single-loop feedback

28 Otline Corse info Introdction Block diagrams

29 Block-diagram of centrifgal governor d p d a Engine Valve Beam linkage r Flball m n r: reqired rotation speed : throttle valve opening : shaft rotation speed m : thrst bearing position d p : plant distrbance d a : actator distrbance n: measrement noise

30 Block-diagram of blood glcose reglation d p d a Blood glcose Liver Pancreas cells r Pancreas cells m n r: reqired glcose level : hormones (inslin / glcagon) : blood glcose level m : glcokinase (enzme) d p : plant distrbance d a : actator distrbance n: measrement noise

31 Different natre / identical logic dp da dp da Engine Valve Beam linkage r Blood glcose Liver Pancreas cells r Flball m Pancreas cells m } n {{ } Centrifgal governor } n {{ } Blood glcose reglation Despite completel different natre of their components, these control sstems have identical operation logic. Hence, from the control viewpoint the can be described b the same block diagram and stdied b the same methods.

32 Different natre / identical logic dp da dp da Engine Valve Beam linkage r Blood glcose Liver Pancreas cells r Flball m Pancreas cells m } n {{ } Centrifgal governor } n {{ } Blood glcose reglation Despite completel different natre of their components, these control sstems have identical operation logic. Hence, from the control viewpoint the can be described b the same block diagram and stdied b the same methods.

33 Abstract control sstem d p d a Plant Actator Controller r Sensor m n r: reference signal : control signal (inpt) : controlled signal (otpt) m : measred signal (otpt) d p : plant distrbance d a : actator distrbance n: measrement noise Control design problem: given plant, sensor and actator design controller garanteeing reqired behavior of

34 Parallel ( = (G 1 + G 2 )): Block-diagrams: basic connections G 1 G 1 + G 2 G 2

35 Parallel ( = (G 1 + G 2 )): Block-diagrams: basic connections G 1 G 1 + G 2 G 2 Series / cascade ( = G 2 G 1 ): G 2 G 1 G 2 G 1

36 Parallel ( = (G 1 + G 2 )): Block-diagrams: basic connections G 1 G 1 + G 2 G 2 Series / cascade ( = G 2 G 1 ): G 2 G 1 G 2 G 1 Feedback ( = G 1 1 G 1 G 2 ): G 1 G 2 ± G 1 1 G 2 G 1

37 Block-diagram maniplation rles: pickoff points Moving pickoff point behind a block: 1 G 1 G 2 1 G 2 Both diagrams describe the relationships 1 = G and 2 =.

38 Block-diagram maniplation rles: pickoff points Moving pickoff point behind a block: 1 G 1 G 2 1 G 2 Both diagrams describe the relationships 1 = G and 2 =. Moving pickoff point ahead of a block: 1 G 2 G 1 G 2 Both diagrams describe the relationship 1 = 2 = G.

39 Block-diagram maniplation rles: smming points Moving smming point behind a block: G 1 G 2 G 2 1 Both diagrams describe the relationship = G( ).

40 Block-diagram maniplation rles: smming points Moving smming point behind a block: G 1 G 2 G 2 1 Both diagrams describe the relationship = G( ). Moving smming point ahead of a block: G 1 G G Both diagrams describe the relationship = G

41 Example G 5 G 4 G 2 G 1 G 3

42 Example G 5 G 4 G 2 G 1 G G 5 G 1 G 5 G 4 G 2 G 1 G 3

43 Example G 5 G 4 G 2 G 1 G G 5 G 1 G 5 G 4 G 2 G 1 G 3 1 G 1 G 5 G 4 G G 4 G 5 G 1 G G 1 G 2 G 3

44 Example G 5 G 4 G 2 G 1 G G 5 G 1 G 5 G 4 G 2 G 1 G 3 1 G 1 G 5 G 4 G G 4 G 5 G 1 G G 1 G 2 G 3 G 1 G 2 G 4 G 5 (1 + G 4 G 5 )(1 + G 1 G 2 G 3 ) + G 2 G 4