1. سیستمهای کنترل خطی پاییز 1389 بسم ا... الرحمن الرحيم دکتر حسين بلندي - دکتر سید مجید اسما عیل زاده

2. Introduction

3. Control The word control is usually taken to mean : - regulate, تنظيم کردن - direct, هدايت کردن - command فرمان ‌ دادن ‌. 3

4. Control system A control system is an arrangement of physical components connected or related in such a manner as to command, direct, or regulate itself or another system. 4

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6. Input The input is the excitation or command applied to a control system. Typically from external energy source, usually in order to produce a specified response from the control system. 6

7. Output The output is the actual response obtained from a control system. It may or may not be equal to specified response implied by the input. 7

8. In Summary Input - Excitation applied to a control system from an external source. Output - The response obtained from a system Feedback - The output of a system that is returned to modify the input. Error - The difference between the reference input and the output. 8

9. Disturbance in a feedback control system Disturbance signal is an unwanted extraneous input signal that affects the system’s output signal. Feedback control can completely or partially eliminate the effect of disturbance signal. 9

10. Negative Feedback Control System CONTROLLER CONTROLLED DEVICE FEEDBACK ELEMENT ++ + - 10

11. Terms and Concepts 11

12. Control system A control system is an interconnection of components forming a system configuration that will provide a desired system response. 12

13. Two Types of Control Systems Open Loop – No feedback – Difficult to control output with accuracy Closed Loop – Must have feedback – Must have sensor on output – Almost always negative feedback 13

14. Open-loop control An open-loop control system utilizes an actuating device to control the process directly without using feedback. Must be closely monitored. A common example of an open-loop control system is an electric toaster in the kitchen. 14

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18. Closed-loop control A closed-loop control system uses a measurement of the output and feedback of this signal to compare it with the desired output. Continually adjusts the process. 18

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21. A person steering an automobile by looking at the auto’s location on the road and making the appropriate adjustments. 21

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23. Manual control system Goal: Regulate the level of fluid by adjusting the output valve. The input is a reference level of fluid and is memorized by operator. The sensor is visual. Operator compares the actual level with the desired level and opens or closes the valve ( actuator). 23

24. The level of fluid in a tank control. 24

25. The roles of feedback Reduce error (eliminating the error) Reduce sensitivity or Enhance robustness Disturbance rejection or elimination Improve dynamic performance or adjust the transient response (such as reduce time constant) Benefits: 25

26. Major Types of Feedback Used øPosition Feedback – Used when the output is a linear distance or angular measurement. øRate & Acceleration Feedback – Feeds back rate of motion or rate of change of motion (acceleration) – Motion smoothing – Uses a electrical/mechanical device call an accelerometer 26

27. Control systems are divided into two classes: a ) If the aim is to maintain a physical variable at some fixed value when there are disturbances, this is a regulator. Example: speed-control system b) The second class is the servomechanism. This is a control system in which a physical variable is required to follow (track) some desired time function. Example: an automatic aircraft landing system, or a robot arm designed to follow a required path in space.

28. Multivariable control system 28

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30. A robot is a computer-controlled machine. Industrial robotics is a particular field of automation in which the robot is designed to substitute for human labor. The Honda P3 humanoid robot. 30

31. Automation - The control of a process by automatic means. Closed-loop feedback control system - A system that uses a measurement of the output and compares it with the desired output. 31

32. Design - The process of conceiving or inventing the forms, parts, and details of a system to achieve a specified purpose. Feedback signal - A measure of the output of the system used for feedback to control the system. Multivariable control system - A system with more than one input variable or more than one output variable. 32

33. Negative feedback - The output signal is fed back so that it subtracts from the input signal. Negative feedback initiates to maintain or regulate physiological functions within a set and narrow range. Open-loop control system - A system that utilizes a device to control the process without using feedback. Optimization - The adjustment of the parameters to achieve the most favorable or advantageous design. 33

34. Positive feedback - The output signal is fed back so that it adds to the input signal. Positive feedback mechanisms are designed to accelerate or enhance the output created by a stimulus that has already been activated. In positive feedback systems the presence of a product (or signal) results in an increase in the production (amplification) of that product (or signal). Process - The device, plant, or system under control. Productivity -The ratio of physical output to physical input of an industrial process. 34

35. Synthesis - The combining of separate elements or devices to form a coherent whole. System - An interconnection of elements and devices for a desired purpose. 35

36. The Control System Design Process

37. Design is the process of conceiving or inventing the forms, parts, and details of a system to achieve a specified purpose. Engineering design 37

38. Engineering design Trade-off The result of making a judgment about how to compromise between conflicting criteria. 38

39. Control system engineers are concerned with understanding and controlling segments of their environment, often called systems, to provide useful economic products. 39

40. Goals Twin goals of understanding and controlling are complementary because effective systems control requires that the systems be understood and modeled. 40

41. Control engineering Control engineering is based on the foundations of feedback theory and linear system analysis, and it integrates the concepts of network theory and communication theory. 41

42. Given a process, how to design a feedback control system? Three steps: Modeling. Obtain mathematical description of the systems. Analysis. Analyze the properties of the system. Design. Given a plant, design a controller based on performance specifications. The course spans each of these steps in that sequence. 42

43. The basis for analysis of a system is the foundation provided by linear system theory, which assumes a cause-effect relationship for the components of a system. 43

44. The design of control systems is a specific example of engineering design. The goal of control engineering design is to obtain the configuration, specifications, and identification of the key parameters of a proposed system to meet an actual need. 44

45. The design process consists of seven main building blocks, which are arrange into three groups: 1. Establishment of goals and variables to be controlled, and definition of specifications against which to measure performance 2. System definition and modeling 3. Control system design and integrated system simulation and analysis 45

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47. Design 1 47

48. Design 2 48

49. Design 3 49

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51. Design examples

52. Rotating disk speed control 52

53. Step 1. Control goal Design a system that will held a rotating disk at a constant speed. Ensure that the actual speed of rotation is within a specified percentage of desired speed. 53

54. Step 2. Variable to be controlled Speed of rotation disc 54

55. Step 3. Control design specification Design a system that will ensure that the actual speed of rotation is within a specified percentage of desired speed. 55

56. Step 4 Preliminary system configuration 56

57. Step 4 Preliminary system configuration 57

58. With precision components, we could expect to reduce the error of the feedback system to one-hundredth of error of the open-loop system. 58

59. Insulin delivery system

60. The blood glucose and insulin concentrations for a healthy person. 60

61. Step 1. Control goal Design a system to regulate the blood sugar concentration of a diabetic by controlled dispensing of insulin. 61

62. Step 2. Variable to be controlled Blood glucose concentration 62

63. Step 3. Control design specification Provide a blood glucose level for the diabetic that closely approximates the glucose level of a healthy person. 63

64. Step 4 Preliminary system configurations 64

65. A drug-delivery system implanted in the body uses an open-loop system, since miniaturized glucose sensors are not yet available. 65

66. 66 E 1: Controlling the position of a missile launcher from a remote location

67. Controlling the position of a missile launcher from a remote location The input is the desired angular position of the missile launcher, The control system consists: of potentiometer, power amplifier, motor, gearing between the motor and the missile launcher, missile launcher. 67

68. A position open loop control The input is the desired angular position of the missile launcher, and the control system consists of potentiometer, power amplifier, motor, gearing between the motor and missile launcher, and missile launcher. 68

69. A position closed loop control Should an error exists, it is amplified and applied to a motor drive which adjusts the output-shaft position until it agrees with the input-shaft position, and the error is zero. 69

70. Applications

71. Control engineering is not limited to any engineering discipline but is equally applicable to: aeronautical, chemical, mechanical, computer science and engineering, civil engineering, electrical engineering. 71

72. Prerequisite by topics Knowledge and proficiency in Matlab Concept and solution of linear ordinary differential equations Laplace transform and its applications Poles, zeros, transfer functions, frequency response, Bode plots Vectors and matrices Complex numbers 72