Lecture _1_ Digital Control Systems.pptx

from my collegues

1. Digital Control Systems lecture No.1 Prof. Dr. Khalaf S Gaeid Electrical Engineering Department/ Tikrit University [email protected]

2. A control system consisting of interconnected components is designed to achieve a desired purpose. Modern control engineering practice includes the use of control design strategies for improving manufacturing processes, the efficiency of energy use, advanced automobile control, including rapid transit, among others. We also discuss the notion of a design gap. The gap exists between the complex physical system under investigation and the model used in the control system synthesis. The iterative nature of design allows us to handle the design gap effectively while accomplishing necessary tradeoffs in complexity, performance, and cost in order to meet the design specifications. Introduction to Control Systems Objectives

3. Introduction System – An interconnection of elements and devices for a desired purpose. Control System – An interconnection of components forming a system configuration that will provide a desired response. Process – The device, plant, or system under control. The input and output relationship represents the cause-and-effect relationship of the process.

4. What is Digital Control? Automatic control is the science that develops techniques to steer, guide, control dynamic systems. These systems are built by humans and must perform a specific task. Examples of such dynamic systems are found in biology, physics, robotics, finance, etc. Digital Control means that the control laws are implemented in a digital device, such as a microcontroller or a microprocessor. Such devices are light, fast and economical. Digital Control Systems  z-Plane Analysis of Discrete Time Control Systems

5. Introduction Digital control offers distinct advantages over analog control that explain its popularity. Accuracy: Digital signals are more accurate than their analogue counterparts. Implementation Errors: Implementation errors are negligible. Flexibility: Modification of a digital controller is possible without complete replacement. Speed: Digital computers may yield superior performance at very fast speeds Cost: Digital controllers are more economical than analogue controllers. 5

6. Disadvantages of digital computer s From the tracking performance side, the analog control system exhibits good performances than digital control system. D igital control system will introduce a delay in the loop. 6 https://www.mathworks.com/academia/books/search.html?q=digital%20control&page=1

7. Structure of a Digital Control System 7

8. Examples of Digitally Controlled Systems Nowadays, digitally controlled systems are everywhere, • Automotive industry: speed regulators in cars, • Aeronautic/space industry: autopilots, automatic take off/landing, cruise control • Chemistry: pharmaceutical industries, oil transformation, liquid level in tanks • Robotics: robot-arm trajectory control, manipulation, • Housing: in-house temperature regulation

9. Introduction Modeling of dynamic systems Model : A representation of a system. Types of Models: 1. Physical models (prototypes) 2. Mathematical models (e.g., input-output relationships) 3. Analytical models (using physical laws) 4. Computer (numerical) models 5. Experimental models (using input/output experimental data) Models for physical dynamic systems: Lumped-parameter models Continuous-parameter models. Example: Spring element (flexibility, inertia, damping)

10. Introduction Signal categories for identifying control system types Continuous-time signal & quantized signal Continuous-time signal is defined continuously in the time domain. Figure on the left shows a continuous-time signal, represented by x(t). Quantized signal is a signal whose amplitudes are discrete and limited. Figure on the right shows a quantized signal. Analog signal or continuous signal is continuous in time and in amplitude. The real word consists of analog signals . The Simulink quantizers as

11. Introduction Discrete -time signal & sampled -data signal Discrete-time signal is defined only at certain time instants. For a discrete-time signal, the amplitude between two consecutive time instants is just not defined. Figure on the left shows a discrete-time signal, represented by y ( kh ), or simply y ( k ), where k is an integer and h is the time interval. Sampled-data signal is a discrete-time signal resulting by sampling a continuous-time signal. Figure on the right shows a sampled-data signal deriving from the continuous-time signal, shown in the figure at the center, by a sampling process. It is represented by x ∗ ( t ). Discrete time signal sampled data signal

12. Introduction Digital signal or binary coded data signal Digital signal is a sequence of binary numbers. In or out from a microprocessor, a semiconductor memory, or a shift register. In practice, a digital signal , as shown in the figures at the bottom, is derived by two processes: sampling and then quantizing.

13. Introduction Control System Types

14. Introduction Controller Design in Digital Control Systems

15. Introduction Controller design in digital control systems - Design in S-domain Digitization (DIG) or discrete control design The above design works very well if sampling period T is sufficiently small.

16. Introduction How to design a Controller: For the approximation methods, used to convert the continuous controller to digital controller, are: Euler method, Trapezoidal method …etc and we can use forward or backward approximation. Afterwards , the differential equation of the controller can be transformed to difference equation where this difference equation can be easily programmed as a control algorithm. Note that the sampling time T should be close to zero. Hw . Design digital controller using simulink

17. backward approximation

18. Introduction Controller design in digital control systems - Design in Z domain Direct (DIR) control design

19. Figure. Piecewise -constant signal  x ZOH ( t ).

20. Examples of Digital control Systems 20 Closed-Loop Drug Delivery System HW(optional ): Implement this system with Matlab / simulink

21. Figure 1.Conversion of antenna azimuth position control system from: a. analog control to b. digital control

22. Examples of Digital control Systems 22 Aircraft Turbojet Engine

23. Introduction Mathematical comparison between analog and digital control systems

24. Difference Equation vs Differential Equation A difference equation expresses the change in some variable as a result of a finite change in another variable. A differential equation expresses the change in some variable as a result of an infinitesimal change in another variable. 24

25. Differential Equation Rearranging above equation in following form 25                    

26. Difference Equation 26                   )  

27. Difference Equations Example-1 : For each of the following difference equations, determine the (a) order of the equation. Is the equation (b) linear, (c) time invariant, or (d) homogeneous? Try to implement all the above difference equations with simulink as HW   27

28. Difference Equations Example-1: For each of the following difference equations, determine the (a) order of the equation. Is the equation (b) linear, (c) time invariant, or (d) homogeneous? Solution: The equation is second order. All terms enter the equation linearly All the terms if the equation have constant coefficients . Therefore the equation is therefore LTI. A forcing function appears in the equation , so it is nonhomogeneous.   28

29. Difference Equations Example-1: For each of the following difference equations, determine the (a) order of the equation. Is the equation (b) linear, (c) time invariant, or (d) homogeneous? Solution: The equation is 4 th order . All terms are linear The second coefficient is time dependent There is no forcing function therefore the equation is homogeneous .   29

30. Difference Equations Example-1: For each of the following difference equations, determine the (a) order of the equation. Is the equation (b) linear, (c) time invariant, or (d) homogeneous? Solution: The equation is 1 st order . Nonlinear Time invariant Homogeneous   30

31. Figure 2a. Placement of the digital computer within the loop; b. detailed block diagram showing placement of A/D and D/A converters

32. Fig.3 .Digital-to-analog converter http://www.uobabylon.edu.iq/eprints/publication_7_11855_163.pdf HW. What are the main D/A and A/D methods, try to implement it in Simulink or any other software?

33. Fig.4 Steps in analog-to-digital conversion: a. analog signal; b . analog signal after sample-and-hold; c. conversion of samples to digital numbers

34. Fig.5 . Two views of uniform-rate sampling: a. switch opening and closing; b. product of time waveform and sampling waveform

35. Fig.6. Model of sampling with a uniform rectangular pulse train

36. Fig.7 .Ideal sampling and the zero-order hold http:// ctms.engin.umich.edu/CTMS/index.php?example=MotorPosition&section=SimulinkControl

37. Table1. Partial table of z - and s -transforms

38. Table2. z -transform theorems

39. Fig.8 .Sampled-data systems: a. continuous; b. sampled input; c. sampled input and output

40. Fig.9. Sampled-data systems and their z -transforms

41. Fig.10. Steps in block diagram reduction of a sampled-data system

42. Fig.11 Digital system for Skill-Assessment Exercise try to solve it

43. Conformal Mapping between s-plane to z-plane Where . Then in polar coordinates is given by   43          

44. Conformal Mapping between s-plane to z-plane We will discuss following cases to map given points on s-plane to z-plane. Case-1: Real pole in s-plane Case-2: Imaginary Pole in s-plane Case-3: Complex Poles   44    

45. Conformal Mapping between s-plane to z-plane Case-1: Real pole in s-plane We know Therefore   45        

46. Conformal Mapping between s-plane to z-plane 46 When                   Case-1: Real pole in s-plane  

47. Conformal Mapping between s-plane to z-plane 47 When                   Case-1: Real pole in s-plane  

48. Conformal Mapping between s-plane to z-plane Case-2: Imaginary pole in s-plane We know Therefore   48        

49. Conformal Mapping between s-plane to z-plane 49 Consider                           Case-2: Imaginary pole in s-plane  

50. Fig.13 .Mapping regions of the s -plane onto the z -plane

51. Mapping regions of the s -plane onto the z -plane 51

52. Fig.14 .Finding stability of a missile control system: a. missile; b. conceptual block diagram; c. block diagram; d. block diagram with equivalent single sampler

53. Fig.25 a. Digital control system showing the digital computer performing compensation; b. continuous system used for design; c. transformed digital system

54. Fig.27.Block diagram showing computer emulation of a digital compensator

55. 55 Discrete-Time Signals: Sequences Discrete-Time signals are represented as In sampling of an analog signal x a ( t ): 1/T (reciprocal of T) : sampling frequency 9/11/2023 Cumbersome, so just use difficult  to do or  manage  and taking a lot of  time  and  effort

56. 56 Figure. Graphical representation of a discrete-time signal 9/11/2023 56 Abscissa: continuous line : is defined only at discrete instants

57. 57 Figure 2 EXAMPLE Sampling the analog waveform

58. 58 9/11/2023 58 Sum of two sequences Product of two sequences Multiplication of a sequence by a number α Delay (shift) of a sequence Basic Sequence Operations

59. 59 Basic sequences Unit sample sequence (discrete-time impulse, impulse, Unit impulse ) 9/11/2023 59 continuous-time unit impulse function δ (t) )

60. 60 Basic sequences 9/11/2023 60 arbitrary sequence A sum of scaled, delayed impulses

61. 1. The acronym DCS stands for ? 2. Many digital control systems utilize Ethernet as a communications network, because . .  3.Resolution refers to in the analog-to-digital conversion portion of a digital control system. 4,Parity bits are used for the purpose of in digital systems . 5.A typical use for an integer variable in a digital control system is : 6.A watchdog timer is a device or a programmed routine used for what purpose in a digital control system? Projects Design Efficient DC-to-DC Power Converters Electric vehicles and charging stations Renewable energy Convert SPICE models into Simscape components Convert SPICE models into Simscape components Implement Power Electronics Control on an Embedded Platform Replace Hand Coding with Code Generation Optimize for C2000 to Improve Execution Performance Strategies Hardware-in-the-Loop (HIL) Testing FPGA-based HIL Relevant to Power Electronics Adaptive control for stability optimization for Induction Motor Intelligent control for stability optimization for Induction Motor Intelligent robotic control for stability optimization

62. 62 Thanks 9/11/2023 62