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Feedback Control System

Feedback Control System. Dr.-Ing. Erwin Sitompul. Textbook: Gene F. Franklin, J. David Powell, Abbas Emami-Naeini, “ Feedback Control of Dynamic Systems ”, 6 th Edition, Pearson International Edition. Textbook and Syllabus. IDR 192,000. Syllabus: Introduction Dynamic Models

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Feedback Control System

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  1. Feedback Control System Dr.-Ing. Erwin Sitompul

  2. Textbook: Gene F. Franklin, J. David Powell, Abbas Emami-Naeini, “Feedback Control of Dynamic Systems”, 6th Edition, Pearson International Edition. Textbook and Syllabus IDR 192,000 • Syllabus: • Introduction • Dynamic Models • Dynamic Response • A First Analysis of Feedback • The Root-Locus Design Method • The Frequency-Response Design Method USD 112.50

  3. Grade Policy Final Grade = 10% Homework + 20% Quizzes + 30% Midterm Exam + 40% Final Exam + Extra Points • Homeworks will be given in fairly regular basis. The average of homework grades contributes 10% of final grade. • Homeworks are to be written on A4 papers, otherwise they will not be graded. • Homeworks must be submitted on time. If you submit late, < 10 min.  No penalty 10 – 60 min.  –20 points > 60 min.  –40 points • There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 20% of final grade.

  4. Grade Policy • Midterm and final exam schedule will be announced in time. • Make up of quizzes and exams will be held one week after the schedule of the respective quizzes and exams, at the latest. • The score of a make up quiz or exam can be multiplied by 0.9 (the maximum score for a make up is 90). • Extra points will be given every time you solve a problem in front of the class. You will earn 1 or 2 points.

  5. Feedback Control System INTRODUCTION Chapter 1 Dr.-Ing. Erwin Sitompul

  6. Control is a series of actions directed for making a system variable adheres to a reference value (can be either constant or variable). The reference valuewhen performing control is the desired output variable. Process, as it is used and understood by control engineers, means the component to be controlled. Introduction • Fundamental structures of control are classified based on the information used along the control process: • Open-loop control / Feedforward control • Closed-loop control / Feedback control

  7. Process Reference Disturbance Measurement noise Performance Input Measurement

  8. Open-loop vs. Feedback Control • The difference: • In open-loop control, the system does not measure the actual output and there is no correction to make the actual output to be conformed with the reference value. • In feedback control, the system includes a sensor to measure the actual output and uses its feedback to influence the control process.

  9. The controller is constructed based on knowledge or experience. The process output is not used in control computation. Examples Open-loop control Feedback control Example: automated filling up system, magic jar, etc. Example: an electric toaster, a standard gas stove. • The output is fed back for control computation.

  10. Plus-Minus of Open-loop Control • Generally simpler than closed-loop control • Does not require sensor to measure the output • Does not, of itself, introduce stability problem • Has lower performance to match the desired output compared to closed-loop control

  11. Plus-Minus of Feedback Control • More complex than open-loop control • May have steady-state error • Depends on the accuracy of the sensor • May have stability problem • Process controlled by well designed feedback control can respond to unforeseen events, such as: disturbance, change of process due to aging, wear, etc. • Eliminates the need of human to adjust the control variable  reduce human workload • Gives much better performance than what is possibly given by open loop control: ability to meet transient response objectives and steady-state error objectives

  12. Feedback Control System DYNAMIC MODELS Chapter 2 Dr.-Ing. Erwin Sitompul

  13. Dynamic Models A Simple System: Cruise Control Model Write the equations of motion for the speed and forward motion of the car shown below, assuming that the engine imparts a force u, and results the car velocity v, as shown. Using the Laplace transform, find the transfer function between the input u and the output v. u (Force) x(Position) v (Velocity)

  14. Dynamic Models Applying the Newton’s Law for translational motion yields: MATLAB (Matrix Laboratory) is the standard software used in control engineering: In the end of this course, you are expected to be able to know how to use MATLAB for basic applications.

  15. Dynamic Models With the parameters: Response of the car velocityv to a step-shaped forceu: In MATLAB windows:

  16. Dynamic Models A Two-Mass System: Suspension Model m1 : mass of the wheel m2 : mass of the car x,y : displacements from equilibrium r : distance to road surface Equation for m1: Equation for m2: Rearranging:

  17. Dynamic Models Using the Laplace transform: to transfer from time domain to frequency domain yields:

  18. Dynamic Models Eliminating X(s) yields a transfer function:

  19. Dynamic Models Bridged TeeCircuit v1 Resistor Inductor Capacitor

  20. Dynamic Models RLCircuit v1 Further calculation and eliminating V1,

  21. Feedback Control System DYNAMIC RESPONSE Chapter 3 Dr.-Ing. Erwin Sitompul

  22. Review of Laplace Transform Time domain Frequency domain Problem difficult operations easy operations Solution

  23. Properties of Laplace Transform 1. Superposition 2. Time delay 3. Time scaling 4. Shift in Frequency 5. Differentiation in Time

  24. Properties of Laplace Transform 6. Integration in Time 7. Differentiation in Frequency 8. Convolution

  25. Table of Laplace Transform unit impulse unit step unit ramp

  26. Laplace Transform Example: Obtain the Laplace transform of

  27. Laplace Transform Example: Find the Laplace transform of the function shown below.

  28. Inverse Laplace Transform • The steps are: • Decompose F(s) into simple terms using partial-fraction expansion. • Find the inverse of each term by using the table of Laplace transform. Example: Find y(t) for

  29. Inverse Laplace Transform Comparing the coefficients

  30. Initial and Final Value Theorem Only applicable to stable system, i.e. a system with convergent step response Example: Find the final value of the system corresponding to

  31. Initial and Final Value Theorem Example: Find the final value of the system corresponding to WRONG Since NOT convergent NO limit value

  32. Initial and Final Value Theorem Example: Find the final value of WRONG Since periodic signal NOT convergent NO limit value

  33. Homework 1 • 2.6 • 3.4 (b) • 3.5 (c) • 3.6 (e) • Deadline: 10.05.2011, 7:30 am.

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