Feedback Control Systems Lecture 1 Dr Ing Erwin

Feedback Control Systems Lecture 1 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com 2 0 President University Erwin Sitompul FCS 1/1

Feedback Control Systems Textbook and Syllabus Textbook: Gene F. Franklin, J. David Powell, Abbas Emami-Naeini, “Feedback Control of Dynamic Systems”, 6 th Edition, Pearson International Edition. Syllabus: 1. Introduction 2. Dynamic Models 3. Dynamic Response 4. A First Analysis of Feedback 5. The Root-Locus Design Method 6. The Frequency-Response Design Method President University Erwin Sitompul FCS 1/2

Feedback Control Systems Grade Policy Final Grade = 4% Attendance + 6% Notes + 10% Homework + 18% Quizzes + 26% Midterm Exam + 36% Final Exam + Extra Points n Attendance will be counted. n Maximum allowed lateness is 15 minutes. n Only sickness with official paper proof will be counted as attending class. n Only permission for duty with official paper proof will be counted as attending class. n Please do not send messages or email regarding missing classes. President University Erwin Sitompul FCS 1/3

Feedback Control Systems Grade Policy Final Grade = 4% Attendance + 6% Notes + 10% Homework + 18% Quizzes + 26% Midterm Exam + 36% Final Exam + Extra Points n You are expected to write a note along the lectures to record your own conclusions or materials which are not covered by the lecture slides. n Your handwritten note should be uploaded to the Gdrive link given to you. n DO NOT make any subdirectory in your folder. One directory for one student only. n To get maximum score, upload the notes in 4 different days (2 before mid-exam and 2 after mid-exam). n The acceptable format is JPG or GIF. No PDF is allowed. n The final allowed upload days is 1 day before final exam week (usually a Sunday). President University Erwin Sitompul FCS 1/4

Feedback Control Systems Grade Policy n Homeworks will be given in fairly regular basis. The homework grades will be averaged. n Homeworks are to be written on A 4 papers, otherwise they will not be graded. Semiconductor Device Physics Homework 2 Ito Chen 009202700008 21 March 2029 (The date when the homework is given) D 6. 2. Answer: . . . . • Heading of Homework Papers (Required) President University Erwin Sitompul FCS 1/5

Feedback Control Systems Grade Policy n Homeworks must be submitted in hardcopy on time, one day before the schedule of the lecture. Late submitted homeworks will not be graded. n There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 18% of final grade. n Make up of quiz must be held within one week after the schedule of the respective quiz. n Extra points will be given every time you solve a problem in front of the class or answer a question. You will earn 1 or 2 points. n The updated version will be available on the lecture homepage around 1 days after class schedule. Please check regularly. http: //zitompul. wordpress. com President University Erwin Sitompul FCS 1/6

Feedback Control Systems Chapter 1 Introduction President University Erwin Sitompul FCS 1/7

Chapter 1 Introduction n Control is a series of actions directed for making a system variable adheres to a reference value (can be either constant or variable). n The reference value when performing control is the desired output variable. n Process, as it is used and understood by control engineers, means the component to be controlled. n Fundamental structures of control are classified based on the information used along the control process: 1. Open-loop control / Feedforward control 2. Closed-loop control / Feedback control President University Erwin Sitompul FCS 1/8

Chapter 1 Introduction Some Terminology n The plant/process is the system being controlled. n The sensors measure the quantity that is subject to control. n The actuators act on the plant. n The controller processes the sensor signals and drives the actuators. n The control law is the rule for mapping sensor signals to actuator signals. Centrifugal governor, invented by James Watt, to control the speed of steam engine President University Erwin Sitompul FCS 1/9

Chapter 1 Introduction Process Reference Disturbance Measurement noise Performance Input Measurement President University Erwin Sitompul FCS 1/10

Chapter 1 Introduction Open-loop vs. Feedback Control The difference: n 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. n In feedback control, the system includes a sensor to measure the actual output and uses its feedback to influence the control process. President University Erwin Sitompul FCS 1/11

Chapter 1 Introduction Examples Open-loop control Feedback control Example: an electric toaster, a standard gas stove. Example: automated filling-up system, magic jar, etc. n The controller is constructed based on knowledge or experience. n The process output is not used in control computation. n The output is fed back for control computation. President University Erwin Sitompul FCS 1/12

Chapter 1 Introduction 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 President University Erwin Sitompul FCS 1/13

Chapter 1 Introduction 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 President University Erwin Sitompul FCS 1/14

Chapter 1 Introduction Some Applications of Feedback Control President University Erwin Sitompul FCS 1/15

Feedback Control Systems Chapter 2 Dynamic Models President University Erwin Sitompul FCS 1/16

Chapter 2 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) President University x (Position) v (Velocity) Erwin Sitompul FCS 1/17

Chapter 2 Dynamic Models A Simple System: Cruise Control Model Applying the Newton’s Law for translational motion yields: MATLAB (Matrix Laboratory) is the standard software used in control engineering: By the end of this course, you are expected to be able to use MATLAB for basic applications. President University Erwin Sitompul FCS 1/18

Chapter 2 Dynamic Models A Simple System: Cruise Control Model With the parameters: Response of the car velocity v to a step-shaped force u: In MATLAB windows: President University Erwin Sitompul FCS 1/19

Chapter 2 Dynamic Models A Two-Mass System: Suspension Model m 1 m 2 x, y r : : mass of the wheel mass of the car displacements from equilibrium distance to road surface Equation for m 1: Equation for m 2: Rearranging: President University Erwin Sitompul FCS 1/20

Chapter 2 Dynamic Models A Two-Mass System: Suspension Model Using the Laplace transform: to transfer from time domain to frequency domain yields: President University Erwin Sitompul FCS 1/21

Chapter 2 Dynamic Models A Two-Mass System: Suspension Model Eliminating X(s) yields a transfer function: President University Erwin Sitompul FCS 1/22

Chapter 2 Dynamic Models Bridged Tee Circuit v 1 Resistor President University Erwin Sitompul Inductor Capacitor FCS 1/23

Chapter 2 Dynamic Models RL Circuit v 1 Further calculation and eliminating V 1, President University Erwin Sitompul FCS 1/24

Feedback Control Systems Chapter 3 Dynamic Response President University Erwin Sitompul FCS 1/25

Chapter 3 Dynamic Response Review of Laplace Transform Time domain Frequency domain Problem difficult operations easy operations Solution President University Erwin Sitompul FCS 1/26

Chapter 3 Dynamic Response Properties of Laplace Transform 1. Superposition 2. Time delay 3. Time scaling 4. Shift in Frequency 5. Differentiation in Time President University Erwin Sitompul FCS 1/27

Chapter 3 Dynamic Response Properties of Laplace Transform 6. Integration in Time 7. Differentiation in Frequency 8. Convolution President University Erwin Sitompul FCS 1/28

Chapter 3 Dynamic Response Table of Laplace Transform unit impulse unit step unit ramp President University Erwin Sitompul FCS 1/29

Chapter 3 Dynamic Response Table of Laplace Transform President University Erwin Sitompul FCS 1/30

Chapter 3 Dynamic Response Laplace Transform Example: Obtain the Laplace transform of President University Erwin Sitompul FCS 1/31

Chapter 3 Dynamic Response Laplace Transform Example: Find the Laplace transform of the function shown below. President University Erwin Sitompul FCS 1/32

Chapter 3 Dynamic Response Inverse Laplace Transform The steps are: 1. Decompose F(s) into simple terms using “Partial-Fraction Expansion Method”. 2. Find the inverse of each term by using the table of Laplace transform. Example: Find y(t) for President University Erwin Sitompul FCS 1/33

Chapter 3 Dynamic Response Inverse Laplace Transform Comparing the coefficients ● Learn also the faster “Cover Up Method” President University Erwin Sitompul FCS 1/34

Chapter 3 Dynamic Response 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 President University Erwin Sitompul FCS 1/35

Chapter 3 Dynamic Response Initial and Final Value Theorem Example: Find the final value of the system corresponding to WRONG Since NOT convergent NO limit value President University Erwin Sitompul FCS 1/36

Chapter 3 Dynamic Response Initial and Final Value Theorem Example: Find the final value of WRONG Since periodic signal NOT convergent NO limit value President University Erwin Sitompul FCS 1/37

Chapter 3 Dynamic Response Homework 1 A 1. Problem 2. 6. 2. Find the transfer function Y(s)/R(s) of the circuit, n Deadline: Monday, 13 January 2019 (Evening Class) Tuesday, 14 January 2019 (Morning Class) President University Erwin Sitompul FCS 1/38

Chapter 3 Dynamic Response Homework 1 B 3. Problem 3. 4 (b), 3. 5 (c), and 3. 6 (e). 4. What is the steady state value of the step response of f(t) if you know that Verify your calculation result using MATLAB. Submit also the printout of the simulation result. Hint: Attachment of MATLAB results is a must. n Deadline: ? ? President University Erwin Sitompul FCS 1/39