Dr.-Ing. Erwin Sitompul President University Lecture 1 Feedback Control Systems President UniversityErwin SitompulFCS 1/1

President UniversityErwin SitompulFCS 1/2 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 IDR 192,000 USD Feedback Control Systems

President UniversityErwin SitompulFCS 1/3 Grade Policy Final Grade =10% Homeworks + 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. Feedback Control Systems

President UniversityErwin SitompulFCS 1/4 Midterm and final exam schedule will be announced in time. Make up of quizzes and exams must be held within one week after the schedule of the respective quizzes and exams. In order to maintain the integrity, the score of a make up quiz or exam can be multiplied by 0.9 (i.e., the maximum score for a make up will be 90). Grade Policy Heading of Homework Papers (Required) Feedback Control Systems

President UniversityErwin SitompulFCS 1/5 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. Lecture slides can be copied during class session. The updated version will be available on the lecture homepage around 2 days after class schedule. Please check regularly. Grade Policy Feedback Control Systems

President UniversityErwin SitompulFCS 1/6 Chapter 1 Introduction Feedback Control Systems

President UniversityErwin SitompulFCS 1/7 Introduction 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 value when performing control is the desired output variable. Process, as it is used and understood by control engineers, means the component to be controlled. 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 Chapter 1Introduction

President UniversityErwin SitompulFCS 1/8 Process Input Performance Measurement Disturbance Reference Measurement noise Chapter 1Introduction

President UniversityErwin SitompulFCS 1/9 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. Open-loop vs. Feedback Control Chapter 1Introduction In feedback control, the system includes a sensor to measure the actual output and uses its feedback to influence the control process.

President UniversityErwin SitompulFCS 1/10 Examples The controller is constructed based on knowledge or experience. The process output is not used in control computation. The output is fed back for control computation. Open-loop controlFeedback control Example: an electric toaster, a standard gas stove. Example: automated filling-up system, magic jar, etc. Chapter 1Introduction

President UniversityErwin SitompulFCS 1/11 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 Chapter 1Introduction

President UniversityErwin SitompulFCS 1/12 Plus-Minus of Feedback Control + 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 – More complex than open-loop control – May have steady-state error – Depends on the accuracy of the sensor – May have stability problem Chapter 1Introduction

President UniversityErwin SitompulFCS 1/13 Chapter 2 Dynamic Models Feedback Control Systems

President UniversityErwin SitompulFCS 1/14 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) Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/15 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. Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/16 A Simple System: Cruise Control Model With the parameters: In MATLAB windows: Response of the car velocity v to a step-shaped force u: Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/17 A Two-Mass System: Suspension Model m 1 : mass of the wheel m 2 : mass of the car x,y: displacements from equilibrium r: distance to road surface Equation for m 1 : Equation for m 2 : Rearranging: Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/18 A Two-Mass System: Suspension Model Using the Laplace transform: to transfer from time domain to frequency domain yields: Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/19 A Two-Mass System: Suspension Model Eliminating X(s) yields a transfer function: Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/20 Bridged Tee Circuit v1v1 ResistorInductorCapacitor Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/21 RL Circuit v1v1 Further calculation and eliminating V 1, Chapter 2Dynamic Models

President UniversityErwin SitompulFCS 1/22 Chapter 3 Dynamic Response Feedback Control Systems

President UniversityErwin SitompulFCS 1/23 Review of Laplace Transform Time domainFrequency domain Problem Solution easy operations difficult operations Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/24 Properties of Laplace Transform 1. Superposition 2. Time delay 3. Time scaling 4. Shift in Frequency 5. Differentiation in Time Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/25 Properties of Laplace Transform 6. Integration in Time 7. Differentiation in Frequency 8. Convolution Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/26 unit impulse unit step unit ramp Table of Laplace Transform Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/27 Example : Obtain the Laplace transform of Laplace Transform Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/28 Laplace Transform Example : Find the Laplace transform of the function shown below. Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/29 Inverse Laplace Transform The steps are: 1.Decompose F(s) into simple terms using partial-fraction expansion. 2.Find the inverse of each term by using the table of Laplace transform. Example : Find y(t) for Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/30 Inverse Laplace Transform Comparing the coefficients Chapter 3Dynamic Response ●Learn also the faster “Cover Up Method”

President UniversityErwin SitompulFCS 1/31 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 Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/32 Initial and Final Value Theorem Example : Find the final value of the system corresponding to WRONG Sinc e NOT convergent NO limit value Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/33 Initial and Final Value Theorem Example : Find the final value of WRONG Sinc e periodic signal NOT convergent NO limit value Chapter 3Dynamic Response

President UniversityErwin SitompulFCS 1/34 Homework (b) 3.5 (c) 3.6 (e) all from FPE (5 th Ed.) Deadline: , 07:30. Chapter 3Dynamic Response