Feedback Control System Dr.-Ing. Erwin Sitompul

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

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.

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.

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

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: Open-loop control / Feedforward control Closed-loop control / Feedback control

Process Reference Disturbance Measurement noise Performance Input

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.

Examples Open-loop control Feedback control Example: an electric toaster, a standard gas stove. Example: automated filling up system, magic jar, etc. 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.

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

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

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

Dynamic Models A Simple System: Cruise Control Model u x (Position) 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)

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.

Dynamic Models With the parameters: Response of the car velocity v to a step-shaped force u: In MATLAB windows:

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:

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

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

Dynamic Models Bridged Tee Circuit v1 Resistor Inductor Capacitor

Dynamic Models RL Circuit v1 Further calculation and eliminating V1,

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

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

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

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

Table of Laplace Transform unit impulse unit step unit ramp

Laplace Transform Example: Obtain the Laplace transform of

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

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

Inverse Laplace Transform Comparing the coefficients

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

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

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

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