Course Objective: To familiarize students with fuzzy logic control systems so that they can. Draft Report 15% 20%

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1 Instructor: Office: ME 581/ ECE 573 Fuzzy Logic Control Systems Fall 2007 Dr. Dean Edwards BEL 319 Office Hours: M,W - 3:30 p.m. to 5:00 p.m. Course Hours: MWF, 10:30 a.m. to 11:20 a.m. in JEB 026 Resource Book: Reference Books: Software: Prerequisites: "Fuzzy Logic" by John Yen and Reza Langari, Prentice Hall. "An Introduction to Fuzzy Control," by Driankou, et.a1., Springer-Verlag. "Modem Control Systems," by Richard C. Dorf, Addison Wesley, 10 th Edition. "Neural Networks and Fuzzy Systems," by Bart Kosko, Prentice Hall. "Fuzzy Control Systems," by A. Kaudel and G. Langholz, CRC Press. Matlab ME 481, EE 470 or permission. Grading: Course Objective: Grade will be based on a semester project. U ofl Video HW Assigned (Notebook) 10% 15% Proposal (Problem Definition) 15% 15% Draft Report 15% 20% Presentation 20% Final Report 40% 50% Total 100% 100% To familiarize students with fuzzy logic control systems so that they can analyze, model, and design these systems. /

2 Chapter 1 Notes Chapter 2 Notes Chapter 3 Chapter 4 Chapter 5 Project Proposal Chapter 6 Chapter 7 Introduction ME 581/ ECE 573 Fuzzy Logic Control Systems Course Outline Review of Classical Control Systems Basic Concepts of Fuzzy Logic Linear Equivalent Fuzzy Logic Control System (LEFLC) Fuzzy Sets Fuzzy Relations, Fuzzy Graphs, and Fuzzy Arithmetic Fuzzy If-Then Rules Fuzzy Implications and Approximate Reasoning Fuzzy Logic and Probability Theory Chapter 8 Fuzzy Logic in Control Engineering Draft Project Report Chapter 14 Chapter 9 Chapter 10 Fuzzy Model Identification Hierarchical Intelligent Control Analytical Issues in Fuzzy Logic Control Project Presentations Final Project Report

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6 580 Fuzzy Control Systems A FUZZY LOGIC CONTROLLER FOR A RIGID DISK DRIVE 1. INTRODUCTION Shuichi Yoshida Information Equipment Research Laboratory Matsushita Electric Industrial Co., Ltd. Osaka, 571 Japan With the recent trends toward more powerful personal computers and workstations has emerged a demand for magnetic rigid disk drives (RDD) and other peripheral storage devices which are smaller in size and provide greater storage capacities with increased rates of data transfer to host computers. (See Fig. 1.) The time for data transfer is determined by the seek time required by the head reading the data. This is the time to move from one data cylinder to the target cylinder. The seek time is limited by the performance of the actuator moving the head as well as by the control method. This chapter shows how to reduce seek time, through a bang-bang controller employing fuzzy logic together with a method for correcting for changes in actuator coil resistance and actuator force unevenness[l,2,3]. Fig. 1 External View of a Rigid Disk Drive

7 COMPARISON OF FUZZY AND NEURAL TRUCK BACKER-UPPER CONTROL SYSTEMS Seon~~Gol'rKong and Bart Kosko 9 FUZZY AND NEURAL CONTROL SYSTEMS In this chapter we develop fuzzy and neural systems to back up a simulated truck, and truck-and-trailer, to a loading dock in a planar parking lot. We use differential competitive learning and the product-space clustering technique, discussed in Chapter 8, to adaptively generate fuzzy-associative-memory (FAM) rules from training data taken from the fuzzy and neural simulations. We developed the neural truck systems on the design recently proposed by Nguyen and Widrow [1989]. We trained the neural truck systems with the backpropagation learning algorithm, discussed in Chapter 5. In principle product-space clustering can convert any neural black-box system into a representative set of FAM rules. 339

8 340 COMPARISON OF FUZZY AND NEURAL CONTROL SYSTEMS CHAP. 9 loading dock (x f Yf) I FIGURE 9.1 BACKING UP A TRUCK front Diagram of simulated truck and loading zone. Figure 9.1 shows the simulated truck and loading zone. The truck corresponds to the cab part of the neural truck in the Nguyen-Widrow neural truck backer-upper system. The three state variables, x, and y exactly determine the truck position. specifies the angle of the truck with the horizontal. The coordinate pair (x, y) specifies the position of the rear center of the truck in the plane. The goal was to make the truck arrive at the loading dock at a right angle ( f = 90 ) and to align the position (x, y) of the truck with the desired loading dock (xf. Yf). We considered only backing up. The truck moved backward by some fixed distance at every stage. The loading zone corresponded to the plane [0. 100] x [0. 100], and (Xf. Yf) equaled (50, 100). At every stage the fuzzy and neural controllers should produce the steering angle e that backs up the truck to the loading dock from any initial position and from any angle in the loading zone. rear Fuzzy Truck Backer-Upper System We first specified each controller's input and output variables. The input variables were the truck angle and the x-position coordinate x. The output variable was the steering-angle signal e. We assumed enough clearance between the truck and the loading dock so we could ignore the y-position coordinate. The variable ranges were as follows: 0~x~ ~ ~ :; e:; 30 Positive values of e represented clockwise rotations of the steering wheel. Negative values represented counterclockwise rotations. We discretized all values to reduce

9 (a) (b) (c) examples of the fuzzy-controlled truck trajectories from different initial positions. The fuzzy control system did not use ("fire") all FAM rules at each iteration. Equjvalently most output consequent sets are empty. In most cases the system used only one or two FAM rules at each it~ration. The system used at most 4 FAM rules at once. 345 BACKING UP A TRUCK FIGURE 9.6 Sample truck trajectories of the fuzzy controller for initial positions (x, y, C/»: (a) (20, 20, 30), (b) (30, 10, 220), and (c) (30, 40, -10).

10 BACKING UP A TRUCK (a) Docking Error Back-up Trial - DCL-AFAM (solid) mean = s.d. = BP-AFAM (dashed): mean = s.d. = (b) Trajector}' Error, 5 ~ :: ~W\i~ (' A, ~!j. j~ hi!b\tl\(:,::;l t : :'L'~"'1\J![V~W\lilVr 'tj vvw~.. II.. Be 1 Back-up Trial - DCL-AFAM (solid) mean = s.d. = BP-AFAM (dashed): mean = s.d. = FIGURE 9.16 (a) Docking errors and (b) trajectory errors of the DCL-AFAM and BP-AFAM control systems. (x, y) (x, y) : Cartesian coordinate of the rear end, [0,100). (u, v) : Cartesian coordinate of the joint. <Pt : Angle of the trailer with horizontal, [-90,270). <Pc: Relative angle of the cab with trailer, [-90,90j. e: Steering angle, [-30,30). ~ : Angle of the trailer updated at each step, [-30,30]. FIGURE 9.17 Diagram of the simulated truck-and-trailer system.

11 COMPARISON OF FUZZY AND KALMAN-FILTER TARGET-TRACKING CONTROL SYSTEMS Peter J. Pacjni and Bart Kosko 11 In Chapter 9, we compared fuzzy and neural systems for the comparatively simple control problem of backing up a truck to a fixed loading dock in an empty parking lot. In this chapter, we compare a fuzzy system with a Kalman filter system for realtime target tracking. The Kalman filter is an optimal stochastic linear adaptive filter, or controller, and requires an explicit mathematical model of how control outputs depend on control inputs. In this sense the Kalman filter is a paragon of math-model controllers-and a challenging benchmark for alternative control systems. FUZZY AND MATH-MODEL CONTROLLERS Fuzzy controllers differ from classical math-model controllers. Fuzzy controllers do not require a mathematical model of how control outputs functionally depend on control inputs. Fuzzy controllers also differ in the type of uncertainty they represent and how they represent it. The fuzzy approach represents ambiguous or fuzzy-system behavior as partial implications or approximate "rules of thumb"-as fuzzy associations (.-1.,. B i ). 379

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