There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Generally, decisions are based on information. To be useful, information must be reliable. Basically, the concept of a Z-number relates to the issue of reliability of information. A Z-number, Z, has two components, Z=(A,B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliability (certainty) of the first component. Typically, A and B are described in a natural language, for example: (about 45 minutes, very sure). Z-number has many applications, especially in the realms of economics, decision analysis, risk assessment, prediction, anticipation, rule-based characterization of imprecise functions and relations, and biomedicine. Different methods, applications, and systems are discussed. Other Fuzzy concepts are also discussed.

Methods and Systems for Applications for Z-numbers

Wind energy is the fastest growing alternate source of energy in the world since its purely economic potential is complemented by its great positive environmental impact. The wind turbine, whether it may be a Horizontal-Axis Wind Turbine (HAWT) or a Vertical-Axis Wind Turbine (VAWT), offers a practical way to convert the wind energy into electrical or mechanical energy. Although this book focuses on the aerodynamic design and performance of VAWTs based on the Darrieus concept, it also discusses the comparison between HAWTs and VAWTs, future trends in design and the inherent socio-economic and environmental friendly aspects of wind energy as an alternate source of energy.

Wind turbine design with emphasis on Darrieus concept Ion Paraschivoiu

Artificial potential fields and optimal controllers are two common methods for path planning of autonomous vehicles. An artificial potential field method is capable of assigning different potential functions to different types of obstacles and road structures and plans the path based on these potential functions. It does not, however, include the vehicle dynamics in the path-planning process. On the other hand, an optimal path-planning controller integrated with vehicle dynamics plans an optimal feasible path that guarantees vehicle stability in following the path. In this method, the obstacles and road boundaries are usually included in the optimal control problem as constraints and not with any arbitrary function. A model predictive path-planning controller is introduced in this paper such that its objective includes potential functions along with the vehicle dynamics terms. Therefore, the path-planning system is capable of treating different obstacles and road structures distinctly while planning the optimal path utilizing vehicle dynamics. The path-planning controller is modeled and simulated on a CarSim vehicle model for some complicated test scenarios. The results show that, with this path-planning controller, the vehicle avoids the obstacles and observes road regulations with appropriate vehicle dynamics. Moreover, since the obstacles and road regulations can be defined with different functions, the path-planning system plans paths corresponding to their importance and priorities.

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A Potential Field-Based Model Predictive Path-Planning Controller for Autonomous Road Vehicles

Control Systems Engineering

Type-2 fuzzy logic systems have recently been utilized in many control processes due to their ability to model uncertainties. This paper proposes a novel inference mechanism for an interval type-2 Takagi-Sugeno-Kang fuzzy logic control system (IT2 TSK FLCS) when antecedents are type-2 fuzzy sets and consequents are crisp numbers (A2-C0). The proposed inference mechanism has a closed form which makes it more feasible to analyze the stability of this FLCS. This paper focuses on control applications for the following cases: 1) Both plant and controller use A2-C0 TSK models, and 2) the plant uses type-1 Takagi-Sugeno (TS) and the controller uses IT2 TS models. In both cases, sufficient stability conditions for the stability of the closed-loop system are derived. Furthermore, novel linear-matrix-inequality-based algorithms are developed for satisfying the stability conditions. Numerical analyses are included which validate the effectiveness of the new inference methods. Case studies reveal that an IT2 TS FLCS using the proposed inference engine clearly outperforms its type-1 TSK counterpart. Moreover, due to the simple nature of the proposed inference engine, it is easy to implement in real-time control systems. The methods presented in this paper lay the mathematical foundations for analyzing the stability and facilitating the design of stabilizing controllers of IT2 TSK FLCSs and IT2 TS FLCSs with significantly improved performance over type-1 approaches.

On the Stability of Interval Type-2 TSK Fuzzy Logic Control Systems

Written by world-class leaders in type-2 fuzzy logic control, this book offers a self-contained reference for both researchers and students. The coverage provides both background and an extensive literature survey on fuzzy logic and related type-2 fuzzy control. It also includes research questions, experiment and simulation results, and downloadable computer programs on an associated website. This key resource will prove useful to students and engineers wanting to learn type-2 fuzzy control theory and its applications.

Introduction to Type-2 Fuzzy Logic Control: Theory and Applications

This paper utilizes an intelligent system which incorporates Kalman filters (KFs) and a fuzzy expert system to track the tip of a fastening tool and to identify the fastened bolt. This system employs one inertial measurement unit and one position sensor to determine the orientation and the center of mass location of the tool. KFs are used to estimate the orientation of the tool and the center of mass location of the tool. Although a KF is used for the orientation estimation, orientation error increases over time due to the integration of angular velocity error. Therefore, a methodology to correct the orientation error is required when the system is used for an extended period of time. This paper proposes a method to correct the tilt angle and orientation errors using a fuzzy expert system. When a tool fastens a bolt, the system identifies the fastened bolt using a fuzzy expert system. Through this bolt identification step, the 3-D orientation error of the tool is corrected by using the location and orientation of the fastened bolt and the position sensor outputs. Using the orientation correction method will, in turn, result in improved reliability in determining the tool tip location. The fastening tool tracking system was experimentally tested in a lab environment, and the results indicate that such a system can successfully identify the fastened bolts.

A Fastening Tool Tracking System Using an IMU and a Position Sensor With Kalman Filters and a Fuzzy Expert System

Recently, there has been a growing interest in using modular and reconfigurable robots (MRRs) in flexible automation to reduce labor and increase throughput. Moreover, the significant facilitation of repair and maintenance of MRRs has attracted manufacturers to respond to the increasing desire for new products and methods of production in today's competitive market. As a result, design and control of such systems have become major topics for investigation in recent years. This paper presents a novel design methodology of interval type-2 Takagi-Sugeno-Kang fuzzy logic controllers (IT2 TSK FLCs) for MRR manipulators with uncertain dynamic parameters. We develop a mathematical framework for the design of IT2 TSK FLCs for tracking purposes that can be effectively used in real-time applications. To verify the effectiveness of the proposed controller, experiments are performed on an MRR with two degrees of freedom, which exhibits dynamic coupling behavior. Results show that the developed controller can outperform some well-known linear and nonlinear controllers for different configurations. Therefore, the proposed structure can be adopted for the position control of MRRs with unknown dynamic parameters in trajectory-tracking applications.

William Melek

Papers

On the Stability of Interval Type-2 TSK Fuzzy Logic Control Systems

Introduction to Type-2 Fuzzy Logic Control: Theory and Applications

A Fastening Tool Tracking System Using an IMU and a Position Sensor With Kalman Filters and a Fuzzy Expert System

Design of Novel Interval Type-2 Fuzzy Controllers for Modular and Reconfigurable Robots: Theory and Experiments

On the robustness of Type-1 and Interval Type-2 fuzzy logic systems in modeling