Fuzzy logic

To assess and evaluate the performance of robots and machine tools dynamically, it
is desirable to have a precision measuring device that performs dynamic measurement
of end-effector positions of such robots and machine tools. Among possible
measurement techniques, Laser Tracking Systems (LTSs) exlnbit the capability of high
accuracy, large workspace, high sampling rate, and automatic target-tracking,. and thus
are well-suited for robot calibration both kinematically and dynamically.
In this dissertation, the design and implementation of a control system for a homemade
laser tracking measurement systems is addressed and calibration of a robot using
the laser tracking system is demonstrated Design and development of a control system for a LTS is a challenging task. It
involves a deep understanding of laser interferometry,. controls, mechanics and optics,.
both in theoretical perspective and in implementation aspect. One of the most important
requirements for a successful design and implementation of a control system for the
LTS is proper installation and alignment of the laser and optical system,. or laser
transducer system. The precision of measurement using the LTS depends highly on the
accuracy of the laser transducer system, as well as the accuracy of the installation and
alignment of the optical system. Hence, in reference to the experimental alignment
method presented in this dissertation, major error sources affecting the system
measurement accuracy are identified and analyzed. A manual compensation method is
developed to eliminate the effects of these error sources effectively in the measurement
system. Considerations on proper design and installation of laser and optical
components are indicated in this dissertation.
As a part of the conventional control system design, a dynamic system model of the
LTS is required. In this study, a detailed derivation and analysis of the dynamic model
of the motor gimbal system using Lagrange-Euler equations of motion is developed for
both ideal and complete gimbal systems. Based on this system model,. a conventional
controller is designed.
Fuzzy Logic Controllers (FLC) are designed in order to suppress noise or
disturbances that exist in the motor driver subsystem. By using the relevant control
strategies. noise and disturbances present in the electrical control channels are shown to
reduce significantly. To improve the system performance further, a spectrum analysis of the error sources and disturbances existing in the system is conducted. Major noise
sources are effectively suppressed by using a two-stage fuzzy logic control strategy. A
comparison study on the performances of different control strategies is given in this
dissertation, in reference to the following: An ideal system model, a system with a long
time delay, a system with various noise sources and a system model with uncertainties.
Both simulation and experimental results are furnished to illustrate the advantages of
the FLC in respect of its transient response, steady-state response, and tracking
performance. Furthermore, noise reduction in the laser tracking system is demonstrated.
Another important issue concerning a successful application of the LTS in the
calibration of a robot is the estimation of system accuracy. Hence, a detailed analysis of
system accuracy of the LTS is presented in this worL This analysis is also verified by
experimental methods by means of tracking a Coordinate Measuring Machine available
in the FAU Robotics Center. Using the developed LTS, a PUMA robot in the FAU
Robotics Center is calibrated. The results obtained are confirmative with the data
available in the literature.
In summary, the proposed methodology towards the design and implementation of a
control system for LTSs has been shown to be successful by performing experimental
tracking and calibration studies at the FAU Robotics Center.

Recent advances in computer engineering make the computational approaches to controller design for high order systems practical. In this dissertation, a series of computational methods based on cell state space for the design and optimization of Takagi-Sugeno (TS) type Fuzzy Logic Controllers (FLCs) are presented. The approaches proposed in this research can be classified into two categories: feed forward design and feedback design. An Optimal Control Table (OCT) based on cell state space is used in all the feed forward design approaches. An FLC can be trained by Least Mean Square (LMS) algorithm with an OCT serving as the training set. For high order systems, due to physical memory limit, the cell resolution is generally low. A specially modified k-d tree representation of cell space is proposed to save the memory while keeping the cell resolution as high as possible. The control command for a point that is not a cell center is approximated by interpolating an OCT. All these commands can be used as training data to train an FLC. An iterative feedback design approach named Incremental Best Estimate Directed Search (IBEDS) is proposed to further optimize a training set. It is a kind of globally directed random search method. The general philosophy is that since the best possible performance of an FLC largely depends on the quality of the training set, if the training set is optimized, an FLC trained by the set would also be optimized. Based on IBEDS, two other feedback FLC design algorithms are also proposed. In one algorithm, subtractive clustering method is used to extract the structure of an FLC from an OCT. The coefficients of the FLC obtained are then optimized with IBEDS. The other algorithm applies IBEDS to three system models and finds the training set that has the worst performance for all the models. This training set is further optimized to improve robustness of a trained FLC.

The problem at hand is developing a controller design methodology that is generally applicable to autonomous systems with fairly accurate models. The controller design process has two parts: synthesis and analysis. Over the years, many synthesis and analysis methods have been proposed. An optimal method for all applications has not yet been found. Recent advances in computer technology have made computational methods more attractive and practical. The proposed method is an iterative computational method that automatically generates non-linear controllers with specified global performance. This dissertation describes this method which consists of using an analysis tool, continued propagation cell mapping (CPCM), as feedback to the synthesis tool, best estimate directed search (BEDS). Optimality in the design can be achieved with respect to time, energy, and/or robustness depending on the performance measure used. BEDS is based on a novel search concept: globally directing a random search. BEDS has the best of two approaches: gradient (or directed) search and random search. It possesses the convergence speed of a gradient search and the convergence robustness of a random search. The coefficients of the best controller at the time direct the search process until either a better controller is found or the search is terminated. CPCM is a modification of simple cell mapping (SCM). CPCM maintains the simplicity of SCM but provides accuracy near that of a point map (PM). CPCM evaluates the controller's complete and global performance efficiently and with easily tunable accuracy. This CPCM evaluation guarantees monotonic progress in the synthesis process. The method is successfully applied to the design of a TSK-type fuzzy logic (FL) controller and a Sliding Mode-type controller for the uncertain non-linear system of an inverted pendulum on a cart for large pole angles (+/-86 degrees). The resulting controller's performance compares favorably to other established methods designed with dynamic programing (DP) and genetic algorithms (GA). When CPCM is used as feedback to BEDS, the resulting design method quickly and automatically generates non-linear controllers with good global performance and without much a priori information about the desired control actions.

Design and Tuning a fuzzy logic controller (FLCs) are usually done in two stages. In the first stage, the structure of a FLC is determined based on physical characteristics of the system. In the second stage, the parameters of the FLC are selected to optimize the performance of the system. The task of tuning FLCs can be performed by a number of methods such as adjusting control gains, changing membership functions, modifying control rules and varying control surfaces. A method for the design and tuning of FLCs through modifying their control surfaces is presented in this dissertation. The method can be summarized as follows. First, fuzzy control surfaces are modeled with Bezier functions. Shapes of the control surface are then adjusted through varying Bezier parameters. A Genetic Algorithm (GA) is used to search for the optimal set of parameters based on the control performance criteria. Then, tuned control surfaces are sampled to create rule-based FLCs. To further improve the system performance, continuity constraints of the curves are imposed. Under the continuity constraints with the same number of tunable parameters, one can obtain more flexible curves that have the potential to improve the overall system performance. An important issue is to develop a new method to self-tune a fuzzy PD controller. The method is based on two building blocks: (I) Bezier functions used to model the control surfaces of the fuzzy PD controller; and, shapes of control surfaces are then adjusted by varying Bezier parameters. (II) The next step involves using a gradient-based optimization algorithm with which the input scaling factors and Bezier parameters are on-line tuned until the controller drives the output of the process as close as possible to the reference position. To protect vendors and consumers from being victimized, various trust models have been used in e-commerce practices. However, a strict verification and authentication process may pose unnecessary heavy cost to the vendor. As an application of the control strategy proposed, this dissertation presents a solution to the reduction of costs of a vendor. With two fuzzy variables (price, credit-history), a trust-surface can be tuned to achieve an optimal solution in terms of profit margin of the vendor. With this new approach, more realistic trust decisions can be reached.

Modern people are becoming more and more dependent on computers in their daily lives. Most industries, from automobile, avionics, oil, and telecommunications to banking, stocks, and pharmaceuticals, require computers to function. As the tasks required become more complex, the complexity of computer software and hardware has increased dramatically. As a consequence, the possibility of failure increases. As the requirements for and dependence on computers increases, the possibility of crises caused by computer failures also increases. High reliability is an important attribute for almost any software system. Consequently, software developers are seeking ways to forecast and improve quality before release. Since many quality factors cannot be measured until after the software becomes operational, software quality models are developed to predict quality factors based on measurements collected earlier in the life cycle. Due to incomplete information in the early life cycle of software development, software quality models with fuzzy characteristics usually perform better because fuzzy concepts deal with phenomenon that is vague in nature. This study focuses on the usage of fuzzy logic in software reliability engineering. Discussing will include the fuzzy expert systems and the application of fuzzy expert systems in early risk assessment; introducing the interval prediction using fuzzy regression modeling; demonstrating fuzzy rule extraction for fuzzy classification and its usage in software quality models; demonstrating the fuzzy identification, including extraction of both rules and membership functions from fuzzy data and applying the technique to software project cost estimations. The following methodologies were considered: nonparametric discriminant analysis, Z-test and paired t-test, neural networks, fuzzy linear regression, fuzzy nonlinear regression, fuzzy classification with maximum matched method, fuzzy identification with fuzzy clustering, and fuzzy projection. Commercial software systems and the COCOMO database are used throughout this dissertation to demonstrate the usefulness of concepts and to validate new ideas.

This thesis develops methodologies for continuous estimation of hydrological variables which infill missing daily rainfall data and the forecast of weekly streamflows from a watershed. Several mathematical programming formulations were developed and used to estimate missing historical rainfall data. Functional relationships were created between radar precipitation and known rain gauge data then are used to estimate the missing data. Streamflow predictions models require highly non-linear mathematical models to capture the complex physical characteristics of a watershed. An artificial neural network model was developed for streamflow prediction. There are no set methods of creating a neural network and the selection of architecture and inputs to a neural network affects the performance. This thesis addresses this issue with automated input and network architecture selection through optimization. MATLABª scripts are developed and used to test many combinations and select a model through optimization.

During the Leukocytapheresis (LCAP) process used to treat patients suffering from acute Ulcerative Colitis, medical practitioners have to continuously monitor the Hematocrit (Ht) level in the blood to ensure it is within the acceptable range. The work done, as a part of this thesis, attempts to create an early warning system that can be used to predict if and when the Ht values will deviate from the acceptable range. To do this we have developed an algorithm based on the Group Method of Data Handling (GMDH) and compared it to other Neural Network algorithms, in particular the Multi Layer Perceptron (MLP). The standard GMDH algorithm captures the fluctuation very well but there is a time lag that produces larger errors when compared to MLP. To address this drawback we modified the GMDH algorithm to reduce the prediction error and produce more accurate results.

Design of intelligent systems that can learn from the environment and adapt to the change in the environment has been pursued by many researchers in this age of information technology. The Group Method of Data Handling (GMDH) algorithm to be implemented is a multilayered neural network. Neural network consists of neurons which use information acquired in training to deduce relationships in order to predict future responses. Most software tool during the simulation of the neural network based algorithms in a sequential, single processor machine like Pascal, C or C++ takes several hours or even days. But in this thesis, the GMDH algorithm was modified and implemented into a software tool written in Verilog HDL and tested with specific application (XOR) to make the simulation faster. The purpose of the development of this tool is also to keep it general enough so that it can have a wide range of uses, but robust enough that it can give accurate results for all of those uses. Most of the applications of neural networks are basically software simulations of the algorithms only but in this thesis the hardware design is also developed of the algorithm so that it can be easily implemented on hardware using Field Programmable Gate Array (FPGA) type devices. The design is small enough to require a minimum amount of memory, circuit space, and propagation delay.