Charles L. Karr

Fuzzy control of pH using genetic algorithms

Abstruct- Establishing suitable control of pH, a requirement in a number of mineral and chemical industries, poses a difficult problem because of inherent nonlinearities and frequently changing process dynamics. Researchers at the U.S. Bureau of Mines have developed a technique for producing adaptive fuzzy logic controllers (FLC’s) that are capable of effectively managing such systems. In this technique, a genetic algorithm (GA) alters the membership functions employed by a conventional FLC, an approach that is contrary to the tactic generally used to provide FLC’s with adaptive capabilities in which the rule set is altered. GA’s are search algorithms based on the mechanics of natural genetics that are able to rapidly locate near-optimal solutions to difficult problems. The Bureau-developed technique is used to produce an adaptive GA-FLC for a laboratory acid-base experiment. Nonlinearities in the laboratory system are associated with the logarithmic pH scale (pH is proportional to the logarithm of HJO’ ions) and changing process dynamics are introduced by altering system parameters such as the desired set point and the concentration and buffering capacity of input solutions. Results indicate that FLC’s augmented with GA’s offer a powerful alternative to conventional process control techniques in the nonlinear, rapidly changing pH systems commonly found in industry.

Helicopter flight control with fuzzy logic and genetic algorithms

Abstract Researchers at the U.S. Bureau of Mines, in conjunction with researchers at the University of Alabama and the U.S. Army, have developed a fuzzy system for controlling the flight of UH-1 helicopters through various maneuvers. Since flying a helicopter is an extremely difficult task, the fuzzy logic controller was necessarily quite complex. In fact, the control tasks were distributed over four individual control units, each of which had its own rules and associated membership functions. Because the fuzzy logic controller was large, and because the rules implemented in the individual control units were not necessarily those a human pilot would use, an efficient technique for writing the rules was required. A genetic algorithm was used to discover rules that provided for effective control of the helicopter. Genetic algorithms are search algorithms based on the mechanics of natural genetics, and have demonstrated the ability to locate rules for fuzzy logic controllers. This paper describes the architecture of the helicopter fuzzy logic controller, provides the details of the genetic algorithm application, and presents the results of an actual flight test using the computer software.

Genetic-algorithm-based fuzzy control of spacecraft autonomous rendezvous

Abstract The combination of the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms is investigated. Fuzzy logic allows for the uncertainty inherent in most control problems to be incorporated into conventional expert systems. Although fuzzy-logic-based expert systems have been used successfully for controlling a number of physical systems, the tasks of selecting acceptable fuzzy membership functions and rule sets have generally been accomplished via subjective decision-making. In this paper, high-performance fuzzy membership functions and efficient rules for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of spacecraft are discovered using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions and rules discovered by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the authors for the rendezvous problem. Thus, genetic algorithms are potentially an effective and structured approach for designing fuzzy systems.

Improved Fuzzy Process Control of Spacecraft Autonomous Rendezvous Using a Genetic Algorithm

The U.S. Bureau of Mines is currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic allows for the uncertainty inherent in most control problems to be incorporated into conventional expert systems. Although fuzzy logic based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective decision. In this paper, high-performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of a spacecraft are learned using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions learned by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the authors for the rendezvous problem. Thus, genetic algorithms are potentially an effective and structured approach for learning fuzzy membership functions.

Solving inverse initial-value, boundary-value problems via genetic algorithm

Abstract There is a growing interest in inverse initial-value, boundary-value (inverse IVBV) problems, and in the development of robust, computationally efficient methods suitable for their solution. Inverse problems are prominent in science and engineering where often an effect is measured and the cause is not known; scientists and engineers observe the response of a system and desire to know the particulars of the system that elicited such a response. IVBV problems result when the equations that govern the behavior of a system are partial differential equations (wave phenomena, diffusion, potential of all kinds, etc.). Thus, inverse IVBV problems stem from systems governed by partial differential equations in which a response has been measured and a characteristic of the system must be computed. In this paper, an approach to solving inverse IVBV problems is presented in which the stated problem is transformed into a nonlinear optimization problem which is then solved using a genetic algorithm. Results are presented demonstrating the effectiveness of this approach for solving inverse problems that result from systems governed by three specific partial differential (1) the heat equation, (2) the wave equation, and (3) Poisson’s equation.

Solutions to systems of nonlinear equations via a genetic algorithm

Abstract Solving systems of nonlinear equations is perhaps the most difficult problem in all of numerical computation. It is also a problem that occurs frequently in a spectrum of engineering applications such as electric power generation and distribution, multi-objective optimization, and trajectory/path-planning applications. Although numerous methods have been developed to attack this class of numerical problems, one of the simplest and oldest methods, Newton’s method, is arguably the most commonly used. Like most numerical methods for solving systems of nonlinear equations, the convergence and performance characteristics of Newton’s method can be highly sensitive to the initial guess of the solution supplied to the method. In this paper, a hybrid scheme is presented, in which a genetic algorithm is used to locate efficient initial guesses, which are then supplied to a Newton method for solving a system of nonlinear equations. The hybrid scheme is tested on a specific example that is representative of this class of problems—one of determining the coefficients used in Gauss-Legendre numerical integration. Results show that the hybrid of a genetic algorithm and Newton’s method is effective, and represents an efficient approach to solving systems of nonlinear equations.

Design of a cart-pole balancing fuzzy logic controller using a genetic algorithm

Scientists at the U.S. Bureau of Mines are currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic affords a mechanism for incorporating the uncertainty inherent in most control problems into conventional expert systems. Although fuzzy logic-based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective and time consuming decision. In this paper, high-performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating a cart-pole balancing system are selected using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions chosen by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the author for the cart-pole balancing problem. Thus, genetic algorithms represent a potentially effective and structured approach for designing fuzzy logic controllers.

Flexible, adaptive, automatic fuzzy-based grade assigning system

In assigning course grades at the end of a term, most instructors are faced with the task of converting a collection of numerical scores into a single letter grade. This conversion process is generally accomplished in two steps: (1) the collection of numerical scores obtained over the course of a grading period is used to compute a weighted average; and (2) the final term average is used to assign a letter grade. The paper addresses the second step in the grade assignment process. The development and testing of a flexible, adaptive, automatic grading system is discussed. The grading system is based on fuzzy mathematics which allows the spreadsheet based grader to model the subjective nature of human grade assigners. A genetic algorithm is then employed to provide the grading system with the adaptive capabilities necessary to alter grade assigning strategies in concert with the attitudes of a particular instructor.

Adaptive Aircraft Flight Control Simulation Based on an Artificial Immune System

Over the past decade much progress has been made in the development of adaptive, model-following flight control systems. These systems are being designed to account for the degradation and even the failure of the actuators used to implement the control laws within aircraft. Typically, these adaptive, model-following flight control systems require software components capable of (1) monitoring system performance, (2) quantifying changes occurring in the performance characteristics of actuators, and (3) adapting control laws based on changes in actuator performance. Interestingly enough, the challenges facing natural immune systems also require the successful completion of three similar tasks: (1) monitoring organism performance, (2) identification of antigens, and (3) distribution of targeted antibodies. Thus, the characteristics inherent in natural immune systems have been captured and employed in computational systems called artificial immune systems (AISs). This paper describes an adaptive, model-following flight control system based on an artificial immune system. The effectiveness of the approach is demonstrated in a system designed to maintain cruise conditions in the simulation of a Boeing 747 aircraft in the presence of atmospheric turbulence and degradations in the performance characteristics of actuators used to manipulate various control surfaces.

Genetic algorithms for modelling, design, and process control

Genetic algorithms (GAs) are becoming increasingly popular as tools for solving search, optimization, and machine learning problems. The true strength of these search techniques lies in their ability to perform impressively across a broad spectrum of problems; they are robust. From system modelling to engineering design to process control, GAs have been used effectively to solve problems that have given more conventional search schemes considerable difficulty. This paper provides an overview of three projects involving GAs that have recently been completed by researchers at the U.S. Bureau of Mines, Tuscaloosa Research Center. The three projects are: (1) using a GA to solve a modelling problem using the Ree-Eyring equation, (2) designing a piece of separation equipment an air injected hydrocyclone, with a GA, and (3) tuning a fizzy logic controller with a GA. These three applications provide an indication of the potential of GAs, and represent “state-of-the-art” of GA use in the minerals industry.