This tutorial is concerned with experimentation and benchmarking algorithms. Continuous Optimizers (COCO) platform, `TWAS Prize' in Engineering Sciences in 2012, `CajAstur Mamdani Prize' in.
Contents.Overview Fuzzy logic is widely used in machine control. The term 'fuzzy' refers to the fact that the logic involved can deal with concepts that cannot be expressed as the 'true' or 'false' but rather as 'partially true'. Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans. History and applications Fuzzy logic was first proposed by of the University of California at Berkeley in a 1965 paper. He elaborated on his ideas in a 1973 paper that introduced the concept of 'linguistic variables', which in this article equates to a variable defined as a fuzzy set. Other research followed, with the first industrial application, a cement built in Denmark, coming on line in 1975.Fuzzy systems were initially implemented in.
Interest in fuzzy systems was sparked by Seiji Yasunobu and Soji Miyamoto of, who in 1985 provided simulations that demonstrated the feasibility of fuzzy control systems for the. Their ideas were adopted, and fuzzy systems were used to control accelerating, braking, and stopping when the opened in 1987. In 1987, Takeshi Yamakawa demonstrated the use of fuzzy control, through a set of simple dedicated fuzzy logic chips, in an ' experiment. This is a classic control problem, in which a vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forth.
Yamakawa subsequently made the demonstration more sophisticated by mounting a wine glass containing water and even a live mouse to the top of the pendulum: the system maintained stability in both cases. Yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the field.
Japanese engineers subsequently developed a wide range of fuzzy systems for both industrial and consumer applications. In 1988 Japan established the Laboratory for International Fuzzy Engineering (LIFE), a cooperative arrangement between 48 companies to pursue fuzzy research. The automotive company Volkswagen was the only foreign corporate member of LIFE, dispatching a researcher for a duration of three years. Japanese consumer goods often incorporate fuzzy systems.
Matsushita vacuum cleaners use microcontrollers running fuzzy algorithms to interrogate dust sensors and adjust accordingly. Hitachi washing machines use fuzzy controllers to load-weight, fabric-mix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergent. Canon developed an camera that uses a (CCD) to measure the clarity of the image in six regions of its field of view and use the information provided to determine if the image is in focus. It also tracks the rate of change of lens movement during focusing, and controls its speed to prevent overshoot. The camera's fuzzy control system uses 12 inputs: 6 to obtain the current clarity data provided by the CCD and 6 to measure the rate of change of lens movement. The output is the position of the lens.
The fuzzy control system uses 13 rules and requires 1.1 kilobytes of memory. An industrial designed by Mitsubishi uses 25 heating rules and 25 cooling rules. A temperature sensor provides input, with control outputs fed to an, a compressor valve, and a fan motor. Compared to the previous design, the fuzzy controller heats and cools five times faster, reduces power consumption by 24%, increases temperature stability by a factor of two, and uses fewer sensors. Other applications investigated or implemented include: character and handwriting recognition; optical fuzzy systems; robots, including one for making Japanese flower arrangements; robot helicopters (hovering is a 'balancing act' rather similar to the inverted pendulum problem); rehabilitation robotics to provide patient-specific solutions (e.g.
.Automatic control belongs to the application areas of theory that have attracted most. In 1974, the first successful application of to the control of a laboratory-scale process was reported (Mamdani and Assilian 1975). Control of cement kilns was an early industrial application (Holmblad and Ostergaard 1982). Since the first consumer product using fuzzy logic was marketed in 1987, the use of fuzzy control has increased substantially. A number of CAD environments for fuzzy control design have emerged together with VLSI hardware for fast execution. Fuzzy control is being applied to various systems in the process industry (Santhanam and Langari 1994, Tani et al. 1994), consumer electronics (Hirota 1993, Bonissone 1994), automatic train operation (Yasunobu and Miyamoto 1985), traffic systems in general (Hellendoorn 1993), and in many other fields (Hirota 1993, Terano et al.
Figure 8: Fuzzy supervisory control.In this way, static or dynamic behavior of the low-level control system can be modified in order to cope with process nonlinearitiesor changes in the operating or environmental conditions. An advantage of a supervisory structure is that it can be added to already existing control systems. Hence, the original controllers can always be used as initial controllers for which the supervisory controller can be tuned for improving the performance. A supervisory structure can be used for implementing different control strategies in a single controller.
An example is choosing proportional control with a high gain, when the system is very far from the desired reference signal and switching to a PI-control in the neighborhood of the reference signal. Because the parameters are changed during the dynamic response, supervisory controllers are in general nonlinear.Many processes in the industry are controlled by PID controllers. Despite their advantages, conventional PID controllers suffer from the fact that the controller must be re-tuned when the operating conditions change. This disadvantage can be reduced by using a fuzzy supervisor for adjusting the parameters of the low-level controller. A set of rules can be obtained from experts to adjust the gains P and D of a PD controller, e.g, based on the current set-point r. The rules may look likeIfprocess output is HighThenreduce proportional gain Slightly andincrease derivative gain ModeratelyThe TS controller can be interpreted as a simple version of supervisory control.
For instance, the TS rules Figure can be written in terms of Mamdani or singleton rules that have the P and D parameters as outputs. These are then passed to a standard PD controller at a lower level.Example: pressure controlA supervisory fuzzy controller has been applied to pressure control in a laboratory fermenter, depicted in Fig. Figure. Figure 11: The supervisory fuzzy control scheme.The volume of the fermenter tank is 40 l, and normally it is filled with 25 l of water.
At the bottom of the tank, air is fed into the water at a constant flow-rate, kept constant by a local mass-flow controller. The air pressure above the water level is controlled by an outlet valve at the top of the tank. With a constant input flow-rate, the system has a single input, the valve position, and a single output, the air pressure. Because of the underlying physical mechanisms, and because of the nonlinear behavior of the control valve, the process has a nonlinear steady-state characteristic, shown in Fig. Figure, as well as a nonlinear dynamic behavior. Figure 12: Membership functions for (u(k).)A single-input, two-output supervisor shown in Fig. Figure was designed. The input of the supervisor is the valve position u(k) and the outputs are the proportional and the integral gain of a conventional PI controller.
The supervisor updates the PI gains at each sample of the low-level control loop ( 5 s).The domain of the valve position between 0 and 100 was modeled with Small, Medium, Big and Very Big as membership functions (cf. Fig. Figure ).The PI gains P and I associated with each of the fuzzy sets are given as follows:Gains (backslash u(k)!)width='50' SmallMediumBigVery bigP50.