controller since you may not be able to measure the operating condition of the plant, so making a best guess or simply placing the membership function centers at zero are common choices To complete the specification of the fuzzy controller, we use minimum or product to represent the conjunction in the premise and the implication(in this book we will use minimum unless otherwise stated) and the standard center-of-gravity defuzzification technique. As an alternative, we could use appropriately initialized singleton output membership functions and centeraverage defuzzification Learning, Memorization, and Controller Input Choice For some applications you may want to use an integral of the error or other preprocessing of the inputs to the fuzzy controller. Sometimes the same guidelines that are used for the choice of the inputs for a nonadaptive fuzzy controller are useful for the FMRLC. We have found, however, times where it is advantageous to replace part of a conventional controller with a fuzzy controller and use the FmrlC to tune it( see the fault-tolerant control application in Section 4.3) In these cases the complex preprocessing of inputs to the fuzzy controller is achieved via a conventional controller Sometimes there is also the need for postprocessing of the fuzzy controller outputs nerally, however, choice of the inputs also involves issues related to the learning dynamics of the FmrLC. As the FMRLC operates, the learning mechanism will tune the fuzzy controller's output membership functions. In particular. in our example, for each different combination of e(kn)and c(kn) inputs, it will try to learn what the best control actions are. In general, there is a close connection between what inputs are provided to the controller and the controllers ability to learn to control the plant for different reference inputs and plant operating conditions. We would like to be able to design the FMRlC so that it will learn and remember different fuzzy controllers for all the different plant operating conditions and reference inputs; hence, the fuzzy controller needs information about these Often, however, we cannot measure the operating condition of the plant, so the FMRlC does not know exactly what operating condition it is learning the controller for. Moreover, it then does not know exactly when it has returned to an operating condition. Clearly, then, if the fuzzy controller has better information about the plant's operating conditions the FmrlC will be able to learn and apply better control actions. If it does not have good information, it will continually adapt, but it will not properly remember For instance, for some plants e(kn)and c(kn)may only grossly characterize the operating conditions of the plant. In this situation the FMrlC is not able to learn different controllers for different operating conditions; it will use its limited information about the operating condition and continually adapt to search for the best controller. It degrades from a learning system to an adaptive system that will not properly remember the control actions(this is not to imply, however, that there will automatically be a corresponding degradation in performance) Generally, we think of the inputs to the fuzzy controller as specifying what conditions we need to learn different controllers for. This should be one guideline used for the choice of the fuzzy controller inputs for practical applicationscontroller since you may not be able to measure the operating condition of the plant, so making a best guess or simply placing the membership function centers at zero are common choices. To complete the specification of the fuzzy controller, we use minimum or product to represent the conjunction in the premise and the implication (in this book we will use minimum unless otherwise stated) and the standard center-of-gravity defuzzification technique. As an alternative, we could use appropriately initialized singleton output membership functions and centeraverage defuzzification. Learning, Memorization, and Controller Input Choice For some applications you may want to use an integral of the error or other preprocessing of the inputs to the fuzzy controller. Sometimes the same guidelines that are used for the choice of the inputs for a nonadaptive fuzzy controller are useful for the FMRLC. We have found, however, times where it is advantageous to replace part of a conventional controller with a fuzzy controller and use the FMRLC to tune it (see the fault-tolerant control application in Section 4.3). In these cases the complex preprocessing of inputs to the fuzzy controller is achieved via a conventional controller. Sometimes there is also the need for postprocessing of the fuzzy controller outputs. Generally, however, choice of the inputs also involves issues related to the learning dynamics of the FMRLC. As the FMRLC operates, the learning mechanism will tune the fuzzy controller's output membership functions. In particular, in our example, for each different combination of e(kT) and c(kT) inputs, it will try to learn what the best control actions are. In general, there is a close connection between what inputs are provided to the controller and the controller's ability to learn to control the plant for different reference inputs and plant operating conditions. We would like to be able to design the FMRLC so that it will learn and remember different fuzzy controllers for all the different plant operating conditions and reference inputs; hence, the fuzzy controller needs information about these. Often, however, we cannot measure the operating condition of the plant, so the FMRLC does not know exactly what operating condition it is learning the controller for. Moreover, it then does not know exactly when it has returned to an operating condition. Clearly, then, if the fuzzy controller has better information about the plant's operating conditions, the FMRLC will be able to learn and apply better control actions. If it does not have good information, it will continually adapt, but it will not properly remember. For instance, for some plants e(kT) and c(kT) may only grossly characterize the operating conditions of the plant. In this situation the FMRLC is not able to learn different controllers for different operating conditions; it will use its limited information about the operating condition and continually adapt to search for the best controller. It degrades from a learning system to an adaptive system that will not properly remember the control actions (this is not to imply, however, that there will automatically be a corresponding degradation in performance). Generally, we think of the inputs to the fuzzy controller as specifying what conditions we need to learn different controllers for. This should be one guideline used for the choice of the fuzzy controller inputs for practical applications