ime signals since it is easier to explain the operation of the Fmrlc for discrete time systems. The FmrLC uses the learning mechanism to observe numerical data from a fuzzy control system(i.e, r(kT)and y(kn) where T is the sampling period). Using this numerical data, it characterizes the fuzzy control systems current performance and automaticall synthesizes or adjusts the fuzzy controller so that some given performance objectives are met These performance objectives(closed-loop specifications) are characterized via the reference model shown in Figure 3. 3. In a manner analogous to conventional MRAC where conventional controllers are adjusted, the learning mechanism seeks to adjust the fuzzy controller so that the closed-loop system( the map from r(kn) to y(kn))acts like the given reference model(the map from r(kn)to ym(kn)). Basically, the fuzzy control system loop(the lower part of Figure 3. 3)operates to make y(kn) track r(kn) by manipulating u(kn), while the upper-level adaptation control loop(the upper part of Figure 3.3)seeks to make the output of the plant y(kn)track the output of the reference model ym(kn by manipulating the fuzzy controller parameters Next, we describe each component of the FMRLC in more detail for the case where there is one input and one output from the plant (we will use the design and implementation case studies in Section 3. 3 to show how to apply the approach to MIMO systems) 3.2.1 The Fuzzy Controller The plant in Figure 3.3 has an input u(kn)and output y(kn). Most often the inputs to the fuzzy controller are generated ia some function of the plant output y(kn)and reference input r(kn). Figure 3. 3 shows a simple example of such a map that has been found to be useful in some applications. For this, the inputs to the fuzzy controller are the error e(kn)=r(kn) y(T)and change in error c(kT) e(kr)-e(kT-T) (i.e. a PD fuzzy controller) There are times when it is beneficial to place a smoothing filter between the r(kt) reference input and the summing junction. Such a filter is sometimes needed to make sure that smooth and reasonable requests are made of the fuzzy controller(e.g, a square wave input for r(kn) may be unreasonable for some systems that you know cannot respond instantaneously ). Sometimes, if you ask for the system to perfectly track an unreasonable reference input, the FmrlC will essentially keep adjusting the"gain"of the fuzzy controller until it becomes too large. Generally, it is important to choose the inputs to the fuzzy controller, and how you process r(kn) and y(kn), properly; otherwise performance can be adversely affected and it may not be possible to maintain stability Returning to Figure 3.3, we use scaling gains ge, ge and gu for the error e(kn), change in error c(kD), and controller output u(kn), respectively. a first guess at these gains can be obtained in the following way: The gain ge, can be chosen so that the range of values that e(kn) typically takes on will not make it so that its values will result in saturation of the corresponding outermost input membership functions. The gain gc can be determined by experimenting with various inputs to the fuzzy control system(without the adaptation mechanism) to determine the normal range of values that c(kt PDF文件使用" pdffactory Pro"试用版本创建ww, fineprint,com,cntime signals since it is easier to explain the operation of the FMRLC for discrete time systems. The FMRLC uses the learning mechanism to observe numerical data from a fuzzy control system (i.e., r(kT) and y(kT) where T is the sampling period). Using this numerical data, it characterizes the fuzzy control system's current performance and automatically synthesizes or adjusts the fuzzy controller so that some given performance objectives are met. These performance objectives (closed-loop specifications) are characterized via the reference model shown in Figure 3.3. In a manner analogous to conventional MRAC where conventional controllers are adjusted, the learning mechanism seeks to adjust the fuzzy controller so that the closed-loop system (the map from r(kT) to y(kT)) acts like the given reference model (the map from r(kT) to ym(kT)). Basically, the fuzzy control system loop (the lower part of Figure 3.3) operates to make y(kT) track r(kT) by manipulating u(kT), while the upper-level adaptation control loop (the upper part of Figure 3.3) seeks to make the output of the plant y(kT) track the output of the reference model ym(kT) by manipulating the fuzzy controller parameters. Next, we describe each component of the FMRLC in more detail for the case where there is one input and one output from the plant (we will use the design and implementation case studies in Section 3.3 to show how to apply the approach to MIMO systems). 3.2.1 The Fuzzy Controller The plant in Figure 3.3 has an input u(kT) and output y(kT). Most often the inputs to the fuzzy controller are generated via some function of the plant output y(kT) and reference input r(kT). Figure 3.3 shows a simple example of such a map that has been found to be useful in some applications. For this, the inputs to the fuzzy controller are the error e(kT) = r(kT) — y(kT) and change in error ( ) e(kT ) e( ) kT T c kT T - - = (i.e.,a PD fuzzy controller). There are times when it is beneficial to place a smoothing filter between the r(kT) reference input and the summing junction. Such a filter is sometimes needed to make sure that smooth and reasonable requests are made of the fuzzy controller (e.g., a square wave input for r(kT) may be unreasonable for some systems that you know cannot respond instantaneously). Sometimes, if you ask for the system to perfectly track an unreasonable reference input, the FMRLC will essentially keep adjusting the "gain" of the fuzzy controller until it becomes too large. Generally, it is important to choose the inputs to the fuzzy controller, and how you process r(kT) and y(kT), properly; otherwise performance can be adversely affected and it may not be possible to maintain stability. Returning to Figure 3.3, we use scaling gains ge,gc and gu for the error e(kT), change in error c(kT), and controller output u(kT), respectively. A first guess at these gains can be obtained in the following way: The gain ge , can be chosen so that the range of values that e(kT) typically takes on will not make it so that its values will result in saturation of the corresponding outermost input membership functions. The gain gc can be determined by experimenting with various inputs to the fuzzy control system (without the adaptation mechanism) to determine the normal range of values that c(kT) PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn