distinction is drawn since the FMRlC will tune and to some extent remember the values that it had tuned in the past, while the conventional approaches for linear systems simply continue to tune the controller parameters. Hence, for some applications when a properly designed FMRLC returns to a familiar operating condition, it will already know how to control for that condition. Many past conventional adaptive control techniques for linear systems would have to retune each time a new operating condition is encountered yn Knowledge-base /neI Knowled zy sets Rule base Know:) 1 Pu h Fuzzy contradict Figure 4.3 Fuzzy model reference learning controller The functional block diagram for the FMrlC is shown in Figure 43. It has four main parts: the plant, the fuzzy controller to be tuned, the reference model, and the learning mechanism(an adaptation mechanism). We use discrete time 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(kD)and y(kn) where T is the sampling period ). Using this numerical data, it characterizes the fuzzy control systems 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 4.3. 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 4.3)operates to make y(kn) track r(kn) by manipulating u(kn), while the upper-level adaptation control loop(the uppe part of Figure 4.3)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 4.3 to show how to apply the approach to MIMO systems)distinction is drawn since the FMRLC will tune and to some extent remember the values that it had tuned in the past, while the conventional approaches for linear systems simply continue to tune the controller parameters. Hence, for some applications when a properly designed FMRLC returns to a familiar operating condition, it will already know how to control for that condition. Many past conventional adaptive control techniques for linear systems would have to retune each time a new operating condition is encountered. Figure 4.3 Fuzzy model reference learning controller The functional block diagram for the FMRLC is shown in Figure 4.3. It has four main parts: the plant, the fuzzy controller to be tuned, the reference model, and the learning mechanism (an adaptation mechanism). We use discrete time 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 4.3. 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 4.3) operates to make y(kT) track r(kT) by manipulating u(kT), while the upper-level adaptation control loop (the upper part of Figure 4.3) 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 4.3 to show how to apply the approach to MIMO systems)