In MMAC, at least implicitly, local linear controllers are patched together to form an approximation to a global nonlinear controller. It is thus possible to take advantage of this fact to compensate some plant nonlinearities. This compensation is only approximate because it relies on a finite number of local controllers being patched. Furthermore, it may not be clear how to design the local controllers in a systematic way to achieve this objective. The examples provided for both a pilot air heating turbofan in Sect. 4.3 and for a DCSF in Sect. 4.4 that rely on the variables that define the operational regimes of these plants, and qualitative physical insight, provide clues for designing this type of controllers.
A much better compensation of the nonlinearities requires the DCSF models discussed in Chap. 2. One possible approach along this line consists of making a change of time variable that depends on the fluid flow. In practice, this transformation can be implemented in a computer control framework with a sampling interval that varies with the flow. Together with the change in the time variable, a virtual manipulated variable is computed such that the plant model becomes linear. The controller that computes this virtual manipulated variable is thus simplified. In turn, the physical manipulated variable (fluid flow) can be easily computed from this virtual control. This approach is followed in Chap.5 to obtain nonlinear MPC controllers, named WARTIC-i/o and WARTIC-state, that allow to make fast jumps of the outlet fluid temperature almost with no overshoot. Adaptation is embedded according to a certainty equivalence assumption, with the control laws being computed with models that depend on parameter estimates obtained online. In the closely related Chap. 7, a similar technique is used to solve the motion planning problem and design an adaptive servo-controller that is able to track time-varying references.
Alternatively, in Chap.6, feedback input-output linearization is used together with a lumped model approximation of the DCSF infinite dimensional model, and adaptation is embedded using a control Lyapunov function technique.
Figure 8.1 shows the “location” of the different types of adaptive controllers considered in a “space” defined by performance and the degree of plant structure embedded in the plant model. As expected, experience shows that, by increasing the degree of physical structure embedded in the models that serve as a basis for controller design, performance increases, but the algorithm becomes more plant specific and may not be used, without significant changes, on plants other than the DCSF for which it is designed. For example, adaptive MPC algorithms like GPC or MUSMAR rely on data-driven linear models and may be used almost unchanged (requiring only a proper selection of the assumed model order and cost function weights) in plants other than DCSFs like a steam super-heater (Sect. 3.7.2) or arc welding (Sect. 3.7.3).
At the other extreme, theWARTIC algorithms in Chap. 5 provide a better performance (they yield a step response with much less overshoot for the same raise time) than the adaptive MPC algorithms of Chap. 3, but may not be used directly on other plants (although the key idea of making a change of the time scale depending on the flow can be used with advantage).
Although not explicitly shown in Fig. 8.1, other algorithms that are important for applications are discussed in detail in the book, in relation to DCSFs. One of these topics is the use of flatness-based methods for planning variations of the outlet fluid temperature, addressed in Chap. 7. These type of methods are usually associated to robotic problems, but they provide valuable tools for solving servo problems for thermodynamic processes (i. e., tracking problems in which the reference is time varying) as well. For distributed parameter plants, their application involves a gauge type change of the time variable, which makes these methods intimately related to the WARTIC algorithms in Chap. 5.