By Alexandre Sanfelice Bazanella
Data-Based Controller layout offers a accomplished research of data-based keep watch over layout. It brings jointly different data-based layout equipment which were awarded within the literature because the overdue 1990’s. To the simplest wisdom of the writer, those data-based layout equipment have by no means been accrued in one textual content, analyzed extensive or in comparison to one another, and this significantly limits their common software. during this booklet those tools can be offered lower than a standard theoretical framework, which inserts additionally a wide family members of adaptive regulate tools: the MRAC (Model Reference Adaptive keep an eye on) equipment. This universal theoretical framework has been built and offered very recently.
The ebook is essentially meant for PhD scholars and researchers - senior or junior - up to the mark platforms. it may function instructing fabric for data-based and adaptive keep an eye on classes on the graduate point, in addition to for reference fabric for PhD theses. it's going to even be precious for complicated engineers prepared to use data-based layout. in fact, the recommendations during this booklet are getting used, less than the author’s supervision, for constructing new software program items in a automation corporation. The ebook will current simulation examples alongside the textual content. functional purposes of the options and methodologies can be offered in a selected chapter.
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Extra info for Data-Driven Controller Design: The H2 Approach
3. 1 Too Ambitious Performance If the reference model Td (z) specifies a performance that is too different from the best that can be achieved within the given controller class, then the solution may have nothing to do with Td (z). Start with the following example. 2 controlled by a purely integral controller C(z, ρ) = ρ . z−1 22 2 H2 Performance Criteria Fig. 2 Reference tracking performance criterion as a function of the scalar controller parameter ρ The performance criterion is reference tracking, with the specification of the deadbeat reference model 1 Td1 (z) = .
42 3 One-Shot Optimization—The VRFT Method Assumption BNMP (Flexible matched control) There exists a pair (η∗ , ρ∗ ) such that J0VR (η∗ , ρ∗ ) = 0; equivalently ∃η∗ , ρ∗ : C(z, ρ∗ ) = T (z, η∗ ) . 1 Let Assumption BNMP be satisfied and all the poles of the controller be either inside or on the unit circle. Then the NMP zeros of G(z) are also zeros of T (z, η∗ ). (z) ∗) Proof Let G(z) = ndGG (z) and T (z, η∗ ) = nTd(z,η be coprime factorizations of G(z) T (z) and T (z, η∗ ), where nG (z), dG (z), nT (z, η∗ ) and dT (z) are polynomials.
26), any unstable root of nG (z) must be canceled by a root of nT (z, η∗ ). 1, if G(z) has NMP zeros and Assumption BNMP is satisfied, then the NMP zeros appear necessarily in the numerator of T (z, η∗ ). Under these conditions, the global minimum of J0VR (η, ρ) gives the desired result: a reference model containing the NMP zeros of the process and the controller that achieves this reference model. But this is a nasty cost function to minimize, as the decision variables appear even in its denominator, and VRFT is all about having a nice cost function to minimize so as to avoid iterative procedures.
Data-Driven Controller Design: The H2 Approach by Alexandre Sanfelice Bazanella