PID Passivity-Based Control of Nonlinear Systems with Applications. Romeo Ortega
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Название: PID Passivity-Based Control of Nonlinear Systems with Applications

Автор: Romeo Ortega

Издательство: John Wiley & Sons Limited

Жанр: Отраслевые издания

Серия:

isbn: 9781119694182

isbn:

СКАЧАТЬ minus upper K Subscript upper P Baseline y 0 minus upper K Subscript upper I Baseline left-bracket gamma left-parenthesis x right-parenthesis minus gamma left-parenthesis x Superscript star Baseline right-parenthesis right-bracket comma"/>

      which exactly coincides with the control generated with the PI‐PBC evaluated at script upper M Subscript kappa Superscript star. Such an implementation does not impose any constraint on x Subscript c Baseline left-parenthesis 0 right-parenthesis and is therefore robust.

      The details of this construction are given in Chapter 6, where we also prove that the set of solutions of the partial differential equations (PDEs) that must be solved to generate the invariant foliation script upper M Subscript kappa in CbI is strictly smaller than the ones needed in the PID‐PBC, yielding a design procedure that is applicable for a broader class of systems.

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      13 M. Zhang, R. Ortega, D. Jeltsema, and H. Su. Further deleterious effects of the dissipation obstacle in control‐by‐interconnection of port‐Hamiltonian systems. Automatica, 61(11): 227–2331, 2015.

      1 1 Essentially, it is necessary to ensure that the control law 2.1 can be computed without differentiation nor singularities. We will elaborate on this issue in Section 2.2.

      2 2 We recall that a necessary condition for passivity of the system is that the relative degree is smaller or equal to one (van der Schaft, 2016).

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