Power-shaping control: Writing the system dynamics into the Brayton–Moser form

Passivity-based nonlinear control of CSTR via asymptotic observers

“…Under (H1), the energy balance is written using the enthalpy H. Hence the material and energy balances are finally given as follows (Favache et al, 2011;Favache & Dochain, 2010;Luyben, 1990):…”

“…CSTRs may exhibit nonminimum phase behavior (Niemiec & Kravaris, 2003), instability and multiple steady states (Favache & Dochain, 2010;Viel, Jadot, & Bastin, 1997). Studies on CSTRs have investigated control synthesis for stabilization (Alvarez et al, 2011;Favache, Dochain, & Winkin, 2011;Georgakis, 1986;Hoang, Couenne, Jallut, & Le Gorrec, 2011; and state observer design (Alvarez-Ramírez, 1995;Dochain, Couenne, & Jallut, 2009;Gibon-Fargeot, Hammouri, & Celle, 1994;Soroush, 1997). The combination of these is an important field of research.…”

Dissipative-based dynamic state feedback design using a geometric decomposition

“…The central problem here is to find an expression that relates the one-form in the original coordinates ω e (χ) to the oneform in the new coordinates (14). In essence, the idea amounts to computing a positive definite function V (χ) by reshaping the dissipative potential ψ(χ).…”

“…This motivated many researchers to study physically-defined storage functions for dissipativity analysis, for example Hamiltonian functions [4] and mixed-potential functions [7] used, in this context, as storage function for dissipativity analysis and dissipative-based feedback design. This approach has been successful in applications, for example using {n.hudon, j.bao}@unsw.edu.au port-Hamiltonian passivity based approaches [8], [9], [10], [11] and power-shaping methods [12], [13], [14], [15]. In particular, in [15], a dynamic feedback extension to powershaping passivity-based control was proposed.…”

“…For a known control affine system and a fixed dynamic controller structure, a parameterized potential function is computed by using a homotopy operator in the extended space. The homotopy operator, which discriminates the exact and the non-exact components of the dynamics, renders possible the application of the Poincaré lemma locally [19], a central element of the derivations in power-shaping methods [12], [14], [15]. The Hessian of the obtained locally-defined approximate potential is then shaped using the parameters of the controller dynamics as in [15].…”