Feedforwarding Under Sampling

Abstract

The paper deals with stabilization of feedforward multiple cascade dynamics under sampling. It is shown that u-average passivity concepts and Lyapunov methods can be profitably exploited to provide a systematic sampled-data design procedure. The proposed methodology recalls the continuous-time feedforwarding steps and can be applied under the same assumptions as those set over the continuous-time cascade dynamics. The final sampled feedback is carried out through a three steps procedure that involves iterative passivation and stabilization in the u-average sense. Constructive aspects are developed to compute approximate solutions which are indeed implemented in practice. An example is worked out upon the paper with comparative simulations with respect to usual sampled-and-hold implementations.

Forwarding stabilization in discrete time

“…However, taking advantage of the continuous-time original system, one might deduce a less conservative sampled-data forwarding strategy which stays in-between the continuous and discrete-time scenarios. In this sense, the work by Mattioni et al (2019) is devoted to the sampling of continuous-time feedforward design where the difference among the two approaches are discussed as well. The paper is organized as follows.…”

Discrete port-controlled Hamiltonian dynamics and average passivation

“…In [15], the notion of u-average passivity from some nominal control valueū ∈ R has been introduced to deal with incremental-like passivity properties in discrete time. The following definition is hence recalled.…”

“…Proposition 3.2: Consider the pcH dynamics (15) with Hamiltonian H(x) = 1 2 x P x with P > 0 and output map h(x, u) = ∇H(x)G(x, u) then, there exists a unique solution to the damping equality (14) which minimizes (16) with…”

“…An interesting discussion is also performed to compare the proposed pcH structure with the one more commonly adopted in the literature which does not explicitly split the dynamics into its free and controlled evolutions but privileges the gradient form to more easily cope with the power conserving or dissipating properties of the dynamics. It is shown that these pcH forms and their associated passivating output can be reinterpreted in terms of average passivity from/around a certain control value [15]. Finally, the pcH models and control strategies here proposed are detailed in the constructive case represented by input-affine dynamics with quadratic Hamiltonian.…”

Interconnection through u-average passivity in discrete time

“…In [18], [19], the notion of u-average passivity from some nominal control valueū has been introduced to deal with incremental-like passivity properties in discrete time. The following definition is hence recalled.…”