On equivalence between internal and external model‐based repetitive learning controllers for nonlinear passive systems

Abstract

In this paper a new class of globally stable finite dimensional repetitive controllers for nonlinear passive systems is proposed. The proposed internal model-based repetitive controller has a structure in the form of a parallel connection of linear oscillators and one integrator. The passive interconnection of the controller and the nonlinear passive systems provides the same stability conditions as the controller with the exact feed-forward compensation of system dynamics. The existing internal and external model-based repetitive controllers can be derived as the special cases of the proposed controller.

Modeling and Control of Heave-Induced Pressure Fluctuations in Managed Pressure Drilling

“…In [20], passivity of the controller (35) is proven, as well as the closed-loop stability of this controller and a passive nonlinear system. The hydraulic transmission line is quite clearly dissipative due to the friction force, but to ensure the correct control action applied to the choke, we must take one more step.…”

A new adaptive control for periodic tracking/disturbance rejection

“…According to (13) in Lemma 2, estimation of the periodic control u m (t) is further reduced to estimation of the unknown constant vector u in (13). According to (13) in Lemma 2, estimation of the periodic control u m (t) is further reduced to estimation of the unknown constant vector u in (13).…”

“…After identifying the existence of the ideal control u m (t), the control design problem becomes the problem of estimating u m (t). According to (13) in Lemma 2, estimation of the periodic control u m (t) is further reduced to estimation of the unknown constant vector u in (13). In order to estimate u , one needs a linear regression form in u .…”

“…When the system is not SPR, the adaptation gain must be constrained to be small in order to maintain stability. Its repetitive controller was further extended to a general class of nonlinear passive systems, and equivalence with existing internal and external model-based repetitive controllers was proven [13]. A modified adaptive algorithm with an extra phase advance is proposed in [12] to expedite the algorithm's convergence.…”

“…Recently, a study on a new class of finite-dimensional internal model-based repetitive controller was proposed. Its repetitive controller was further extended to a general class of nonlinear passive systems, and equivalence with existing internal and external model-based repetitive controllers was proven [13].…”