MIMO Super-Twisting Controller using a passivity-based design

Garcia-Mathey, Juan F.; Moreno, Jaime A.

doi:10.48550/arxiv.2208.04276

Cited by 1 publication

(2 citation statements)

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“…where K 1 ∈ ℜ mc×mc , K 2 ∈ ℜ mc×mc are matrices to be designed, and l ∈ [−1, 0] is a freely chosen parameter [34], [35]. Note that such control has a discontinuous integral term when l = −1 and it is known as the Super-Twisting algorithm [36].…”

Section: Remarkmentioning

confidence: 99%

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Robust Tracking for the Diffusion Equation using Sliding-Mode Boundary Control

Gutiérrez‐Oribio

Orlov

Stefanou

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Robust output tracking is addressed in this paper for a diffusion equation with Neumann boundary conditions and anti-collocated boundary input and output. The desired reference tracking is solved using the well-known flatness and Lyapunov approaches. The reference profile is obtained by solving the motion planning problem for the nominal plant. To robustify the closed-loop system in the presence of the disturbances and uncertainties, it is then augmented with PI feedback plus a discontinuous component responsible for rejecting matched disturbances with a priori known magnitude bounds. Such control law only requires the information of the system at the same boundary as the control input is located. The resulting dynamic controller globally exponentially stabilizes the error dynamics while also attenuating the influence of Lipschitz-intime external disturbances and parameter uncertainties. The proposed controller relies on a discontinuous term that however passes through an integrator, thereby minimizing the chattering effect in the plant dynamics. The performance of the closedloop system, thus designed, is illustrated in simulations under different kinds of reference trajectories in the presence of external disturbances and parameter uncertainties.

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Section: Remarkmentioning

confidence: 99%

“…Proof: Following [34], [35], the trajectories (y e , x I ) of system ( 14)-( 15) are ensured to reach the origin if the control gains are designed as K 1 > 0, K 2 > 0. Then, the stability of the diffusion system (3) has to be analysed.…”

Section: Remarkmentioning

confidence: 99%