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Register a new userBarrier function-Based Variable Gain Super-Twisting Controller
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In this paper, a variable gain super-twisting algorithm based on a barrier function is proposed for a class of first order disturbed systems with uncertain control coefficient and whose disturbances derivatives are bounded but they are unknown. The specific feature of this algorithm is that it can ensure the convergence of the output variable and maintain it in a predefined neighborhood of zero independent of the upper bound of the disturbances derivatives. Moreover, thanks to the structure of the barrier function, it forces the gain to decrease together with the output variable which yields the non-overestimation of the control gain.
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In this paper, a practical fractional-order variable-gain super-twisting algorithm (PFVSTA) is proposed to improve the tracking performance of wafer stages for semiconductor manufacturing. Based on the sliding mode control (SMC), the proposed PFVSTA enhances the tracking performance from three aspects: 1) alleviating the chattering phenomenon via super-twisting algorithm and a novel fractional-order sliding surface~(FSS) design, 2) improving the dynamics of states on the sliding surface with fast response and small overshoots via the designed novel FSS and 3) compensating for disturbances via variable-gain control law. Based on practical conditions, this paper analyzes the stability of the controller and illustrates the theoretical principle to compensate for the uncertainties caused by accelerations. Moreover, numerical simulations prove the effectiveness of the proposed sliding surface and control scheme, and they are in agreement with the theoretical analysis. Finally, practice-based comparative experiments are conducted. The results show that the proposed PFVSTA can achieve much better tracking performance than the conventional methods from various perspectives.
In this paper, we present a generalization of the super-twisting algorithm for perturbed chains of integrators of arbitrary order. This Higher Order Super-Twisting (HOST) controller, which extends the approach of Moreno and als., is homegeneous with respect to a family of dilations and can be continuous. Its design is derived from a first result obtained for pure chains of integrators, the latter relying on a geometric condition introduced by the authors. The complete result is established using a homogeneous strict Lyapunov function which is explicitely constructed. The effectiveness of the controller is finally illustrated with simulations for a chain of integrator of order four, first pure then perturbed, where we compare the performances of two HOST controllers.
In this paper, we present Lyapunov-based {color{black}time varying} controllers for {color{black}fast} stabilization of a perturbed chain of integrators with bounded uncertainties. We refer to such controllers as {color{black}time varying} higher order sliding mode controllers since they are designed for nonlinear Single-Input-Single-Output (SISO) systems with bounded uncertainties such that the uncertainty bounds are unknown. %{color{blue} OLD: Our main result states that, given any neighborhood $varepsilon$ of the origin, we determine a controller insuring, for every uncertainty bounds, that every trajectory of the corresponding closed loop system enters $varepsilon$ and eventually remains there. Furthermore, based on the homogeneity property, a new asymptotic accuracy, which depends on the size of $varepsilon$, is presented.} We provide a time varying control feedback law insuring verifying the following: there exists a family $(D(t))_{tgeq 0}$ of time varying open sets decreasing to the origin as $t$ tends to infinity, such that, for any unknown uncertainty bounds and trajectory $z(cdot)$ of the corresponding system, there exists a positive positve $t_z$ for which $z(t_z)in D(t_z)$ and $z(t)in D(t)$ for $tgeq t_z$. %enters convergence in finite time of all the trajectories to a time varying domain $D(t)$ shrinking to the origin and their maintenance there. Hence, since the function $eta(t)$ tends to zero, this leads the asymptotic convergence of all the trajectories to zero. The effectiveness of these controllers is illustrated through simulations.
We present a new continuous Lyapunov Redesign (LR) methodology for the robust stabilization of a class of uncertain time-delay systems that is based on the so-called Super Twisting Algorithm. The main feature of the proposed approach is that allows one to simultaneously adjust the chattering effect and achieve asymptotic stabilization of the uncertain system, which is lost when continuous approximation of the unit control is considered. At the basis of the Super Twisting based LR methodology is a class of Lyapunov-Krasovskii functionals, whose particular form of its time derivative allows one to define a delay-free sliding manifold on which some class of smooth uncertainties are compensated.
We study linear quadratic Gaussian (LQG) control design for linear port-Hamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which leads to an LQG controller which is port-Hamiltonian and, thus, in particular stable and passive. Furthermore, we construct a reduced-order controller via balancing and subsequent truncation. This approach is closely related to classical LQG balanced truncation and shares a similar a priori error bound with respect to the gap metric. By exploiting the non-uniqueness of the Hamiltonian, we are able to determine an optimal pH representation of the full-order system in the sense that the error bound is minimized. In addition, we discuss consequences for pH-preserving balanced truncation model reduction which results in two different classical H-infinity-error bounds. Finally, we illustrate the theoretical findings by means of two numerical examples.
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