We propose an integral sliding surface for linear time-invariant implicit systems (descriptor systems). We show that, under reasonable assumptions (regularity, stabilizability) it is possible to design a stabilizing controller that compensates the matched perturbations exactly. Higher-order sliding motions are required since, for the solutions of the implicit system to be well defined, special care must be taken on the degree of smoothness of the controller and the perturbations. The algorithm is tested on a system where the perturbation enters through an algebraic equation.
We show that the well-known formula by Ackermann and Utkin can be generalized to the case of higher-order sliding modes. By interpreting the eigenvalue assignment of the sliding dynamics as a zero-placement problem, the generalization becomes straightforward and the proof is greatly simplified. The generalized formula retains the simplicity of the original one while allowing to construct the sliding variable of a single-input linear time-invariant system in such a way that it has desired relative degree and desired sliding-mode dynamics. The formula can be used as part of a higher-order sliding-mode control design methodology, achieving high accuracy and robustness at the same time.
Singular systems with matched Lipschitz perturbations and uncertainties are considered in this paper. Since continuous solutions of an impulse-free singular system require continuous input signals, a two-step continuous sliding-mode control strategy to compensate matched Lipschitz perturbations and uncertainties in singular systems is proposed. Our suggested methodology is tested in a singular representation of a DC motor pendulum of relative degree two. The performance of the proposed strategy is assessed by comparing the accuracy, in both cases, with and without considering small noise in the output, obtained through other continuous sliding-mode control, and reconstruction/compensation of perturbations and uncertainties techniques.Recently, CSM controllers for sliding outputs of relative degree r have been developed. Such controllers provide:1. finite-time theoretically exact compensation of Lipschitz P/U; 2. sliding accuracy of order (r+1) with respect to the output ((r+1)th order of precision) in the face of time discretizations of the control input and actuator time constant; 3. robust convergence of the output and its first r time derivatives to the origin in finite time ((r + 1)-sliding motion) while assuming only the information of the output and its first (r − 1) time derivatives.Examples of CSM controllers for systems of relative degree two are: continuous twisting (CT) algorithm, 17 continuous terminal SM, 18 and discontinuous integral controller. 19 For an arbitrary relative degree, continuous algorithms have also been derived (eg, see other works [19][20][21][22] ).
We propose an integral sliding surface for linear time-invariant implicit descriptions (descriptor systems). We show that, under reasonable assumptions (regularity, stabilizability and a corresponding matching condition), it is possible to design a controller that drives the descriptor variables to zero, even in the presence of disturbances. Higher-order sliding motions are required since, for the solutions of the implicit description to be well defined, special care must be taken on the degree of smoothness of the controller and the perturbations.
Abstract. In this article, a H∞ control methodology is proposed for a hybrid power generation system composed by a 500 W PEM fuel cell and a 58F supercapacitor. The control strategy consists in synthetizing a multivariable PI controller with H∞ performance in order to manage powers between two electrochemical sources. The controller is then designed through an optimization procedure based on solving some Linear Matrix Inequalities (LMI). The control performance in time and frequency domains are then analyzed and compared with classical controllers. Results show the efficiency of the proposed methodology in order to reduce time spent for design.
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