Robust singular optimization for linear time varying systems by integral high‐order sliding mode

This paper presents an approach to solve a singular quadratic optimization problem for linear time varying systems based on the so‐called integral high‐order sliding mode control. The plant which is time varying is affected for some bounded disturbances, and the criterion to minimize is degenerated, in the sense that the weighting matrix can possess any rank. It is shown the natural connection between the order of singularity of the time varying quadratic criterion, which is connected to the rank of the cost matrix and the order of the sliding mode. An integral high‐order sliding mode is proposed to control the behavior of the transit phase before arriving toward the corresponding higher order singular time varying optimal manifold in prescribed time. The transformation to the phase‐variable form for the Linear Time Variant Systems (LTVS) becomes the key step to solve the problem, and the proposed solution provides the insensitivity of trajectory w.r.t. matched bounded uncertainties. Such a design is applied to a probe landing problem to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal integral sliding mode control for a class of uncertain discrete‐time systems

This paper considers the problem of sliding mode control for a class of uncertain discrete‐time systems. Firstly, an optimal control law for the nominal system is derived to satisfy linear quadratic performance index. And then, an optimal integral sliding surface is designed to ensure the robustness for sliding dynamics. By combining with the discrete reaching law, the existence condition of the sliding mode is proved, and the bandwidth of the quasi‐sliding mode is given. It is shown that the present method utilizes a lower control gain to attain stronger robustness and eliminate the chattering. Finally, illustrative simulation results are provided. Copyright © 2013 John Wiley & Sons, Ltd.     

Hybridized gravitational search algorithm tuned sliding mode controller design for load frequency control system with doubly fed induction generator wind turbine

In this paper, the load frequency regulation problem of 2‐area interconnected power system is resolved using the sliding mode control (SMC) methodology. Interconnected 2‐area power systems with and without doubly fed induction generator wind turbines are considered for implementing the proposed optimal control methodology. Here, a heuristic gravitational search algorithm (GSA) and its variants such as opposition learning–based GSA (OGSA), disruption‐based GSA (DGSA), and disruption based oppositional GSA (DOGSA) are employed to optimize the switching vector and feedback gains of SMC. In order to overcome the inherent chattering problem in SMC, the control signals are considered in the objective function. The robustness of optimized SMC is analyzed by the inclusion of nonlinearities such as generation rate constraint (GRC), governor deadband, and time delay during the signal processing between the control areas, which are present in the real‐time power system. The insensitiveness of the optimal controller is shown by variation in system parameters like loading condition, speed governor constant, turbine constant, and tie‐line power coefficient. Further, the optimal SMC has been studied with significant load variations and wind power penetration levels in the control areas. The potential of proposed SMC design with chattering reduction feature is shown and validated by comparing the results obtained with the other reported methods in the literature.     

Design of sliding mode control for neutral delay systems with perturbation in control channels

This paper considers the problem of sliding mode control for a class of uncertain neutral delay systems. There are uncertainties not only in the state matrices, but also in the control matrix that results from perturbation in the control channels. By means of a sliding surface dependent on both the current states and delayed states, a sliding mode controller is designed such that the asymptotic stability of closed‐loop systems can be ensured. The design of both the sliding surface and the sliding mode controller can be obtained via convex optimization. It is shown that the state trajectories are driven onto the specified sliding surface in finite time and remain there for subsequent time. Finally, a numerical simulation example is provided. Copyright © 2011 John Wiley & Sons, Ltd.