Proposed Switching Function Research Articles

Stabilization of rank-deficient continuous-time switched affine systems

This paper treats the global stabilization problem of continuous-time switched affine systems that have rank-deficient convex combinations of their dynamic matrices. For these systems, the already known set of attainable equilibrium points has higher dimensionality than in the full-rank case due to the existence of what we define as singular equilibrium points. Our main goal is to design a state-dependent switching function to ensure global asymptotic stability of a chosen point inside this set with conditions expressed in terms of linear matrix inequalities. For this class of systems, global exponential stability is generally impossible to be guaranteed. Hence, the proposed switching function is shown to ensure global asymptotic and local exponential stability of the desired equilibrium point. The position control and the velocity control with integral action of a dc motor driven by a h-bridge fed via a boost converter are used for validation. This practical application example is composed of eight subsystems, and all possible convex combinations of the dynamic matrices are singular.

Anti-Unwinding Sliding Mode Attitude Maneuver Control for Rigid Spacecraft

In this article, anti-unwinding attitude maneuver control for rigid spacecraft is considered. First, in order to avoid the unwinding phenomenon when the system states are restricted to the switching surface, a novel switching function is designed by a hyperbolic sine function such that the switching surface contains the two equilibriums. Then, a sliding mode attitude maneuver controller is developed based on the proposed switching function to ensure the robustness of the closed-loop system to disturbance and inertia uncertainty. Another important feature of the presented attitude control law is that a dynamic parameter is constructed to guarantee the unwinding-free performance before the system states reach the switching surface. Furthermore, a boundary layer is introduced for the designed controller to avoid the chattering phenomenon. Moreover, the convergence property and unwinding-free performance when the system states within the boundary layer are proven. The simulation results demonstrate that the unwinding problem is settled during attitude maneuver for rigid spacecraft by adopting the newly developed switching function and the presented attitude control scheme.

Design of Discrete-Time Sliding Mode Control With Disturbance Compensator-Based Switching Function

In this brief, a new disturbance compensator based switching function is proposed for disturbed discrete-time systems. A sliding mode controller is developed based on this switching function. A high order disturbance compensator is embedded in the new switching function to achieve accurate disturbance rejection. Rigorous analysis on system dynamics of the corresponding closed-loop system is performed where it is shown that the proposed switching function is invariant to disturbances and has the ability to achieve the ideal quasi-sliding mode (QSM). In other words, the proposed method enables the convergence of the system trajectory and keeps it on the sliding surface independent of disturbances, which is rarely achieved in the discrete-time sliding mode control (DSMC). Moreover, the presented method is capable of delivering a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ) control accuracy of the system states, which is much higher than most previous methods. Simulation results on a MAGnetic LEViation system illustrate the main characteristics and performance of the proposed method.

Switched control of a three-phase AC–DC power converter

In this paper, a new switched control strategy for three-phase AC-DC power converters, also known as controlled rectifiers, is proposed. More specifically, a switching function is determined to command the converter switches at each instant of time assuring global asymptotic tracking of a desired reference trajectory, which is related to a constant output voltage and sinusoidal phase currents. This is generally a desired situation for AC-DC power converters as it can ensure unitary power factor and rectified steady-state D C voltage simultaneously. The proposed switching function must also assure a guaranteed performance cost. The design conditions are based on a Lyapunov function, which is dependent on the electrical angle, and are expressed in terms of linear matrix inequalities (LMIs). Simulation results put in evidence the effectiveness of the proposed methodology and motivate future related works.

Identification of GMS friction model using a new switching function: experimental investigation

The objective of this paper is the identification of generalised Maxwell slip (GMS) friction model using a new proposed switching function. The GMS friction model is composed of two phases and a switching function, which guarantee the transition from one phase to another. The switching function is based on the friction model and its parameters which are unknown. Hence, a new switching function is proposed in this paper. The new switching function is validated experimentally. The identification of the GMS friction model is done using online least square estimator combined with filtering approaches and a linearisation in order to adopt the formulation of the friction model to the estimator mechanism. Moreover, the new proposed switching function is integrated with the process of the identification and it is validated using an experimental test. The experimental results show that the switching function proposed is convenient for the identification of the friction model.

그래프에 기초한 스위칭함수 구현

본 논문에서는 그래프에 기초하여 유한체상의 스위칭함수를 도출하는 알고리즘과 이를 바탕으로 스위칭함수를 회로로 구현하는 방법을 제안하였다. 방향성그래프의 경로 수로부터 행렬방정식을 유도한 후에 이에 따른 스위칭 함수회로설계 알고리즘을 제안하였으며, 설계된 회로와 함께 방향성 그래프의 특성을 만족할 수 있게 노드들에 대한 코드를 할당하는 알고리즘을 제안하였다. 본 논문에서 제안한 알고리즘을 통해 설계한 스위칭함수회로는 기존의 방법에 비해 좀 더 최적화된 스위칭함수회로를 구현할 수 있었으며, 제안한 스위칭함수회로설계 알고리즘을 통해 임의의 자연수의 경로 수를 갖는 방향성 그래프에 대한 설계가 가능하였다. 또한, 입출력단자 수의 감소, 회로구성의 간략화, 연산속도의 향상과 비용감소 등의 이점이 있었다. This paper proposes the method of switching function implementation using switching function extraction based on graph over finite fields. After we deduce the matrix equation from path number of directional graph, we propose the switching function circuit algorithm, also we propose the code assignment algorithm for nodes which is satisfied the directional graph characteristics with designed circuits. We can implement more optimal switching function compare with former algorithm, also we can design the switching function circuit which have any natural number path through the proposed switching function circuit implementation algorithms. Also the proposed switching function implementation using graph theory over finite fields have decrement number of input-output, circuit construction simplification, increment arithmetic speed and decrement cost etc.

Computation of the I/V characteristic of a molecular switch

We report on the study of a molecular torsional switch made up of two distinct aromatic moieties bound by an acetynil group. The mechanism of operation is based on the action of a static electric field perpendicular to the ring–ring bond which modifies the torsional angle and, as a consequence, the inter-ring conjugation. The current is computed with a method based on the molecular Green’s function, in which the electrodes are taken into account in an effective way. The current/voltage profile at several dihedral angles shows that the current is maximum for the planar conformation and decreases by a factor ∼1000 for the orthogonal conformation, suggesting the potential applicability of the proposed switching function in devices at the molecular scale.

A Switching Adaptive Output Feedback Control System Based on Almost Strictly Positive Real-ness

In this paper, a new design method for adaptive output feedback control systems with a switching function for sets of compensators is proposed. The proposed switching function can automatically select an appropriate parallel feedforward compensator and pre-compensator so that the resulting augmented plant is almost strictly positive real (or stabilizable). This paper also shows that all of the signals in the switching adaptive control system are bounded and that the switching action ceases after a finite number of switches.

Finite dimensional variable structure control design for distributed delay systems

A general design method for the variable structure control of distributed time-delay systems is studied in this paper. The proposed switching function and variable structure controller are of finite dimension. The basic idea is to construct a finite dimensional system which contains all the unstable poles of the original time-delay system and hence those unstable poles of the time delay system will be absorbed by the developed variable structure controller. The proposed method is applied to the stabilization of combustion in a liquid monopropellant rocket motor and satisfactory results are obtained by simulation study. Simulation results show that the developed variable structure controller can still stabilize the combustion when the two key parameters, pressure exponent and maximal time lag r, change from their nominal value down to 0.0 and 0.1 respectively. By this result, we can somewhat overestimate the two parameters to obtain a reliable controller for the rocket motor control systems.

Finite-dimensional variable structure control design for systems with a single time delay

A design method for the variable structure control of point time-delay systems is studied in this paper. The proposed switching function and variable structure controller are of finite dimension. The basic idea is to construct a finite-dimensional system which contains all the unstable poles of the original time-delay system and hence those unstable poles of the time delay system will be absorbed by the developed variable structure controller. The proposed method is applied to the stabilization of combustion in a liquid monopropellant rocket motor and satisfactory results are obtained by simulation study. Smooth dependence of the closed-loop system response on the two parameters, the pressure exponent y and time lag ∞, are shown by simulation results.

Robust closed-loop control design for spacecraft slew maneuver using thrusters

In this paper, a closed-loop switching function for on-off thruster firings is proposed to provide good attitude control performance in the presence of modeling errors for single-axis slew maneuver of a rigid spacecraft and to eliminate double-sided thruster firings. The size of a single-sided deadband in the switching function provides the capability of a tradeoff between maneuver time and fuel expenditure. The application of this switching function for the single-axis slew maneuvers of flexible spacecraft is also analyzed. The analytical simulations and experimental results demonstrate that the proposed switching function provides significant improvement in the slew maneuver performance.