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This work aims to propose and compare trajectory tracking controllers for mobile robots. At first the mathematical requirements to propose a feasible strategy for a unicyclelike robot are presented, as well as the necessary condition to guarantee the stability in the sense of Lyapunov. In the sequence, the controllers are tuned in simulation and then validated in real experiments. The performance...
A Lyapunov-based construction of a predefined-time stabilizing function (a function that stabilizes a system in fixed-time with settling time as function of the controller parameters) for scalar systems is considered in this paper. The constructed function involves the inverse incomplete gamma function, causing this function to be semi-global, i.e., the domain of definition of the function can be...
For stability analysis of discrete-time arbitrary switching positive linear systems, we introduce a new class of switched copositive Lyapunov functions (abbreviated as CLFs) and we investigate their test power. The new class means “switched max-type CLFs” and it is defined by generalizing the “mode-independent max-type CLFs” (that were introduced and characterized by our previous works). This generalization...
For underactuated overhead cranes, this paper designs a novel sliding mode control method. Specifically, similar to the idea of backstepping method, the overall dynamic system is divided into two cascaded subsystems; thus the control algorithm consists of two steps. At first, the payload swing angle is kept in a bounded area by tracking a target trajectory. Second, the positioning error is indirectly...
A fixed-time sliding mode control scheme is designed in this paper for the high-order linear systems in the pure-feedback form with system uncertainties. A recursive procedure is utilized where a set of switching manifolds have been resorted to realize the fixed-time stability. The initial conditions of the system variables are confined in a particular region so as to avoid the singularity problem...
In this paper, an event-triggered distributed receding horizon control algorithm is proposed for dynamically coupled continuous-time linear systems. First, an event-triggered rule that is realized by monitoring the error between subsystem state and its optimal prediction is designed, and an extra constraint that restricts the discrepancy between each subsystem's assumed and predicted state and input...
The predefined-time stabilization of second-order systems, i.e. the fixed-time stabilization with settling time as a function of the controller parameters, is revisited in this paper. The proposed controller is a time-based switched controller which first drive the system trajectories to a linear manifold in predefined time and then uses a nested second-order controller. The application of the results...
Implantable medical devices are increasingly employed for neurorehabilitation to restore lost motor function through brain computer interfacing. Proper circuit design for both sensing and stimulation is key to technology success, including the optimization of device capabilities and the exploitation of neural coding properties, while enhancing patient safety. To date peripheral nerve and brain implant...
In this paper, the finite-time boundedness (FTB) and the finite-time stability (FTS) for fractional order linear time invariant (LTI) systems are studied. By using the generalized Gronwall inequality, the sufficient conditions expressed in terms of matrix inequality to guarantee the FTB and FTS are derived. The proposed conditions are less conservative than the the ones in recent literature. Based...
A method of stability analysis of nonlinear systems using Lyapunov densities has been proposed by Rantzer: almost all trajectories of the system are guaranteed to converge to the equilibrium point if a Lyapunov density exists for the nonlinear system. However, only the convergence of trajectories is considered in the Rantzer's original result and the speed of convergence has never been taken care...
In this paper, the stochastic excitations in single machine infinite bus power systems have been modeled as alpha-stable Levy processes. Through the simulations of the corresponding stochastic differential equations, we have shown that the impulsiveness and/or asymmetry in the distributions of the load fluctuations can cause the instability of the rotor angle. Hence, the synchronism is lost and the...
Permanent magnet linear motors (PMLM) are widely used in high precision machineries. With the removal of the transmission elements, the positioning performances of PMLM are easily affected by parameter variations and external disturbances. Various control approaches were proposed, yet it was noticed that majority of these controllers have complex design procedures, and require accurate model parameters...
How to bound the state vector trajectory of a nonlinear system in a way so that the obtained bound be of practical value is an open problem. If some norm is employed for bounding the state vector trajectory, then this norm should be carefully selected and the state vector components suitably scaled. In addition, practical applications usually require separate bounds on every state variable. Bearing...
This paper presents a design methodology for the rejection of wind gusts during flight. The proposed application is based on the Simple Adaptive Controller (SAC) methodology, but differs from other SAC applications in the sense that the reference model utilised is an Unknown Input Observer (UIO). As a consequence, the adaptive controller is fed by an estimate of the wind gust and will only act in...
A simple Line-Of-Sight (LOS) based trajectory tracking algorithm intended for underactuated vehicles is presented. Time parametrized trajectories in two dimensions are considered. Local exponential stability for straight trajectories and ultimate boundedness for general trajectories is shown for the guidance law error dynamics, using Lyapunov perturbation analysis. The results are verified in simulations...
The problem of exponential stability of a linear mixed continuous-discrete systems is considerate. Such system is built basing on periodic sampling of the second order. The sufficient conditions basing on eigenvalues of the state matrix of the considered system are given. Obtained results are illustrated on the example.
The paper addresses the finite time stability analysis of continuous-time LTI systems. Based on its definition, the necessary and sufficient condition can be derived easily. Verification of the condition is almost impossible because an infinite numbers of checking points are required. Therefore, by using the well-known Bellman-Gronwall inequality, a set of more efficient and practical LMI-based conditions...
The paper concerns the development of a adaptive sliding mode control based on super twisting (ASTW) and can be applied to a Human-Driven Knee Joint Orthosis. Therefore, a model of the shank-orthosis system is given considering the human effort as an external torque acting on the system. The main objective of this paper is to bring together two approaches to reduce the phenomenon of chattering, adaptation...
Short circuit in the power system can lead problems in term of stability system. Transient stability becomes the main focus because it can determine the critical clearing time (CCT) to find critical time before generator loss of synchronization. The Critical trajectory method can be used to determine trajectory from the disturbance occurs to just before the generator loses its synchronization. The...
Constant-Power Load (CPL) introduces destabilizing effect to dc-dc converters, which may lead to voltage oscillation or collapse. To mitigate the destabilizing problem brought by CPL, a nonlinear boundary controller is proposed in this paper, which has a nonlinear switching line. The converters' dynamics on the state space plane is analyzed through phase portrait. The proposed controller is verified...
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