Finite-Time Integral Sliding Mode Control for Motion Control of Permanent-Magnet Linear Motors

The finite-time motion control problem of permanent-magnet linear motor (PMLM) is studied in this paper. Firstly, based on finite-time integral sliding mode (FTISM) technique, a finite-time control (FTC) law is proposed such that the PMLM can track the desired trajectory in finite time in the presence of disturbances. Secondly, to alleviate the chattering caused by discontinuous property of the control law, a novel saturation function is introduced to replace the signum function in the proposed FTC law. Finally, the effectiveness of the proposed method is shown by simulation results and comparisons

Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs) subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC) is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC) law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO) is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach

Global output-feedback finite-time stabilization for a class of stochastic nonlinear cascaded systems

summary:In this paper, the problem of global finite-time stabilization via output-feedback is investigated for a class of stochastic nonlinear cascaded systems (SNCSs). First, based on the adding a power integrator technique and the homogeneous domination approach, a global output-feedback finite-time control law is constructed for the driving subsystem. Then, based on homogeneous systems theory, it is shown that under some mild conditions the global finite- time stability in probability of the driving subsystem implies the global finite-time stability in probability of the whole SNCS. Finally, a simulation example is given to illustrate the effectiveness of the proposed control design approach

Transition behaviors of system energy in a bi-stable van Ver Pol oscillator with fractional derivative element driven by multiplicative Gaussian white noise

The stochastic P-bifurcation behavior of system energy in a bi-stable Van der Pol oscillator with fractional damping under multiplicative Gaussian white noise excitation is investigated. Firstly, using the principle of minimal mean square error, the non-linear stiffness terms can be equivalent to a linear stiffness which is a function of the system amplitude, and the original system is simplified to an equivalent integer order Van der Pol system. Secondly, the system amplitude’s stationary probability density function is obtained by stochastic averaging. Then, according to the singularity theory, the critical parametric conditions for the system amplitude’s stochastic P-bifurcation are found. Finally, the types of the system’s stationary probability density function curves of amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical results and the numerical results obtained from Monte-Carlo simulation verifies the theoretical analysis in this paper, and the method used in this paper can directly guide the design of the fractional-order controller to adjust the response of the system

Stochastic transition behaviors in a tri-stable van der Pol oscillator with fractional delayed element subject to Gaussian white noise

The stochastic P-bifurcation behavior of tri stability in a generalized Van der Pol system with fractional derivative under additive Gaussian white noise excitation is investigated. Firstly, based on the minimal mean square error principle, the fractional derivative is found to be equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the stationary probability density function of the system amplitude is obtained by stochastic averaging, and according to the singularity theory, the critical parameters for stochastic P-bifurcation of the system are found. Finally, the nature of stationary probability density function curves of the system amplitude is qualitatively analyzed by choosing the corresponding parameters in each region divided by the transition set curves. The consistency between the analytical solutions and Monte-Carlo simulation results verifies the theoretical results in this paper