Stabilization of the cart pole system: by sliding mode control

This paper presents a control strategy designed as a combination of a PD controller and a twisting-like algorithm to stabilize the damped cart pole system, provided that the pendulum is initially placed within the upper-half plane. To develop the strategy, the original system is transformed into a four-order chain of integrator form, where the damping force is included through an additional nonlinear perturbation. The strategy consists of simultaneously bringing the position and velocity of the pendulum to within a compact region by applying the PD controller. Meanwhile, the system state variables are brought to the origin by the twisting-like algorithm. The corresponding convergence analysis is done using several Lyapunov functions. The control strategy is illustrated with numerical simulations.     

Large eddy simulation of separation control over a backward-facing step flow by suction

Separation control over a backward-facing step (BFS) flow by continuous suction was numerically investigated using the turbulence model of large eddy simulation (LES). The effect of suction control on the flow fields was scrutinised by altering the suction flow coefficient, and the results indicate that suction is not only very effective in shortening the reattachment length but also very influential in reducing the tangential velocity gradient and turbulence fluctuations of the reattached flows. With increasing increments of the absolute suction flow coefficient, the effect of suction control is more significant. Furthermore, the detailed flow fields (including the time-averaged stream and velocity fields) and turbulence characteristics (including the time-averaged resolved kinetic energy and RMS velocity) for the BFS models with or without suction are presented to discuss the mechanism of suction control. Comparisons of the time-averaged statistics between the numerical simulations and corresponding experiments are conducted, and it shows that the LES based on the dynamic kinetic energy subgrid-scale model (DKEM) can acquire exact results. Therefore, feasibility of the numerical methods to simulate suction-controlled models is validated.     

Stabilization control of a hovering model insect: lateral motion

Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability (passive stability),because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion.Controllability analysis shows that although inherently unstable,the lateral disturbance motion is controllable.By feeding back the state variables (i.e.lateral translation velocity,yaw rate,roll rate and roll angle,which can be measured by the sensory system of the insect) to produce anti-symmetrical changes in stroke amplitude and/or in angle of attack between the left and right wings,the motion can be stabilized,explaining why the drone flies can fly stably even if the flight is passively unstable.     

Stabilization control of a bumblebee in hovering and forward flight

Our previous study shows that the hovering and forward flight of a bumblebee do not have inherent stability （passive stability）. But the bumblebees are observed to fly stably. Stabilization control must have been applied. In this study, we investigate the longitudinal stabilization control of the bumblebee. The method of computational fluid dynamics is used to compute the control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion. Controllability analysis shows that at all flight speeds considered, although inherently unstable, the flight is controllable. By feedbacking the state variables, i.e. vertical and horizontal velocities, pitching rate and pitch angle （which can be measured by the sensory system of the insect）, to produce changes in stroke angle and angle of attack of the wings, the flight can be stabilized, explaining why the bumblebees can fly stably even if they are passively unstable.     

Stabilization control of a hovering model insect:lateral motion

Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability (passive stability),because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue...     

Stabilization of a nonlinear rotating disk-beam system with localized thermal effect

This paper presents two methods for finite-time topology identification for the complex spatio- temporal networks with coupling time delay. By introducing the auxiliary systems, a relationship between the unknown topology and two measurable matrix signals is developed. Based on the relationship, one method of identifying the topology is to compute the invertibility of the matrix. Besides this method, an adaptive law is developed to infer the topology online in finite time. The proposed methods do not require the differentiability of the time-varying delay. Furthermore, the methods can also be applied to complex spatio-temporal networks with unknown system parameters. Finally, an illustrative example is provided to show the effectiveness of the proposed methods.     

Stabilization problems for a system with output feedback (review)

Algorithms for solving the problem of design of static output feedback controllers for stationary linear systems with continuous and discrete time are reviewed. The inverse problem is considered. The algorithms of synthesis of output feedback controllers are generalized to the case of a periodic discrete-time system. To solve such problems, it might be more natural to use an approach based on multi-criterion optimization. It is also shown that these algorithms can be used for the optimal stabilization of unstable systems with delay. In this connection, the parameters of a controller with given structure for a controlled unstable scalar system with delay are optimized. To this end, the system is first approximated by a system without delay, with the exponent approximated by a fractionally rational function. Since the structure of the controller is given, the quality of approximation is estimated as the difference (in the space of controller coefficients) between the stability domains of the original and approximating systems. At the next stage, the gain coefficients of the controller for the reduced system are optimized. The efficiency of the thus synthesized controller is assessed through mathematical modeling of a system with delay whose feedback loop is defined by the gain coefficients found. The approach is illustrated by stabilizing an inverted simple pendulum with a proportional–derivative controller with delay. The problem of synthesis of a robust controller for this example is considered. Some examples of designing a robust controller, including for a third-order system in which the delay rather than some parameter is uncertain are presented     

Automatic control of a modified tractor to work on steep side slopes

The main purpose of this paper is to investigate the control and stability of a tractor moving over obstacles on steep side slopes. To this end, a modified slope tractor is considered and the lateral stability of the vehicle is studied. The modified tractor is able to roll against the side slope and change the position of its mass centre. The tractor behaviour in a sloped field on a straight path is simulated in ADAMS software environment. A two-layer controller consisting of a Fuzzy upper layer and a PI lower layer is designed for the control of tractor stability. The dynamics of hydraulic actuators adjusting the body roll angle is also included. The stability of controlled and uncontrolled tractors is investigated by several simulations. It is shown that in comparison with the two types of ordinary and uncontrolled slope tractors, the controller is capable of maintaining the stability of modified tractor and preventing it from rollover and instability on various side slopes and obstacles.     

双面理想完整约束系统的机械能守恒律

研究双面理想完整约束系统在约束不是定常且主动力不是有势时的机械能守恒律. 建立系统的能量变化方程,给出存在机械能守恒律的充分必要条件. 分析有机械能守恒律的12种情况. 最后给出说明性算例.     

Stabilization of impulsive switched linear systems with saturated control input

This paper considers the stabilization problem of impulsive switched linear systems with saturated control input, in which the impulses are viewed as control or disturbances. Under arbitrary switching rule and dwell time switching rule, the local stabilization conditions are obtained in terms of LMIs, respectively. The corresponding optimization problems are formulated to obtain a bigger attractive region. Our results show that impulsive control can recover part of attractive region, or allow a wide range of switching signals. If the impulses occur as disturbances, we have to increase the dwell time of switching signals to offset the effects of disturbances. Numerical examples are given to show the effectiveness of the results proposed.     

Stabilization of an alternating-current-carrying plasma filament by a quadrupole magnetic field

Dynamic stabilization of straight and toroidal current-carrying plasma jets by a high-frequency quadrupole magnetic field was proposed by Osovets [1]. A more rigorous theoretical analysis of the problem was performed by Levin and Rabinovich [2], who obtained a Routh function for studying the dynamics of the filament in various magnetic fields for a thin filament experiencing longwave serpentine- and construction-type disturbances. In this paper, the method proposed in [2] is applied to the stabilization of a plasma filament in which (as distinct from [1,2]) flows an alternating current while the quadrupole field is either constant, or varies at a high frequency, as in [1,2].The author is indebted to M. L. Levin for useful discussions and advice.     

Stabilization of a laminar boundary layer by an active surface-localized action

A method for rapidly damping instability waves is proposed as a means of actively controlling a perturbed gas boundary layer flow. The method is based on the use of an active body surface segment which reacts to an instantaneous local pressure variation by producing a proportional local wall displacement normal to the surface with a constant time lag calculated to result in the optimal suppression of unstable disturbances. It is shown that in the one-frequency case the wave number spectrum of the optimal control law contains multiple eigenvalues. The effectiveness of the method is demonstrated over a wide range of variation of the instability wave frequencies and directions. The propagation of an instability wave over an active segment of finite length is calculated using an integral-equation method based on solving the problem of boundary layer flow receptivity to surface vibration. Explicit formulas describing the process of scattering of the instability wave into stable modes at the junction point of the rigid and active surfaces are obtained using the Fourier method and the integral Cauchy theorem.     

Stability analysis of a noise control system in a duct by using delay differential equation

The paper deals with the criteria for the closed- loop stability of a noise control system in a duct. To study the stability of the system, the model of delay differential equation is derived from the propagation of acoustic wave governed by a partial differential equation of hyperbolic type. Then, a simple feedback controller is designed, and its closed- loop stability is analyzed on the basis of the derived model of delay differential equation. The obtained criteria reveal the influence of the controller gain and the positions of a sensor and an actuator on the closed-loop stability. Finally, numerical simulations are presented to support the theoretical results.     

Chaos control of a new 3D autonomous system by stability transformation method

This paper sheds new insights into the stability transformation method (STM) for chaos control of dynamical system. The STM is applied to stabilize both multiple equilibrium points and unstable periodic orbits (UPOs) embedded in the chaotic attractor of a new 3D autonomous system. Firstly, the different equilibrium points of chaotic system are stabilized with STM by choosing specific initial points and involutory matrices. Then, the stability matrix is derived based on a priori information of equilibrium points, which indicates that the non-involutory matrix can also be used to control the unstable equilibrium points of chaotic systems. Finally, it is found that the STM can be regarded as a special form of speed feedback control method (SFCM), which facilitates the practical implementation of STM scheme. The chaotic system can be controlled by adopting the corresponding feedback control strategy once the stability matrices are determined. In this way, the blindness of choice for control strategy in the SFCM is avoided, and the difficulty for determining the state variables to be controlled is overcome.     

Dynamics of prolate jellyfish with a jet-based locomotion

Swimming jellyfish deliver momentum to the surrounding fluid in the form of vortices. A three-dimensional computational model was adopted to investigate the characteristic flow patterns produced by jellyfish with a jet-based locomotion and the process of vortex generation. The interaction between jellyfish and the surrounding fluid may be simulated using the immersed boundary method. The vortex structures generated in the wake were elucidated in detail. The vortices were formed due to the contraction and expansion of the elastic bell. A dimensionless temporal parameter was employed to analyze the vortex formation process. During the early stage of contraction, the vortices were dominantly generated by the stroke. The ejected fluid from the inside of the bell was then entrained into the vortices, thereby decreasing the vorticity at the core and increasing the total circulation within the vortex ring. The Froude propulsion efficiency increased as the vortex formation number increased, implying that the propulsion in the way of growing the vortex structures was favorable in terms of the efficiency.     

Open-channel waves generated by propagation of a discontinuous wave over a bottom step

This paper presents the results of theoretical and experimental studies of open-channel waves generated by the propagation of a discontinuous dam-break wave over a bottom step. The cases where the initial tailwater level is higher than the step height (the step is under water) and where this value is smaller than the step height (at the initial time, water is absent on the step) are considered. Exact solutions are constructed using modified first-approximation equations of shallow-water theory, which admit the propagation of discontinuous waves in a dry channel. On the stationary hydraulic jump formed above the bottom step, the total free-stream energy is assumed to be conserved. These solutions agree with experimental data on various parameters (types of waves, wave propagation velocity, asymptotic depths behind the wave fronts). __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 31–44, January–February, 2008.