Arbitrary Disturbances Research Articles

Model for Estimating the Transient Response of the Global Mean Surface Temperature to Changes in the Concentrations of Atmospheric Aerosols and Radiatively Active Gases

A two-component energy-balance climate model (EBM) is considered, which allows estimating the transient response of the global mean surface temperature (i.e., the Earth climate system response) to radiative forcing due to atmospheric aerosols and radiatively active gases in accordance with the specified scenarios of their atmospheric content. An expression for the impulse response function of EBM is analytically derived. The response of the climate system to arbitrary external radiative forcing is calculated as a convolution of two functions – an impulse response function and a function describing the radiative forcing. The comparative analysis of the numerical calculation results for two idealized scenarios of radiative forcing (step function and linearly increasing radiative disturbance) and the exact solution analytically derived shows a fairly high accuracy of the approach. Using the impulse response function, we estimate the response of the global mean surface temperature to radiative forcing specified by several scenarios of an increase in the concentrations of greenhouse gases (four RCP scenarios) and volcanic aerosol (1991 eruption of the Pinatubo volcano). Since the technique suggested for estimating the transient climate response to radiative forcing is quite accurate and computationally inexpensive, it can be used as an express analysis tool for estimating the climate system response to arbitrary radiative disturbance caused by natural and anthropogenic aerosols and radiatively active gases including greenhouse gases.

Pinning Controllability for a Boolean Network With Arbitrary Disturbance Inputs.

In this paper, pinning controllability for a Boolean network (BN) under arbitrary disturbance inputs is considered. By selecting a fraction of nodes as the pinning nodes and injecting controllers that depend on the values of the disturbance inputs of the previous time instant, the controllability can be guaranteed for any BNs under arbitrary disturbance inputs. First, based on the necessary and sufficient conditions for the controllability of a BN with arbitrary disturbance inputs obtained in this paper, a constructive method for designing the transition matrix of the BN is presented, which further provides a method for selecting the pinning nodes. Second, a logical relationship between the control input nodes and system nodes is provided through solving logical matrix equations. Third, the control input sequence algorithm is also given. Finally, an example is presented to show the effectiveness of the proposed results.

Human inspired fall prediction method for humanoid robots

Humanoid robots are anticipated to work like humans in unstructured environments, and in such cases, falling over is inevitable due to the inherent postural instabilities and external disturbances arising from the environments. Since falling over may annihilate both the robot and its surroundings, we introduce in this work a generic method to predict the falling over of humanoid robots in a reliable, robust, and agile manner across various terrains, and also amidst arbitrary disturbances. The aforementioned characteristics have been strived to attain by proposing a prediction principle inspired by the human balance sensory systems. Accordingly, the fusion of multiple sensors such as inertial measurement unit and gyroscope (IMU), foot pressure sensor (FPS), joint encoders, and stereo vision sensor, which are equivalent to the human’s vestibular, proprioception, and vision systems are considered. For the prediction process, we first define a set of feature-based fall indicator variables (FIVs) from the different sensors, introduce prediction window parameters, and the thresholds for the FIVs are extracted using those parameters for four major disturbance scenarios. Further, an online threshold interpolation technique and an impulse adaptive counter limit are proposed to manage more generic disturbances. Finally, an instantaneous integer value is computed for each FIVs using their respective thresholds and the cumulative sum of them are normalized to predict the fall over by setting a suitable value as the critical limit. To determine the best combination and the usefulness of multiple sensors, the prediction performance is evaluated on four different types of terrains, in three unique combinations: first, each feature individually with their respective FIVs; second, an intuitive performance-based (PF); and finally, Kalman filter based (KF) techniques, which involve the usage of multiple features. For PF and KF techniques, prediction performance evaluations are carried out with and without adding noise to ascertain the influence of sensor noise. Overall, it is reported that KF performed better than PF and individual sensor features under different conditions. Also, the method’s ability to predict fall overs during the robot’s simple dynamic motion is also tested and verified through simulations. Experimental verification of the proposed prediction method on flat and uneven terrains is carried out with the WALK-MAN humanoid robot.

An internal model approach to estimation of systems with arbitrary unknown inputs

Estimation of systems with arbitrary unknown inputs, for which no models or statistical properties are assumed to be known, has received much attention. Given that no prior knowledge is assumed for the unknown inputs, the estimator has to be designed to be dissociated from their effects, i.e., the problem at hand has also been called unknown input decoupled estimation. The most significant results in the literature, pioneered by Hautus and others, show that the strong∗ detectability requirements, namely, (1) a rank matching condition; (2) the system is minimum phase, are necessary and sufficient for stable estimation of the state/unknown input. Recent research has sought alternative methods, when the above conditions do not hold. However, existing results have only addressed a few specific scenarios. For the most general case with the unknown inputs affecting both the state dynamics and the output, the essential question of whether and under what conditions it is still possible to obtain instantaneous and asymptotically stable estimation of the full state, when the strong∗ detectability conditions do not hold, has remained open for a long time. Answering such a question is critical for real-time feedback control with closed-loop stability and offset free regulation/tracking performance guarantees. The current paper will fill this gap via an internal model approach. We make a crucial observation that albeit without any model or statistical properties for the unknown inputs, one does have a model for their sum over time (to illustrate, here we consider the discrete-time case), which is an integrator driven by the unknown inputs. By incorporating this model into the original system model to form an augmented system, we establish conditions under which the augmented system is strong∗ detectable so that a strong observer exists and can be constructed to estimate the augmented state variable, comprised of the original system state and the unknown input sum, with asymptotically stable error. Moreover, the former conditions prove to encompass well-known results in the existing literature on offset free tracking with known disturbance models as special cases. Hence, the proposed results generalize the classical internal model principle from the conventional case when models of the disturbances are assumed to be known to the case with arbitrary unknown disturbances.

A New Approach to Calculate the Shielding Factor of Magnetic Shields Comprising Nonlinear Ferromagnetic Materials under Arbitrary Disturbances

To enable the realization of ultra-low magnetic fields for scientific and technological research, magnetic shielding is required to create a space with low residual magnetic field and high shielding factors. The shielding factors of magnetic shields are due to nonlinear material properties, the geometry and structure of the shields, and the external magnetic fields. Magnetic shielding is used in environments full of random realistic disturbances, resulting in an arbitrary and random external magnetic field, and in this case, the shielding effect is hard to define simply by the shielding factors. A new method to simulate and predict a dynamic internal space magnetic field wave is proposed based on the Finite Element method (FEM) combined with the Jiles-Atherton (JA) model. By simulating the hysteresis behavior of the magnetic shields and establishing a dynamic model, the new method can simulate dynamic magnetic field changes inside magnetic shields as long as the external disturbances are known. The shielding factors under an AC external field with a sine wave and certain frequencies are calculated to validate the feasibility of the new method. A real-time wave of internal magnetic flux density under an AC triangular wave external field is simulated directly with the new method versus a method that splits the triangular wave into several sine waves by a Fourier transform, divides the shielding factors, and then adds the quotients together. Moreover, real-time internal waves under some arbitrary fields are measured. Experimental internal magnetic flux density waves of a 4-layer magnetically shielded room (MSR) at the Harbin Institute of Technology (HIT) fit the simulated results well, taking experimental errors into account.

Применение технологии вложения систем для исследования инвариантности выхода сложной электрической системы по переменным состояния

The presented technique for synthesizing the electric system controller based on the system nesting technology is sufficiently simple because it is based on the modern theory of matrices suited for computer applications and therefore can be recommended for investigating complex automatically controlled electric power systems. The conditions for invariance of the electric system output with a synthesized controller to arbitrary external disturbances are substantiated using the matrix canonization method, which serves as a basis of the system nesting technology. The main distinctive feature of using the system nesting technology consists in a reduced amount of computation efforts because this technology rests on matrix analysis techniques, for which software packages have been developed. Another important aspect is that the class of controllers imparting the required dynamic properties to the studied systems, including invariance, is described analytically. The obtained results demonstrate high efficiency of the system nesting technology, due to which it can be recommended for being used in performing dispatch control of complex electrical systems.

Theoretical analysis of Rayleigh–Taylor instability on a spherical droplet in a gas stream

A linear analysis of the Rayleigh–Taylor (R–T) instability on a spherical viscous liquid droplet in a gas stream is presented. Different from the most previous studies in which the external acceleration is usually assumed to be radial, the present study considers a unidirectional acceleration acting on a spherical droplet with arbitrary initial disturbances and therefore can provide insights into the influence of R–T instability on the atomization of spherical droplets. A general recursion relation coupling different spherical modes is derived and two physically prevalent limiting cases are discussed. In the limiting case of inviscid droplet, the critical Bond numbers to excite the instability and the growth rates for a given Bond number are obtained by solving two eigenvalue problems. In the limiting case of large droplet acceleration, different spherical modes are asymptotically decoupled and an explicit dispersion relation is derived. For given Bond number and Ohnesorge numbers, the critical size of stable droplet, the most-unstable mode and its corresponding growth rate are determined theoretically.

Physics-based Learning for Aircraft Dynamics Simulation

The accurate prediction of flight trajectories is crucial for the real-time prognostics of air transportation system. However, the computation costs of predictions can be expensive or even prohibitive especially for a large number of aircrafts in the air traffic system. This study proposes the concept of physics-based learning, a hybrid approach based on data-driven learning and physical models, as a computationally efficient method for the simulation of aircraft dynamics. The physics-based learning integrates the underlying physics of dynamical systems into learning models such as neural networks to reduce the training and simulation costs. The application of physics-based learning for simulating aircraft dynamics is demonstrated using a recently introduced physics-aware network known as the deep residual recurrent neural network (DR-RNN) on a Boeing 747-100 aircraft. The aircraft dynamics are described using a six degrees-of-freedom aircraft model. The DR-RNN is first trained using the simulated responses of the aircraft and then the trained network is used to predict the response of aircraft under arbitrary control inputs and disturbances. The results show that the DR-RNN can accurately predict aircraft responses and has excellent extrapolation capabilities. Moreover, the DR-RNN exhibits superior computation efficiency compared with a classical numerical method, the fourth-order Runge-kutta method, highlighting its suitability in serving as surrogating models for aircraft dynamical systems.

On steady-state disturbance compensability for actuator placement in adaptive structures

Abstract Adaptive structures in civil engineering are mechanical structures with the ability to modify their response to external loads. Actuators strongly affect a structure’s adaptivity and have to be placed thoughtfully in the design process to effectively compensate external loads. For constant loads, this property is introduced as steady-state disturbance compensability. This property can be linked to concepts from structural engineering such as redundancy or statical indeterminacy, thus representing an interdisciplinary approach. Based on the disturbance compensability matrix, a scalar performance metric is derived as quantitative measure of a structure’s ability to compensate the output error for arbitrary constant disturbances with a given set of actuators. By minimizing this metric, an actuator configuration is determined. The concept is applied to an example of a truss structure.

Dynamic response of free span pipelines via linear and nonlinear stability analyses

A thorough stability analysis of submerged pipeline dynamics has been performed. The problem of current-induced vibrations in a free spanning pipeline was analyzed using both linear and non-linear methodologies. While most investigations dedicated to the analysis of this type of problem use either approximate analytical methods or traditional numerical methods, two alternative approaches are presented: Linear Stability Analysis (LSA) and the Generalized Integral Transform Technique (GITT). Although strictly valid when the pipeline is subject to small amplitude disturbances, LSA is simple to apply and yields accurate either explicit or transcendental analytical relations that predict dominant pipeline vibration frequencies and wavelengths as well as the onset of buckling. On the other hand, the GITT can predict pipeline behavior for arbitrary disturbance amplitudes more efficiently than traditional numerical methods. These features are illustrated by considering the problem of a submerged pipeline subjected to soil conditions and ocean currents. This problem was solved using LSA, the GITT and the Finite Element Method (FEM) for comparison purposes. Moreover, the DNV-RP-F105 standard was also used for verifying the proposed methods. The alternative methods offered in this paper can overcome limitations associated with traditional analytical and numerical approaches, and are employed to produce previously unreported results.

Energy extraction from vortex-induced vibrations using period-1 rotation of an autoparametric pendulum

We propose and analyse the feasibility of extracting energy from vortex-induced vibrations using rotating motion of an attached pendulum. The resulting autoparametric pendulum system is studied primarily to understand the effect of pendulum motion on the performance of the harvester which is typically ignored to result in a simple parametric pendulum. We find that rotating motions are possible only for small values of the pendulum mass when compared with the effective mass of the vibrating structure. However, the pendulum motion reduces the basin of attraction as well as the range of system parameters corresponding to the existence of rotary solutions. This significantly alters the harvester performance. By contrast, the evolution of the pendulum coordinates (angular position and velocity) remains largely unaffected by this interaction. Hence, for the purpose of design of controllers to robustly initiate/maintain rotation from arbitrary disturbances, the simplification to a parametric pendulum is reasonable while for the design of the harvester, this exercise is completely unsatisfactory.

Discrete-Time Robust Hierarchical Linear-Quadratic Dynamic Games

In this paper, the theory of robust min–max control is extended to hierarchical and multiplayer dynamic games for linear quadratic discrete time systems. The proposed game model consists of one leader and many followers, while the performance of all players is affected by disturbance. The Stackelberg–Nash-saddle equilibrium point of the game is derived and a necessary and sufficient condition for the existence and uniqueness of such a solution is obtained. In the infinite time horizon, it is shown that the solution of the Riccati equation is upper bounded under a condition that is called individual controllability. By assuming such a condition and using a time-varying Lyapunov function the input-to-state stability of the hierarchical dynamic game is achieved, considering the optimal feedback strategies of the players and an arbitrary disturbance as the input.

Pareto-optimal Choice of Controller Dimension for Plasma Stabilization System

Abstract The approach to synthesis and implementation of the controller of ITER plasma stabilization system is considered. The advantage of the presented approach is that the controllers of various dimensions are optimized. Software computes the controllers whose dimension and integral quality criterion are Pareto-optimal. It is described the algorithm to choose the proper controller to final implementation when equations of the plasma stabilization system have a high dimension. The presented integral quality criterion evaluates the upper bound of the ensemble of transient processes for some arbitrary plasma disturbances.

Gain scheduled dynamic surface control for a class of underactuated mechanical systems using neural network disturbance observer

A gain scheduled dynamic surface control (GSDSC) based on neural network disturbance observer (NNDOB) is developed for a class of uncertain underactuated mechanical systems with multiple equilibria. Equilibrium manifold linearization (EML) transforms the nonlinear system into an equivalent model using scheduling variables. The NNDOB with a filtering adaptive law is constructed to approximate arbitrary disturbances. The dynamic surface controller is designed based on the NNDOB and EML model, which efficiently solves the mismatches and overcomes the problem of “explosion of complexity” resulting from repeated differentiation of virtual control variables. Moreover, the robust stability of the closed-loop system is proved by Lyapunov stability theorem. Finally, we apply the proposed control scheme to a power line inspection robotic system. The simulation results illustrate the approximation capability of NNDOB and the effectiveness of the presented control scheme.

Robust Stabilization for a Logical System

This brief studies robust stabilization for a logical system under arbitrary disturbance inputs. Feedback control and pinning control design algorithms, which relying on the disturbance inputs, are developed to stabilize the logical system. In order to design feedback controller, necessary and sufficient conditions for the existence of a state feedback controller are derived. Then, constructive procedures for feedback control are provided. For the purpose of designing pinning control, an algorithm to select the pinning nodes is provided. Besides, a pinning control design algorithm is given. Finally, illustrative examples are given to show the proposed results.

Novel Semi-Parametric Algorithm for Interference-Immune Tunable Absorption Spectroscopy Gas Sensing.

One of the most common limits to gas sensor performance is the presence of unwanted interference fringes arising, for example, from multiple reflections between surfaces in the optical path. Additionally, since the amplitude and the frequency of these interferences depend on the distance and alignment of the optical elements, they are affected by temperature changes and mechanical disturbances, giving rise to a drift of the signal. In this work, we present a novel semi-parametric algorithm that allows the extraction of a signal, like the spectroscopic absorption line of a gas molecule, from a background containing arbitrary disturbances, without having to make any assumption on the functional form of these disturbances. The algorithm is applied first to simulated data and then to oxygen absorption measurements in the presence of strong fringes.To the best of the authors’ knowledge, the algorithm enables an unprecedented accuracy particularly if the fringes have a free spectral range and amplitude comparable to those of the signal to be detected. The described method presents the advantage of being based purely on post processing, and to be of extremely straightforward implementation if the functional form of the Fourier transform of the signal is known. Therefore, it has the potential to enable interference-immune absorption spectroscopy. Finally, its relevance goes beyond absorption spectroscopy for gas sensing, since it can be applied to any kind of spectroscopic data.

Design, modelling and estimation of a novel modular multi-speed transmission system for electric vehicles

The efficiency of electric vehicles (EVs) should be improved to make them viable, especially in light of the current low energy-storage capacity of electric batteries. Research demonstrates that applying a multi-speed transmission (MST) in an EV can reduce the energy consumption of the vehicle through gear-shifting. However, for effective gear-shifting control in MSTs, first of all, the model of the transmission is required. Moreover, reliable methods should be employed for estimation of the unmeasurable loads and states of the system, under model-based control. This study establishes the mathematical model and estimation algorithms for a novel MST designed for EVs. The main advantages of the designed MST are simplicity and modularity. After devising the dynamics of our proposed transmission, the Kalman filter, the Luenberger obsever and neural networks (NNs) are used to estimate the states, the unknown arbitrary disturbance and the unknown clutch torque applied to the system. Simulation results demonstrate that the proposed approach is suitable for estimation purposes. Experiments were conducted using an in-house prototyped transmission testbed, to validate the simulation results and assess the estimation algorithms.

Stochastic model predictive control with joint chance constraints

ABSTRACTThis article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input constraints and joint state chance constraints in the presence of unbounded additive disturbances. The Cantelli–Chebyshev inequality is used in combination with risk allocation to obtain computationally tractable but accurate surrogates for the joint state chance constraints when only the mean and variance of the arbitrary disturbance distributions are known. An algorithm is presented for determining the optimal feedback gain and optimal risk allocation by iteratively solving a series of convex programs. The proposed stochastic MPC approach is demonstrated on a continuous acetone–butanol–ethanol fermentation process, which is used in the production of biofuels.

Global and exact HOSM differentiator with dynamic gains for output-feedback sliding mode control

In this paper we introduce a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains to solve the problem of trajectory tracking via output-feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state-dependent and time-varying. Uniform global stability and robust exact tracking are guaranteed employing the proposed HOSM based exact differentiator. The obtained results are not restricted to first-order sliding mode control feedback, but applies for second order sliding mode algorithms (twisting, super-twisting and variable gain super-twisting) as well as quasi-continuous HOSM finite-time controllers. Simulations with an aircraft pitch-control application illustrate the claimed properties, even in the presence of measurement noise.

On triply diffusive convection in completely confined fluids

The present paper carries forward Prakash et al. [21] analysis for triple diffusive convection problem in completely confined fluids and derives upper bounds for the complex growth rate of an arbitrary oscillatory disturbance which may be neutral or unstable through the use of some non-trivial integral estimates obtained from the coupled system of governing equations of the problem.