EFFECT OF RISK-SENSITIVE STOCHASTIC OPTIMAL CONTROL WITH TRACKING IN AN EVAPORATOR

This work presents an application of the Risk-Sensitive (R-S) control with tracking applied to a stochastic nonlinear system which models the operation of an electronic expansion valve (EEV) in a conventional evaporator. A novel dynamical stochastic equation represents the mathematical model of the evaporator system. The R-S stochastic optimal problem consists of the design of an optimal control u(t) such that the state reaches setpoint values (SP) and minimizes the exponential quadratic cost function. The presence of disturbances and errors in the sensor measurements is represented by Gauss white noise in the state equation, with the coefficient v(e/(2?^2 )) . One novel characteristic in this proposal is that the coefficient of the control into the state equation contains the state term. The error and exponential quadratic cost function show that the R-S control has a better performance versus the classical PID (Proportional, Integral Derivative) control. Key Words: Optimal Risk-Sensitive control with tracking, modelling of the evaporator.

New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations

In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the system to 12 and 14 parameters, respectively. Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. On the one hand of the special state equation, the submodel describes an isochoric vortex motion of particles, isobaric along each world line and restricted by a moving plane. The motions of particles occur along parabolas and along rays in parallel planes. The spherical volume of particles turns into an ellipsoid at finite moments of time, and as time tends to infinity, the particles end up on an infinite strip of finite width. On the other hand of the state equation of a monatomic gas, the submodel describes vortex compaction to the origin and the subsequent expansion of gas particles in half-spaces. The motion of any allocated volume of gas retains a spherical shape. It is shown that for any positive moment of time, it is possible to choose the radius of a spherical volume such that the characteristic conoid beginning from its center never reaches particles outside this volume. As a result of the generalization of the solutions with a linear velocity field, exact solutions of a wider class are obtained without conditions of invariance of density and pressure with respect to the selected three-dimensional subalgebras.

A Chaotic Oscillator Based on Meminductor, Memcapacitor, and Memristor

In this paper, a hyperchaotic circuit consisting of a series memristor, meminductor, and memcapacitor is proposed. The dimensionless mathematical model of the system is established by the state equation of the circuit. The stability of equilibrium point of the system is analyzed by using the traditional dynamic analysis method. Then, the dynamical characteristics of the chaotic system with parameters are analyzed in detail. In addition, the system also has some particular phenomena such as attractor coexistence and state transition. Finally, the circuit is realized by DSP, and the result is consistent with that of numerical simulation. This proves the accuracy of the theoretical analysis. Numerical simulation result shows which hyperchaotic system has very abundant dynamical characteristics.

Analytical study on discharge process of multiphase air-core pulsed alternators

This paper has investigated the discharge process of a four-phase air-core pulsed alternator. A mathematical model of the short-circuit current, relating to firing angles of discharge thyristors and taking the current coupling and field current attenuation into account, is established. Compared with the conventional trial-and-error method and existing phase peak current model, the proposed model has considered the attenuation trend of the filed current in the discharge process and derived the intuitive expression of the resultant short-circuit current. Firstly, the state equation model of a four-phase air-core pulsed alternator is established. Meanwhile, the simulation comparison indicates that the results of the state equation model are close to the finite-element model. Then, the segmented formula of resultant short-circuit current is derived based on the voltage equations of the armature winding circuits and the approximate attenuation coefficient of the field current. Finally, the segmented formula is verified with the finite-element method, and some preliminary experiments for field windings are carried out. The results show that this method can well describe the decay trend of field current and discharge current. It is helpful for selecting firing angles to generate the desired current amplitude and waveform in the future.

Liquid-Liquid Phase Transition in Supercooled H2O and D2O: A Path-Integral Computer Simulation Study

We perform path-integral molecular dynamics (PIMD) and classical MD simulations of H2O and D2O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density ρ(T), isothermal compressibility κT(T), and self-diffusion coefficients D(T) of H2O and D2O are in excellent agreement with available experimental data; the isobaric heat capacity CP(T) obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H2O and D2O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H2O and D2O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H2O, from PIMD simulations, is located at Pc = 167±9 MPa, Tc = 159±6 K, and ρc = 1.02±0.01 g/cm3. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D2O is estimated to be Pc = 176 ± 4 MPa, Tc = 177 ± 2 K, and ρc = 1.13±0.01 g/cm3. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, Pc = 203 ± 4 MPa, Tc = 175 ± 2 K, and ρc = 1.03 ± 0.01 g/cm3). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of Tc for D2O and, particularly, H2O suggest that improved water models are needed for the study of supercooled water.

Active disturbance rejection motion control of spherical robot with parameter tuning

Purpose The characteristics of spherical robots, such as under-drive, non-holonomic constraints and strong coupling, make it difficult to establish its motion control model accurately. To improve the anti-interference performance of spherical robots in practical engineering, this paper proposes a spherical robot motion controller based on auto-disturbance rejection control (ADRC) with parameter tuning. Design/methodology/approach This paper considers the influences of the spherical shell, internal frame and pendulum on the movement of the spherical robot during the rotation to establish the multi-body dynamics model of the XK-I spherical robot. Due to the serious coupling problem of the dynamic model, the motion control state equation is constructed using linearization and decoupling. The XK-I spherical robot PSO-ADRC motion controller with parameter tuning function is designed by combining the state equation with the particle swarm optimization (PSO) algorithm. Finally, experiments are performed to evaluate the feasibility of PSO-ADRC in an actual case compared to ADRC, PSO-PID and PID. Findings By analyzing the required time to reach the expected value, the control stability and the fluctuation range of the standard deviation after reaching the expected value, the superiority of PSO-ADRC to ADRC, PSO-PID and PID is demonstrated in terms of the speed and anti-interference ability. Practical implications The proposed method can be applied to the robot control field. Originality/value A parameter-tuning method for auto-disturbance-rejection motion control of the spherical robot is proposed. According to the experimental results, the anti-interference ability of the spherical robot moving on uneven ground is improved. Therefore, it provides a foundation for the autonomous environmental monitoring of the spherical robot equipped with sensors.

Asymptotic stability of 3D functional Brinkman-Forchheimer equation

This paper is concerned with the asymptotic stability of global weak and strong solutions for a 3D incompressible functional Brinkman-Forchheimer equation with delay. Under some appropriate assumptions on the external forces especially the averaged state, the well-posedness of 3D functional Brinkman-Forchheimer flow model and its steady state equation have been obtained rstly, then the asymptotic stability of global solutions also derived via the convergence of trajectories for the corresponding systems.

Optimal Control of Plasticity with Inertia

The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic strain by controlling volume forces. The idea given in [10] is used to transform the state equation into an evolution variational inequality (EVI) involving a certain maximal monotone operator. Results from [27] are then used to analyze the EVI. A regularization is obtained via the Yosida approximation of the maximal monotone operator, this approximation is smoothed further to derive optimality conditions for the smoothed optimal control problem.

Clothoid curve optimization for parallel parking path planning and tracking control

In order to solve the problem of abrupt curvature change at the connection between arcs and straight lines in circle-line-circle (C-L-C) combined parallel parking paths, curvature optimization was carried out by using a cycloid curve, and the trajectory curvature and heading Angle were made to meet the pose requirements of parallel parking. By establishing the kinematics model state equation and taking the optimized C-L-C trajectory as the reference trajectory, the error model was obtained. The model predictive controller based on the error model was designed, and the effectiveness of the path planning and model predictive controller was verified on Carsim and Matlab/Simulink co-simulation platform.