CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME_DELAY CASE

The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of periodic systems are presented, respectively.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME_DELAY CASE

The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of aperiodic systems are presented,respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

The controllability for switched linear system with time_delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time_delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.

Finite time stability and stabilization of hybrid dynamic systems

Finite time stability and stabilization are studied for hy-brid dynamic systems. By combining multiple Lyapunov function and finite time Lyapunov function, a sufficient condition of finite time stability is given for the system. Compared with the previ-ous works, our results have less conservativeness. Furthermore, based on the state partition of continuous and resetting parts of system, a hybrid feedback controller is constructed, which stabi-lizes the closed-loop systems in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the pro-posed method.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS

In this paper, we consider a class of optimal control problem for the singularly perturbed hybrid dynamical systems. By means of variational method, we obtain the necessary conditions of the hybrid dynamical systems. Meanwhile, the existence of solution for the hybrid dynamical system is proved by the sewing method and the uniformly valid asymptotic expansion of the optimal trajectory is constructed by the boundary function method. Finally,an example is presented to illustrate the result.

MLD-MPC Approach for Three-Tank Hybrid Benchmark Problem

The present paper aims at validating a Model Predictive Control(MPC),based on the Mixed Logical Dynamical(MLD)model,for Hybrid Dynamic Systems(HDSs)that explicitly involve continuous dynamics and discrete events.The proposed benchmark system is a three-tank process,which is a typical case study of HDSs.The MLD-MPC controller is applied to the level control of the considered tank system.The study is initially focused on the MLD approach that allows consideration of the interacting continuous dynamics with discrete events and includes the operating constraints.This feature of MLD modeling is very advantageous when an MPC controller synthesis for the HDSs is designed.Once the MLD model of the system is well-posed,then the MPC law synthesis can be developed based on the Mixed Integer Programming(MIP)optimization problem.For solving this MIP problem,a Branch and Bound(B&B)algorithm is proposed to determine the optimal control inputs.Then,a comparative study is carried out to illustrate the effectiveness of the proposed hybrid controller for the HDSs compared to the standard MPC approach.Performances results show that the MLD-MPC approach outperforms the standardMPCone that doesn’t consider the hybrid aspect of the system.The paper also shows a behavioral test of the MLDMPC controller against disturbances deemed as liquid leaks from the system.The results are very satisfactory and show that the tracking error is minimal less than 0.1%in nominal conditions and less than 0.6%in the presence of disturbances.Such results confirm the success of the MLD-MPC approach for the control of the HDSs.

Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing （RTDHT）. This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Pad6 approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.

Mathematical Model and Its Hybrid Dynamic Mechanism in Intelligent Control of Ironmaking

A hybrid dynamic model was proposed, which considered both the hydrokinetic and the chaotic properties of the blast furnace ironmaking process; and great emphasis was put on its mechanism. The new model took the high complexity of the blast furnace as well as the effects of main parameters of the model into account, and the predicted results were in very good agreement with actual data.

Simulation of large-scale numerical substructure in real-time dynamic hybrid testing

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom （DOFs）. Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

A Hybrid Statistical-Dynamical Downscaling of Air Temperature over Scandinavia Using the WRF Model

An accurate simulation of air temperature at local scales is crucial for the vast majority of weather and climate applications.In this work,a hybrid statistical–dynamical downscaling method and a high-resolution dynamical-only downscaling method are applied to daily mean,minimum and maximum air temperatures to investigate the quality of localscale estimates produced by downscaling.These two downscaling approaches are evaluated using station observation data obtained from the Finnish Meteorological Institute over a near-coastal region of western Finland.The dynamical downscaling is performed with the Weather Research and Forecasting(WRF)model,and the statistical downscaling method implemented is the Cumulative Distribution Function-transform(CDF-t).The CDF-t is trained using 20 years of WRF-downscaled Climate Forecast System Reanalysis data over the region at a 3-km spatial resolution for the central month of each season.The performance of the two methods is assessed qualitatively,by inspection of quantile-quantile plots,and quantitatively,through the Cramer-von Mises,mean absolute error,and root-mean-square error diagnostics.The hybrid approach is found to provide significantly more skillful forecasts of the observed daily mean and maximum air temperatures than those of the dynamical-only downscaling(for all seasons).The hybrid method proves to be less computationally expensive,and also to give more skillful temperature forecasts(at least for the Finnish near-coastal region).

Hybrid dynamic model of polymer electrolyte membrane fuel cell stack using variable neural network

The polymer electrolyte membrane（PEM） fuel cell has been regarded as a potential alternative power source,and a model is necessary for its design,control and power management.A hybrid dynamic model of PEM fuel cell,which combines the advantages of mechanism model and black-box model,is proposed in this paper.To improve the performance,the static neural network and variable neural network are used to build the black-box model.The static neural network can significantly improve the static performance of the hybrid model,and the variable neural network makes the hybrid dynamic model predict the real PEM fuel cell behavior with required accuracy.Finally,the hybrid dynamic model is validated with a 500 W PEM fuel cell.The static and transient experiment results show that the hybrid dynamic model can predict the behavior of the fuel cell stack accurately and therefore can be effectively utilized in practical application.

DYNAMIC CHARACTERISTICS OF ELECTRO-HYDRAULIC PROPORTIONAL PRESSURE-FLOW HYBRID VALVE

The structure principles under the flow and pressure working conditions are studied, in order to investigate the dynamic characteristics of the electro-hydraulic proportional pressure-flow hybrid valve. According to the structure principles under the two different working conditions, the transfer functions under such conditions are derived. With the transfer functions, some structure elements that may affect its performance, are investigated, afterwards some principles of optimality and effective methods for improving the dynamic performance of the valve are proposed. The conclusions can be used to instruct engineering applications and products designing. The test results conform to the results of the theoretical analysis and simulation, which proves the correctness of the study and simulation works.

Consensus control for heterogeneous uncertain multi-agent systems with hybrid nonlinear dynamics via iterative learning algorithm

In this study,We propose a compensated distributed adaptive learning algorithm for heterogeneous multi-agent systems with repetitive motion,where the leader's dynamics are unknown,and the controlled system's parameters are uncertain.The multiagent systems are considered a kind of hybrid order nonlinear systems,which relaxes the strict requirement that all agents are of the same order in some existing work.For theoretical analyses,we design a composite energy function with virtual gain parameters to reduce the restriction that the controller gain depends on global information.Considering the stability of the controller,we introduce a smooth continuous function to improve the piecewise controller to avoid possible chattering.Theoretical analyses prove the convergence of the presented algorithm,and simulation experiments verify the effectiveness of the algorithm.

MODELING AND IMPLEMENTATION OF SPEED GOVERNOR FOR THE HYBRID ELECTRIC VEHICLE ENGINE

A speed control analysis for an in-line gasoline fueled internal combustion （IC） engine is presented for the purpose of alleviation of high frequency oscillations in engine revolutions. A dynamic cylinder-by-cylinder model is proposed, base on slider-crank mechanism, which is extended to develop a digital governor providing a high fidelity estimation of rotary speed oscillation for hybrid vehicle engines. A modified PID controller that P and I gain is placed in feedback path is also described for hybrid electric vehicle （HEV） engine speed regulation, By comparison between measured and estimated signals, it is demonstrated that a good agreement has been achieved and the governor behaves an excellent damping speed ripple.

Function Observer Based Event-triggered Control for Linear Systems with Guaranteed L_∞-Gain

This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the difference between the current value of the system and its previously transmitted value which includes the plant output or the function observer output exceeds an additional threshold. For such an eventtriggered mechanism, we derive conditions in terms of matrix inequality to guarantee the stability as well as longer inter-event time. We propose two approaches to investigate the closed-loop model, namely, reformulating the event-triggered control system as a hybrid system and interpreting the event-induced error as exogenous disturbance. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results.

Geographically distributed hybrid testing & collaboration between geotechnical centrifuge and structures laboratories

Distributed Hybrid Testing（DHT） is an experimental technique designed to capitalise on advances in modern networking infrastructure to overcome traditional laboratory capacity limitations. By coupling the heterogeneous test apparatus and computational resources of geographically distributed laboratories, DHT provides the means to take on complex, multi-disciplinary challenges with new forms of communication and collaboration. To introduce the opportunity and practicability afforded by DHT, here an exemplar multi-site test is addressed in which a dedicated fibre network and suite of custom software is used to connect the geotechnical centrifuge at the University of Cambridge with a variety of structural dynamics loading apparatus at the University of Oxford and the University of Bristol. While centrifuge time-scaling prevents real-time rates of loading in this test, such experiments may be used to gain valuable insights into physical phenomena, test procedure and accuracy. These and other related experiments have led to the development of the real-time DHT technique and the creation of a flexible framework that aims to facilitate future distributed tests within the UK and beyond. As a further example, a real-time DHT experiment between structural labs using this framework for testing across the Internet is also presented.

Dynamic torque response analysis of IPMSM in flux weakening region for HEV applications

An over-modulation based vector control strategy for interior permanent magnet synchronous machine（ IPMSM） is proposed and investigated. The strategy increases the reference flux weakening voltage to improve efficiency in flux weakening region of IPMSMwith the same dynamic torque response performance in standard SV Mtechnique. The relationship between dynamic torque performance and the reference flux weakening voltage is also discussed. In order to achieve fast and smooth shift process,the torque response must be less than 20 ms in the parallel hybrid electric vehicle（ HEV）,according to this,modeling and experimental studies were carried out. The results show that the proposed strategy can achieve the same dynamic and steady state torque performance with higher reference flux weakening voltage,which means higher efficiency.

Numerical Simulation of PMM Tests for A Ship in Close Proximity to Sidewall and Maneuvering Stability Analysis

As the maneuverability of a ship navigating close to a bank is influenced by the sidewall, the assessment of ship maneuvering stability is important. The hydrodynamic derivatives measured by the planar motion mechanism （PMM） test provide a way to predict the change of ship maneuverability. This paper presents a numerical simulation of PMM model tests with variant distances to a vertical bank by using unsteady RANS equations. A hybrid dynamic mesh technique is developed to realize the mesh configuration and remeshing of dynamic PMM tests when the ship is close to the bank. The proposed method is validated by comparing numerical results with results of PMM tests in a circulating water channel. The first-order hydrodynamic derivatives of the ship are analyzed from the time history of lateral force and yaw moment according to the multiple-run simulating procedure and the variations of hydrodynamic derivatives with the ship-sidewall distance are given. The straight line stability and directional stability are also discussed and stable or unstable zone of proportional-derivative （PD） controller parameters for directional stability is shown, which can be a reference for course keeping operation when sailing near a bank.

Implementable Strategy Research of Brake Energy Recovery Based on Dynamic Programming Algorithm for a Parallel Hydraulic Hybrid Bus

The purpose of this paper is to develop an implementable strategy of brake energy recovery for a parallel hydraulic hybrid bus. Based on brake process analysis, a dynamic programming algorithm of brake energy recovery is established. And then an implementable strategy of brake energy recovery is proposed by the constraint variable trajectories analysis of the dynamic programming algorithm in the typical urban bus cycle. The simulation results indicate the brake energy recovery efficiency of the accumulator can reach 60% in the dynamic programming algorithm. And the hydraulic hybrid system can output braking torque as much as possible.Moreover, the accumulator has almost equal efficiency of brake energy recovery between the implementable strategy and the dynamic programming algorithm. Therefore, the implementable strategy is very effective in improving the efficiency of brake energy recovery.The road tests show the fuel economy of the hydraulic hybrid bus improves by 22.6% compared with the conventional bus.