State Space Of System Research Articles

Full and Partial Eigenvalue Placement for Minimum Norm Static Output Feedback Control

The controller design for linear time-invariant state space systems seems to be straightforward and well established. This is not true for static output feedback control, which is still a challenging task. This paper deals with controller design based on eigenvalue assignment. We consider the placement of distinct as well as multiple real eigenvalues or complex conjugate pairs. The desired eigenvalue configurations are characterised in terms of algebraic divisibility of the characteristic polynomial of the closed-loop system. We also consider the problem of partial eigenvalue placement, where not all eigenvalues are fixed by feedback. Degrees of freedom in the controller design are used for the minimization of various matrix norms of the feedback gain matrix.

An MOR Algorithm Based on the Immittance Zero and Pole Eigenvectors for Fast FEM Simulations of Two-Port Microwave Structures

The aim of this article is to present a novel model-order reduction (MOR) algorithm for fast finite-element frequency-domain simulations of microwave two-port structures. The projection basis used to construct the reduced-order model (ROM) comprises two sets: singular vectors and regular vectors. The first set is composed of the eigenvectors associated with the poles of the finite-element method (FEM) state-space system, while the second one is made up from the eigenvectors corresponding to the zeros of the diagonal elements of the matrix-valued immittance transfer function. Importantly, just one LU factorization of the FEM system is required to construct the projection basis during the reduction process, due to the application of a new formulation based on the Schur complement. The sets of eigenvectors that are used in the basis are independent of one another, which makes the new technique better suited for parallel computing compared with previously developed methods, which are sequential in nature. The reliability and accuracy of the proposed scheme are compared with that of the standard MOR technique, namely, the reduced-basis method (RBM), and verified through the analysis of three microwave structures: an eighth-order dual-mode waveguide filter, a dielectric resonator filter, and a folded waveguide filter.

State space and binary decision diagram models for discrete standby systems with multistate components

A state space model for exact analysis of discrete time heterogeneous general standby systems applicable for hot, warm, and cold backups in any combination of them is proposed. The systems have multistate components whose lifetimes follow independent discrete phase-type distributions. The approach is by incorporating a deceleration matrix into the survival matrix of a component while as a backup and proving that such an approach results in a discrete phase-type representation of the system lifetime distribution. The method is applicable for dynamic reliability analyses of general structure systems having combinations of series, parallel, and standby structures. A binary decision diagram model for the same systems is also proposed by representing a multistate component as a single node. The performance of the two models in generating system reliability measures are compared numerically and qualitatively. Applications for a real-world system and finding optimal backup orderings are given.

Deep Q-learning based optimal resource allocation method for energy harvested cognitive radio networks

In this article, we propose a deep Q-learning based algorithm for optimal resource allocation in energy harvested cognitive radio networks (EH-CRN). In EH-CRN, channel resources of primary users (PU) networks are shared with secondary users (SU) and energy harvesting allows nodes of the CRN to acquire energy from the environment for operation sustainability. However, amount of energy harvested from the environment is not fixed and requires dynamic allocation of resources for obtaining optimum network and throughput capacity. In this work, we overcome the limitations of existing Q-learning based resource allocation schemes which are constrained by large state-space systems and have slow convergence. Proposed deep Q-learning based algorithm improves the resource allocation in EH-CRN, while considering quality of service (QoS), energy and interference constraints. Simulation results show that proposed algorithm provide improved convergence and better resource utilization compared to other techniques in literature.

CO2 Removal via an Environmental Green Solvent, K2CO3-Glycine (PCGLY): Investigative Analysis of a Dynamic and Control Study.

Promoted potassium carbonate with glycine has been actively investigated as a chemical solvent for the removal of CO2. Though a vast number of studies have been reported for potassium carbonate, dynamic studies regarding this promoted solvent are not yet extensively reported in the literature. In this work, a steady-state simulation has been performed via an equilibrium stage model in Aspen Plus V10 using the experimental data of an absorber from the bench scale pilot plant (MINI CHAS) located in Universiti Teknologi PETRONAS. In this study, 15 wt % K2CO3 + 3 wt % glycine is utilized as the medium for absorption, and the operating pressure is set at 40 bar to imitate the natural gas treatment process. The removal observed from the pilot plant is about 75% and the steady-state simulation with a tuned vaporization efficiency managed to replicate a similar result. The transient analysis is performed via activating a flow-driven method, and the simulation is transferred into Aspen Dynamic. A simple control strategy using a proportional–integral (PI) controller is installed at the gas outlet to monitor the CO2 composition, and further disturbances are introduced at the inlet gas flow rate using a step test and ramp test. The controller is tuned using a trial-and-error method and a satisfactory response is achieved under varying changes in the inlet gas flow rate. Further investigation is carried out using the model predictive controller (MPC), in which 5000 data points are generated through pseudorandom binary sequence (PRBS) analysis for state-space model system identification. The state-space model identified as the best is then used to design the MPC controller. A disturbance rejection test on the MPC controller is conducted via changing the gas flow rate at 5% and a quick response is observed. In conclusion, both MPC and PI controllers managed to produce a good response once the disturbance was introduced within the CO2–potassium carbonate–glycine (PCGLY) system.

Geometric decomposition of geodesics and null-phase curves using Majorana star representation

Geodesics are the shortest curves between any two points on a given surface. Geodesics in the state space of quantum systems play an important role in the theory of geometric phases, as these are also the curves along which the acquired geometric phase is zero. Null phase curves (NPCs) are the generalization of the geodesics, which are defined as the curves along which the acquired geometric phase is zero even though they need not be the shortest curves between two points. Here we present a geometric decomposition of geodesics and NPCs in higher-dimensional state space, which allows understanding the intrinsic symmetries of these curves. We use Majorana star representation to decompose a geodesic in the $n$-dimensional Hilbert space to $n-1$ curves on the Bloch sphere and show that all the $n-1$ curves are circular segments with specific properties that are determined by the inner product of the end states connected by the given geodesic. We also propose a method to construct infinitely many NPCs between any two arbitrary states for $(n>2)$-dimensional Hilbert space using our geometric decomposition.

A systematic method for the optimization of gas supply reliability in natural gas pipeline network based on Bayesian networks and deep reinforcement learning

This study proposes a method based on Bayesian networks (BNs) to optimize the reliability of gas supply in natural gas pipeline networks. The method integrates probabilistic safety analysis with preventive maintenance to achieve the targets of minimizing gas shortage risk and reducing maintenance costs. For this, the tasks of unit failure probability calculation, system maximum supply capacity analysis, gas supply reliability assessment and system maintenance planning are performed. A stochastic capacity network model is coupled with a Markov model and graph theory to generate the state space of the pipeline network system. BN, is then, proposed as the modeling framework to describe the stochastic behavior of unit failures and customer gas shortage. The system maintenance problem is converted into a Markov decision process (MDP), and solved by using deep reinforcement learning (DRL). The effectiveness of the proposed method is validated on a case study of a European gas pipeline network. The results show that the proposed method outperforms others in identifying optimal maintenance strategies. The DRL-optimized maintenance strategy is capable of responding to a dynamic environment through continuous online learning, considering the randomness of the unit failures and the uncertainty in gas demand profiles.

Data-driven state estimation toward blade individual load-reduction of wind turbines1

As wind turbines tend to be build larger every year, the importance of load-reducing controls to damp the rotor blade oscillations increases. For a control algorithm to perform blade individual load-reducing strategies, online information about each rotor blade’s deflection is needed. An approach for wind turbine state estimation with special attention to the rotor blade deflections is given using a Hammerstein model driven by simulation data in a Kalman Filter (KF). The Hammerstein’s linear submodel is mainly derived as time discrete state space system via least squares, while nonlinear effects are defined in terms of their proportionality. The model noise definition required by the KF is calculated by the system model’s one-step prediction error. The simulation results show the estimate to have a standard deviation of less than 2 % in edge and 9% in flap-wise direction when using an appropriate sensor configuration. Using state-of-the-art sensors, standard deviations of less than 4% and 25% respectively are achieved. The approach is particularly attractive due to the low level of tuning required. The usage of the state estimation in a closed control loop as well as the Hammerstein model in a model-based control system offer room for promising further investigations.

Zero-order hold discretization of general state space systems with input delay

Abstract Plethora of applications in physics and engineering are dealing with systems that are subject to input delays. Despite the scientific focus, previous research investigated only state space systems with input delays. Here, we investigate the discretization of generalized state space system with input delay by using the zero-order hold method. Firstly, the solution of a continuous time, generalized state space system with input delay is addressed. By applying the appropriate zero-order hold sampling method, we transform a continuous time linear system into the equivalent discrete time system, while the discrete time solution of the equivalent system is analytically presented. Finally, we use local error metric to estimate the difference between the continuous time and discrete time solutions.

Modal characteristics of electric vehicle powertrain considering electromagnetic effect

In this paper, the modal characteristics of an electric powertrain considering electromagnetic effect are directly obtained by solving the parameter matrix of the system state space equation. Open loop controller and PI controller are applied to the electric powertrain respectively. The natural frequencies and mode shapes under different loads and PI controller gains are studied. The influence of electromagnetic effect on gear load and motor current under impact load is also analyzed. Results indicate that the magnetic field and the PI controller introduce a low-order rotational mode respectively. These two modes play a significant role in the load impact process. Furthermore, the natural frequencies of the low-order modes change with the load and PI controller gains. The results provide theoretical support for electromechanical system design and dynamic load research.

Composition of Multipartite Quantum Systems: Perspective from Timelike Paradigm.

Figuring out the physical rationale behind natural selection of quantum theory is one of the most acclaimed quests in quantum foundational research. This pursuit has inspired several axiomatic initiatives to derive a mathematical formulation of the theory by identifying the general structure of state and effect space of individual systems as well as specifying their composition rules. This generic framework can allow several consistent composition rules for a multipartite system even when state and effect cones of individual subsystems are assumed to be quantum. Nevertheless, for any bipartite system, none of these compositions allows beyond quantum spacelike correlations. In this Letter, we show that such bipartite compositions can admit stronger-than-quantum correlations in the timelike domain and, hence, indicates pragmatically distinct roles carried out by state and effect cones. We discuss consequences of such correlations in a communication task, which accordingly opens up a possibility of testing the actual composition between elementary quanta.

A high-fidelity building performance simulation test bed for the development and evaluation of advanced controls

We present an open-source building performance simulation test bed, the Advanced Controls Test Bed (ACTB), that interfaces high-fidelity Spawn of EnergyPlus building models, with advanced controllers implemented in Python. The ACTB leverages the Building Optimization Testing and Alfalfa platforms for managing simulations, providing an external clock, a representational state transfer (REST) application programming interface (API), and key performance indicators for evaluating the effectiveness of control strategies. The REST API allows the development of external controllers programmed in languages such as Python, which provides flexibility and a rich choice of scientific libraries for designing control sequences. We present three test cases based on the U.S. Department of Energy's Reference Small Office Building to demonstrate the ACTB's capabilities: (a) rule-based controls compliant with ASHRAE Guideline 36 control sequences; (b) an economic model predictive control implemented using do-mpc; and (c) a deep Q-network reinforcement learning agent implemented using OpenAI Gym. Abbreviations: ACTB: Advanced Controller Test Bed; AHU: Air Handling Unit; AI:Artificial Intelligence; API: Application Programming Interface; BEM: Building EnergyModeling; BSS: Best Subset Selection; DOE: Department of Energy; DQN: Deep-QNetwork; EKF: Extended Kalman Filter; FMI: Functional Mock-up Interface; FMU:Functional Mock-up Unit; FSS: Forward Stepwise Selection; HVAC: Heating; Ventilationand Air Conditioning; KPI: Key Performance Indicator; LTI: Linear Time-Invariant; MBL: Modelica Buildings Library; MHE: Moving Horizon Estimator; MPC: ModelPredictive Control; N4SID: Numerical Subspace State-Space System Identification; REST: Representational State Transfer; RL: Reinforcement Learning; ROM: Reducedorder model

Average Controllability of Complex Networks With Laplacian Dynamics

The trace of the controllability Gramian quantifies the average controllability in all directions in the system state space. In this paper, we investigate the average controllability of a semistable networked system with Laplacian dynamics and derive upper and lower bounds on the trace of its pseudo-controllability Gramian matrix. We show that these bounds are solely determined by the network topology, which can be obtained without computing any higher-dimensional matrix. We find that a sparse or a scale-free network is easy to control in terms of the average controllability. We then investigate the effect of the edges with negative weights on the average controllability for a signed network with Laplacian dynamics. We find that a small number of negatively-weighted edges can significantly affect the average controllability of the signed network. We finally demonstrate that many real-world networks are easy to control via manipulating negatively-weighted edges.

Molecular Weight Distribution Control for Polymerization Processes Based on the Moment-Generating Function.

The molecular weight distribution is an important factor that affects the properties of polymers. A control algorithm based on the moment-generating function was proposed to regulate the molecular weight distribution for polymerization processes in this work. The B-spline model was used to approximate the molecular weight distribution, and the weight state space equation of the system was identified by the subspace state space system identification method based on the paired date of B-spline weights and control inputs. Then, a new performance criterion mainly consisting of the moment-generating function was constructed to obtain the optimal control input. The effectiveness of the proposed control method was tested in a styrene polymerization process. The molecular weight distribution of the styrene polymers can be approximated by the B-spline model effectively, and it can also be regulated towards the desired one under the proposed control method.

Disturbance Rejection Analysis of a Droop-Controlled DC Microgrid Through a Novel Mathematical Modeling

DC microgrids are gaining interest by the increase in dc loads and renewable resource penetrations. Photovoltaic (PV) arrays are the primary renewable resources utilized in dc microgrids with variations in their productions. Power variations are seen as disturbances from other sources’ point of view. The droop control method is frequently used to control dc microgrids and assures power sharing among parallel-connected converters. It is of great interest to assess droop controller functionality in rejecting disturbances, and maintain constant output voltage. Therefore, there is a need for a comprehensive converter and controller modeling to study the effect of disturbances on the system behavior. In this article, the converter’s small-signal model is utilized in deriving the system state space model. Via the derived model, the effect of different circuit parameters on time and frequency responses is studied. The line resistances’ effect on the parallel operation of converters is also studied. To verify the droop controller’s functionality, the converter’s output impedance is derived. Disturbances are applied to the load current, and the system response is analyzed. Finally, the dc microgrid plug and play feature is addressed by proposing an algorithm for deriving the multiple converters’ mathematical model. Simulations and hardware-in-the-loop (HIL) experiments are conducted to verify the mathematical model and controllers’ performance.

Singular Spectrum Analysis for Modal Estimation from Stationary Response Only.

Conventional experimental modal analysis uses excitation and response information to estimate the frequency response function. However, many engineering structures face excitation signals that are difficult to measure, so output-only modal estimation is an important issue. In this paper, singular spectrum analysis is employed to construct a Hankel matrix of appropriate dimensions based on the measured response data, and the observability of the system state space model is used to treat the Hankel matrix as three components containing system characteristics, excitation and noise. Singular value decomposition is used to factorize the data matrix and use the characteristics of the left and right singular matrices to reduce the dimension of the data matrix to improve calculation efficiency. Furthermore, the singular spectrum is employed to estimate the minimum order to reconstruct the Hankel matrix; then, the excitation and noise components can be removed, and the system observability matrix can be obtained. By appropriately a factorizing system observability matrix, we obtain the system matrix to estimate the modal parameters. In addition, the fictitious modes produced by increasing the order of the matrix can be eliminated through the stabilization diagram.

Modal identification of high-rise buildings under earthquake excitations via an improved subspace methodology

The subspace state-space system identification method has drawn extensive attention in structural modal identification, which is generally involved with the stabilization diagram for estimating structural modal parameters. However, the conventional stabilization diagram has an inherent problem, i.e., some spurious modes may be identified as stable results, leading to the adverse effect on structural modal identification. To address this issue, this paper proposes an improved subspace algorithm, in which a Monte Carlo-based stabilization diagram is involved. The performance of the Monte Carlo-based stabilization diagram for discriminating the poles denoting the physical modes from those representing spurious modes is demonstrated through a numerical study. The simulation results further prove that the proposed method can accurately estimate the time-varying structural modal parameters. Moreover, the proposed method is applied to field measurements on a 218-m-tall building during the 1994 Northridge earthquake event, and the identified results verify the applicability and effectiveness of the proposed method in field measurements. This paper aims to provide an effective tool for modal identification of high-rise buildings under earthquake excitations.

Process knowledge-based random forest regression for model predictive control on a nonlinear production process with multiple working conditions

In process industry, predictive control approaches have been widely used for nonlinear production processes. Practically, the predictor in a predictive controller is extremely important since it provides future states for the optimization problem of controllers. The conventional predictive controller with precise mathematical predictors approximating the state space of physical systems is difficult and time-consuming for nonlinear production processes, and it performs poorly over a wide range of working conditions and with significant disturbances. To address the challenges, the trend of applying artificial intelligence emerges. However, the industrial process-specific knowledge is ignored in most cases. In this study, a predictive controller with a control process knowledge-based random forest (RF) model is proposed. Specifically, working data are clustered at first to handle diverse working conditions. Then, a process knowledge-based forest predictor, namely MIW-RF model with a redesigned cascading RF structure, is proposed to incorporate control process knowledge into modeling. Thus, future states of controlled variables could be more accurately acquired for the optimizer. A simplified version of the predictive model is also developed with quick model training and updating. The proposed predictive methods are finally introduced into the controller design. According to the empirical results, the proposed methods deliver a better control performance against benchmarks, including more accurate anticipated controlled-variable responses, better set-point tracking and disturbance rejection capability.

Proactive inhibition is marked by differences in the pattern of motor cortex activity during movement preparation and execution.

Successful human behavior relies on the ability to flexibly alter movements depending on the context in which they are made. One such context-dependent modulation is proactive inhibition, a type of behavioral inhibition used when anticipating the need to stop or change movements. We investigated how the motor cortex might prepare and execute movements made under different contexts. We used transcranial magnetic stimulation (TMS) in different coil orientations [postero-anterior (PA) and antero-posterior (AP) flowing currents] and pulse widths (120 and 30 µs) to probe the excitability of different inputs to corticospinal neurons while participants performed two reaction time tasks: a simple reaction time task and a stop-signal task requiring proactive inhibition. We took inspiration from state space models to assess whether the pattern of motor cortex activity changed due to proactive inhibition (PA and AP neuronal circuits represent the x and y axes of a state space upon which motor cortex activity unfolds during motor preparation and execution). We found that the rise in motor cortex excitability was delayed when proactive inhibition was required. State space visualizations showed altered patterns of motor cortex activity (combined PA120 and AP30 activity) during proactive inhibition, despite adjusting for reaction time. Overall, we show that the pattern of neural activity generated by the motor cortex during movement preparation and execution is dependent upon the context under which the movement is to be made.NEW & NOTEWORTHY Using directional TMS, we find that the human motor cortex flexibly changes its pattern of neural activity depending on the context in which a movement is due to be made. Interestingly, this occurs despite adjusting for reaction time. We also show that state space and dynamical systems models of movement can be noninvasively visualized in humans using TMS, thereby offering a novel method to study these powerful models in humans.

Parameter Sensitivity Analysis of a Brake Pressure Control System in Aviation Using an Electro-Hydraulic Servo Valve

The landing gear system has the task of bearing the weight of the aircraft, bearing the impact load, and providing the braking function in the process of the aircraft taxiing, take-off, and landing. There are many parameters in the aviation brake pressure servo valve-controlled cylinder system (ABPSVCS) which will have a significant influence on the dynamic behavior of the system. Sensitivity analysis is an effective method to analyze the influence of system parameters on system characteristics, especially for nonlinear systems. The trajectory sensitivity method based on the description of system state space is used for the parameter sensitivity analysis of the ABPSVCS. By grouping various parameters for sensitivity analysis, the law of parameter sensitivity of each group is obtained, and the results are verified by experiments. The results can lay a theoretical and experimental foundation for the related research work of the aviation brake pressure servo valve.