Reduced-order Dynamic Model Research Articles

Dynamic reduced order modeling of an entrained-flow slagging gasifier using a new recirculation ratio correlation

This study presents a dynamic reduced order model (ROM) that describes the transient behaviour of an entrained-flow slagging gasifier. A new correlation for estimation of the recirculation ratio in the ROM’s reactor network is presented in this work by using the ROM and experimental data. The proposed correlation improves the well-known method of Thring and Newby for jet-flow recirculation by adding a term that takes into account the changes in the feed streams (multi-phase jet and secondary flows) on the recirculation. This feature enhances the prediction capabilities of the reactor network, especially in dynamic simulations where the inlet flowrates may change over time, e.g., for load-following power plants. The proposed dynamic ROM has been validated using steady-state and transient experimental data. Furthermore, the dynamic responses of dry syngas composition, temperature distribution, cold gas efficiency, slag thickness and flowrate were studied under load-following and co-firing (petroleum coke/coal) scenarios.

A Fast, Memory-Efficient Discrete-Time Realization Algorithm for Reduced-Order Li-Ion Battery Models

Research into reduced-order models (ROM) for Lithium-ion batteries is motivated by the need for a real-time embedded model possessing the accuracy of physics-based models, while retaining computational simplicity comparable to equivalent-circuit models. The discrete-time realization algorithm (DRA) proposed by Lee et al. (2012, “One-Dimensional Physics-Based Reduced-Order Model of Lithium-Ion Dynamics,” J. Power Sources, 220, pp. 430–448) can be used to obtain a physics-based ROM in standard state-space form, the time-domain simulation of which yields the evolution of all the electrochemical variables of the standard pseudo-2D porous-electrode battery model. An unresolved issue with this approach is the high computation requirement associated with the DRA, which needs to be repeated across multiple SoC and temperatures. In this paper, we analyze the computational bottleneck in the existing DRA and propose an improved scheme. Our analysis of the existing DRA reveals that singular value decomposition (SVD) of the large Block–Hankel matrix formed by the system's Markov parameters is a key inefficient step. A streamlined DRA approach that bypasses the redundant Block–Hankel matrix formation is presented as a drop-in replacement. Comparisons with existing DRA scheme highlight the significant reduction in computation time and memory usage brought about by the new method. Improved modeling accuracy afforded by our proposed scheme when deployed in a resource-constrained computing environment is also demonstrated.

Structured Identification of Reduced-Order Models of Power Systems in a Differential-Algebraic Form

In a recent paper, we proposed a system identification method for constructing reduced-order models for the electro-mechanical dynamics of large power systems, divided into multiple coherent clusters, using Synchrophasors. Every cluster in the actual model was represented as an aggregate generator in the reduced-order model. An aggregate network graph connected one aggregate generator to another. In this paper, we extend this identification approach to differential-algebraic (DAE) models. First, every cluster is associated with a unique terminal bus, referred to as the pilot bus, that couples its internal network to the rest of the system. The proposed algorithm uses Synchrophasor measurements from the pilot buses to identify the dynamic model of the aggregate generator for each cluster using nonlinear least squares while retaining the identity of all the pilot buses. The resulting reduced-order model is in the form of a nonlinear electric circuit described by aggregate differential and algebraic equations. We illustrate our results using two case studies, one for the IEEE 9-bus power system and another for the IEEE 39-bus power system. We also discuss how these reduced-order DAE models may be useful for designing shunt controllers at the pilot buses by using Synchrophasor feedback.

Dynamic Balance Optimization and Control of Quadruped Robot Systems With Flexible Joints

This paper investigates dynamic balance optimization and control of quadruped robots with compliant/flexible joints under perturbing external forces. First, we formulate a constrained dynamic model of compliant/flexible joints for quadruped robots and a reduced-order dynamic model is developed considering the robot interaction with the environment through multiple contacts. A dynamic force distribution approach based on quadratic objective function is proposed for evaluating the optimal contact forces to cope with the external wrench, and fuzzy-based adaptive control of compliant/flexible joints for quadruped robots is proposed to suppress uncertainties in the dynamics of the robot and actuators. The dynamic surface control approaches and fuzzy learning algorithms are combined in the proposed framework. All the signals of the closed-loop system have proven to be uniformly ultimately bounded through Lyapunov synthesis. Simulation experiments were performed for a quadruped robot with compliant/flexible joints. The benefits of its tracking accuracy and robustness indicate that the proposed framework is promising for the robots with payload uncertainties and external disturbances.

A Wideband Equivalent Model of Type-3 Wind Power Plants for EMT Studies

This paper presents the development and validation of an accurate and computationally efficient wideband reduced-order dynamic equivalent model for the Type-3-based wind power plant (WPP). The proposed Type-3 WPP equivalent model reproduces the dynamic behavior of the WPP in response to an electromagnetic transient in the host power system and is composed of two parts: 1) a static frequency-dependent network equivalent model which represents the response of all passive components of the WPP in a wideband frequency range, and 2) a dynamic low-frequency equivalent model that represents the aggregated dynamic model of the doubly-fed asynchronous generator (which is also referred to as doubly-fed induction generator) wind turbine generators, their local controls, and the WPP supervisory control. The proposed model significantly reduces the hardware/software computational burden and the computation time, as compared to the WPP detailed models, without compromising the accuracy of the simulation results. The proposed model is incorporated as a software module in the PSCAD/EMTDC environment and its computational efficiency and accuracy are verified based on comparing the results with those of a detailed model.

Hierarchical Model Predictive Control of independent systems with joint constraints

This paper describes a hierarchical scheme for the control of independent stable systems subject to joint constraints. At the higher layer of the control structure reduced order dynamic models are used to minimize an economic cost function by adopting a long sampling time, while at the lower layer independent shrinking horizon MPC controllers working at a faster rate are designed for the original models to guarantee stability and convergence. A novel model reduction procedure is developed and simulation results are reported to witness the potentialities of the approach.

A Kalman Latency Compensation Strategy for Model Predictive Control to Damp Inter-Area Oscillations in Delayed Power Systems

Power systems control strategies that use global signals have shown better results than those based on local signals, but the remote signals are usually taken far away from the control center. Because of that, wide area power systems controlled using global signals are inherently delayed, and time delays jeopardize the stability of power systems. This paper presents a Kalman based time delay compensation strategy, which feed a Model Predictive Control (MPC) scheme to damp inter-area oscillations in power systems with latencies in their communications. A Kalman state estimator is employed to get the states. The proposal uses a dynamic reduced order model obtained using Hankel singular values. The methodology is promissory because it considers time delays in control schemes design processes, useful for either centralized or distributed wide area power system controllers based on widespread metering. This approach was validated for controlling inter-area oscillations in a test power system with two areas, 4 generators and a tie power line. Results suggest an enhancement of the power system dynamic performance upon the application of the method proposed.

An Approximate Analytical Solution for Dynamic Response of a Large Nonlinear Rotor-Bearing System

Large nonlinear rotor-bearing system is an important structure in rotating machinery, such as NC machine. Due to the mass imbalance of the system, vibrations induced by centrifugal forces inevitably exist in rotating machinery. So, nonlinear dynamic response of a complex rotor-bearing system was dealt with in this paper. The system considered was modeled using the finite element method and has 124 DOFs (degrees of freedom). A linear reduction method was used and a reduced-order dynamic model of the system with two DOFs had been obtained. Harmonic balance method was applied to the reduced-order dynamic model of the system and an approximate analytical expression of the solution for nonlinear dynamic response of the system at steady state was derived. The analytical solution obtained from the reduced-order dynamic model of the system was compared with the numerical one obtained from the direct integration of the equations of motion of the original system.

Dynamical balance optimization and control of biped robots in double-support phase under perturbing external forces

To realize the dynamic balance optimization and control of biped robots under the perturbing external forces in the double-support phase, a systematic scheme is proposed in this paper. First, a constrained dynamic model of biped robots and a reduced order dynamical model for the double-support phase are formulated. Considering the dynamic external wrench applied on biped robots, we present a dynamic force distribution approach based on quadratic objective function for computing the optimal contact forces to equilibrate the dynamic external wrench. As a result, the sum of the normal force components is minimized for enhancing safety and energy saving. Then, one primary recurrent neural network (RNN) is adopted to solve the optimization problem subject to both equality and inequality constraints. For the derived optimized contact force and motion, hybrid motion/force control is proposed based on another RNN to approximate unknown dynamic functions. Adaptive learning algorithms for learning the parameters of the RNN are provided as well. The proposed control can deal with the uncertainties including approximation errors and external disturbances. Extensive simulations are presented to demonstrate the effectiveness of the proposed optimization and control approach.

Christchurch Women’s Hospital: Performance Analysis of the Base-Isolation System during the Series of Canterbury Earthquakes 2011–2012

AbstractLive monitoring data and simple dynamic reduced-order models of the Christchurch Women’s Hospital (CWH) help explain the performance of the base-isolation (BI) system of the hospital during the series of Canterbury earthquakes in 2011–2012. A Park-Wen-Ang hysteresis model is employed to simulate the performance of the BI system and results are compared to measured data recorded above the isolation layer and on the sixth story. Simplified single, two, and three degree-of-freedom models (SDOF, 2DOF, and 3DOF) show that the CWH structure did not behave as an isolated but as a fixed-base structure. Comparisons of accelerations and deflections between simulated and monitored data show a good match for isolation stiffness values of approximately two times of the value documented in the design specification and test protocol. Furthermore, an analysis of purely measured data revealed very little to no relative motion across the isolators for large events of moment magnitude scale (Mw) 5.8 and 6.0 that occ...

Linear and nonlinear free vibrations of electrostatically actuated micro-/nanomechanical resonators

This paper is concerned with linear and nonlinear free vibrations of an axially stressed clamped---clamped micro-/nanobeam actuated by one-sided electrode configuration. Galerkin procedure and a proper shape function are used to establish a dynamic reduced-order model, where the integral of the electromechanical forcing term is obtained in an explicit and closed form. This model makes the analysis of dynamic behaviors convenient for the micro-/nanobeam. For linear free vibration, the fundamental natural frequency formulas of the system are validated by comparing with published experiment data while the Newton method coupled with the harmonic balance method is developed to obtain analytical approximate period and periodic solution for the nonlinear system. These approximate solutions have explicit expressions and they can readily be used to derive the effects of various physical parameters on dynamic behavior of micro-/nanobeams. Exact solution in an integral form is also presented. For small as well as large amplitudes of nonlinear vibration, the new analytical approximate solutions show excellent agreement with respect to the numerically integrated solutions obtained from the integral-form exact solutions.

Dynamic response and governor tuning of a long penstock pumped-storage hydropower plant equipped with a pump-turbine and a doubly fed induction generator

In this paper, the dynamic response of a long penstock pumped-storage hydropower plant which is equipped with a single pump-turbine and a doubly-fed induction machine, is analyzed in detail in generating mode. The pumped-storage hydropower plant is connected to a small island power system with thermal generation, and provides load–frequency control under the orders of an automatic generation control system. The output power of the pumped-storage hydropower plant is assumed to be controlled by the rotor-side frequency converter. The unit running speed is controlled by an isochronous PI governor. The dynamic response of the pumped-storage hydropower plant is analyzed by using a linearized reduced order dynamic model, which considers the elastic water column effects in the penstock. Two governor tuning criteria are proposed in the paper: one is devised from the root locus analysis of the plant dynamic model, and the other one is based on a Pareto approach. The proposed tuning criteria are compared with each other and with a recently published tuning criterion through a set of commonly used performance indexes and by means of simulations with a nonlinear dynamic model.

Hybrid position–force control for constrained reconfigurable manipulators based on adaptive neural network

This article presents a hybrid position–force control method based on adaptive neural network for addressing the problems of position and force tracking of a constrained reconfigurable manipulator. The reduced-order dynamic model of a reconfigurable manipulator is formulated considering the model uncertainty and the external constraint. Combining decentralized control with centralized control scheme, a hybrid position–force controller is designed for controlling the position and force of the constrained reconfigurable manipulator. The dynamic model uncertainty and the dynamic coupling effect are compensated by radial basis function neural network. The stability of the closed-loop system is proved using the Lyapunov theory. Finally, simulations are performed to study the effectiveness of the proposed method.

Control of a Cable-Driven Platform in a Master–Slave Robotic System: Linear Parameter Varying Approach

Space restrictions prevent surgeons to directly interact with the patient during magnetic resonance imaging (MRI)-guided procedures. One practical solution would be to develop a robotic system that can act as an interface between surgeon and patient during those interventions. The proposed system consists of a commercial PHANTOM device (product of The Sensable Technologies) as the master robot and an MRI-compatible patient-mounted parallel platform (that we name ROBOCATHETER) designed to serve as the slave mechanism inside the scanner bore. As the main contribution of this paper, a linear parameter varying (LPV) gain-scheduling controller is designed and implemented to obtain the desired performance of the slave robot in tracking set points and reference trajectories. To do so, a reduced-order dynamic model of the robot based on the Lagrange method is derived to capture the nonlinear dynamics of the platform. The model is then used for the design of an output-feedback LPV controller to command the robot to position the catheter in any desired states. During the course of control, appropriate selection of scheduling parameters not only helps to compensate for the nonlinearities of the system dynamics but also leads to a set of decoupled models for the system, where each degree-of-freedom (DOF) could be treated separately. The performance of the controller is compared with a variable-gain proportional-derivative-integral (PID) controller. Experimental results show that the proposed control scheme has significant advantages in terms of set point tracking and actuator saturation over the baseline PID controller.

Dynamic Reduced Order Models for Simulating Bubbling Fluidized Bed Adsorbers

Spatially distributed first-principles process models provide an accurate physical description of chemical processes, but lead to large-scale models whose numerical solution can be challenging and computationally expensive. Therefore, fast reduced order models are required for model-based real-time applications, such as advanced process control and dynamic real-time optimization. In this paper, we focus on the model reduction of a bubbling fluidized bed (BFB) adsorber, which is a key component of a postcombustion carbon capture system. From a temporal aspect, dynamic reduced models are generated using the nullspace projection and eigenvalue analysis method, with the basic idea of quasi-steady state approximation for the states with fast dynamics. From a spatial aspect, dynamic reduced models are developed using orthogonal collocation and proper orthogonal decomposition to reduce the size of the rigorous model. Finally, a computationally efficient and accurate dynamic reduced model is developed for the BFB...

Impedance Matching in Photovoltaic Systems Using Cascaded Boost Converters and Sliding-Mode Control

Switching dc–dc converters are widely used to interface the dc output of renewable energy resources with power distribution systems in order to facilitate the use of energy at the customer side. In the case of residential photovoltaic (PV) applications, high conversion ratio is usually required, in order to adapt the low output voltages of PV modules to a dc bus voltage, while dealing with the appropriate impedance matching. In this paper, a system connected to a PV panel consisting of two cascaded dc–dc boost converters under sliding-mode control and working as loss-free resistors is studied. The modeling, simulation, and design of the system are addressed. First, an ideal reduced-order sliding-mode dynamics model is derived from the full-order switched model taking into account the sliding constraints, the nonlinear characteristic of the PV module, and the dynamics of the MPPT controller. For this model, a design-oriented averaged model is obtained and its dynamic behavior is analyzed showing that the system is asymptotically globally stable. Moreover, the proposed system can achieve a high conversion ratio with an efficiency close to 95 $\%$ for a wide range of working power. Numerical simulations and experimental results corroborate the theoretical analysis and illustrate the advantages of this architecture in PV systems.

Dynamic data-driven reduced-order models

Abstract Data-driven model reduction constructs reduced-order models of large-scale systems by learning the system response characteristics from data. Existing methods build the reduced-order models in a computationally expensive offline phase and then use them in an online phase to provide fast predictions of the system. In cases where the underlying system properties are not static but undergo dynamic changes, repeating the offline phase after each system change to rebuild the reduced-order model from scratch forfeits the savings gained in the online phase. This paper proposes dynamic reduced-order models that break with this classical but rigid approach. Dynamic reduced-order models exploit the opportunity presented by dynamic sensor data and adaptively incorporate sensor data during the online phase. This permits online adaptation to system changes while circumventing the expensive rebuilding of the model. A computationally cheap adaptation is achieved by constructing low-rank updates to the reduced operators. With these updates and with sufficient and accurate data, our approach recovers the same model that would be obtained by rebuilding from scratch. We demonstrate dynamic reduced-order models on a structural assessment example in the context of real-time decision making. We consider a plate in bending where the dynamic reduced-order model quickly adapts to changes in structural properties and achieves speedups of four orders of magnitude compared to rebuilding a model from scratch.

Parametric reduced order dynamical model construction of a fluid flow control problem

The problem of approximating a given fluid flow control problem, governed by the Navier-Stokes equations at varying Reynolds number, with a low-order parametric linear dynamical model, is presented. To this aim, a three steps approach is proposed: first, (i) the original Reynolds number dependent fluid flow problem is spatially and parametrically discretized, then (ii) each resulting local very large-scale Linear Time Invariant (LTI) Differential Algebraic Equations (DAE) models are approximated using the IRKA approach proposed by Gugercin et al. (2008), and finally (iii), the reduced order models are interpolated and transformed into a low-complexity Linear Fractional Representation (LFR). The overall process is illustrated in a top down framework using a generic flow configuration, namely, an open cavity flow. Numerical simulations assess the validity of the approach.

Electrochemical state and internal variables estimation using a reduced-order physics-based model of a lithium-ion cell and an extended Kalman filter

This paper addresses the problem of estimating the present value of electrochemical internal variables in a lithium-ion cell in real time, using readily available measurements of cell voltage, current, and temperature. The variables that can be estimated include any desired set of reaction flux and solid and electrolyte potentials and concentrations at any set of one-dimensional spatial locations, in addition to more standard quantities such as state of charge. The method uses an extended Kalman filter along with a one-dimensional physics-based reduced-order model of cell dynamics. Simulations show excellent and robust predictions having dependable error bounds for most internal variables.

On model reduction for quantum dynamics: symmetries and invariant subspaces

Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized quantum Hamiltonians. In particular, we first formulate an algebraic condition that certifies the existence of invariant subspaces for a model defined by a parameterized Hamiltonian and an initial state. Following this we develop and analyze two methods to explicitly construct a reduced-order model, if one exists. In addition to general results characterizing invariant subspaces of arbitrary finite dimensional Hamiltonians, by exploiting properties of the generalized Pauli group we develop practical tools to speed up simulation of dynamics generated by certain spin Hamiltonians. To illustrate the methods developed we apply them to several paradigmatic spin models.