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Dabadghao, V., D.A. Allan, M. Li, J.C. Eslick, J. Ma, S.E. Zitney, D. Bhattacharyya, and L.T. Biegler, “Nonlinear Model Predictive Control for Solid-Oxide Electrolysis Cell Systems,” AIChE 2022 Annual Meeting, Phoenix, AZ, November 13-18 (2022).
The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.
Abstract Despite the significant potential of solar thermochemical process technology for storing solar energy as solid-state solar fuel, several challenges have made its industrial application difficult. It is important to note that solar energy has a transient nature that causes instability and reduces process efficiency. Therefore, it is crucial to implement a robust control system to regulate the process temperature and tackle the shortage of incoming solar energy during cloudy weather. In our previous works, different model-based control strategies were developed namely a proportional integral derivative controller (PID) with gain scheduling and adaptive model predictive control (MPC). These methods were tested numerically to regulate the temperature inside a high-temperature tubular solar reactor. In this work, the proposed control strategies were experimentally tested under various operation conditions. The controllers were challenged to track different setpoints (500 °C, 1000 °C, and 1450 °C) with different amounts of gas/particle flowrates. Additionally, the flow controller was tested to regulate the reactor temperature under a cloudy weather scenario. The ultimate goal was to produce 5 kg of reduced solar fuel magnesium manganese oxide (MgMn2O4) successfully, and the controllers were able to track the required process temperature and reject disturbances despite the system's strong nonlinearity. The experimental results showed a maximum error in the temperature setpoint of less than 0.5% (6 °C), and the MPC controller demonstrated superior performance in reducing the control effort and rejecting disturbances.
The flavor evolution of neutrinos in core collapse supernovae and neutron star mergers is a critically important unsolved problem in astrophysics. Following the electron flavor evolution of the neutrino system is essential for calculating the thermodynamics of compact objects as well as the chemical elements they produce. Accurately accounting for flavor transformation in these environments is challenging for a number of reasons, including the large number of neutrinos involved, the small spatial scale of the oscillation, and the nonlinearity of the system. We take a step in addressing these issues by presenting a method which describes the neutrino fields in terms of angular moments. We apply our moment method to neutron star merger conditions and show it simulates fast flavor neutrino transformation in a region where this phenomenon is expected to occur. By comparing with particle-in-cell calculations we show that the moment method is able to capture the three phases of growth, saturation, and decoherence, and correctly predicts the lengthscale of the fastest growing fluctuations in the neutrino field.
Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem.
The decoupled control of the nonlinear, multiinput-multioutput, and highly coupled space station furnace facility (SSFF) thermal control system is addressed. Sliding mode control theory, a subset of variable-structure control theory, is employed to increase the performance, robustness, and reliability of the SSFF's currently designed control system. This paper presents the nonlinear thermal control system description and develops the sliding mode controllers that cause the interconnected subsystems to operate in their local sliding modes, resulting in control system invariance to plant uncertainties and external and interaction disturbances. The desired decoupled flow-rate tracking is achieved by optimization of the local linear sliding mode equations. The controllers are implemented digitally and extensive simulation results are presented to show the flow-rate tracking robustness and invariance to plant uncertainties, nonlinearities, external disturbances, and variations of the system pressure supplied to the controlled subsystems.
Analysis of a typical nonlinear electrohydraulic servo-model establishes the dynamic-performance capabilities of servo-actuation systems.
Approach for generating stability criteria, applying odd function and power law nonlinearity
Wavelets present a method for signal processing that may be useful for analyzing responses of dynamical systems. This paper describes several wavelet-based tools that have been developed to improve the efficiency of flight flutter testing. One of the tools uses correlation filtering to identify properties of several modes throughout a flight test for envelope expansion. Another tool uses features in time-frequency representations of responses to characterize nonlinearities in the system dynamics. A third tool uses modulus and phase information from a wavelet transform to estimate modal parameters that can be used to update a linear model and reduce conservatism in robust stability margins.
Wavelets present a method for signal processing that may be useful for analyzing responses of dynamical systems. This paper describes several wavelet-based tools that have been developed to improve the efficiency of flight flutter testing. One of the tools uses correlation filtering to identify properties of several modes throughout a flight test for envelope expansion. Another tool uses features in time-frequency representations of responses to characterize nonlinearities in the system dynamics. A third tool uses modulus and phase information from a wavelet transform to estimate modal parameters that can be used to update a linear model and reduce conservatism in robust stability margins.
The inverse problem of the optimal regulator is considered for a general class of multi-input systems with integral-type performance indices. A new phase variable canonical form is shown to be convenient for this analysis. The advantage of the canonical form is to separate the state variables into subvectors of directly controlled, indirectly controlled, and uncontrollable components. Necessary and sufficient conditions for optimized performance indices are given. With the nonlinearities of the system restricted to functions of the directly controlled state variables, additional results are developed about the nonnegative property of optimized loss functions.
The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.
Two acentric thiophosphate compounds, HfP 2 S 6 and α-Ag 4 P 2 S 6 , are revisited and studied as infrared nonlinear optical materials. HfP 2 S 6 and α-Ag 4 P 2 S 6 were structurally characterized without any property measurements. Here, in this work, HfP 2 S 6 and α-Ag 4 P 2 S 6 were synthesized via high temperature salt flux reactions. Low-temperature polymorph acentric α-Ag 4 P 2 S 6 was purified and grown as mm-sized crystals with the aid of AgBr flux. The AgBr flux was revealed to play an important role in stabilizing the acentric α-Ag 4 P 2 S 6 . The acentric α-Ag 4 P 2 S 6 transforms to centrosymmetric β-Ag 4 P 2 S 6 at 850(5) K, which is revealed by differential scanning calorimetry (DSC) analysis and powder X-ray diffraction experiments. HfP 2 S 6 and α-Ag 4 P 2 S 6 are discovered by UV-vis spectrum measurements as indirect bandgap semiconductors with bandgaps of 2.2(1) eV and 2.5(1) eV, respectively, which is supported by DFT calculations and TB-LMTO-ASA calculations. The bonding pictures of α-Ag 4 P 2 S 6 were studied by crystal orbital Hamilton population calculations (COHP) coupled with electron localization function (ELF) analysis. DFT calculations predict that HfP 2 S 6 and α-Ag 4 P 2 S 6 would exhibit different optical performances regardless of being constructed from identical [P 2 S 6 ] motifs. HfP 2 S 6 exhibits a low second harmonic generation (SHG) response, ~0.21 × AGS (for the sample of particle size of 25 μm). α-Ag 4 P 2 S 6 possesses moderate SHG response, ~0.61 × AGS (for the sample of particle size of 225 μm) coupled with a high laser damage threshold (LDT) of ~3.2 × AGS. Characteristics of high ambient stability, moderate bandgap and SHG response, type-I phase-matching capability, and high LDT together with the easy growth of large crystals make α-Ag 4 P 2 S 6 attractive for future infrared nonlinear optical applications. Photocurrent measurements found that α-Ag 4 P 2 S 6 and β-Ag 4 P 2 S 6 have high photocurrent response, 165 nA cm -2 and 135 nA cm -2 , respectively. α-Ag 4 P 2 S 6 is a new multifunctional material of the ternary Ag–P–S system, which combines nonlinear optical (NLO) properties and photocurrent response.
A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.
Foil bearings provide noncontacting rotor support through a number of thin metal strips attached around the circumference of a stator and separated from the rotor by a fluid film. The resulting support stiffness is dominated by the characteristics of the foils and is a nonlinear function of the rotor deflection. The present study is concerned with characterizing this nonlinear effect and investigating its influence on rotordynamical behavior. A finite element model is developed for an existing bearing, the force versus deflection relation characterized, and the dynamics of a sample rotor system are studied. Some conclusions are discussed with regard to appropriate ranges of operation for such a system.
Patterned nanomagnet arrays (PNAs) have been shown to exhibit a strong geometrically frustrated dipole interaction. Some PNAs have also shown emergent domain wall dynamics. Previous works have demonstrated methods to physically probe these magnetization dynamics of PNAs to realize neuromorphic reservoir systems that exhibit chaotic dynamical behavior and high-dimensional nonlinearity. These PNA reservoir systems from prior works leverage echo state properties and linear/nonlinear short-term memory of component reservoir nodes to map and preserve the dynamical information of the input time-series data into nondelay spatial embeddings. Such mappings enable these PNA reservoir systems to imitate and predict/forecast the input time series data. However, these prior PNA reservoir systems are based solely on the nondelay spatial embeddings obtained at component reservoir nodes. As a result, they require a massive number of component reservoir nodes, or a very large spatial embedding (i.e., high-dimensional spatial embedding) per reservoir node, or both, to achieve acceptable imitation and prediction accuracy. These requirements reduce the practical feasibility of such PNA reservoir systems. To address this shortcoming, we present a mixed delay/nondelay embeddings-based PNA reservoir system. Our system uses a single PNA reservoir node with the ability to obtain a mixture of delay/nondelay embeddings of the dynamical information of the time-series data applied at the input of a single PNA reservoir node. Our analysis shows that when these mixed delay/nondelay embeddings are used to train a perceptron at the output layer, our reservoir system outperforms existing PNA-based reservoir systems for the imitation of NARMA 2, NARMA 5, NARMA 7, and NARMA 10 time series data, and for the short-term and long-term prediction of the Mackey Glass time series data.
A digital Nonlinear Proportional-Integral-Derivative (NPID) control algorithm was proposed to control a 1-kW, PWM, DC/DC, switching power converter. The NPID methodology is introduced and a practical hardware control solution is obtained. The design of the controller was completed using Matlab (trademark) Simulink, while the hardware-in-the-loop testing was performed using both the dSPACE (trademark) rapid prototyping system, and a stand-alone Texas Instruments (trademark) Digital Signal Processor (DSP)-based system. The final Nonlinear digital control algorithm was implemented and tested using the ED408043-1 Westinghouse DC-DC switching power converter. The NPID test results are discussed and compared to the results of a standard Proportional-Integral (PI) controller.
A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.