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The local error of single step methods is modelled as a function of the state derivative multiplied by bias and zero-mean white noise terms. The deterministic Taylor series expansion of the local error depends on the state derivative meaning that the local error magnitude is zero in steady state and grows with the rate of change of the state vector. The stochastic model of the local error may include a constant, “catch-all” noise term. A continuous time extension of the local error model is developed and this allows the original continuous time state differential equation to be represented by a combination of the simulation method and a stochastic term. This continuous time stochastic differential equation model can be used to study the propagation of the simulation error in Monte Carlo experiments, for step size control, or for propagating the mean and variance. This simulation error model can be embedded into continuous-discrete state estimation algorithms. Two illustrative examples are included to highlight the application of the approach.

This article presents a new refinement design routine aimed at solving the robust multivariable tracking error problem with reduced conservatism. The prevailing multivariable quantitative feedback theory (QFT) approach is to implicitly overbound the model‐error tracking set frequency response in magnitude using the triangle inequality, with the intention of arriving at a set of univariate design constraints that independently describe the feedback controller solution space. While this method is effective in the low‐frequency range (where the loop gain tends to be large), the mid‐ to high‐frequency design regions (where diagonal dominance is not possible in general) suffers from arbitrarily large design conservatism. This inhibits minimum gain‐phase solutions and necessitates undesirable over‐design in the frequency band that can contribute to large, expensive control action. The proposed method follows a refinement approach that makes use of information from an a priori feedback control design. In this way, the tracking error problem is reposed as a differential design, and gain‐phase information from the previous iteration can be captured to reduce the conservatism imposed when applying the triangle inequality. Additionally, a constrained optimization routine is used to select a prototype feedforward filter that can relax the constraint set, thereby increasing the accessible solution space of the diagonal feedback controller. Finally, a nondiagonal, multivariable feedforward filter bound generation routine is defined that relies on existence conditions and is free of induced design conservatism. The viability of this design methodology is demonstrated on two benchmark problems of varying complexity, in order to demonstrate the widespread efficacy. [ABSTRACT FROM AUTHOR]

Construction of reduced order models using the conventional quasi-steady-state (QSS) or singular perturbation approach may not yield good low frequency approximations, especially if there is not a distinct time scale separation into slow and fast subsystems. An implicit QSS technique is proposed for general nonlinear models. The resulting reduced order model is accurate to first order in the perturbation parameter and its linearization is accurate to first order in frequency. An example is included showing the application of the proposed method to model reduction on a power plant evaporator. [DOI: 10.1115/1.2397153] Keywords: implicit quasi-steady state, model reduction, stiff systems, singular perturbation, power plant boiler, once through steam generator

An algorithm for calculating design bounds in multivariable quantitative feedback theory (QFT) tracking design is presented. The algorithm solves the problem of trade-off between on- and off-diagonal constraints.

Summary: This article presents a solution to the 2 × 2 multivariable tracking error problem. Current quantitative feedback theory methods commonly employ plant‐inverting splittings in order to arrive at an approximately decoupled design on the feedback control elements. This results in suitable design regions in the high‐gain, low‐frequency range, but can result in conservative design at and above the gain‐crossover frequency, resulting in overdesigned feedback controllers. Our method aims to reduce this conservatism by supplementing a plant‐inverting design with a non‐plant‐inverting design, which tends to perform well at higher frequencies. Decoupling the design of the controller elements is facilitated by making use of appropriate existence conditions. The union of the two resulting design regions then describes a larger solution space, and by enlarging the admissible design regions for the feedback controller, lower gain feedback controller design at all design frequencies of interest may be possible. A benchmarking example is presented, showing the viability of the proposed method. [ABSTRACT FROM AUTHOR]

Discrete Fourier transforms or inverse transform pairs with uniformly spaced input data but with output data required only at exponentially spaced intervals are evaluated by means of fast algorithms. Results suggest that the use of the algorithms reduces the number of arithmetic operations involved in the solution of discrete Fourier transforms by minimizing the number of output data points.

Summary: This paper presents a method for designing a robust two‐degree‐of‐freedom control scheme, capable of satisfying multiple model‐error specifications on a plant by plant basis. Traditional quantitative feedback theory methods generally use a single model‐error or above‐below magnitude tracking specification, which can result in overdesign for plants located away from the bounding conditions. The performance specifications are also generally hand‐tuned, or iteratively adjusted to keep the underlying time‐domain signals within permissible levels. Our method aims to perform a model‐error design on a per‐plant basis, such that each plant's corresponding model tracking has equal weighting given the plant's inherent feedback requirements and capability. The quantitative feedback theory method allows this per‐plant approach to be undertaken with ease. Additionally, sufficiently low‐order model specifications are designed using simple optimisation, which take into account performance limiting effects, such as non‐minimum phase behaviour and signal constraints. A worked example is presented, showing the viability and transparency of the proposed method. [ABSTRACT FROM AUTHOR]

The Perron-Frobenius root is used to measure the level of interaction in MIMO quantitative feedback design (QFT). A design approach to reduce interaction in uncertain plants via a precompensator is presented. A decentralized stability result applies if the interaction index can be made less than unity by design. [DOI: 10.1115/1.1343463]

To reduce the computational overhead in quantitative feedback theory (QFT) bound computation, only the (nonconvex) outside edge of a template should be used. This note presents an algorithm to calculate the nonconvex hull with minimum concave radius defined by the system specifications. [S0022-0434(00)01301-0]

An actuated tail can impart large angular impulse over short time spans, but swinging in a plane results in inevitable tail angle saturation. Cheetahs (Acinonyx jubatus) are observed swinging the tail in a cone during turns [1], and this paper develops a simplified two-degree-of-freedom (pitch and roll) rigid tail model to investigate this motion. Trajectory optimization and experiments on a robotic platform confirm the observed cone motion as a useful solution to roll stabilization. These results are relevant to the understanding of tail motions in biomechanics and bioinspired tailed robots. [ABSTRACT FROM PUBLISHER]

This paper presents a method to classify flow regime and vapor quality in vertical two-phase (vapor-liquid) flow, using a video of the flow as the input; this represents the first high-performing and entirely camera image-based method for the classification of a vertical flow regime (which is effective across a wide range of regimes) and the first image-based tool for estimating vapor quality. The approach makes use of computer vision techniques and deep learning to train a convolutional neural network (CNN), which is used for individual frame classification and image feature extraction, and a deep long short-term memory (LSTM) network, used to capture temporal information present in a sequence of image feature sets and to make a final vapor quality or flow regime classification. This novel architecture for two-phase flow studies achieves accurate flow regime and vapor quality classifications in a practical application to two-phase CO2 flow in vertical tubes, based on offline data and an online prototype implementation, developed as a proof of concept for the use of these models within a feedback control loop. The use of automatically selected image features, produced by a CNN architecture in three distinct tasks comprising flow-image classification, flow-regime classification, and vapor quality prediction, confirms that these features are robust and useful, and offer a viable alternative to manually extracting image features for image-based flow studies. The successful application of the LSTM network reveals the significance of temporal information for image-based studies of two-phase flow. [ABSTRACT FROM AUTHOR]

Abstract: The behaviour of single input, single output, continuous time systems sampled with various types of jitter in both measurement and control action is investigated. It is shown that the effects of jitter can be modelled by approximations for the plant dynamics, and additive noise constructed by the modulation of plant signals with the jitter. These approximations give useful insights for digital controller design. [Copyright &y& Elsevier]

This paper examines the distributed parameter model of a main steam header system and simplifies it to retain only the significant dynamics of the pipe wall temperature and quasisteady-state behavior of the steam in the headers. An augmented linear optimal filter is developed for estimating the steam and pipe wall temperatures along the interconnected main steam headers, between the superheater outlet and the turbine. The filter algorithm is illustrated using data from a power plant. [ABSTRACT FROM AUTHOR]