High-order volterra model predictive control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but the existing design and implementation methods are restricted to linear process models. A chemical process involves, however, severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC), and also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design which relieves practising engineers from the need for first deriving a physical-principles based model. An on-line realisation technique for implementing the NMPC is also developed. The NMPC is then applied to a Mitsubishi Chemicals polymerisation reaction process. The results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the approach developed lie not only in control performance superior to existing NMPC methods, but also in relieving practising engineers from the need for deriving an analytical model and then converting it to a Volterra model through which the model can only be obtained up to the second order

Temporal Correlations and Persistence in the Kinetic Ising Model: the Role of Temperature

We study the statistical properties of the sum $S_t=\int_{0}^{t}dt' \sigma_{t'}$, that is the difference of time spent positive or negative by the spin $\sigma_{t}$, located at a given site of a $D$-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of $S_{t}$ and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ($T>T_{c}$), criticality ($T=T_c$), and low temperature ($T<T_{c}$). We discuss in particular the question of the temperature dependence of the persistence exponent $\theta$, as well as that of the spectrum of exponents $\theta(x)$, in the low temperature phase. The probability that the temporal mean $S_t/t$ was always larger than the equilibrium magnetization is found to decay as $t^{-\theta-\frac12}$. This yields a numerical determination of the persistence exponent $\theta$ in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model.Comment: 21 pages, 11 PostScript figures included (1 color figure

Effect of anisotropy and destructuration on behavior of Haarajoki test embankment

This paper investigates the influence of anisotropy and destructuration on the behavior of Haarajoki test embankment, which was built by the Finnish National Road Administration as a noise barrier in 1997 on a soft clay deposit. Half of the embankment is constructed on an area improved with prefabricated vertical drains, while the other half is constructed on the natural deposit without any ground improvement. The construction and consolidation of the embankment is analyzed with the finite-element method using three different constitutive models to represent the soft clay. Two recently proposed constitutive models, namely S-CLAY1 which accounts for initial and plastic strain induced anisotropy, and its extension, called S-CLAY1S which accounts, additionally, for interparticle bonding and degradation of bonds, were used in the analysis. For comparison, the problem is also analyzed with the isotropic modified cam clay model. The results of the numerical analyses are compared with the field measurements. The simulations reveal the influence that anisotropy and destructuration have on the behavior of an embankment on soft clay

Toxicity and Applications of Internalised Magnetite Nanoparticles Within Live Paramecium caudatum Cells

© 2017, The Author(s). The nanotechnology revolution has allowed us to speculate on the possibility of hybridising nanoscale materials with live substrates, yet significant doubt still remains pertaining to the effects of nanomaterials on biological matter. In this investigation, we cultivate the ciliated protistic pond-dwelling microorganism Paramecium caudatum in the presence of excessive quantities of magnetite nanoparticles in order to deduce potential beneficial applications for this technique, as well as observe any deleterious effects on the organisms’ health. Our findings indicate that this variety of nanoparticle is well-tolerated by P. caudatum cells, who were observed to consume them in quantities exceeding 5–12% of their body volume: cultivation in the presence of magnetite nanoparticles does not alter P. caudatum cell volume, swimming speed, growth rate or peak colony density and cultures may persist in nanoparticle-contaminated media for many weeks. We demonstrate that P. caudatum cells ingest starch-coated magnetite nanoparticles which facilitates their being magnetically immobilised whilst maintaining apparently normal ciliary dynamics, thus demonstrating that nanoparticle biohybridisation is a viable alternative to conventional forms of ciliate quieting. Ingested magnetite nanoparticle deposits appear to aggregate, suggesting that (a) the process of being internalised concentrates and may therefore detoxify (i.e. render less reactive) nanomaterial suspensions in aquatic environments, and (b) P. caudatum is a candidate organism for programmable nanomaterial manipulation and delivery

Cellular automata modelling of slime mould actin network signalling

© 2016, The Author(s). Actin is a cytoskeletal protein which forms dense, highly interconnected networks within eukaryotic cells. A growing body of evidence suggests that actin-mediated intra- and extracellular signalling is instrumental in facilitating organism-level emergent behaviour patterns which, crucially, may be characterised as natural expressions of computation. We use excitable cellular automata modelling to simulate signal transmission through cell arrays whose topology was extracted from images of Watershed transformation-derived actin network reconstructions; the actin networks sampled were from laboratory experimental observations of a model organism, slime mould Physarum polycephalum. Our results indicate that actin networks support directional transmission of generalised energetic phenomena, the amplification and trans-network speed of which of which is proportional to network density (whose primary determinant is the anatomical location of the network sampled). Furthermore, this model also suggests the ability of such networks for supporting signal-signal interactions which may be characterised as Boolean logical operations, thus indicating that a cell’s actin network may function as a nanoscale data transmission and processing network. We conclude by discussing the role of the cytoskeleton in facilitating intracellular computing, how computation can be implemented in such a network and practical considerations for designing ‘useful’ actin circuitry

Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC

Optimal control of a linear system subject to partially specified input noise

One of the most basic problems in control theory is that of controlling a discrete-time linear system subject to uncertain noise with the objective of minimising the expectation of a quadratic cost. If one assumes the noise to be white, then solving this problem is relatively straightforward. However, white noise is arguably unrealistic: noise is not necessarily independent and one does not always precisely know its expectation. We first recall the optimal control policy without assuming independence, and show that in this case computing the optimal control inputs becomes infeasible. In a next step, we assume only knowledge of lower and upper bounds on the conditional expectation of the noise, and prove that this approach leads to tight lower and upper bounds on the optimal control inputs. The analytical expressions that determine these bounds are strikingly similar to the usual expressions for the case of white noise

Performance of Sensitivity based NMPC Updates in Automotive Applications

In this work we consider a half car model which is subject to unknown but measurable disturbances. To control this system, we impose a combination of model predictive control without stabilizing terminal constraints or cost to generate a nominal solution and sensitivity updates to handle the disturbances. For this approach, stability of the resulting closed loop can be guaranteed using a relaxed Lyapunov argument on the nominal system and Lipschitz conditions on the open loop change of the optimal value function and the stage costs. For the considered example, the proposed approach is realtime applicable and corresponding results show significant performance improvements of the updated solution with respect to comfort and handling properties.Comment: 6 pages, 2 figure

Human immunodeficiency virus infection in Northern Ireland 1980-1989.

To 31st December 1989, 71 persons are known to have attended medical practitioners in Northern Ireland with a diagnosis of Human Immunodeficiency Virus (HIV) infection. Twenty-one of these persons have had the diagnosis of Acquired Immune Deficiency Syndrome (AIDS) and 11 have died. The distribution of reports in the "at risk" categories of homosexual/bisexual males, injecting drug users, heterosexual males and females was significantly different (p less than 0.001) from those reported in the United Kingdom as a whole. Of tests for HIV infection carried out in patients attending the genitourinary medicine department of the Royal Victoria Hospital between 1987-1989, 0.16% have been positive. The prognostic value of the T4 lymphocyte count at presentation for the subsequent development of AIDS was significant (p = 0.0011). The commonest AIDS indicator disease diagnosed was Pneumocystis carinii pneumonia which was seen in seven of the 21 patients (33%)

Robust constrained model predictive control based on parameter-dependent Lyapunov functions

The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques