Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Robust STATCOM control for the stabilisation of fixed-speed wind turbines during low voltages

This paper presents a robust voltage control scheme for fixed-speed wind generators using a static synchronous compensator (STATCOM) controller. To enable a linear and robust control framework with structured uncertainty, the overall system is represented by a linear part plus a nonlinear part that covers an operating range of interest required to ensure stability during severe low voltages. The proposed methodology is flexible and readily applicable to larger wind farms of different configurations. The performance of the control strategy is demonstrated on a two area test system. Large disturbance simulations demonstrate that the proposed controller enhances voltage stability as well as transient stability of induction generators during low voltage ride through (LVRT) transients and thus enhances the LVRT capability. (C) 2011 Elsevier Ltd. All rights reserved.

Robust state prediction for descriptor systems

This paper deals with the problem of state prediction for descriptor systems subject to bounded uncertainties. The problem is stated in terms of the optimization of an appropriate quadratic functional. This functional is well suited to derive not only the robust predictor for descriptor systems but also that for usual state-space systems. Numerical examples are included in order to demonstrate the performance of this new filter. (C) 2008 Elsevier Ltd. All rights reserved.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Optimization of the rheological properties of probiotic yoghurts supplemented with milk proteins

This study aimed to optimize the rheological properties of probiotic yoghurts supplemented with skimmed milk powder (SMP) whey protein concentrate (WPC) and sodium caseinate (Na-Cn) by using an experimental design type simplex-centroid for mixture modeling It Included seven batches/trials three were supplemented with each type of the dairy protein used three corresponding to the binary mixtures and one to the ternary one in order to increase protein concentration in 1 g 100 g(-1) of final product A control experiment was prepared without supplementing the milk base Processed milk bases were fermented at 42 C until pH 4 5 by using a starter culture blend that consisted of Streptococcus thermophilus Lactobacillus delbrueckii subsp bulgaricus and Bifidobacterium (Humans subsp lactis The kinetics of acidification was followed during the fermentation period as well the physico-chemical analyses enumeration of viable bacteria and theological characteristics of the yoghurts Models were adjusted to the results (kinetic responses counts of viable bacteria and theological parameters) through three regression models (linear quadratic and cubic special) applied to mixtures The results showed that the addition of milk proteins affected slightly acidification profile and counts of S thermophilus and B animal`s subsp lactis but it was significant for L delbrueckii subsp bulgaricus Partially-replacing SMP (45 g/100 g) with WPC or Na-Cn simultaneously enhanced the theological properties of probiotic yoghurts taking into account the kinetics of acidification and enumeration of viable bacteria (C) 2010 Elsevier Ltd All rights reserved

H(infinity) filtering for rectangular discrete-time descriptor systems

This paper deals with the H(infinity) recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to find an estimate that brings the estimation cost to a minimum. A solution exists for a specified gamma-level if the resulting cost is positive. In order to present some computational alternatives to the H(infinity) filters developed, they are rewritten in information form along with the respective array algorithms. (C) 2009 Elsevier Ltd. All rights reserved.

Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems Of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Information Filtering and Array Algorithms for Discrete-Time Markovian Jump Linear Systems

This technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete-time Markovian jump linear systems. A numerical example for a two-mode Markovian jump linear system, to show the advantage of using array algorithms to filter this class of systems, is provided.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

Comparing performance of instrumental drift correction by linear and quadratic adjusting in inductive electromagnetic data

Electromagnetic induction (EMI) method results are shown for vertical magnetic dipole (VMD) configuration by using the EM38 equipment. Performance in the location of metallic pipes and electrical cables is compared as a function of instrumental drift correction by linear and quadratic adjusting under controlled conditions. Metallic pipes and electrical cables are buried at the IAG/USP shallow geophysical test site in Sao Paulo City. Brazil. Results show that apparent electrical conductivity and magnetic susceptibility data were affected by ambient temperature variation. In order to obtain better contrast between background and metallic targets it was necessary to correct the drift. This correction was accomplished by using linear and quadratic relation between conductivity/susceptibility and temperature intending comparative studies. The correction of temperature drift by using a quadratic relation was effective, showing that all metallic targets were located as well deeper targets were also improved. (C) 2010 Elsevier B.V. All rights reserved.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Fuzzy pole placement based on piecewise Lyapunov functions

This paper presents a controller design method for fuzzy dynamic systems based on piecewise Lyapunov functions with constraints on the closed-loop pole location. The main idea is to use switched controllers to locate the poles of the system to obtain a satisfactory transient response. It is shown that the global fuzzy system satisfies the requirements for the design and that the control law can be obtained by solving a set of linear matrix inequalities, which can be efficiently solved with commercially available softwares. An example is given to illustrate the application of the proposed method. Copyright (C) 2009 John Wiley & Sons, Ltd.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.