Showing papers on "Control variable published in 2011"

Modeling and control insights into demand-side energy management through setpoint control of thermostatic loads

Abstract: This paper examines the problem of using thermostat offset signals to directly control distributed air conditioning loads attached to the grid. The paper models these loads using a novel partial differential equation framework that builds on existing diffusion-based load modeling ideas in the literature. Both this PDE model and its finite-difference discretizations are bilinear in the state and control variables. This key insight creates a unique opportunity for designing nonlinear direct load control algorithms with theoretically guaranteed Lyapunov stability properties. The paper's main contribution to the literature is the development of the bilinear PDE model and Lyapunov-stable controller for real-time management of thermostatic air conditioning loads.

Hierarchical Long-Term and Short-Term Production Optimization

Abstract: Model-based dynamic optimization of oil production has a significant potential to improve economic life-cycle performance, as has been shown in various studies. However, within these studies, short-term operational objectives are generally neglected. As a result, the optimized injection and production rates often result in a considerable decrease in short-term production performance. In reality, however, it is often these short-term objectives that dictate the course of the operational strategy. Incorporating short-term goals into the life-cycle optimization problem, therefore, is an essential step in model-based life-cycle optimization. We propose a hierarchical optimization structure with multiple objectives. Within this framework, the life-cycle performance in terms of net present value (NPV) serves as the primary objective and short-term operational performance is the secondary objective, such that optimality of the primary objective constrains the secondary optimization problem. This requires that optimality of the primary objective does not fix all degrees of freedom (DOF) of the decision variable space. Fortunately, the life-cycle optimization problem is generally ill-posed and contains many more decision variables than necessary. We present a method that identifies the redundant DOF in the life-cycle optimization problem, which can subsequently be used in the secondary optimization problem. In our study, we used a 3D reservoir in a fluvial depositional environment with a production life of 7 years. The primary objective is undiscounted NPV, while the secondary objective is aimed at maximizing short-term production. The optimal life-cycle waterflooding strategy that includes short-term performance is compared to the optimal strategy that disregards short-term performance. The experiment shows a very large increase in short-term production, boosting first-year production by a factor of 2, without significantly compromising optimality of the primary objective, showing a slight drop in NPV of only ?0.3%. Our method to determine the redundant DOF in the primary objective function relies on the computation of the Hessian matrix of the objective function with respect to the control variables. Although theoretically rigorous, this method is computationally infeasible for realistically sized problems. Therefore, we also developed a second, more pragmatic, method relying on an alternating sequence of optimizing the primary- and secondary-objective functions. Subsequently, we demonstrated that both methods lead to nearly identical results, which offers scope for application of hierarchical long-term and short-term production optimization to realistically sized flooding-optimization problems.

Quantile Regression with Censoring and Endogeneity

Abstract: In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol.

Two-Loop Digital Sliding Mode Control of DC–DC Power Converters Based on Predictive Interpolation

Abstract: Digital implementation of sliding-mode current control applied to dc-dc switching converters is analyzed and developed in this paper. It is based on an interpolation predictive strategy that avoids problems associated to continuous sampling process of the controlled variable and minimizes quasi-sliding effects. In addition to inherent advantages of digital implementation, as programmability, flexibility, complex calculation capability and noise immunity, the proposed strategy maintains robustness and has similar behavior than analog sliding-mode current control implementations. In order to obtain output voltage regulation, an outer proportional-integral digital output voltage control loop is added. Simulated and experimental results in a boost converter are in good agreement with the theoretical predictions.

Quadratic order conditions for bang-singular extremals

Abstract: This paper deals with optimal control problems for systems affine in the control variable We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state First, we obtain second order necessary optimality conditions Secondly, we derive a second order sufficient condition for the scalar control case

Maximum principle for optimal control problems with intermediate constraints

Abstract: We consider optimal control problems with constraints at intermediate points of the trajectory. A natural technique (propagation of phase and control variables) is applied to reduce these problems to a standard optimal control problem of Pontryagin type with equality and inequality constraints at the trajectory endpoints. In this way we derive necessary optimality conditions that generalize the Pontryagin classical maximum principle. The same technique is applied to so-called variable structure problems and to some hybrid problems. The new optimality conditions are compared with the results of other authors and five examples illustrating their application are presented.

Minimum-Cost Cruise at Constant Altitude of Commercial Aircraft Including Wind Effects

Abstract: A IRCRAFT trajectory optimization is a subject of great importance in air traffic management from the point of view of defining optimal flight procedures that lead to energy-efficient flights. In practice, the airlines consider a cost index (CI) and define the direct operating cost (DOC) as the combined cost of fuel consumed and flight time weighted by the CI. Their goal is to minimize the DOC. However, in the presence of unexpected winds, the flight timemay differ considerably from the scheduled time, which leads to an arrival-error cost that can be added to the DOC to obtain the total cost (TC). Minimum-DOC trajectories have been studied by different authors [1–6]. The related problem of minimum fuel with fixed final time has been analyzed as a minimum-DOC problem with free final time in [3,5,7] (the problem is to find the time cost for which the corresponding free final time DOC-optimal trajectory arrives at the assigned time); this same problem is addressed in [8], analyzing the effects of mismodeled winds in a scenario formed by the final cruise and descent segments. The problem of minimum-cost flight, considering not only the DOC but also the arrival-error cost, is analyzed in [9,10], taking into account factors such as crew overtime cost, passenger dissatisfaction cost, and losses due to missed connections. In this Note, the problem of minimum-cost cruise at constant altitude in the presence of strong winds, including the arrival-error cost, is analyzed, considering the general unsteady problem, with variable aircraft mass, and without any restriction on cruise altitude. The main objective is to analyze the optimal trajectories that lead to minimum cost, defined as optimal speed laws (speed as a function of aircraft mass). The analysis is made using the theory of singular optimal control (see [11]), which has the great advantage of providing feedback control laws (control variables as functions of the state variables) that can be directly used to guide the aircraft along the optimal path. These optimal control laws are analyzed as well. In this work, the initial and final speeds are given, so that the optimal control is of the bang-singular-bang type, and the optimal paths are formed by a singular arc and two minimum/maximumthrust arcs joining the singular arc with the given initial and final points (see [6,12]). In previous work related to optimum cruise at constant altitude [13,14], only the singular arc was studied; hence, a more general formulation of the optimal problem is addressed now, apart from considering the arrival-error cost and including wind effects (average horizontal winds). In this analysis of the minimum-TC problem, the arrival-error cost depends on the difference between the actual and the scheduledflight times, and it is defined to be positive, so that both late and early arrivals are penalized (the objective is to achieve high arrival-time accuracy). It will be shown that, for some values of the parameters of the problem, minimum cost is obtained when the final time coincides with the scheduled time of arrival; that is, when the arrival-error cost is zero. This critical case is in fact a problem with fixed final time. Results are presented for a model of a Boeing 767-300ER.

Quantile Regression with Censoring and Endogeneity

Abstract: In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors The CQIV estimator is obtained in two stages that are nonadditive in the unobservables The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution We verify these conditions for quantile and distribution regression estimation of the control variable We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol

Stochastic Maximum Principle for Optimal Control Problems of Forward-Backward Systems Involving Impulse Controls

Abstract: We consider a stochastic optimal control problem of a forward-backward system in which the control variable consists of two components: the continuous control and the impulse control. The domain of the control is assumed to be convex. Necessary optimality conditions of the Pontryagin maximum principle type are obtained for this stochastic optimal control problem. We also give additional conditions, under which the necessary optimality conditions turn out to be sufficient.

Dynamic Optimization of a Slab Reheating Furnace With Consistent Approximation of Control Variables

Abstract: A dynamic optimization method is developed for temperature control of steel slabs in a continuous reheating furnace. The work was stimulated by the need for furnace control concepts that are computationally undemanding, robust, accurate, and capable of non-steady-state operating scenarios, where the properties and the temperature goals of slabs may vary significantly. The proposed hierarchical control structure is based on a continuous-time switched nonlinear model and uses the furnace zone temperatures as intermediate control variables. Consistent approximation is applied to obtain a parametric optimization problem that can be efficiently solved with the quasi-Newton method. Constraints on system states and control variables are considered by penalty terms in the cost function and saturation functions, respectively. The optimization method plans temperature trajectories for both the furnace and the slabs, which may be useful for open-loop control and feedforward branches of two-degrees-of-freedom control structures. The capabilities of the method are demonstrated in an example problem.

Pontryagin's maximum principle of optimal control problems with time-delay

Abstract: In this paper, we consider an optimal control problem with time-delay. The state and the control variables contain various constant time-delays. This allows us to represent the necessary conditions in an explicit form. Solution of this problem with infinite terminal time is also given.

Review Article: One machine multiple-product problem with production-inventory system under fuzzy inequality constraint

Abstract: This paper presents a one machine multiple-product problem with bounded production rate to minimize the total linear cost of inventory under imprecise space constraint. The demand is dependent on time and known. Also the production is a control variable and unknown. The net discount rate of inflation is fuzzy in nature. At first defined the expected value of fuzzy number, then the system is transferred to the fuzzy expected value model. The model is formulated as an optimal control problem and then reduced to an equivalent deterministic model and solved for optimum production function using Pontryagin's Optimal Control policy, the Kuhn-Tucker conditions and generalized reduced gradient (GRG) technique. The model is illustrated numerically and values of demand, optimal production and stock level are presented in both tabular and pictorial forms.

Direct method for optimal power management in hybrid electric vehicles

Abstract: Hybrid electric vehicles are powered by an electric system and an internal combustion engine. The components of a hybrid electric vehicle need to be coordinated in an optimal manner to deliver the desired performance. This paper presents an approach based on direct method for optimal power management in hybrid electric vehicles with inequality constraints. The approach consists of reducing the optimal control problem to a set of algebraic equations by approximating the state variable which is the energy of electric storage, and the control variable which is the power of fuel consumption. This approximation uses orthogonal functions with unknown coefficients. In addition, the inequality constraints are converted to equal constraints. The advantage of the developed method is that its computational complexity is less than that of dynamic and non-linear programming approaches. Also, to use dynamic or non-linear programming, the problem should be discretized resulting in the loss of optimization accuracy. The propsed method, on the other hand, does not require the discretization of the problem producing more accurate results. An example is solved to demonstrate the accuracy of the proposed approach. The results of Haar wavelets, and Chebyshev and Legendre polynomials are presented and discussed.

Predictive control of systems with Markovian jumps under constraints and its application to the investment portfolio optimization

Abstract: In the paper, we study a problem of control with a predictive model for discrete systems with Markovian jumps and multiplicative noises. A strategy to control with regard for explicit constraints on control variables is defined. The results are applied to control an investment portfolio under constraints on investment amounts.

Model Predictive Control and Optimization for Papermaking Processes

Abstract: Papermaking is a large-scale two-dimensional process. It has to be monitored and controlled continuously in order to ensure that the qualities of paper products stay within their specifications. There are two types of control problems involved in papermaking processes: machine directional (MD) control and cross directional (CD) control. Machine direction refers to the direction in which paper sheet travels and cross direction refers to the direction perpendicular to machine direction. The objectives of MD control and CD control are to minimize the variation of the sheet quality measurements in machine direction and cross direction, respectively. This chapter considers the design and applications of model predictive control (MPC) for papermaking MD and CD processes. MPC, also known as moving horizon control (MHC), originated in the late seventies and has developed considerably in the past two decades (Bemporad and Morari 2004; Froisy 1994; Garcia et al. 1998; Morari & Lee 1999; Rawlings 1999; Chu 2006). It can explicitly incorporate the process’ physical constraints in the controller design and formulate the controller design problem into an optimization problem. MPC has become the most widely accepted advanced control scheme in industries. There are over 3000 commercial MPC implementations in different areas, including petro-chemicals, food processing, automotives, aerospace, and pulp and paper (Qin and Badgwell 2000; Qin and Badgwell 2003). Honeywell introduced MPC for MD controls in 1994; this is likely the first time MPC technology was applied to MD controls (Backstrom and Baker, 2008). Increasingly, paper producers are adopting MPC as a standard approach for advanced MD controls. MD control of paper machines requires regulation of a number of quality variables, such as paper dry weight, moisture, ash content, caliper, etc. All of these variables may be coupled to the process manipulated variables (MV’s), including thick stock flow, steam section pressures, filler flow, machine speed, and disturbance variables (DV’s) such as slice lip adjustments, thick stock consistency, broke recycle, and others. Paper machine MD control is truly a multivariable control problem. In addition to regulation of the quality variables during normal operation, a modern advanced control system for a paper machine may be expected to provide dynamic economic optimization on the machine to reduce energy costs and eliminate waste of raw materials. For machines that produce more than one grade of paper, it is desired to have an automatic grade change feature that will create and track controlled variable (CV) and MV

Optimal control of polymer flooding based on mixed-integer iterative dynamic programming

Abstract: Polymer flooding is one of the most important technologies for enhanced oil recovery. In this article, a mixed-integer optimal control model of distributed parameter systems (DPS) for the injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding and some inequalities constraints, such as polymer concentration and injection amount limitation. The control variables are the volume size, the injection concentration of each slug and the terminal flooding time. For the constant injection rate, the slug size is determined by the integer time stage length, and thus the integer variables are introduced in the DPS. To cope with the optimal control problem (OCP) of this DPS, a mixed-integer iterative dynamic programming incorporating a special truncation procedure to handle integer restrictions on stage lengths is proposed. First, the OCP with variable time stage lengths is transformed into a fixed time ...

Local following control method of multiple mobile robots

Abstract: The invention discloses a local following control method of multiple mobile robots. In the method, a following robot uses information provided by a self vision system to realize the control of the following of a pilot robot of the following robot. The following robot depends on visual measurement for acquiring a relative distance d and an observed azimuth theta to the pilot robot; by combining with a given distance dp, the following robot calculates a distance deviation e and a deviation change rate ec, adjusts the distance by using a fuzzy control method and outputs a control variable mu to realize speed control; and by combining with a given observed azimuth thetap, the following robot calculates an azimuth deviation etheta, adjusts the azimuth through proportional control and outputs acontrol variable mutheta to realize the control of the movement direction of the robot. The method is expected to provide a coordinate control method for a multi-robot system under a condition of poor communication quality, particularly invalid communication. In addition, the method provides a technical guarantee for the applications of the multi-robot system in military, security and other aspects.

Maximum principle for forward-backward doubly stochastic control systems and applications

Abstract: The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short). And as an example of the SMP, we solve a kind of forward-backward doubly stochastic linear quadratic optimal control problems as well. In the last section, we use the solution of FBDSDEs to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and open-loop Nash equilibrium point for nonzero sum stochastic differential games problem.

Voltage control apparatus, method, and program

Abstract: The voltage control apparatus ( 202 ) includes: a first information obtaining unit ( 302 ) obtaining an output value of active power output from each of the distributed generations, and a voltage deviation amount or a voltage value at a point of common coupling of each of the distributed generations; and a control variable calculating unit ( 303 ) calculating a control variable corresponding to an amount of the active power or reactive power that should be changed and is to be output from each of the distributed generations to the distribution system so that the voltage deviation amount or the voltage value at one of the points of common coupling falls within a predetermined proper range in advance, wherein the control variable calculating unit calculates the control variable to be larger, as the output value of the active power output from one of the distributed generations is larger.

Model Predictive Control Synthesis Approach of Electrode Regulator System for Electric Arc Furnace

Abstract: In electric arc furnace smelting, electrode regulator system is a key link. A good electrode control algorithm will reduce energy consumption effectively and shorten smelting time greatly. The offline design online synthesis model predictive control algorithm is proposed for electrode regulator system with input and output constraints. On the offline computation, the continuum of terminal constraint sets will be constructed. On the online synthesis, the time-varying terminal constraint sets will be adopted and at least one free control variable will be introduced to solve the min-max optimization control problem. Then Lyapunov method will be adopted to analyze closed-loop system stability. Simulation and field trial results show that the proposed offline design online synthesis model predictive control method is effective.

Optimal power flow calculation of power system with wind farms

Abstract: With the rapid development of wind power generation, integrated wind farms will exert a growing influence in the economic operation of power system. This paper build an OPF model with wind farms which includes the stable model of wind generator and the added up spinning reserve and down spinning reserve caused by the uncertainty of wind power. In order to make this model become more reasonable, the cost of wind power generation is added into the objective function and the real output of wind power generator is dealed with a control variable. A quadratic penalty function with variable penalty is employed to realize successive discretization of the discrete control variables in optimization process. The IEEE 118 system is used to analyze the effect of connected wind farm and its spinning reserve demand on the total generation cost and verify the rationality of proposed optimal power flow model and the validity of proposed algorithm.

Intervention in Biological Phenomena Modeled by S-Systems

Abstract: Recent years have witnessed extensive research activity in modeling biological phenomena as well as in developing intervention strategies for such phenomena. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of biological phenomena. In this paper, two different intervention strategies, namely direct and indirect, are proposed for the S-system model. In the indirect approach, the prespecified desired values for the target variables are used to compute the reference values for the control inputs, and two control algorithms, namely simple sampled-data control and model predictive control (MPC), are developed for transferring the control variables from their initial values to the computed reference ones. In the direct approach, a MPC algorithm is developed that directly guides the target variables to their desired values. The proposed intervention strategies are applied to the glycolytic-glycogenolytic pathway and the simulation results presented demonstrate the effectiveness of the proposed schemes.

Tree-based variable selection for dimensionality reduction of large-scale control systems

Abstract: This paper is about dimensionality reduction by variable selection in high-dimensional real-world control problems, where designing controllers by conventional means is either impractical or results in poor performance.

Analysis and numerical simulation of a nonlinear mathematical model for testing the manoeuvrability capabilities of a submarine

Abstract: The aim of this work is to provide a mathematical and numerical tool for the analysis of the manoeuvrability capabilities of a submarine. To this end, we consider a suitable optimal control problem with constraints in both state and control variables. The state law is composed of a highly coupled and nonlinear system of twelve ordinary di erential equations. Control inputs appear in linear and quadratic form and physically are linked to rudders and propeller forces and moments. We consider a nonlinear Bolza type cost function which represents a commitment between reaching a final desired state and a minimal expense of control. In a first part, following recent ideas in [F. Periago and J. Tiago, A local existence result for an optimal control problem modeling the manoeuvring of an underwater vehicle, Nonlinear Analysis: Real World Applications (2009), doi:10.1016/j.nonrwa.2009.09.002] , we prove a local existence result for the above mentioned optimal control problem. In a second part, we address the numerical resolution of the problem by using a descent method with projection and optimal step-size parameter. To illustrate the performance of the method proposed in this paper and to show its application in a real engineering problem we include three di erent numerical experiments for a standard manoeuvre.