Nikolaos A. Bozinis

On-line optimization via off-line parametric optimization tools

In this paper, model predictive control (MPC) based optimization problems with a quadratic performance criterion and linear constraints are formulated as multi-parametric quadratic programs (mp-QP), where the input and state variables, corresponding to a plant model, are treated as optimization variables and parameters, respectively. The solution of such problems is given by (i) a complete set of profiles of all the optimal inputs to the plant as a function of state variables, and (ii) the regions in the space of state variables where these functions remain optimal. It is shown that these profiles are linear and the corresponding regions are described by linear inequalities. An algorithm for obtaining these profiles and corresponding regions of optimality is also presented. The key feature of the proposed approach is that the on-line optimization problem is solved off-line via parametric programming techniques. Hence (i) no optimization solver is called on-line, and (ii) only simple function evaluations are required, to obtain the optimal inputs to the plant for the current state of the plant.

A multiparametric programming approach for mixed-integer quadratic engineering problems

Abstract In this work we propose algorithms for the solution of multiparametric quadratic programming (mp-QP) problems and multiparametric mixed-integer quadratic programming (mp-MIQP) problems with a convex and quadratic objective function and linear constraints. For mp-QP problems it is shown that the optimal solution, i.e. the vector of continuous variables and Lagrange multipliers, is an affine function of parameters. The basic idea of the algorithm is to use this affine expression for the optimal solution to systematically characterize the space of parameters by a set of regions of optimality. The solution of the mp-MIQP problems is approached by decomposing it into two subproblems, which converge based upon an iterative methodology. The first subproblem, which is an mp-QP, is obtained by fixing the integer variables and its solution represents a parametric upper bound. The second subproblem is formulated as a mixed-integer non-linear programming (MINLP) problem and its solution provides a new integer vector, which can be fixed to obtain a parametric solution, which is better than the current upper bound. The algorithm terminates with an envelope of parametric profiles corresponding to different optimal integer solutions. Examples are presented to illustrate the basic ideas of the algorithms and their application in model predictive and hybrid control problems.

Anaerobic codigestion of agricultural industries' wastewaters

Wastewaters generated from agricultural industries are usually hard to treat due to a high organic content. The basic treatment process to be used can only be anaerobic digestion, a process with the additional advantages of (i) limited production of stabilized sludge and (ii) utilization of the produced biogas. The cotreatment of such seasonally produced wastewaters is proposed in order to secure the economically favorable and stable year-round operation of a treatment plant, with the additional benefits of smaller capital costs (due to the use of centrally located rather than distributed treatment facilities) and the exploitation of complementarity in waste characteristics (e.g. avoidance of nutrients (N,P) addition when a codigested wastewater contains nutrients in excess). A mathematical model for codigesting piggery, olive-mill and dairy wastewaters was developed based on batch kinetic experiments. An organic loading rate of 3.84 g COD/l·d was found to be safe for a digester operating on a year-round basis, fed sequentially with piggery, piggery-olive-mill and piggery-dairy wastewaters.

Model predictive control: a multi-parametric programming approach

In this paper, linear model predictive control problems are formulated as multi-parametric quadratic programs, where the control variables are treated as optimization variables and the state variables as parameters. It is shown that the control variables are affine functions of the state variables and each of these affine functions is valid in a certain polyhedral region in the space of state variables. An approach for deriving the explicit expressions of all the affine functions and their corresponding polyhedral regions is presented. The key advantage of this approach is that the control actions are computed off-line: the on-line computation simply reduces to a function evaluation problem.

Output feedback Parametric Controllers for an Active Valve Train Actuation System

The first commercial camless car engines featuring continuously variable valve timing are expected to be available by 2010 to meet the strict legislation on NOx and COx emissions. A key factor for the development of this technology is the design of controllers that can maintain accurate signal tracking in the presence of variations in engine parameters and running conditions. Towards this direction, we present a control design methodology and a new control implementation of an advanced optimizing parametric controller (Parco) for a research active valve train system at Lotus Engineering. The controller is based on a mathematical model for the active valve train and is derived off-line using novel parametric programming techniques. The simple explicit form of the controller enables its implementation on the currently available commercial microprocessor with sampling times of 0.1 ms. Simulation and experimental results demonstrated the superiority of the parametric controller in comparison with a conventional proportional derivative (PD) control scheme

PARAMETRIC MODEL PREDICTIVE CONTROL OF AIR SEPARATION

Abstract This paper describes the application of Parametric Model Predictive Control to small processing units, in particular small Air Separation plants. Multiparametric optimization techniques are used to rigorously solve the MPC problem in two steps: an offline solution which generates a parametric mapping of the optimal control adjustments, and an online solution which reduces to a simple lookup operation. Because of the speed and simplicity of this lookup operation we are able to implement MPC in low-end computing devices such as PLCs, reaping the benefits of model-based control by implementing it at low cost in small plants where otherwise it would not be justified by the cost/benefit ratio.

A new multiparametric mixed-integer quadratic programming algorithm

Publisher Summary A number of important engineering problems, such as mixed logical dynamic systems, which simultaneously involve process dynamics and logical constraints, can be reformulated as multiparametric mixed-integer quadratic programs (mp-MIQP) by treating the control variables as the optimization variables and the state variables as parameters—the quadratic terms appear only in the objective function. This chapter presents an algorithm for the solution of mp-MIQPs. The solution of mp-MIQPs is given by an enclosure of the nonlinear profiles of the control variables as a function of the state variables. The optimal solution is then obtained, online, by evaluating the profiles for a given value of the state variables and then choosing the minimum of the values corresponding to different profiles. The mathematical foundations and the algorithm for the solution of mp-MIQPs are proposed.