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This paper presents a rigorous dynamic rate based model suitable for simulation of distillation of mixtures in packed columns. The model equations are described in detail considering structure exploitation at simulation level in order to alleviate the large number of states involved in the model description. Moreover, this kind of model leads to differential-algebraic equations with a differentiation index higher than one. Here this issue is analyzed and a differentiation-index reduction procedure based on the incidence of model states in the Jacobian and the properties of the model dynamics is proposed. This procedure allows for a simplified index-1 model with a reduced stiffness so that dynamic simulation can be performed with off-the-shelf solvers.

This paper presents a convexity-based homotopy solution procedure to non-convex optimal control problems (OCPs) arising in model predictive control. The approach deals with a special class of OCP formulations, where the dynamic system involved is control-affine and the objective is a penalty on deviations from a state reference trajectory. The non-convex OCP is modified by introducing a penalized pseudo state and a homotopy parameter which gradually transforms the original problem into a convex one. The method solves first this convex formulation and uses the result to initialize the solution of the next problem on the zero path, recovering the original OCP. The proposed methodology is evaluated for the benchmark control problem of an isothermal chemical reactor with Van de Vusse reactions and input multiplicity. For the simple case with control horizon one, the method is able to find the global solution due to the convex initialization, while local optimization techniques only lead to a local minimum. convex relaxation of Bolza-type functionals has been also proposed for the solution of finite dimensional non-convex OCPs [3]. However, there is still a lot of work in improving the computational demand of B&B methods and finding tighter convex relaxations to functionals with embedded ODEs [4]. On the other hand, mathematicians and practitioners have realized that several non-convex optimization problems can be reformulated such that the new formulation exhibits convexity [5]. The advantages of using convex formulations lie not only in the fact that local solutions are global, but also in that they exhibit polynomial-time convergence, and that efficient and reliable methods to solve such convex problems are well developed [6].This work proposes a method to solve non-convex OCP with a particular structure in the cost and constraints. In particular, a control-affine model structure is assumed together with an objective, which penalizes deviations from a desired reference trajectory. Many nonlinear dynamic systems of practical interest present the control-affine structure which enables the applicability of the method. Examples of these kinds of systems arise for instance in the chemical industry (e.g. distillation columns and continuous stirred tank reactors-CSTRs) and mechanical engineering (e.g. car maneuvering and robot arm manipulators). The convergence to the global optimum, for these OCPs, can be improved by first solving a related convex formulation, which is connected by a homotopy path to the original problem, and using this solution to initialize the original OCP. The proposed technique resembles a continuation method for global optimization [7] where, by means of filtering techniques, the original cost is gradually transformed into a smoother function with fewer local minimizers. An optimization algorithm is then applied to the transformed function, tracing the minimizers back to the original cost.This paper is organized as follows: in Section 2 the basis of dynamic optimization in the Nonlinear Model Predi...

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This paper presents a Newton optimization technique applied to the Nonlinear Model Predictive Controller (NMPC) for a DC-DC converter. The nonlinear predictor, used in this NMPC algorithm, is approximated by means of a dynamic model which is cubic in the input. This approximation allows the formulation of an explicit MPC law in terms of the states of the model. The proposed controller is tailored for this specific application, taking into account simplicity in the calculation of the control law. The approach followed makes the control law easy to implement and able to deal with the fast response dynamics presented by electronic drivers. The performance of the proposed controller is evaluated under simulation and compared with the response presented by a linear MPC. Although robustness and tracking test are performed over the whole operating range, stability results for the nonlinear MPC are not addresed.Keywords: Predictive control, Nonlinear systems, Electronic applications INTRODUCTIONPower electronic devices are nowadays applied to different areas, from power generation and distribution to embedded solutions for communication, automotive and computers industries. This wide range of applications has motivated this field to be an active research area where several topologies and control strategies have been investigated. Among all these topologies, the DC-DC boost converter presents interesting challenges from the control point of view. It exhibits a non-linear, hybrid behavior (including continuous and logical variables), non-minimum phase and additionally, very short time responses requiring nonlinear and fast control strategies which have to be implemented in real-time. However, in spite of this challenging features, boost converters are usually regulated by simple linear analog techniques based on a linear low frequency approximation of the system. Nevertheless the performance of the closed loop system can be improved by the use of nonlinear control, especially if the circuit has to apply a wide-range time-varying output voltage. A number of non-linear control techniques has been reported in the literature, such as: sliding mode controllers (Silva, 1999) The paper is organized as follows: in section 2, the hybrid model is formulated for a real low power boost converter. Section 3 shows the development of a linear MPC algorithm for a linear simplified State Space Average (SSA) model, while section 4 deals with the NMPC design for a nonlinear SSA model. The designed controllers are evaluated in section 5 and the paper is concluded in section 6. SYSTEM MODELThe modeling of switched power drives can be classified depending on whether the switching signal q(t) is directly manipulated 1 or a pulse width modulator (PWM) is needed to drive the state of the switch. Figure 1 shows the electric circuit for a boost converter assuming internal losses in the components. It is assumed in general that v o (t) > v s (t). Losses in the diode will be represented by its internal resistance R D and its forward voltage...