José M. Igreja

Adaptive Receding Horizon Control of a Distributed Collector Solar Field

This paper presents an adaptive receding horizon control algorithm for a distributed collector solar field which explicitly explores its distributed parameter character. The plant considered is a distributed collector solar field, being described by a nonlinear hyperbolic partial differential equation (PDE) which models the temperature dynamics. A lumped parameter model is obained by applying Orthogonal Collocation. This model is then used as a basis for controller design. Stability is ensured for the lumped parameter model by resorting to Control Lyapunov function methods. Simulation results using a detailed physically based simulator of the solar field are provided.

Nonlinear Adaptive Control

Exact linear models are obtained using the technique known as input–output feedback linearization, that is applied to a bilinear finite-dimensional state-space approximation of the dynamics of a distributed collector solar field. A control Lyapunov function is then used to jointly design the adaptation law for the uncertain parameter that measures the mirror efficiency, and the gain of the pole-placement controller. Provided that the plant is represented by the finite-dimensional bilinear model considered, this approaches ensures the stability of the overall controlled system, and that the outlet fluid temperature asymptotically approaches the reference. A reduced complexity controller designed along these lines is obtained and the resulting internal state dynamics is studied. Experimental results on a distributed collector solar field are shown.

Control of a water delivery canal with cooperative distributed MPC

This article addresses the problem of controlling pool levels in a water delivery canal using a novel cooperative distributed MPC control algorithm that incorporates stability constraints. According to a distributed control strategy, a local control agent is associated to all canal gates (actuators). In order to achieve cooperative action, each control agent computes the corresponding gate position (manipulated variable) by performing the minimization of a cost function that considers not only its local control objectives, but also the ones of their immediate neighbors. For this purpose, a MPC algorithm with stability constraints is used (SIORHC). At the beginning of each sampling interval, local control agents exchange information with their neighbors and adjust their decisions in an iterative way. The resulting distributed MPC is denoted D-SIORHC and yields a stable closed-loop. Experimental results are provided to show the influence of the controller configuration parameters on the resulting performance.

Nonlinear Model Predictive Control of a Water Distribution Canal Pool

Water distribution canals provide interesting examples of distributed parameter plants for which nonlinear model predictive control may be applied. Canals are formed by a sequence of pools separated by gates. Output variables are the pool level at certain points, manipulated variables are the position of the gates and disturbances are the outlet water flows for agricultural use. The operation of this system is subject to a number of constraints. These are the minimum and maximum positions of the gates, gate slew-rate and the minimum and maximum water level. The objective considered in this paper is to drive the canal level to track a reference in the presence of the disturbances. The pool level is a function of both time and space that satisfies the Saint-Venant equations. These are a set of hyperbolic partial differential equations that embody mass and momentum conservation. In order to develop a NMPC algorithm, the Saint-Venant equations are approximated by a set of ordinary differential equations corresponding to the variables at the so called collocation points. Together with the boundary conditions, this forms a nonlinear reduced predictive model. In this way, a nonlinear prediction of future canal levels is obtained. The paper details the control general formulation along with a computationally efficient algorithm as well as the results obtained from its application.

Application of distributed model predictive control to a water delivery canal

Water delivery canals are large, spatially distributed structures whose objective is to bring in a continuous way water from the sources to the points were it is used. Due to their large scale character, the backbone of water delivery canals modeling is made of partial differential equations, in particular the Saint-Venant equations that embody mass and moment conservation. As a consequence this type of plants have an infinite dimension and are difficult to control due to phenomena like wave formation and a strong interaction between different parts. In this work, a canal made of four sequential pools is considered, the gates between adjacent pools being the actuators. In order to tackle the above dynamic characteristics, in particular the strong interaction between canal subsystems, a distributed model predictive control (MPC) algorithm is used. As such, the controllers driving each gate communicate with each other in order to make coordinate moves. The resulting algorithm is a sub-optimal version of a centralized, multivariable, MPC controller. The paper presents the distributed MPC algorithm applied to the canal and shows that it is a near optimum approximation.

NONLINEAR PREDICTIVE CONTROL OF A SOLAR PLANT BASED ON REDUCED COMPLEXITY MODELS

Abstract This paper is concerned with predictive controller design for the outlet oil temperature in distributed collector solar fields. The design method proposed combines feedback linearization cascade with an outer loop consisting of a predictive controller incorporating constraints. A relevant feature is the use of a reduced complexity model, selected according to a nonlinearity measure.

Robust Pointwise Min-Norm Control of distributed systems with fluid flow

This paper reports a Pointwise Min-Norm control (PWMN) general result for a class of distributed systems that include transport phenomena associated with fluid flow in pipes and open pool canals. The main goal is to find a numerical control scheme that ultimately can be embedded in a more general Nonlinear Model Predictive Control formulation as an alternative to ensure closed-loop stability, for moderate values of the receding horizon without increasing dramatically the computational effort. In fact the PWMN control can be viewed as the NMPC limit stabilizing solution when the predictive horizon value goes to zero. A tubular system with finite escape traveling time is used to illustrate the control performance. An application to a canal pool modeled by Saint-Venants equations is also given. Canals are formed by a sequence of pools separated by gates. Water distribution canals provide interesting examples of distributed parameter plants for nonlinear control application.

Controlling Distributed Hyperbolic Plants with Adaptive Nonlinear Model Predictive Control

A number of plants of technological interest include transport phenomena in which mass, or energy, or both, flow along one space dimension, with or without reactions taking place, but with neglected dispersion. This type of processes are described by hyperbolic partial differential equations [4] and is receiving an increasing attention in what concerns the application of Predictive Control [6]. Two examples considered are distributed collector solar fields [3, 10] and tubular bioreactors [5]. In both cases the manipulated variable is assumed to be the flow. For lack of space, only the first example is considered hereafter.

Adaptive Receding Horizon Control of Tubular Bioreactors

This paper presents a case study of application of an adaptive nonlinear predictive control algorithm to tubular bioreactors. According to the control strategy proposed, the system of PDEs describing the reactor is approximated by a lumped parameter model obtained using the Orthogonal Collocation Method. An adaptive receding horizon controller is then designed using Control Lyapunov Function methods. The design procedure and the resulting performance is illustrated by simulations in a two reactions model with Contois kinetics.

LPV water delivery canal control based on prescribed order models

This article addresses the problem of designing an LPV controller for a water delivery canal based on reduced complexity linear models with a priori chosen order. For that sake, by applying a method based on the Laplace transform and the linearization of the Saint-Venant equations, a finite dimensional rational transfer function is obtained for each canal reach. An LPV gain-scheduling controller that relies on H∞ optimization is then designed for local upstream canal control. The scheduling variables are the inlet canal flow and the downstream-reach mean level. The uncertainty bound is computed on the basis of the high frequency error of the frequency response of the model used with respect to the one of the infinite-dimensional model by linearizing the Sain-Venant equations. This approach has the advantage of yielding an LPV controller that relies on a model with specified complexity and to relate model uncertainty to physical canal parameters, allowing operation over an extended envelop of water flow and level equilibria.